http://wiki.magicc.org/api.php?action=feedcontributions&user=Antonius+Golly&feedformat=atomMAGICC6 Wiki - User contributions [en]2024-03-28T20:10:18ZUser contributionsMediaWiki 1.25.2http://wiki.magicc.org/index.php?title=Model_Description&diff=56Model Description2015-08-30T12:02:31Z<p>Antonius Golly: </p>
<hr />
<div>'''NOTE: formulae are not displayed correctly since our wikimedia update.<br />
'''<br />
<br />
<br />
*[[Model Description|model description]]<br />
**[[The Carbon Cycle| carbon cycle]]<br />
**[[Non-CO2 Concentrations | non-CO2 concentrations]]<br />
**[[Radiative Forcing | radiative forcing routines]]<br />
**[[Upwelling_diffusion_climate_model | climate model]]<br />
**[[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]]<br />
<br />
<br />
==Model description==<br />
<br />
=== Overview ===<br />
<br />
The 'Model for the Assessment of Greenhouse Gas Induced Climate Change' (MAGICC) is a simple/reduced complexity climate model. MAGICC was originally developed by Tom Wigley (National Centre for Atmospheric Research, Boulder, US, and University of Adelaide, Australia) and Sarah Raper (Manchester Metropolitan University, UK) in the late 1980s and continuously developed since then. It has been one of the widely used climate models in various IPCC Assessment Reports. The latest version, MAGICC6, is co-developed by Malte Meinshausen (Potsdam Institute for Climate Impact Research, Germany, and the University of Melbourne, Australia). These pages provide an extensive model description, sourced from a 2011 publication in Atmospheric Chemistry & Physics [http://www.atmos-chem-phys.net/11/1417/2011/ (M. Meinshausen, S. Raper and T. Wigley, 2011)]. <br />
<br />
This Page provides a detailed description of MAGICC6 and its<br />
different modules (see [[#Fig_A1|Fig-A1]] below). A basic [[Model_Documentation|model description]] is given, while subsections describe MAGICC's <br />
[[The Carbon Cycle| carbon cycle]], the atmospheric-chemistry<br />
parameterizations and derivation of <br />
[[Non-CO2 Concentrations | non-CO<sub>2</sub> concentrations]], <br />
[[Radiative Forcing | radiative forcing routines]], and the climate module to get from<br />
radiative forcing to hemispheric (land and ocean, separately) to<br />
global-mean temperatures ([[Upwelling_diffusion_climate_model|climate model]]), as<br />
well as oceanic heat uptake. Finally, details are provided on the implementation scheme for the [[UDB Implementation | upwelling-diffusion-entrainment ocean]]<br />
climate module. A technical upgrade is that MAGICC6 has been re-coded in Fortran95,<br />
updated from previous Fortran77 versions. Nearly all of the MAGICC6 code is directly based on the earlier<br />
MAGICC versions programmed by Wigley and Raper <br />
([[References#Wigley_Raper_1987_ThermalExpansion_SeaWater_Nature| 1987]], [[References#Wigley_Raper_1992_ImplicationsWarmingIPCC_Nature | 1992]], [[References#Wigley_Raper_2001_Science_InterpretationHighProjections | 2001]]).<br />
<br />
[[File:OverviewGraph Fig1.png|frame|right|'''Fig-A1''' Schematic overview of MAGICC calculations showing the key steps<br />
from emissions to global and hemispheric climate responses.<br />
Black circled numbers denote the sections in the Appendix<br />
describing the respective algorithms used. Source: Fig A.1. in Meinshausen et al. 2011, ACP]]<span id="fig_A1"></span> <br />
<br />
===Basic model description===<br />
<br />
MAGICC has a hemispherically averaged upwelling-diffusion ocean coupled to an atmosphere layer and a globally averaged carbon cycle model. As with most other simple models, MAGICC evolved from a simple global average energy-balance equation. The energy balance equation for the perturbed climate system can be written as:<br />
<br />
<math>\Delta Q_G = \lambda_G \Delta T_G + \frac{d H}{d t}\label{eq_globalenergybalance}</math><span id="eq_1"></span><div style="float: right; clear: right;">('''1''')</div><br />
<br />
where <math>\Delta Q_G</math> is the global-mean radiative forcing at the top of the troposphere. This extra energy influx is partitioned into increased outgoing energy flux and heat content changes in the ocean <math>\frac{d H}{d t}</math>. The outgoing energy flux is dependent on the global-mean feedback factor, <math>\lambda_G</math>, and the surface temperature perturbation <math>\Delta T_G</math>.<br />
<br />
While MAGICC is designed to provide maximum flexibility in order to match different types of responses seen in more sophisticated models, the approach in MAGICC's model development has always been to derive the simple equations as much as possible from key physical and biological processes. In other words, MAGICC is as simple as possible, but as mechanistic as necessary. This process-based approach has a strong conceptual advantage in comparison to simple statistical fits that are more likely to quickly degrade in their skill when emulating scenarios outside the original calibration space of sophisticated models.<br />
<br />
The main improvements in MAGICC6 compared to the version used in the IPCC AR4 are briefly highlighted in this section (Note that there is an intermediate version, MAGICC 5.3, described in [[References#Wigley_etal_2009_UncertaintiesClimateStabilization|Wigley et al., 2009]]). The options introduced to account for variable climate sensitivities are described in Sect. [[#introduction of variable climate sensitivities|introduction of variable climate sensitivities]]. With the exception of the updated carbon cycle routines [[#updated carbon cycle|updated carbon cycle]], the MAGICC 4.2 and 5.3 parameterizations are covered as special cases of the 6.0 version, i.e., the IPCC AR4 version, for example, can be recovered by appropriate parameter settings.<br />
<br />
===Introduction of variable climate sensitivities===<br />
<br />
Climate sensitivity (<math>\Delta T_{2x}</math>) is a useful metric to compare models and is usually defined as the equilibrium global-mean warming after a doubling of CO<math>_2</math> concentrations. In the case of MAGICC, the equilibrium climate sensitivity is a primary model parameter that may be identified with the eventual global-mean warming that would occur if the CO<math>_2</math> concentrations were doubled from pre-industrial levels. Climate sensitivity is inversely related to the feedback factor <math>\lambda</math>:<br />
<br />
<math>\label{eq_climatesensitivity}\Delta T_{2x} = \frac{\Delta Q_{2x}}{\lambda}</math><span id="eq_2"></span><div style="float: right; clear: right;">('''2''')</div><br />
<br />
where <math>\Delta T_{2x}</math> is the climate sensitivity, and <math>\Delta Q_{2x}</math> the radiative forcing after a doubling of CO<math>_2</math> concentrations (see energy balance<br />
Eq. [[#eq_A45|A45]]).<br />
<br />
The (time- or state-dependent) effective climate sensitivity (<math>S^t</math>)([[References#Murphy_Mitchell_1995_SpatialTemporalResponse|Murphy and Mitchell, 1995]]) is defined using the transient energy balance Eq. ([[#eq_1|1]]) and can be diagnosed from model output for any part of a model run where radiative forcing and ocean heat uptake are both known and their sum is different from zero, so that:<br />
<br />
<math>\label{eq_effective_climatesensitivity} S^t = \frac{\Delta Q_{2x}}{\lambda^t} = \Delta Q_{2x} \frac{\Delta T_{G}^t}{\Delta Q^t - \frac{d H}{dt}|^t}</math><span id="eq_3"></span><div style="float: right; clear: right;">('''3''')</div><br />
<br />
where <math>\Delta Q_{2x}</m> is the model-specific forcing for doubled CO<math>_2</math> concentration, <math>\lambda_t</math> is the time-variable feedback factor, <math>\Delta Q^t</math> the radiative forcing, <math>\Delta T_{GL}^t</math> the global-mean temperature perturbation and <math>\frac{dH}{dt}|^t</math> the climate system's heat uptake at time <math>t</math>. By definition, the traditional (equilibrium) climate sensitivity (<math>\Delta T_{2x}</math>) is equal to the effective climate sensitivity <math>S^t</math> at equilibrium (<math>\frac{dH}{dt}|^t</math>=0) after doubled (pre-industrial) CO<math>_2</math> concentration.<br />
<br />
If there were only one globally homogenous, fast and constant feedback process, the diagnosed effective climate sensitivity would always equal the equilibrium climate sensitivity <math>\Delta T_{2x}</math>. However, many CMIP3 AOGCMs exhibit variable effective climate sensitivities, often increasing over time (e.g. models CCSM3, CNRM-CM3, GFDL-CM2.0, GFDL-CM2.1, GISS-EH - see Figs. (B1, B2, B3 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html). This is consistent with earlier results of increasing effective sensitivities found by ([[References#Senior_Mitchell_2000_TimeDependence_ClimateSensitivity|Senior and Mitchell (2000)]];[[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2000)]]) for the HadCM2 model. In addition, some models present significantly higher sensitivities for higher forcing scenarios (1pctto4x) than for lower forcing scenarios (1pctto2x) (e.g. ECHAM5/MPI-OM and GISS-ER, see [[#fig_increasing_ClimSens_CCSM3_ECHAM5|Fig.1 ]]<br />
<br />
In order to better emulate these time-variable effective climate sensitivities, this version of MAGICC incorporates two modifications: Firstly, an amended land-ocean heat exchange<br />
formulation allows effective climate sensitivities to increase on the path to equilibrium warming. In this formulation, changes in effective climate sensitivity arise from a geometrical effect: spatially non-homogenous feedbacks can lead to a time-variable effective global-mean climate sensitivity, if the spatial warming distributions change over time. Hence, by modifying land-ocean heat exchange in MAGICC, the spatial evolution of warming is altered, leading to changes in effective climate sensitivities ([[References#Raper_2004_GeometricalEffectClimsens|Raper, 2004]]) given that MAGICC has different equilibrium sensitivities over land and ocean. Secondly, the climate sensitivities, and hence the feedback parameters, can be made explicitly dependent on the current forcing at time <math>t</math>. Both amendments are detailed in the [[Upwelling_Diffusion_Entrainment_Implementation#Revised land-ocean heat formulation|Revised land-ocean heat formulation]], and [[Upwelling_Diffusion_Entrainment_Implementation#Accounting for climate-state dependent feedbacks|Accounting for climate-state dependent feedbacks]] sections. Although these two amendments both modify the same diagnostic, i.e., the time-variable effective sensitivities in MAGICC, they are distinct: the land-ocean heat exchange modification changes the shape of the effective climate sensitivity's time evolution to equilibrium, but keeps the equilibrium sensitivity unaffected. In contrast, making the sensitivity explicitly dependent on the forcing primarily affects the equilibrium sensitivity value.<br />
<br />
Note that time-varying effective sensitivities are not only empirically observed in AOGCMs, but they are necessary here in order for MAGICC to accurately emulate AOGCM results. Alternative parameterizations to emulate time-variable climate sensitivities are possible, e.g.~assuming a dependence on temperatures instead of forcing, or by implementing indirect radiative forcing effects that are most often regarded as feedbacks see Section 6.2 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html. However, this study chose to limit the degrees of freedom with respect to time-variable climate sensitivities given that a clear separation into three (or more) different parameterizations seemed unjustified based on the AOGCM data analyzed here.<br />
<br />
[[file:Fig-1.png|350px|thumb|The effective climate sensitivity diagnosed from low-pass filtered CCSM3 (a) and ECHAM5/MPI-OM (b) output for two idealized<br />
scenarios assuming an annual 1% increase in CO2 concentrations until twice pre-industrial values in year 70 (1pctto2×) or quadrupled concentration in year 140 (1pctto4×), with constant<br />
concentrations thereafter. Additionally, the reported slab ocean model equilibrium climate sensitivity (“slab”) and the sensitivity estimates by Forster and Taylor (2006) are shown (“F&T(06)”). ]] <br />
<span id="fig_increasing_ClimSens_CCSM3_ECHAM5"></span><br />
<br />
===Updated carbon cycle=== <br />
<br />
MAGICC's terrestrial carbon cycle model is a globally integrated box model, similar to that in [[References#Harvey_1989_ManagingAtmCO2|Harvey (1989)]] and [[References#Wigley_1993_BalancingCarbonBudget|Wigley (1993)]]. The MAGICC6 carbon cycle can emulate temperature-feedback effects on the heterotrophic respiration carbon fluxes. One improvement in MAGICC6 allows increased flexibility when accounting for CO<sub>2</sub> fertilization. This increase in flexibility allows a better fit to some of the more complex carbon cycle models reviewed in C<math>^4</math>MIP([[References#Friedlingstein_2006_climatecarbonInteraction_C4MIP|Friedlingstein, 2006]])(see [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]).<br />
<br />
Another update in MAGICC6 relates to the relaxation in carbon pools after a deforestation event. The gross CO<sub>2</sub> emissions related to deforestation and other land use activities are subtracted from the plant, detritus and soil carbon pools (see Fig. [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]]. While in previous versions only the regrowth in the plant carbon pool was taken into account to calculate the net deforestation, MAGICC6 now includes an effective relaxation/regrowth term for all three terrestrial carbon pools (see [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]).<br />
<br />
The original ocean carbon cycle model used a convolution representation ([[References#Wigley_1991_simpleInverseCarbonCycleModel|Wigley, 1991]]) to quantify the ocean-atmosphere CO<math>_2</math> flux. A similar representation is used here, but modified to account for nonlinearities. Specifically, the impulse response representation of the Princeton 3D GFDL model ([[References#Sarmiento_etal_1992_perturbationCO2_ocean_general_circulation_model|Sarmiento, 1992]]) is used to approximate the inorganic carbon perturbation in the mixed layer (for the impulse response representation see, [[References#Joos_Bruno_etal_1996_efficient_accurate_carbonuptake|Joos, 1991]]). The temperature sensitivity of the sea surface partial pressure is implemented based on [[References#Takahashi_etal_1993_surfaceOceans_CO2|Takahashi et al. (1993)]] as given in [[References#Joos_Prentice_etal_2001_feedbacks_biosphere_IPCC|Joos et al. (2001)]]. For details on the updated carbon cycle routines, see the [[The Carbon Cycle|The carbon cycle]].<br />
<br />
===Other additional capabilities compared to MAGICC4.2===<br />
<br />
Five additional amendments to the climate model have been implemented in MAGICC6 compared to the MAGICC4.2 version that has<br />
been used in IPCC AR4.<br />
<br />
====Aerosol indirect effects====<br />
<br />
It is now possible to account directly for contributions from black carbon, organic carbon and nitrate aerosols to indirect (i.e., cloud albedo) effects ([[References#Twomey_1977_albedo|Twomey, 1977]]). The first indirect effect, affecting cloud droplet size and the second indirect effect, affecting cloud cover and lifetime, can also be modeled separately. Following the convention in IPCC AR4 ([[References#Forster_Ramaswamy_etal_2007_IPCCAR4_Chapter2_radiativeForcing|Forster et al., 2007]]), the second indirect effect is modeled as a prescribed change in efficacy of the first indirect effect. See [[Non-CO2 Concentrations|Tropospheric aerosols]] for details.<br />
<br />
====Depth-variable ocean with entrainment====<br />
<br />
Building on the work by [[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2007)]], MAGICC6 includes the option of a depth-dependent ocean area profile with entrainment at each of the ocean levels (default, 50 levels) from the polar sinking water column. The default ocean area profile decreases from unity at the surface to, for example, 30<math>%</math>, 13<math>%</math> and 0<math>%</math> at depths of 4000, 4500 and 5000 m. Although comprehensive data on depth-dependent heat uptake profiles of the CMIP3 AOGCMs were not available for this study, this entrainment update provides more flexibility and allows for a better simulation of the characteristic depth-dependent heat uptake as observed in one analyzed AOGCM, namely HadCM2 ([[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al., 2000]]).<br />
<br />
====Vertical mixing depending on warming gradient====<br />
<br />
Simple models, including earlier versions of MAGICC, sometimes overestimated the ocean heat uptake for higher warming scenarios when applying parameter sets chosen to match heat uptake for lower warming scenarios, see e.g. Fig. 17b in [[References#Harvey_etal_1997_IPCC_IntroductionSimpleClimateModels|Harvey et al. (1997)]]. A strengthened thermal stratification and hence reduced vertical mixing might contribute to the lower heat uptake for higher warming cases. To model this effect, a warming-dependent vertical gradient of the thermal diffusivity is implemented here(see[[Upwelling diffusion climate model#Depth-dependent ocean with entrainment|Depth-dependent ocean with entrainment]]).<br />
<br />
====Forcing efficacies====<br />
<br />
Since the IPCC TAR, a number of studies have focussed on forcing efficacies, i.e., on the differences in surface temperature response due to a unit forcing by different radiative forcing agents with different geographical and vertical distributions ([[References#Joshi_etal_2003_improvedmetric_climatechange|Joshi et al., 1997]]). This version of MAGICC includes the option to apply different efficacy terms for the different forcings agents (see the [[Upwelling_Diffusion_Entrainment_Implementation#Depth-dependent ocean with entrainment|efficacies]] section for details and supplement pdf in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html for default values).<br />
<br />
====Radiative forcing patterns====<br />
<br />
Earlier versions of MAGICC used time-independent (but user-specifiable) ratios to distribute the global-mean forcing of tropospheric ozone and aerosols to the four atmospheric boxes, i.e., land and ocean in both hemispheres. This model structure and the simple 4-box forcing patterns are retained as it is able to capture a large fraction of the forcing agent characteristics of interest here. However, we now use patterns for each forcing individually, and allow for these patterns to vary over time. For example, the historical forcing pattern evolutions for tropospheric aerosols are based on results from [[References#Hansen_etal_2005_Efficacies|Hansen et al. (2005)]], which are interpolated to annual values and extrapolated into the future using hemispheric emissions. Additionally, MAGICC6 now incorporates forcing patterns for the long-lived greenhouse gases as well, although these patterns are assumed to be constant in time and scaled with global-mean radiative forcing (supplement pdf in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html for details on the default forcing patterns and time series).</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Model_Description&diff=55Model Description2015-08-30T12:02:11Z<p>Antonius Golly: </p>
<hr />
<div>NOTE: formulae are not displayed correctly since our wikimedia update.<br />
<br />
*[[Model Description|model description]]<br />
**[[The Carbon Cycle| carbon cycle]]<br />
**[[Non-CO2 Concentrations | non-CO2 concentrations]]<br />
**[[Radiative Forcing | radiative forcing routines]]<br />
**[[Upwelling_diffusion_climate_model | climate model]]<br />
**[[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]]<br />
<br />
<br />
==Model description==<br />
<br />
=== Overview ===<br />
<br />
The 'Model for the Assessment of Greenhouse Gas Induced Climate Change' (MAGICC) is a simple/reduced complexity climate model. MAGICC was originally developed by Tom Wigley (National Centre for Atmospheric Research, Boulder, US, and University of Adelaide, Australia) and Sarah Raper (Manchester Metropolitan University, UK) in the late 1980s and continuously developed since then. It has been one of the widely used climate models in various IPCC Assessment Reports. The latest version, MAGICC6, is co-developed by Malte Meinshausen (Potsdam Institute for Climate Impact Research, Germany, and the University of Melbourne, Australia). These pages provide an extensive model description, sourced from a 2011 publication in Atmospheric Chemistry & Physics [http://www.atmos-chem-phys.net/11/1417/2011/ (M. Meinshausen, S. Raper and T. Wigley, 2011)]. <br />
<br />
This Page provides a detailed description of MAGICC6 and its<br />
different modules (see [[#Fig_A1|Fig-A1]] below). A basic [[Model_Documentation|model description]] is given, while subsections describe MAGICC's <br />
[[The Carbon Cycle| carbon cycle]], the atmospheric-chemistry<br />
parameterizations and derivation of <br />
[[Non-CO2 Concentrations | non-CO<sub>2</sub> concentrations]], <br />
[[Radiative Forcing | radiative forcing routines]], and the climate module to get from<br />
radiative forcing to hemispheric (land and ocean, separately) to<br />
global-mean temperatures ([[Upwelling_diffusion_climate_model|climate model]]), as<br />
well as oceanic heat uptake. Finally, details are provided on the implementation scheme for the [[UDB Implementation | upwelling-diffusion-entrainment ocean]]<br />
climate module. A technical upgrade is that MAGICC6 has been re-coded in Fortran95,<br />
updated from previous Fortran77 versions. Nearly all of the MAGICC6 code is directly based on the earlier<br />
MAGICC versions programmed by Wigley and Raper <br />
([[References#Wigley_Raper_1987_ThermalExpansion_SeaWater_Nature| 1987]], [[References#Wigley_Raper_1992_ImplicationsWarmingIPCC_Nature | 1992]], [[References#Wigley_Raper_2001_Science_InterpretationHighProjections | 2001]]).<br />
<br />
[[File:OverviewGraph Fig1.png|frame|right|'''Fig-A1''' Schematic overview of MAGICC calculations showing the key steps<br />
from emissions to global and hemispheric climate responses.<br />
Black circled numbers denote the sections in the Appendix<br />
describing the respective algorithms used. Source: Fig A.1. in Meinshausen et al. 2011, ACP]]<span id="fig_A1"></span> <br />
<br />
===Basic model description===<br />
<br />
MAGICC has a hemispherically averaged upwelling-diffusion ocean coupled to an atmosphere layer and a globally averaged carbon cycle model. As with most other simple models, MAGICC evolved from a simple global average energy-balance equation. The energy balance equation for the perturbed climate system can be written as:<br />
<br />
<math>\Delta Q_G = \lambda_G \Delta T_G + \frac{d H}{d t}\label{eq_globalenergybalance}</math><span id="eq_1"></span><div style="float: right; clear: right;">('''1''')</div><br />
<br />
where <math>\Delta Q_G</math> is the global-mean radiative forcing at the top of the troposphere. This extra energy influx is partitioned into increased outgoing energy flux and heat content changes in the ocean <math>\frac{d H}{d t}</math>. The outgoing energy flux is dependent on the global-mean feedback factor, <math>\lambda_G</math>, and the surface temperature perturbation <math>\Delta T_G</math>.<br />
<br />
While MAGICC is designed to provide maximum flexibility in order to match different types of responses seen in more sophisticated models, the approach in MAGICC's model development has always been to derive the simple equations as much as possible from key physical and biological processes. In other words, MAGICC is as simple as possible, but as mechanistic as necessary. This process-based approach has a strong conceptual advantage in comparison to simple statistical fits that are more likely to quickly degrade in their skill when emulating scenarios outside the original calibration space of sophisticated models.<br />
<br />
The main improvements in MAGICC6 compared to the version used in the IPCC AR4 are briefly highlighted in this section (Note that there is an intermediate version, MAGICC 5.3, described in [[References#Wigley_etal_2009_UncertaintiesClimateStabilization|Wigley et al., 2009]]). The options introduced to account for variable climate sensitivities are described in Sect. [[#introduction of variable climate sensitivities|introduction of variable climate sensitivities]]. With the exception of the updated carbon cycle routines [[#updated carbon cycle|updated carbon cycle]], the MAGICC 4.2 and 5.3 parameterizations are covered as special cases of the 6.0 version, i.e., the IPCC AR4 version, for example, can be recovered by appropriate parameter settings.<br />
<br />
===Introduction of variable climate sensitivities===<br />
<br />
Climate sensitivity (<math>\Delta T_{2x}</math>) is a useful metric to compare models and is usually defined as the equilibrium global-mean warming after a doubling of CO<math>_2</math> concentrations. In the case of MAGICC, the equilibrium climate sensitivity is a primary model parameter that may be identified with the eventual global-mean warming that would occur if the CO<math>_2</math> concentrations were doubled from pre-industrial levels. Climate sensitivity is inversely related to the feedback factor <math>\lambda</math>:<br />
<br />
<math>\label{eq_climatesensitivity}\Delta T_{2x} = \frac{\Delta Q_{2x}}{\lambda}</math><span id="eq_2"></span><div style="float: right; clear: right;">('''2''')</div><br />
<br />
where <math>\Delta T_{2x}</math> is the climate sensitivity, and <math>\Delta Q_{2x}</math> the radiative forcing after a doubling of CO<math>_2</math> concentrations (see energy balance<br />
Eq. [[#eq_A45|A45]]).<br />
<br />
The (time- or state-dependent) effective climate sensitivity (<math>S^t</math>)([[References#Murphy_Mitchell_1995_SpatialTemporalResponse|Murphy and Mitchell, 1995]]) is defined using the transient energy balance Eq. ([[#eq_1|1]]) and can be diagnosed from model output for any part of a model run where radiative forcing and ocean heat uptake are both known and their sum is different from zero, so that:<br />
<br />
<math>\label{eq_effective_climatesensitivity} S^t = \frac{\Delta Q_{2x}}{\lambda^t} = \Delta Q_{2x} \frac{\Delta T_{G}^t}{\Delta Q^t - \frac{d H}{dt}|^t}</math><span id="eq_3"></span><div style="float: right; clear: right;">('''3''')</div><br />
<br />
where <math>\Delta Q_{2x}</m> is the model-specific forcing for doubled CO<math>_2</math> concentration, <math>\lambda_t</math> is the time-variable feedback factor, <math>\Delta Q^t</math> the radiative forcing, <math>\Delta T_{GL}^t</math> the global-mean temperature perturbation and <math>\frac{dH}{dt}|^t</math> the climate system's heat uptake at time <math>t</math>. By definition, the traditional (equilibrium) climate sensitivity (<math>\Delta T_{2x}</math>) is equal to the effective climate sensitivity <math>S^t</math> at equilibrium (<math>\frac{dH}{dt}|^t</math>=0) after doubled (pre-industrial) CO<math>_2</math> concentration.<br />
<br />
If there were only one globally homogenous, fast and constant feedback process, the diagnosed effective climate sensitivity would always equal the equilibrium climate sensitivity <math>\Delta T_{2x}</math>. However, many CMIP3 AOGCMs exhibit variable effective climate sensitivities, often increasing over time (e.g. models CCSM3, CNRM-CM3, GFDL-CM2.0, GFDL-CM2.1, GISS-EH - see Figs. (B1, B2, B3 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html). This is consistent with earlier results of increasing effective sensitivities found by ([[References#Senior_Mitchell_2000_TimeDependence_ClimateSensitivity|Senior and Mitchell (2000)]];[[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2000)]]) for the HadCM2 model. In addition, some models present significantly higher sensitivities for higher forcing scenarios (1pctto4x) than for lower forcing scenarios (1pctto2x) (e.g. ECHAM5/MPI-OM and GISS-ER, see [[#fig_increasing_ClimSens_CCSM3_ECHAM5|Fig.1 ]]<br />
<br />
In order to better emulate these time-variable effective climate sensitivities, this version of MAGICC incorporates two modifications: Firstly, an amended land-ocean heat exchange<br />
formulation allows effective climate sensitivities to increase on the path to equilibrium warming. In this formulation, changes in effective climate sensitivity arise from a geometrical effect: spatially non-homogenous feedbacks can lead to a time-variable effective global-mean climate sensitivity, if the spatial warming distributions change over time. Hence, by modifying land-ocean heat exchange in MAGICC, the spatial evolution of warming is altered, leading to changes in effective climate sensitivities ([[References#Raper_2004_GeometricalEffectClimsens|Raper, 2004]]) given that MAGICC has different equilibrium sensitivities over land and ocean. Secondly, the climate sensitivities, and hence the feedback parameters, can be made explicitly dependent on the current forcing at time <math>t</math>. Both amendments are detailed in the [[Upwelling_Diffusion_Entrainment_Implementation#Revised land-ocean heat formulation|Revised land-ocean heat formulation]], and [[Upwelling_Diffusion_Entrainment_Implementation#Accounting for climate-state dependent feedbacks|Accounting for climate-state dependent feedbacks]] sections. Although these two amendments both modify the same diagnostic, i.e., the time-variable effective sensitivities in MAGICC, they are distinct: the land-ocean heat exchange modification changes the shape of the effective climate sensitivity's time evolution to equilibrium, but keeps the equilibrium sensitivity unaffected. In contrast, making the sensitivity explicitly dependent on the forcing primarily affects the equilibrium sensitivity value.<br />
<br />
Note that time-varying effective sensitivities are not only empirically observed in AOGCMs, but they are necessary here in order for MAGICC to accurately emulate AOGCM results. Alternative parameterizations to emulate time-variable climate sensitivities are possible, e.g.~assuming a dependence on temperatures instead of forcing, or by implementing indirect radiative forcing effects that are most often regarded as feedbacks see Section 6.2 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html. However, this study chose to limit the degrees of freedom with respect to time-variable climate sensitivities given that a clear separation into three (or more) different parameterizations seemed unjustified based on the AOGCM data analyzed here.<br />
<br />
[[file:Fig-1.png|350px|thumb|The effective climate sensitivity diagnosed from low-pass filtered CCSM3 (a) and ECHAM5/MPI-OM (b) output for two idealized<br />
scenarios assuming an annual 1% increase in CO2 concentrations until twice pre-industrial values in year 70 (1pctto2×) or quadrupled concentration in year 140 (1pctto4×), with constant<br />
concentrations thereafter. Additionally, the reported slab ocean model equilibrium climate sensitivity (“slab”) and the sensitivity estimates by Forster and Taylor (2006) are shown (“F&T(06)”). ]] <br />
<span id="fig_increasing_ClimSens_CCSM3_ECHAM5"></span><br />
<br />
===Updated carbon cycle=== <br />
<br />
MAGICC's terrestrial carbon cycle model is a globally integrated box model, similar to that in [[References#Harvey_1989_ManagingAtmCO2|Harvey (1989)]] and [[References#Wigley_1993_BalancingCarbonBudget|Wigley (1993)]]. The MAGICC6 carbon cycle can emulate temperature-feedback effects on the heterotrophic respiration carbon fluxes. One improvement in MAGICC6 allows increased flexibility when accounting for CO<sub>2</sub> fertilization. This increase in flexibility allows a better fit to some of the more complex carbon cycle models reviewed in C<math>^4</math>MIP([[References#Friedlingstein_2006_climatecarbonInteraction_C4MIP|Friedlingstein, 2006]])(see [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]).<br />
<br />
Another update in MAGICC6 relates to the relaxation in carbon pools after a deforestation event. The gross CO<sub>2</sub> emissions related to deforestation and other land use activities are subtracted from the plant, detritus and soil carbon pools (see Fig. [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]]. While in previous versions only the regrowth in the plant carbon pool was taken into account to calculate the net deforestation, MAGICC6 now includes an effective relaxation/regrowth term for all three terrestrial carbon pools (see [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]).<br />
<br />
The original ocean carbon cycle model used a convolution representation ([[References#Wigley_1991_simpleInverseCarbonCycleModel|Wigley, 1991]]) to quantify the ocean-atmosphere CO<math>_2</math> flux. A similar representation is used here, but modified to account for nonlinearities. Specifically, the impulse response representation of the Princeton 3D GFDL model ([[References#Sarmiento_etal_1992_perturbationCO2_ocean_general_circulation_model|Sarmiento, 1992]]) is used to approximate the inorganic carbon perturbation in the mixed layer (for the impulse response representation see, [[References#Joos_Bruno_etal_1996_efficient_accurate_carbonuptake|Joos, 1991]]). The temperature sensitivity of the sea surface partial pressure is implemented based on [[References#Takahashi_etal_1993_surfaceOceans_CO2|Takahashi et al. (1993)]] as given in [[References#Joos_Prentice_etal_2001_feedbacks_biosphere_IPCC|Joos et al. (2001)]]. For details on the updated carbon cycle routines, see the [[The Carbon Cycle|The carbon cycle]].<br />
<br />
===Other additional capabilities compared to MAGICC4.2===<br />
<br />
Five additional amendments to the climate model have been implemented in MAGICC6 compared to the MAGICC4.2 version that has<br />
been used in IPCC AR4.<br />
<br />
====Aerosol indirect effects====<br />
<br />
It is now possible to account directly for contributions from black carbon, organic carbon and nitrate aerosols to indirect (i.e., cloud albedo) effects ([[References#Twomey_1977_albedo|Twomey, 1977]]). The first indirect effect, affecting cloud droplet size and the second indirect effect, affecting cloud cover and lifetime, can also be modeled separately. Following the convention in IPCC AR4 ([[References#Forster_Ramaswamy_etal_2007_IPCCAR4_Chapter2_radiativeForcing|Forster et al., 2007]]), the second indirect effect is modeled as a prescribed change in efficacy of the first indirect effect. See [[Non-CO2 Concentrations|Tropospheric aerosols]] for details.<br />
<br />
====Depth-variable ocean with entrainment====<br />
<br />
Building on the work by [[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2007)]], MAGICC6 includes the option of a depth-dependent ocean area profile with entrainment at each of the ocean levels (default, 50 levels) from the polar sinking water column. The default ocean area profile decreases from unity at the surface to, for example, 30<math>%</math>, 13<math>%</math> and 0<math>%</math> at depths of 4000, 4500 and 5000 m. Although comprehensive data on depth-dependent heat uptake profiles of the CMIP3 AOGCMs were not available for this study, this entrainment update provides more flexibility and allows for a better simulation of the characteristic depth-dependent heat uptake as observed in one analyzed AOGCM, namely HadCM2 ([[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al., 2000]]).<br />
<br />
====Vertical mixing depending on warming gradient====<br />
<br />
Simple models, including earlier versions of MAGICC, sometimes overestimated the ocean heat uptake for higher warming scenarios when applying parameter sets chosen to match heat uptake for lower warming scenarios, see e.g. Fig. 17b in [[References#Harvey_etal_1997_IPCC_IntroductionSimpleClimateModels|Harvey et al. (1997)]]. A strengthened thermal stratification and hence reduced vertical mixing might contribute to the lower heat uptake for higher warming cases. To model this effect, a warming-dependent vertical gradient of the thermal diffusivity is implemented here(see[[Upwelling diffusion climate model#Depth-dependent ocean with entrainment|Depth-dependent ocean with entrainment]]).<br />
<br />
====Forcing efficacies====<br />
<br />
Since the IPCC TAR, a number of studies have focussed on forcing efficacies, i.e., on the differences in surface temperature response due to a unit forcing by different radiative forcing agents with different geographical and vertical distributions ([[References#Joshi_etal_2003_improvedmetric_climatechange|Joshi et al., 1997]]). This version of MAGICC includes the option to apply different efficacy terms for the different forcings agents (see the [[Upwelling_Diffusion_Entrainment_Implementation#Depth-dependent ocean with entrainment|efficacies]] section for details and supplement pdf in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html for default values).<br />
<br />
====Radiative forcing patterns====<br />
<br />
Earlier versions of MAGICC used time-independent (but user-specifiable) ratios to distribute the global-mean forcing of tropospheric ozone and aerosols to the four atmospheric boxes, i.e., land and ocean in both hemispheres. This model structure and the simple 4-box forcing patterns are retained as it is able to capture a large fraction of the forcing agent characteristics of interest here. However, we now use patterns for each forcing individually, and allow for these patterns to vary over time. For example, the historical forcing pattern evolutions for tropospheric aerosols are based on results from [[References#Hansen_etal_2005_Efficacies|Hansen et al. (2005)]], which are interpolated to annual values and extrapolated into the future using hemispheric emissions. Additionally, MAGICC6 now incorporates forcing patterns for the long-lived greenhouse gases as well, although these patterns are assumed to be constant in time and scaled with global-mean radiative forcing (supplement pdf in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html for details on the default forcing patterns and time series).</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Changelog&diff=53Changelog2014-05-02T15:54:10Z<p>Antonius Golly: </p>
<hr />
<div><br />
== MAGICC 6 version history ==<br />
<br />
===6.8.01 BETA===<br />
Date: 7th July 2012 (Currently used in [http://live.magicc.org liveMAGICC])<br />
* n.y.a<br />
* n.y.a<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
== General information ==<br />
For liveMAGICC you find the version used to create the results in the output files.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Changelog&diff=52Changelog2014-05-02T15:53:48Z<p>Antonius Golly: </p>
<hr />
<div><br />
== MAGICC 6 version history ==<br />
<br />
===6.8.01 BETA===<br />
Date: 7th July 2012 (Currently used in [http://live.magicc.org|liveMAGICC])<br />
* n.y.a<br />
* n.y.a<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
== General information ==<br />
For liveMAGICC you find the version used to create the results in the output files.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Main_Page&diff=51Main Page2014-05-02T15:50:55Z<p>Antonius Golly: </p>
<hr />
<div>Welcome to the MAGICC Wiki. Here, we provide you with model descriptions, FAQs, user instructions and more ... all around the latest version of the "Model for the Assessment of Greenhouse Gas Induced Climate Change", i.e. MAGICC. <br />
<br />
<br />
[[File:MAGICC_logo_small.jpg|right]]<br />
<br />
<br />
[[Model_Description|Model Description]] - See what is behind MAGICC, a complete scientific description of datasets and parameterisations used in MAGICC6. ([[Changelog|MAGICC changelog]])<br />
<br />
[[Online_Help|Access MAGICC6 online]] - Help files and instructions for using our online interface [http://live.magicc.org live.magicc.org] for running MAGICC6 on our servers. <br />
<br />
[[Download MAGICC6|Download MAGICC6]] - Download and installation instructions for MAGICC6 executable.<br />
<br />
[[MAGICC6 User FAQ|Frequently Asked Questions]] - Find answers to the frequently asked questions regarding the Magicc6 model.<br />
<br />
[[For IAM Modellers|For IAM Modellers]] - Find information if you like to include MAGICC in an Integrated Assessment Model.<br />
<br />
[[MAGICC_projects|MAGICC Projects]] - See a list of publications that have made various uses of MAGICC in the past. <br />
<br />
[[MAGICC_team|MAGICC Team]] - Meet the MAGICC Development Team, Tom Wigley, Sarah Raper and Malte Meinshausen.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Changelog&diff=50Changelog2014-05-02T15:50:09Z<p>Antonius Golly: Created page with " == MAGICC 6 version history == *6.8.01 BETA*, 7th July 2012 (Currently used in [http://live.magicc.org|liveMAGICC]) - n.y.a - n.y.a == General information == For live..."</p>
<hr />
<div><br />
== MAGICC 6 version history ==<br />
<br />
*6.8.01 BETA*, 7th July 2012 (Currently used in [http://live.magicc.org|liveMAGICC])<br />
- n.y.a<br />
- n.y.a<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
== General information ==<br />
For liveMAGICC you find the version used to create the results in the output files.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Main_Page&diff=49Main Page2014-05-02T15:45:23Z<p>Antonius Golly: </p>
<hr />
<div>Welcome to the MAGICC Wiki. Here, we provide you with model descriptions, FAQs, user instructions and more ... all around the latest version of the "Model for the Assessment of Greenhouse Gas Induced Climate Change", i.e. MAGICC. <br />
<br />
<br />
[[File:MAGICC_logo_small.jpg|right]]<br />
<br />
<br />
[[Model_Description|Model Description]] - See what is behind MAGICC, a complete scientific description of datasets and parameterisations used in MAGICC6. ([[Changelog| MAGICC changelog]])<br />
<br />
[[Online_Help|Access MAGICC6 online]] - Help files and instructions for using our online interface [http://live.magicc.org live.magicc.org] for running MAGICC6 on our servers. <br />
<br />
[[Download MAGICC6|Download MAGICC6]] - Download and installation instructions for MAGICC6 executable.<br />
<br />
[[MAGICC6 User FAQ|Frequently Asked Questions]] - Find answers to the frequently asked questions regarding the Magicc6 model.<br />
<br />
[[For IAM Modellers|For IAM Modellers]] - Find information if you like to include MAGICC in an Integrated Assessment Model.<br />
<br />
[[MAGICC_projects|MAGICC Projects]] - See a list of publications that have made various uses of MAGICC in the past. <br />
<br />
[[MAGICC_team|MAGICC Team]] - Meet the MAGICC Development Team, Tom Wigley, Sarah Raper and Malte Meinshausen.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=MAGICC6_User_FAQ&diff=48MAGICC6 User FAQ2013-08-01T10:19:58Z<p>Antonius Golly: </p>
<hr />
<div>This page provides answers to common questions, encountered when using MAGICC6 via our [http://live.magicc.org webinterface] or when using the [http://www.magicc.org/download downloadable Windows executable]. <br />
<br />
== General Questions == <br />
<br />
=== Is MAGICC6 the best climate model ever? ===<br />
Certainly not. MAGICC6 is a reduced-complexity climate model that attempts to synthesize current scientific understanding about many different gas-cycles, including the carbon cycle, climate feedbacks and radiative forcing. The strength of MAGICC is that it is sufficiently flexible to be able to closely emulate the large and complex climate models, sufficiently physically based to allow credible interpolations and indicative extrapolation near the calibration range. Furthermore, MAGICC6 is fast. That is an advantage, particularly for producing probabilistic projections for new emission scenarios, a process that is computationally unfeasible with the complex climate models. Thus, with due respect, if the question is whether MAGICC6 is the best method around to synthesize a whole range of climate and carbon cycle knowledge for probabilistic projections over the 21st century and beyond, we are inclined to say "yes". Thus, MAGICC6 aims to complement, rather than replace, any complex climate models (simply because MAGICC6 is closely calibrated towards these "big brothers").<br><br><br />
<br />
=== I am teaching a class on climate. How can I use MAGICC? ===<br />
Probably the best method is to use our online web-interface [http://live.magicc.org live.magicc.org]<br />
<br />
== Questions related to live.magicc.org ==<br />
=== Which version does liveMAGICC use? ===<br />
liveMAGICC currently uses MAGICC6, the same version which was used to generate the RCP greenhouse gas concentrations. <br />
<br><br><br />
<br />
=== How do I know what the different emission scenarios actually mean? ===<br />
<br>There are many possible global emission pathways for different purposes and assumptions. For example, the RCP scenarios are the new standard, used by the Coupled Model Intercomparison excercise Phase 5. The highest scenario is RCP8.5 with a steady increase of emissions throughout the century. RCP.6 is the next lower one, approximately a middle range non-climate-policy scenarios, when compared to the previous SRES scenarios. RCP4.5 is the next lower emission scenario, often considered as a lax mitigation scenarios. The lowest scenario is RCP2.6, or as well called RCP3-PD, which represents a stringent mitigation scenario. Out of the four RCPs, only the latter scenario RCP2.6/RCP3-PD has a likely chance to stay below 2-degree warming. In general, it is probably best, if you go to the first tab on live.magicc.org. If you select your emissions scenarios and select the emissions you want to see, you can see their emission trajectories graphically. Thus, you can compare any other emission scenario to the RCPs, for example. <br><br />
<br />
=== If I select an emissions variable like "Fossil CO2" on Tab 1 - Emissions will I get different climate results ? ===<br />
The selection of a emission path variable in the emission chart has no effect to the Magicc run. The emission chart is just for your information. <br />
<br><br><br />
<br />
=== Can I run multiple emission scenarios at the same time? ===<br />
You can do multiple selection of emission scenarios in the '''scenario select''' box on '''Tab 1 - Emissions'''. The procedure is dependent on your OS / browser. For Windows users: hold CTRL while selecting scenarios with the mouse or hold SHIFT to select a range of scenarios.<br />
<br />
The multiple scenario selection will result in several tasks in ''Tab 3 - Climate'' that are queued to the users task list. MAGICC will process them in sequence.<br />
<br />
'''Note''' that multiple selection of scenarios is also available in Bulk Run Mode. This may result in a long term processing queue.<br />
<br><br><br />
<br />
=== How can I select multiple climate or carbon cycle settings? === <br />
Choose a desired climate or carbon cycle setting and switch to '''Tab 3 - Climate'''. The run will be queued. Now return to '''Tab 2 - Model Settings''' (you don't have to wait for the results) and choose another desired climate or carbon cycle setting. You can repeat these steps as often as desired. Identical model configurations will not be executed twice, so you don't need to take care of this.<br />
<br><br><br />
<br />
=== How can I compare the same emission scenario for two different climate settings? ===<br />
Choose a desired climate or carbon cycle setting and switch to '''Tab 3 - Climate'''. The run will be queued. Now return to '''Tab 2 - Model Settings''' and choose another desired climate or carbon cycle setting. You can repeat these steps as often as desired. <br />
<br><br><br />
<br />
=== How can I change only the climate sensitivity or other parameters? ===<br />
Return to '''Tab 2 - Model Settings''' and change only the desired parameters. Once you switch to '''Tab 3 - Climate''' the forms of Tab 1 and Tab 2 will be evaluated and if changes were made MAGICC will be executed.<br />
<br><br><br />
<br />
=== Why is the carbon cycle setting important when I want to know about the climate ? ===<br />
<br>The carbon cycle is important as it determines the CO2 concentrations that result from CO2 emission pathways. There is some uncertainty on that link. The coupled carbon-cycle climate model MAGICC includes a simple terrestrial carbon cycle and oceanic component. You can select various C4MIP model calibrations to get a feeling for the uncertainty and importance of the carbon cycle response. <br><br />
<br />
<br />
=== Where can I see my outputs? ===<br />
You can see your outputs on '''Tab 3 - Climate'''. On the left you will see your individual run list. Checkboxes indicate the already processed runs. By checking / unchecking the checkboxes you select the runs that will be plotted in the chart on the right.<br />
<br><br><br />
<br />
=== Can I plot different variables in the same plot? ===<br />
No, that is not possible because different climate variables require different y-axes and units. The variable list is therefore a single select box.<br />
<br><br><br />
<br />
=== Can I download the data that live.magicc.org created? ===<br />
You are able to download the results when you are registered and logged in. In your run list on Tab 3 - Climate you find a download link in the tooltips of the runs.<br />
<br><br><br />
<br />
=== How can I run create GHG concentrations according to the RCP default settings ? ===<br />
<br>If you choose the DEFAULT settings for both the climate and carbon cycle settings "SINGLERUN", your setting is the same as we used for creating the official RCP GHG concentrations. The reason, why you will get tiny differences in the concentration results (if you were to use the RCP emission pathways) compared to the official recommendations are things like ozone-depleting substance emissions. We had adapted those emissions for each RCP, but use a default emission profile in the background for this web-interface. <br><br />
<br />
=== How can I share my results with another user? ===<br />
This feature is scheduled on high priority. Please, stay tuned to [http://live.magicc.org live.magicc.org].<br />
<br><br><br />
<br />
=== Why would I want to sign up with a User Account on live.magicc.org? === <br />
This allows you to resume a session as well as share your results with other users (This feature is scheduled on high priority. Please, stay tuned to our [http://live.magicc.org live.magicc.org]). Also it allows to upload own emission scenarios and to download the results of the MAGICC runs.<br />
<br><br><br />
<br />
=== What are the system requirements for participating in live.magicc.org? === <br />
You need a browser that is able to display our website. We tested our website for IE6, FF4, Opera7. You will need to enable JavaScript. There are no requirements for your processor or any of your hardware as MAGICC runs on our server.<br />
<br><br><br />
<br />
=== How can I extend the output inteval to e.g. 2500 ===<br />
That feature is not offered or planned in the online version. Please use the desktop version of MAGICC6 and change the paramtere ENDYEAR in /MAGICC_MAIN/MAGCFG_NMLYEARS.CFG to do so.<br />
<br />
=== How much does it cost? ===<br />
The service is free to use. If you make any use of this work, please cite:<br />
<br />
Meinshausen, M., S. C. B. Raper and T. M. L. Wigley (2011). "Emulating coupled atmosphere-ocean and carbon cycle models with a simpler model, MAGICC6: Part I – Model Description and Calibration." Atmospheric Chemistry and Physics 11: 1417-1456. doi:[http://dx.doi.org/10.5194/acp-11-1417-2011 10.5194/acp-11-1417-2011]<br />
<br><br><br />
<br />
=== How can I save the graphs that I create? ===<br />
This feature is scheduled on high priority. Please, stay tuned to [http://live.magicc.org live.magicc.org]. <br />
<br><br></div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=MAGICC6_User_FAQ&diff=47MAGICC6 User FAQ2013-08-01T10:16:41Z<p>Antonius Golly: </p>
<hr />
<div>This page provides answers to common questions, encountered when using MAGICC6 via our [http://live.magicc.org webinterface] or when using the [http://www.magicc.org/download downloadable Windows executable]. <br />
<br />
== General Questions == <br />
<br />
=== Is MAGICC6 the best climate model ever? ===<br />
Certainly not. MAGICC6 is a reduced-complexity climate model that attempts to synthesize current scientific understanding about many different gas-cycles, including the carbon cycle, climate feedbacks and radiative forcing. The strength of MAGICC is that it is sufficiently flexible to be able to closely emulate the large and complex climate models, sufficiently physically based to allow credible interpolations and indicative extrapolation near the calibration range. Furthermore, MAGICC6 is fast. That is an advantage, particularly for producing probabilistic projections for new emission scenarios, a process that is computationally unfeasible with the complex climate models. Thus, with due respect, if the question is whether MAGICC6 is the best method around to synthesize a whole range of climate and carbon cycle knowledge for probabilistic projections over the 21st century and beyond, we are inclined to say "yes". Thus, MAGICC6 aims to complement, rather than replace, any complex climate models (simply because MAGICC6 is closely calibrated towards these "big brothers").<br><br><br />
<br />
=== I am teaching a class on climate. How can I use MAGICC? ===<br />
Probably the best method is to use our online web-interface [http://live.magicc.org live.magicc.org]<br />
<br />
== Questions related to live.magicc.org ==<br />
=== Which version does liveMAGICC use? ===<br />
liveMAGICC currently uses MAGICC6, the same version which was used to generate the RCP greenhouse gas concentrations. <br />
<br><br><br />
<br />
=== How do I know what the different emission scenarios actually mean? ===<br />
<br>There are many possible global emission pathways for different purposes and assumptions. For example, the RCP scenarios are the new standard, used by the Coupled Model Intercomparison excercise Phase 5. The highest scenario is RCP8.5 with a steady increase of emissions throughout the century. RCP.6 is the next lower one, approximately a middle range non-climate-policy scenarios, when compared to the previous SRES scenarios. RCP4.5 is the next lower emission scenario, often considered as a lax mitigation scenarios. The lowest scenario is RCP2.6, or as well called RCP3-PD, which represents a stringent mitigation scenario. Out of the four RCPs, only the latter scenario RCP2.6/RCP3-PD has a likely chance to stay below 2-degree warming. In general, it is probably best, if you go to the first tab on live.magicc.org. If you select your emissions scenarios and select the emissions you want to see, you can see their emission trajectories graphically. Thus, you can compare any other emission scenario to the RCPs, for example. <br><br />
<br />
=== If I select an emissions variable like "Fossil CO2" on Tab 1 - Emissions will I get different climate results ? ===<br />
The selection of a emission path variable in the emission chart has no effect to the Magicc run. The emission chart is just for your information. <br />
<br><br><br />
<br />
=== Can I run multiple emission scenarios at the same time? ===<br />
You can do multiple selection of emission scenarios in the '''scenario select''' box on '''Tab 1 - Emissions'''. The procedure is dependent on your OS / browser. For Windows users: hold CTRL while selecting scenarios with the mouse or hold SHIFT to select a range of scenarios.<br />
<br />
The multiple scenario selection will result in several tasks in ''Tab 3 - Climate'' that are queued to the users task list. MAGICC will process them in sequence.<br />
<br />
'''Note''' that multiple selection of scenarios is also available in Bulk Run Mode. This may result in a long term processing queue.<br />
<br><br><br />
<br />
=== How can I select multiple climate or carbon cycle settings? === <br />
Choose a desired climate or carbon cycle setting and switch to '''Tab 3 - Climate'''. The run will be queued. Now return to '''Tab 2 - Model Settings''' (you don't have to wait for the results) and choose another desired climate or carbon cycle setting. You can repeat these steps as often as desired. Identical model configurations will not be executed twice, so you don't need to take care of this.<br />
<br><br><br />
<br />
=== How can I compare the same emission scenario for two different climate settings? ===<br />
Choose a desired climate or carbon cycle setting and switch to '''Tab 3 - Climate'''. The run will be queued. Now return to '''Tab 2 - Model Settings''' and choose another desired climate or carbon cycle setting. You can repeat these steps as often as desired. <br />
<br><br><br />
<br />
=== How can I change only the climate sensitivity or other parameters? ===<br />
Return to '''Tab 2 - Model Settings''' and change only the desired parameters. Once you switch to '''Tab 3 - Climate''' the forms of Tab 1 and Tab 2 will be evaluated and if changes were made MAGICC will be executed.<br />
<br><br><br />
<br />
=== Why is the carbon cycle setting important when I want to know about the climate ? ===<br />
<br>The carbon cycle is important as it determines the CO2 concentrations that result from CO2 emission pathways. There is some uncertainty on that link. The coupled carbon-cycle climate model MAGICC includes a simple terrestrial carbon cycle and oceanic component. You can select various C4MIP model calibrations to get a feeling for the uncertainty and importance of the carbon cycle response. <br><br />
<br />
<br />
=== Where can I see my outputs? ===<br />
You can see your outputs on '''Tab 3 - Climate'''. On the left you will see your individual run list. Checkboxes indicate the already processed runs. By checking / unchecking the checkboxes you select the runs that will be plotted in the chart on the right.<br />
<br><br><br />
<br />
=== Can I plot different variables in the same plot? ===<br />
No, that is not possible because different climate variables require different y-axes and units. The variable list is therefore a single select box.<br />
<br><br><br />
<br />
=== Can I download the data that live.magicc.org created? ===<br />
This feature is scheduled on high priority. Please, stay tuned to [http://live.magicc.org live.magicc.org].<br />
<br><br><br />
<br />
=== How can I run create GHG concentrations according to the RCP default settings ? ===<br />
<br>If you choose the DEFAULT settings for both the climate and carbon cycle settings "SINGLERUN", your setting is the same as we used for creating the official RCP GHG concentrations. The reason, why you will get tiny differences in the concentration results (if you were to use the RCP emission pathways) compared to the official recommendations are things like ozone-depleting substance emissions. We had adapted those emissions for each RCP, but use a default emission profile in the background for this web-interface. <br><br />
<br />
=== How can I share my results with another user? ===<br />
This feature is scheduled on high priority. Please, stay tuned to [http://live.magicc.org live.magicc.org].<br />
<br><br><br />
<br />
=== Why would I want to sign up with a User Account on live.magicc.org? === <br />
This allows you to resume a session as well as share your results with other users (This feature is scheduled on high priority. Please, stay tuned to our [http://live.magicc.org live.magicc.org]). Also it allows to upload own emission scenarios and to download the results of the MAGICC runs.<br />
<br><br><br />
<br />
=== What are the system requirements for participating in live.magicc.org? === <br />
You need a browser that is able to display our website. We tested our website for IE6, FF4, Opera7. You will need to enable JavaScript. There are no requirements for your processor or any of your hardware as MAGICC runs on our server.<br />
<br><br><br />
<br />
=== How much does it cost? ===<br />
The service is free to use. If you make any use of this work, please cite:<br />
<br />
Meinshausen, M., S. C. B. Raper and T. M. L. Wigley (2011). "Emulating coupled atmosphere-ocean and carbon cycle models with a simpler model, MAGICC6: Part I – Model Description and Calibration." Atmospheric Chemistry and Physics 11: 1417-1456. doi:[http://dx.doi.org/10.5194/acp-11-1417-2011 10.5194/acp-11-1417-2011]<br />
<br><br><br />
<br />
=== How can I save the graphs that I create? ===<br />
This feature is scheduled on high priority. Please, stay tuned to [http://live.magicc.org live.magicc.org]. <br />
<br><br></div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Creating_MAGICC_Scenario_Files&diff=46Creating MAGICC Scenario Files2013-07-16T16:35:38Z<p>Antonius Golly: /* How do I format my scenario data? */</p>
<hr />
<div>= How to create your own emission scenario file for MAGICC6? =<br />
<br />
This is a quick recipe of how you can put your data into a ASCII fileformat that will work with MAGICC. Example files of the RCP scenarios can be downloaded from [http://www.pik-potsdam.de/~mmalte/rcps/ the RCP concentration calculations site] [only links labled "MAGICC"], e.g. [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP3PD.SCEN RCP3-PD] (sometimes as well called RCP2.6), [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP45.SCEN RCP45], [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP6.SCEN RCP6], or [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP85.SCEN RCP85]. Suitable scenario files have always the extension *.SCEN.<br />
<br />
== What ingredients do you need? ==<br />
<br />
1. In order to create an emission scenario file, you need the emission scenario data. Specifically, you need: <br />
* Fossil / Industrial carbon dioxide CO2 emissions in units GtC/yr (to convert from GtCO2/yr to GtC/yr, multiply by '12/44')<br />
* Landuse carbon dioxide CO2 emissions in units GtC/yr<br />
* Methane CH4 emissions in units MtCH4/yr<br />
* Nitrous oxide N2O emissions in units MtN/yr (note that to convert from MtN2O/yr to MtN/yr, multiply by '28/(28+16)')<br />
* Sulphate dioxide SO2 emissions in units MtS/yr<br />
* Carbon monoxide CO emissions in units MtCO/yr<br />
* Non-Methane Volatile Organic compounds NMVOC in units Mt/yr<br />
* Nitrogen Oxides NOx in units MtN/yr<br />
* Black Carbon BC in units Mt/yr<br />
* Organic Carbon OC in units Mt/yr <br />
* Ammonium NH3 in MtN/yr <br />
* Perfluorocarbons PFCs in the units kt/yr, namely CF4, C2F6, C6F14 <br />
* Hydrofluorocarbons HFCs in the units kt/yr, namely HFC23, HFC32, HFC43-10, HFC125, HFC134a, HFC143a, HFC227ea, HFC245fa <br />
* Sulfur hexafluoride SF6 in units kt/yr<br />
<br />
2. You need all these emission trajectories on the same points in time. MAGICC assumes linear interpolation between any years that are not provided. Thus, your time axis could either be 2000, 2005, 2050 and 2100, or, annual values or any other sequence of years as long as they monotonically increase. Note that historical emissions files are overwritten from the startpoint onwards, i.e. with the startpoint being your first year of your emission scenario, i.e. 2000 or 1990 or 2005. <br />
<br />
3. Optionally, you can prescribe all this data regionally. This has the advantage that MAGICC does not have to make guesses on what the regional distribution of your emissions are over time. The regional split up follows the five RCP regions, i.e. OECD, REF, ASIA, MAF and LAM, (where MAF and LAM are together the former ALM region of the SRES scenarios), as defined [http://www.iiasa.ac.at/web-apps/tnt/RcpDb/dsd?Action=htmlpage&page=about#regiondefs here]. In addition, you should specify emissions from international transport (i.e. the sum of aviation and shipping emissions) separately as the sixth region. Note that if you provide regional data, MAGICC expects the order of these data blocks to be GLOBAL, OECD, REF, ASIA, MAF, LAM, BUNKERS. And yes, globally aggregate emissions should be provided as well (although they will be ignored, if MAGICC is told to use the regional data..). <br />
<br />
== How do I format my scenario data? == <br />
<br />
Now that you have all your data, you have to take into account some formatting requirements of your ASCII .SCEN file. <br />
* Your file ending should be ".SCEN" and it should be an ASCII file under DOS standard. <br />
* The first line in your ASCII file consists of only one integer, ("20" in the example below), which specifies the number of prescribed years of your emission trajectory. For example, if your emission scenario is specified for the years, 2000, 2005, 2050 and 2100, then "4" is the number you should put into the top left corner of your ASCII file. <br />
* The second line consists of only one integer. Simplified speaking, this integer stands for whether you provide global data or regional data. The options are: <br />
** 11 - Global/World data only. <br />
** 21 - Global/World data plus the four SRES regions OECD90, REF, ASIA and ALM. See regional definition [http://www.ipcc.ch/ipccreports/sres/emission/index.php?idp=149 here]. <br />
** 31 - Global/World data plus the five RCP regions OECD, REF, ASIA, MAF and LAM. <br />
** 41 - Global/World data plus the five RCP regions OECD, REF, ASIA, MAF and LAM and international transport "BUNKERS". <br />
* The third line specifies the scenario name. Usually identical to the filename. <br />
* The fourth and fifth line are there for describing your scenario. <br />
* The sixth line is empty. <br />
* '''The seventh line contains WORLD as the regional definition for the first datablock.''' <br />
* The eights line contains first the YEARS column header and then the headers with the list of gases (note, column order is not variable, but fixed as shown in the example below). <br />
* The ninth line contains the units (only for the viewer as MAGICC expects the data to be in units as specified above). <br />
* '''The tenth line is the first data line.''' Note that the field width has to be 11 for every data column - with the years being integers and the other emissions being floating point numbers with four digits after the dot, as MAGICC uses the Fortran command READ(FILE_ID , '(I11 , 24F11.4)') to read in these datablock lines. <br />
* There are X data lines in total (including line 10), with X being the integer read in in the first line. <br />
* Afterwards, there are TWO empty lines as separator <br />
* Then, if regional flag is not set to 11, the header for the next regional block comes, i.e. "OECD". <br />
* Then there is one line with column headers (i.e. years and gas names) <br />
* Then there is one line with Units <br />
* Then comes the next data block and so on.. <br />
* After the last data block, two empty lines are again provided as separator. <br />
* Below these two empty lines, additional comments can be inserted, which will be ignored by MAGICC.<br />
<br />
== Please note: If you create unexpected curves with your scenario ==<br />
Please make sure that your data start in line 10 and end in line 10 + ''the value from line 1''. For example, adding an extra empty line between YEARS and UNITS or discard a comment line (line 3 or 4) will corrupt the SCEN file.<br />
<br />
== Example file ==<br />
<br />
This is how the header and first dataline of an emission scenario .SCEN file should look like. In this example, an array of 20 annual datapoints has been provided (hence first integer in line 1 being "20"), and the data is provided with regional detail of the RCP regions (plus bunkers) (hence "41" in second line, see description above). For full examples, see these files [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP3PD.SCEN RCP3-PD] (sometimes as well called RCP2.6), [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP45.SCEN RCP45], [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP6.SCEN RCP6], or [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP85.SCEN RCP85]. <br />
<br />
<pre><br />
20<br />
41<br />
RCP3PD<br />
HARMONISED, EXTENDED FINAL RCP3-PD (Peak&Decline) Emission scenario for MAGICC6<br />
DATE: 26/11/2009 11:29:06; MAGICC-VERSION: 6.3.09, 25 November 2009<br />
<br />
WORLD<br />
YEARS FossilCO2 OtherCO2 CH4 N2O SOx CO NMVOC NOx BC OC NH3 CF4 C2F6 C6F14 HFC23 HFC32 HFC43-10 HFC125 HFC134a HFC143a HFC227ea HFC245fa SF6<br />
Yrs GtC GtC MtCH4 MtN2O-N MtS MtCO Mt MtN Mt Mt MtN kt kt kt kt kt kt kt kt kt kt kt kt<br />
2000 6.7350 1.1488 300.2070 7.4567 53.8413 1068.0009 210.6230 38.1623 7.8048 35.5434 40.0185 12.0000 2.3750 0.4624 10.3949 4.0000 0.0000 8.5381 75.0394 6.2341 1.9510 17.9257 5.5382 <br />
2001 6.8960 1.1320 303.4093 7.5029 54.4192 1066.7447 211.5938 38.2888 7.8946 35.7143 40.3916 11.9250 2.4344 0.4651 10.4328 5.3987 0.6470 9.0301 84.0409 7.4947 1.6450 19.7183 5.6990 <br />
2002 6.9490 1.2317 306.5787 7.5487 54.9960 1065.4692 212.5632 38.4153 7.9841 35.8846 40.7647 11.8480 2.4915 0.4058 10.4708 6.7974 1.2941 9.8853 94.7162 8.7389 2.5080 21.5109 5.8596 <br />
2003 7.2860 1.2256 309.7165 7.5942 55.5716 1064.1742 213.5311 38.5418 8.0734 36.0543 41.1377 11.7692 2.5464 0.3939 10.5083 8.1961 1.9411 12.0788 101.4157 9.9776 3.3410 23.3034 6.0202 <br />
2004 7.6720 1.2428 312.8241 7.6394 56.1461 1062.8596 214.4977 38.6683 8.1624 36.2233 41.5107 11.6885 2.5990 0.4062 10.5455 9.5948 2.5881 12.5074 113.9297 11.2136 4.2690 25.0960 6.1806<br />
<br />
...<br />
</pre><br />
<br />
Then, simply upload your scenario file on live.magicc.org and calculate climate effects following your own emission scenario.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Creating_MAGICC_Scenario_Files&diff=45Creating MAGICC Scenario Files2013-07-16T16:29:14Z<p>Antonius Golly: /* How do I format my scenario data? */</p>
<hr />
<div>= How to create your own emission scenario file for MAGICC6? =<br />
<br />
This is a quick recipe of how you can put your data into a ASCII fileformat that will work with MAGICC. Example files of the RCP scenarios can be downloaded from [http://www.pik-potsdam.de/~mmalte/rcps/ the RCP concentration calculations site] [only links labled "MAGICC"], e.g. [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP3PD.SCEN RCP3-PD] (sometimes as well called RCP2.6), [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP45.SCEN RCP45], [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP6.SCEN RCP6], or [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP85.SCEN RCP85]. Suitable scenario files have always the extension *.SCEN.<br />
<br />
== What ingredients do you need? ==<br />
<br />
1. In order to create an emission scenario file, you need the emission scenario data. Specifically, you need: <br />
* Fossil / Industrial carbon dioxide CO2 emissions in units GtC/yr (to convert from GtCO2/yr to GtC/yr, multiply by '12/44')<br />
* Landuse carbon dioxide CO2 emissions in units GtC/yr<br />
* Methane CH4 emissions in units MtCH4/yr<br />
* Nitrous oxide N2O emissions in units MtN/yr (note that to convert from MtN2O/yr to MtN/yr, multiply by '28/(28+16)')<br />
* Sulphate dioxide SO2 emissions in units MtS/yr<br />
* Carbon monoxide CO emissions in units MtCO/yr<br />
* Non-Methane Volatile Organic compounds NMVOC in units Mt/yr<br />
* Nitrogen Oxides NOx in units MtN/yr<br />
* Black Carbon BC in units Mt/yr<br />
* Organic Carbon OC in units Mt/yr <br />
* Ammonium NH3 in MtN/yr <br />
* Perfluorocarbons PFCs in the units kt/yr, namely CF4, C2F6, C6F14 <br />
* Hydrofluorocarbons HFCs in the units kt/yr, namely HFC23, HFC32, HFC43-10, HFC125, HFC134a, HFC143a, HFC227ea, HFC245fa <br />
* Sulfur hexafluoride SF6 in units kt/yr<br />
<br />
2. You need all these emission trajectories on the same points in time. MAGICC assumes linear interpolation between any years that are not provided. Thus, your time axis could either be 2000, 2005, 2050 and 2100, or, annual values or any other sequence of years as long as they monotonically increase. Note that historical emissions files are overwritten from the startpoint onwards, i.e. with the startpoint being your first year of your emission scenario, i.e. 2000 or 1990 or 2005. <br />
<br />
3. Optionally, you can prescribe all this data regionally. This has the advantage that MAGICC does not have to make guesses on what the regional distribution of your emissions are over time. The regional split up follows the five RCP regions, i.e. OECD, REF, ASIA, MAF and LAM, (where MAF and LAM are together the former ALM region of the SRES scenarios), as defined [http://www.iiasa.ac.at/web-apps/tnt/RcpDb/dsd?Action=htmlpage&page=about#regiondefs here]. In addition, you should specify emissions from international transport (i.e. the sum of aviation and shipping emissions) separately as the sixth region. Note that if you provide regional data, MAGICC expects the order of these data blocks to be GLOBAL, OECD, REF, ASIA, MAF, LAM, BUNKERS. And yes, globally aggregate emissions should be provided as well (although they will be ignored, if MAGICC is told to use the regional data..). <br />
<br />
== How do I format my scenario data? == <br />
<br />
Now that you have all your data, you have to take into account some formatting requirements of your ASCII .SCEN file. <br />
* Your file ending should be ".SCEN" and it should be an ASCII file under DOS standard. <br />
* The first line in your ASCII file consists of only one integer, ("20" in the example below), which specifies the number of prescribed years of your emission trajectory. For example, if your emission scenario is specified for the years, 2000, 2005, 2050 and 2100, then "4" is the number you should put into the top left corner of your ASCII file. <br />
* The second line consists of only one integer. Simplified speaking, this integer stands for whether you provide global data or regional data. The options are: <br />
** 11 - Global/World data only. <br />
** 21 - Global/World data plus the four SRES regions OECD90, REF, ASIA and ALM. See regional definition [http://www.ipcc.ch/ipccreports/sres/emission/index.php?idp=149 here]. <br />
** 31 - Global/World data plus the five RCP regions OECD, REF, ASIA, MAF and LAM. <br />
** 41 - Global/World data plus the five RCP regions OECD, REF, ASIA, MAF and LAM and international transport "BUNKERS". <br />
* The third line specifies the scenario name. Usually identical to the filename. <br />
* The fourth and fifth line are there for describing your scenario. <br />
* The sixth line is empty. <br />
* '''The seventh line contains WORLD as the regional definition for the first datablock.''' <br />
* The eights line contains first the YEARS column header and then the headers with the list of gases (note, column order is not variable, but fixed as shown in the example below). <br />
* The ninth line contains the units (only for the viewer as MAGICC expects the data to be in units as specified above). <br />
* '''The tenth line is the first data line.''' Note that the field width has to be 11 for every data column - with the years being integers and the other emissions being floating point numbers with four digits after the dot, as MAGICC uses the Fortran command READ(FILE_ID , '(I11 , 24F11.4)') to read in these datablock lines. <br />
* There are X data lines in total (including line 10), with X being the integer read in in the first line. <br />
* Afterwards, there are TWO empty lines as separator <br />
* Then, if regional flag is not set to 11, the header for the next regional block comes, i.e. "OECD". <br />
* Then there is one line with column headers (i.e. years and gas names) <br />
* Then there is one line with Units <br />
* Then comes the next data block and so on.. <br />
* After the last data block, two empty lines are again provided as separator. <br />
* Below these two empty lines, additional comments can be inserted, which will be ignored by MAGICC.<br />
<br />
== Example file ==<br />
<br />
This is how the header and first dataline of an emission scenario .SCEN file should look like. In this example, an array of 20 annual datapoints has been provided (hence first integer in line 1 being "20"), and the data is provided with regional detail of the RCP regions (plus bunkers) (hence "41" in second line, see description above). For full examples, see these files [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP3PD.SCEN RCP3-PD] (sometimes as well called RCP2.6), [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP45.SCEN RCP45], [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP6.SCEN RCP6], or [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP85.SCEN RCP85]. <br />
<br />
<pre><br />
20<br />
41<br />
RCP3PD<br />
HARMONISED, EXTENDED FINAL RCP3-PD (Peak&Decline) Emission scenario for MAGICC6<br />
DATE: 26/11/2009 11:29:06; MAGICC-VERSION: 6.3.09, 25 November 2009<br />
<br />
WORLD<br />
YEARS FossilCO2 OtherCO2 CH4 N2O SOx CO NMVOC NOx BC OC NH3 CF4 C2F6 C6F14 HFC23 HFC32 HFC43-10 HFC125 HFC134a HFC143a HFC227ea HFC245fa SF6<br />
Yrs GtC GtC MtCH4 MtN2O-N MtS MtCO Mt MtN Mt Mt MtN kt kt kt kt kt kt kt kt kt kt kt kt<br />
2000 6.7350 1.1488 300.2070 7.4567 53.8413 1068.0009 210.6230 38.1623 7.8048 35.5434 40.0185 12.0000 2.3750 0.4624 10.3949 4.0000 0.0000 8.5381 75.0394 6.2341 1.9510 17.9257 5.5382 <br />
2001 6.8960 1.1320 303.4093 7.5029 54.4192 1066.7447 211.5938 38.2888 7.8946 35.7143 40.3916 11.9250 2.4344 0.4651 10.4328 5.3987 0.6470 9.0301 84.0409 7.4947 1.6450 19.7183 5.6990 <br />
2002 6.9490 1.2317 306.5787 7.5487 54.9960 1065.4692 212.5632 38.4153 7.9841 35.8846 40.7647 11.8480 2.4915 0.4058 10.4708 6.7974 1.2941 9.8853 94.7162 8.7389 2.5080 21.5109 5.8596 <br />
2003 7.2860 1.2256 309.7165 7.5942 55.5716 1064.1742 213.5311 38.5418 8.0734 36.0543 41.1377 11.7692 2.5464 0.3939 10.5083 8.1961 1.9411 12.0788 101.4157 9.9776 3.3410 23.3034 6.0202 <br />
2004 7.6720 1.2428 312.8241 7.6394 56.1461 1062.8596 214.4977 38.6683 8.1624 36.2233 41.5107 11.6885 2.5990 0.4062 10.5455 9.5948 2.5881 12.5074 113.9297 11.2136 4.2690 25.0960 6.1806<br />
<br />
...<br />
</pre><br />
<br />
Then, simply upload your scenario file on live.magicc.org and calculate climate effects following your own emission scenario.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Upwelling_Diffusion_Entrainment_Implementation&diff=40Upwelling Diffusion Entrainment Implementation2013-06-17T15:12:04Z<p>Antonius Golly: </p>
<hr />
<div>*[[Model Description|model description]]<br />
**[[The Carbon Cycle| carbon cycle]]<br />
**[[Non-CO2 Concentrations | non-CO2 concentrations]]<br />
**[[Radiative Forcing | radiative forcing routines]]<br />
**[[Upwelling_diffusion_climate_model | climate model]]<br />
**[[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]]<br />
<br />
<br />
==Implementation of upwelling-diffusion-entrainment equations==<br />
<br />
This section details how the equations governing the upwelling-diffusion-entrainment (UDE) ocean (Eqs. [[#eq_62|A62]], [[#eq_63|A63]]) are implemented and modified by entrainment terms and depth-dependent ocean area (see Fig. [[#Fig-A2a|A2]]). These equations represent the core of the UDE model and build on the initial work by ([[References#Hoffert_1980_Role_DeapSea, Harvey_Schneider_1985_PartII, Harvey_Schneider_1985_PartI|Hoffert et al. (1980)]].<br />
<br />
The entrainment is here modeled so that the upwelling velocity in the main column is the same in each layer. Thus, the three area correction factors, <math>\theta_z^{\rm top}</math>, <math>\theta_z^{b}</math> and<br />
<math>\theta_z^{\rm dif}</math>, applied below are:<br />
<br />
<math>\theta_z^{\rm top} = \frac{A_z}{(A_{z+1}+A_z)/2}</math><br />
<br />
<math>\theta_z^{b} = \frac{A_{z+1}}{(A_{z+1}+A_z)/2} </math><br />
<br />
<math>\theta_z^{\rm dif} = \frac{A_{z+1}-A_{z}}{(A_{z+1}+A_z)/2}\label{eq_areacorrection_thetatop}</math><span id="eq_A67"></span><div style="float: right; clear: right;">('''A67''')</div><br />
<br />
<br />
where <math>A_z</math> is the area at the top of layer z or bottom of layer z-1 and the denominator is thus an approximation for the mean area of each ocean layer.<br />
<br />
For the mixed layer, all terms in Eq. ([[#eq_62|A62]]) involving <math>\Delta T^{t+1}_{\rm NO,1}</math> are collected on the left hand side in variable <math>A(1)</math>. All terms involving <math>\Delta T^{t+1}_{\rm NO,2}</math> are collected in variable <math>B(1)</math> on the left hand side. All other terms are held in variable <math>D(1)</math> on the right hand side, so that the<br />
equation reads:<br />
<br />
{| <br />
| <math>\Delta T_{\rm NO,1}^{t+1} = -\frac{B(1)}{A(1)}\Delta T_{\rm NO,2}^{t+1} + \frac{D(1)}{A(1)} \label{eq_udebm_coding_ALL1}</math> || || <span id="eq_A68"></span><div style="float: right; clear: right;">('''A68''')</div><br />
|- <br />
| with || || <br />
|- <br />
| <math>A(1) = 1.0+\theta_1^{\rm top}\Delta t\frac{ \lambda_O\alpha}{\zeta_o}</math> || :feedback over ocean || <span id="eq_A69"></span><div style="float: right; clear: right;">('''A69''')</div><br />
|- <br />
| <math>+\theta_1^{b}\Delta t\frac{ K_z}{0.5h_m h_d}</math> || :diffusion to layer 2 || <br />
|- <br />
| <math>+\theta_1^{b}\Delta t\frac{ w^t \beta}{h_m}</math> || :downwelling || <br />
|- <br />
| <math>+\theta_1^{\rm top}\Delta t\frac{ k_{\rm LO}\lambda_L\mu\alpha }{\zeta_o f_{\rm NO} (\frac{k_{\rm LO}}{f_{\rm NL}} + \lambda_L)}</math> || :feedback over land || <br />
|- <br />
| <math>B(1) = -\theta_1^{b}\Delta t\frac{ K_z}{0.5h_m h_d}</math> || :diffusion from layer 2 || <span id="eq_A70"></span><div style="float: right; clear: right;">('''A70''')</div><br />
|- <br />
| <math>-\theta_1^{b}\Delta t\frac{ w^t}{h_m}</math> || :upwelling from layer 2 || <br />
|- <br />
| <math>D(1) = \Delta T_{\rm NO,1}^{t}</math> || :previous temp || <span id="eq_A71"></span><div style="float: right; clear: right;">('''A71''')</div><br />
|- <br />
| <math>+ \theta_1^{\rm top}\Delta t\frac{1}{\zeta_o}DeltaQ_{NO}</math> || : forcing ocean || <br />
|- <br />
| <math>+ \theta_1^{\rm top}\Delta t\frac{\alpha k_{NS}}{\zeta_o f_{NO}}(\Delta T^t_{\rm SO,1}-\Delta T^t_{NO,1})</math> || :inter-hemis. exch. || <br />
|- <br />
| <math>+ \theta_1^{\rm top}\Delta t\frac{ k_{LO}\Delta Q_{NL}}{\zeta_o f_{NO} (\frac{k_{LO}}{f_{NL}} + \lambda_L)} </math> || : land forcing || <br />
|- <br />
| <math>+ \theta_1^{b}\Delta t\frac{\Delta w^t}{h_m}(T^0_{\rm NO,2}-T^0_{NO,sink})</math> || : variable upwelling || <br />
|}<br />
<br />
For the interior layers (2<math>{\leq}</math>z<math>{\leq}</math><math>n</math>), i.e., all layers except the top mixed layer and the bottom layer, the terms are re-ordered, so that <math>A(z)</math> comprises the terms for <math>\Delta T^{t+1}_{\rm NO,z-1}</math>, <math>B(z)</math> the terms for <math>\Delta T^{t+1}_{\rm NO,z}</math>, <math>C(z)</math> the terms for <math>\Delta T^{t+1}_{\rm NO,z+1}</math> and <math>D(z)</math> the remaining terms, according to:<br />
<br />
<br />
<br />
{| <br />
| <math>\Delta T_{\rm NO,z-1}^{t+1} = -\frac{B(z)}{A(z)}\Delta T_{\rm NO,z}^{t+1} - \frac{C(z)}{A(z)}\Delta T_{\rm NO,z+1}^{t+1} + \frac{D(z)}{A(z)}</math> || || <span id="eq_A72"></span><div style="float: right; clear: right;">('''A72''')</div><br />
|- <br />
| with || || <br />
|- <br />
| <math>A(z) = - \theta_z^{top}\Delta t\frac{K_z}{0.5(h_d+h_d')h_d}</math>|| : diffusion from layer above || <span id="eq_A73"></span><div style="float: right; clear: right;">('''A73''')</div><br />
|- <br />
| <math>B(z) = 1.0 + \theta_z^{b}\Delta t\frac{K_z}{h_d^2}</math> || :diffusion to layer below || <br />
|- <br />
| <math>+\theta_z^{top}\Delta t\frac{K_z}{0.5(h_d+h_d')h_d}</math> || :diffusion to layer above || <br />
|- <br />
| <math>+\theta_z^{top}\Delta t\frac{ w^t}{h_d}</math> || :upwelling to layer above || <span id="eq_A74"></span><div style="float: right; clear: right;">('''A74''')</div><br />
|- <br />
| <math>C(z) = - \theta_z^{b}\Delta t\frac{K_z}{h_d^2}</math> || :diffusion from layer below || <br />
|- <br />
| <math>-\theta_z^{b}\Delta t\frac{ w^t}{h_d}</math> || :upwelling from layer below || <span id="eq_A75"></span><div style="float: right; clear: right;">('''A75''')</div><br />
|- <br />
| <math>D(z) = \Delta T_{\rm NO,z}^{t}</math> || :previous temp || <br />
|- <br />
| <math>+\Delta t\frac{\Delta w^t}{h_d} (\theta_z^{b}T^{0}_{\rm NO,z+1}-\theta_z^{top}T^{0}_{\rm NO,z})</math> || :variable upwelling || <br />
|- <br />
| <math>+\theta_z^{\rm dif}\Delta t\frac{ w^t}{h_d}\beta\Delta T_{\rm NO,1}^{t-1}</math> || :entrainment || <br />
|- <br />
| <math>+\theta_z^{\rm dif}\Delta t\frac{\Delta w^t}{h_d} T^{0}_{\rm NO,sink}</math> || :variable entrainment || <span id="eq_A76"></span><div style="float: right; clear: right;">('''A76''')</div><br />
|}<br />
<br />
where <math>h_d'</math> is zero for the layer below the mixed layer and <math>h_d</math> otherwise. For the bottom layer, the respective sum factor <math>A(n)</math> for <math>\Delta T^{t+1}_{\rm NO,n-1}</math>, <math>B(n)</math> for <math>\Delta T^{t+1}_{\rm NO,n}</math> and <math>D(n)</math> for the remaining terms is:<br />
<br />
{|<br />
| <math>\Delta T_{{\rm NO},n-1}^{t+1} = -\frac{B(n)}{A(n)}\Delta T_{{\rm NO},n}^{t+1} + \frac{D(n)}{A(n)}</math> || || <span id="eq_A77"></span><div style="float: right; clear: right;">('''A77''')</div><br />
|- <br />
| with || || <br />
|- <br />
| <math>A(n) = - \theta_{n}^{\rm top}\Delta t\frac{K_z}{h_d^2}</math> || :diffusion from layer n-1 || <span id="eq_A78"></span><div style="float: right; clear: right;">('''A78''')</div><br />
|- <br />
| <math>B(n) = 1.0 + \theta_{n}^{\rm top}\Delta t\frac{K_z}{h_d^2}</math> || :diffusion to layer n-1 || <span id="eq_A79"></span><div style="float: right; clear: right;">('''A79''')</div><br />
|- <br />
| <math>+\theta_{n}^{\rm top}\Delta t\frac{ w^t}{h_d}</math> || :upwelling to layer n-1 || <br />
|- <br />
| <math>D(n) = \Delta T_{{\rm NO},n}^{t}</math> || :previous temp || <span id="eq_A80"></span><div style="float: right; clear: right;">('''A80''')</div><br />
|- <br />
| <math>+\theta_{n}^{\rm top}\Delta t\frac{w^t}{h_d} \beta\Delta T^{t-1}_{\rm NO,1}</math> || :downwelling from top layer || <br />
|- <br />
| <math>-\theta_{n}^{\rm top}\Delta t\frac{\Delta w^t}{h_d} T^{0}_{{\rm NO},n}</math> || :variable upwelling || <br />
|- <br />
| <math>+\theta_{n}^{\rm top}\Delta t\frac{\Delta w^t}{h_d} T^{0}_{\rm NO,sink}</math> || :variable downweilling || <br />
|}<br />
<br />
With these Eqs. ([[#eq_68|A68]]-[[#eq_80|A80]]), the ocean temperatures can be solved consecutively from the bottom to the top layer at each time step.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Upwelling_diffusion_climate_model&diff=39Upwelling diffusion climate model2013-06-17T15:11:31Z<p>Antonius Golly: </p>
<hr />
<div>*[[Model Description|model description]]<br />
**[[The Carbon Cycle| carbon cycle]]<br />
**[[Non-CO2 Concentrations | non-CO2 concentrations]]<br />
**[[Radiative Forcing | radiative forcing routines]]<br />
**[[Upwelling_diffusion_climate_model | climate model]]<br />
**[[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]]<br />
<br />
<br />
==From forcing to temperatures: the upwelling-diffusion climate model==<br />
<br />
In the early stages, MAGICC's climate module evolved from the simple climate model introduced by [[References#Hoffert_1980_Role_DeapSea|Hoffert et al. (1980)]]. MAGICC's atmosphere has four boxes with zero heat capacity, one over land and one over ocean for each hemisphere. The atmospheric boxes over the ocean are coupled to the mixed layer of the ocean hemispheres, with a set of n-1 vertical layers below (see [[#upd_model_structure|Fig-A3]]). The heat exchange between the oceanic layers is driven by vertical diffusion and advection. In the previous model versions, the ocean area profile is uniform with<br />
depth and the corresponding downwelling is modeled as a stream of polar sinking water from the top mixed layer to the bottom layer. In this study, an updated upwelling-diffusion-entrainment (UDE) ocean model is implemented with a depth-dependent ocean area (from HadCM2). For simplicity, the following equations govern the uniform area upwelling-diffusion version of the model. The [[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]] section provides details on the UDE algorithms.<br />
<br />
[[file:Fig-A1.jpg|330px|thumb|left|'''Fig-A3''' The schematic structure of MAGICC's upwelling-diffusion energy balance module with land and ocean boxes in eache hemisphere. The processes for heat transport in the ocean are deepw-watwe formation, upwelling diffusion, and heat exchange between the hemispheres. Not shown is the entrainment and the vertically depth-dependent area of the ocean layers (see [[Fig-A2a|fig.A2]] and text)]] <br />
<span id="upd_model_structure"></span> <br />
<br />
===Partitioning of feedbacks===<br />
<br />
In order to improve the comparability between MAGICC and AOGCMs, and following earlier versions of MAGICC, we use different feedback parameters over land and ocean. This requires an adjustable land to<br />
ocean warming ratio in equilibrium based on AOGCM results. Given that in equilibrium the oceanic heat uptake is zero, the global energy balance equation can be written as:<br />
<br />
<math>C\Delta Q_G=\lambda_G\Delta T_G=f_{L}\lambda_L \Delta T_{L} + f_{O}\lambda_O \Delta T_{O}\label{eq_globalenergybalance_equilibrium}</math><span id="eq_A45"></span><div style="float: right; clear: right;">('''A45''')</div><br />
<br />
where <math>\Delta Q_G</math>, <math>\lambda_G</math> and <math>\Delta T_G</math> are the global-mean forcing, feedback, and temperature change, respectively. The right hand side uses the area fractions <math>f</math>, feedbacks <math>\lambda</math>, and mean temperature changes, <math>\Delta T</math> for ocean (<math>O</math>) and land (<math>L</math>). As in earlier versions of MAGICC, the non-linear set of equations that determines <math>\lambda_O</math> and <math>\lambda_L</math> for a given set of equilibrium land-ocean warming ratio <math>RLO</math>=<math>\Delta T_L/ \Delta T_O</math>), global-mean feedback <math>\lambda_G</math>, heat exchange and enhancement factors (<math>k</math>, <math>\mu</math>), is solved by an iterative procedure involving the set of linear Eqs. ([[#A46|A46]]-[[#A49|A49]]), seeking the solution for <math>\lambda_L</math> closest to <math>\lambda_G</math>. The procedure in version 6 has been modified slightly to take into account the time-constant radiative forcing pattern by CO<sub>2</sub> for the four boxes with hemispheric land/ocean regions, if prescribed.<br />
<br />
<br />
Following [[References#Wigley_Schlesinger_1985_AnalyticalSolutionsTemperature|Wigley and Schlesinger (1985)]], it is assumed that the atmosphere is in equilibrium with the underlying ocean mixed layer, so that the energy balance equation for the Northern Hemispheric ocean (NO) is:<br />
<br />
{| <br />
| <math>&f_{\rm NO}\lambda_{O}\Delta T_{\rm NO} =</math> || <math>\textrm{:infrared outgoing flux}</math><br />
|- <br />
| <math>f_{\rm NO}\Delta Q_{\rm NO}</math> || <math>\textrm{:forcing}</math> <br />
|-<br />
| <math>+ k_{\rm LO}(\Delta T_{\rm NL} - \mu \Delta T_{\rm NO})</math> || <math>\textrm{:land-ocean heat exchange}</math><br />
|- <br />
| <math>+ k_{\rm NS}\alpha(\Delta T_{\rm SO} - \Delta T_{\rm NO})</math> || <math>\textrm{:hemispheric heat exch.}</math> <br />
|}<span id="eq_A46"></span><div style="float: right; clear: right;">('''A46''')</div><br />
<br />
<br />
where <math>\Delta T_{\rm NO}</math> is the surface temperature change over the Northern Hemisphere ocean, <math>\Delta Q_{\rm NO}</math> the radiative forcing over that region, <math>f_{\rm NO}</math> the northern ocean's area fraction of the earth surface, <math>k_{\rm LO}</math> the land-ocean heat exchange coefficient [Wm<sup>-2</sup><sup><math>^\circ</math></sup>C<sup>-1</sup>], a heat transport enhancement factor <math>\mu</math> allowing for asymmetric heat exchange between land and ocean (1<math>\leq</math><math>\mu</math> (see Sect. [[#Revised land-ocean heat exchange formation|Revised land-ocean heat exchange formation]] below), <math>k_{\rm NS}</math> is the hemispheric heat exchange coefficient in the mixed layer. Following [[References#Raper_Cubasch_1996_Emulation_AOGCM_simplemodel|Raper and Cubasch (1996))]] <math>\alpha</math> is a sea-ice related adjustment factor to relate upper ocean temperature change to surface air temperature change (see [[#Revised land-ocean heat exchange formation|Revised land-ocean heat exchange formation]]). Correspondingly, the equilibrium energy balance equations for the Northern Hemisphere land (NL), Southern Hemisphere ocean (SO) and Southern Hemisphere land (SL) are:<br />
<br />
<br />
<br />
<math>f_{\rm NL}\lambda_{L}\Delta T_{\rm NL} &=& f_{\rm NL}\Delta Q_{\rm NL}+ k_{\rm LO}(\mu \Delta T_{\rm NO} - \Delta T_{\rm NL})\label{eq_fourboxequations_NL}</math><span id="eq_A47"></span><div style="float: right; clear: right;">('''A47''')</div><br />
<br />
<br />
<math>f_{\rm SO}\lambda_{O}\Delta T_{\rm SO} &=& f_{\rm SO}\Delta Q_{\rm SO}+ k_{\rm LO}(\Delta T_{\rm SL} - \mu \Delta T_{\rm SO})+ k_{\rm NS}\alpha(\Delta T_{\rm NO} - \Delta T_{\rm SO})\label{eq_fourboxequations_SO}</math><span id="eq_A48"></span><div style="float: right; clear: right;">('''A48''')</div><br />
<br />
<br />
<math>f_{\rm SL}\lambda_{L}\Delta T_{\rm SL} &=& f_{SL}\Delta Q_{SL}+ k_{\rm LO}(\mu \Delta T_{\rm SO} - \Delta T_{\rm SL})\label{eq_fourboxequations_SL}</math><span id="eq_A49"></span><div style="float: right; clear: right;">('''A49''')</div><br />
<br />
As detailed below ([[#Accounting for climate-state dependent feedbacks|Accounting for climate-state dependent feedbacks]]), if the sensitivity factor <math>\xi</math> is set different from zero (see Eq.[[#A51|A51]]), it is possible to make the feedback factors <math>\lambda</math> in the energy balance equation dependent on the total radiative forcing. This forcing dependence of the feedback factors and the heat exchange enhancement factors are newly introduced in this version of MAGICC. The following two sections ([[#Revised land-ocean heat exchange formation|Revised land-ocean heat exchange formation]] and [[#Accounting for climate-state dependent feedbacks|Accounting for climate-state dependent feedbacks]]) are intended to provide both the motivation and details of these new parameterizations.<br />
<br />
===Revised land-ocean heat exchange formulation===<br />
<br />
This section highlights a "geometric" effect that can cause effective climate sensitivities to change over time. The global-mean sensitivity may increase simply due to decreasing land-ocean warming ratios, given that climate feedbacks over land and ocean areas are different. To control the relative temperature changes over ocean and land, a heat transport enhancement factor <math>\mu</math> is introduced. Enhancing the ocean-to-land heat transport (<math>\mu{\geq}</math>1) has the benefit that the simple climate model can better simulate some characteristic AOGCM responses. In the idealized forcing runs, AOGCMs often show a transient land-ocean warming ratio that slightly decreases over time, but stays above unity, combined with an increasing effective climate sensitivity in some models (see bottom rows in Fig. B1, B2, and B3 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html). The higher land than ocean warming (RLO<math>{>}</math>1) could be achieved by a smaller feedback (greater climate sensitivity) over land compared to the ocean boxes. However, as the land-ocean warming ratio decreases over time (due to less and less ocean heat uptake towards equilibrium), so would the effective global-mean climate sensitivity in previous model versions. The method used here, to allow both a RLO above unity and a non-decreasing effective climate sensitivity, assumes that ocean temperature perturbations influence the heat exchange more than land temperature changes. This asymmetric heat exchange formulation is then given by:<br />
<br />
<math>{\rm HX}_{\rm LO}=k_{\rm LO}(\Delta T_{L} - \mu \Delta T_{O})\label{eq<math>eatxchange}</math><span id="eq_A50"></span><div style="float: right; clear: right;">('''A50''')</div><br />
<br />
where <math>HX_{\rm LO}</math> is the land-ocean heat exchange (positive in direction land to ocean), <math>\mu</math> is the ocean-to-land enhancement factor and <math>\Delta T_L</math> and <math>\Delta T_O</math> are the temperature<br />
perturbations for the land and ocean region, respectively (cf. Eq. [[#eq_A46|A46]] ff.). Typical values for <math>\mu</math> range between 1 and 1.4 as estimated from calibrating the CMIP3 ensemble.<br />
<br />
===Accounting for climate-state dependent feedbacks===<br />
<br />
Some AOGCM runs indicate higher effective climate sensitivities for higher forcings and/or temperatures. For example, the ECHAM5/MPI-OM model shows an effective climate sensitivity of approximately 3.5<sup><math>\circ</math></sup>C after stabilization at twice pre-industrial CO<sub>2</sub> concentrations and 4<sup><math>\circ</math></sup>C for stabilization at quadrupled pre-industrial CO<sub>2</sub> concentrations (see [[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al., 2001]], [[References#Hansen_etal_2005_Efficacies|Hansen et al., 2005]]). Given that the transient land-ocean warming ratio is the same for the 1pctto2x and 1pctto4x runs ( see Fig. B1.last row in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html), the 'geometric' effect discussed in the Sect. [[#Revised land-ocean heat exchange formation|Revised land-ocean heat exchange formation]] would not explain this increase in climate sensitivity. An alternative explanation could be that climate feedbacks are climate-state dependent. The assumption in the standard energy balance with a constant global feedback (<math>\lambda</math>), with its attendant requirement that the outgoing energy flux scales proportionally with temperature change, may be an oversimplification. For example, the slow feedback due to retreating ice-sheets can lead to changes in the diagnosed effective sensitivities in AOGCMs (see e.g. [[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al., 2001]]) over long time-scales. [[References#Hansen_etal_2005_Efficacies|Hansen et al., 2005]] show that the 100-year climate response in the GISS model is more sensitive to higher forcings than to lower or negative forcings. Hansen et al.~(2005) express this effect by increasing efficacies for increasing radiative forcing. Table 1 in [[References#Hansen_etal_2005_Efficacies|Hansen et al., 2005]] suggests a gradient of roughly 1 % increase in efficacy for each additional Wm<sup>-2</sup> (OLS-regression of Ea versus Fa across the full range of CO<sub>2</sub> experiments), although some intervals (e.g. from 1.25 to 1.5<math>\times</math>CO<sub>2</sub>) show a slightly higher sensitivity of efficacy to forcing, i.e., 3% per Wm<sup>-2</sup>.<br />
<br />
Rather than making the efficacies dependent on forcing, an alternative is to make the climate sensitivity dependent on the forcing level. This distinction, on whether to modify forcing or sensitivity, is not important when the climate system is at or close to equilibrium. However, if the efficacies of the forcing, instead of the feedback parameters are allowed to vary with forcing, the transient climate response after a change in forcing will be slightly faster. In this MAGICC version, if a forcing dependency of the sensitivity is assumed, the land and ocean feedback parameters<br />
<math>\lambda_L</math> and <math>\lambda_O</math> are scaled as<br />
<br />
<math>\lambda =\frac{\Delta Q_{2x}}{\frac{\Delta Q_{2x}}{\lambda_{2x}}+\xi(\Delta Q- \Delta Q_{2x})} \label{eq_feedback_dependency_forcing}</math><span id="eq_A51"></span><div style="float: right; clear: right;">('''A51''')</div><br />
<br />
where <math>\lambda_{2x}</math> is the feedback parameter (=<math>\frac{\Delta Q_{2x}}{\Delta T_{2x}}</math>) at the forcing level for twice pre-industrial CO<sub>_2</sub> concentrations. The sensitivity factor <math>\xi</math> (KW<sup>-1</sup>m<sup>2</sup>) scales the climate sensitivity in proportion to the difference of forcing away from the model-specific "twice pre-industrial CO<math>_2</math> forcing level" (<math>\Delta Q{-} \Delta Q_{2x}</math>). The 1% increase in efficacy for each additional unit forcing in Hansen's findings translates into a feedback sensitivity factor <math>\xi</math> of 0.03 KW<sup>-1</sup>m<sup>2</sup>> (assuming a climate sensitivity <m\Delta T_{2x}</math>} of 3<sup><math>\circ</math></sup>C. Note that this scaling convention ([[#eq_51|A51]]) ensures that climate sensitivities are comparable for the equilibrium warming that corresponds to twice preindustrial CO<sub>_2</sub> concentration levels (see Table. 3 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html).<br />
<br />
===Efficacies===<br />
<br />
Efficacy is defined as the ratio of global-mean temperature response for a particular radiative forcing divided by the global-mean temperature response for the same amount of global-mean radiative forcing induced by CO<sub>_2</sub> (see Sect. 2.8.5 in [[References#Forster_Ramaswamy_etal_2007_IPCCAR4_Chapter2_radiativeForcing|Forster et al., 2005]]). In most cases, the efficacies are different for different forcing agents because of the geographical and vertical distributions of the forcing ([[References#Boer_Yu_2003_ClimateSensitivityResponse|Boer and Yu, 2003]];[[References#Joshi_etal_2003_improvedmetric_climatechange|Joshi et al., 2003]];[[References#Hansen_etal_2005_Efficacies|Hansen et al., 2005]]). The effective radiative forcing (<math>\Delta Q_e</math>) is the product of the standard climate forcing (<math>\Delta Q_a</math>), calculated after thermal adjustment of the stratosphere, and the efficacy (E<math>_a</math>). It is the effective forcings that are used in the energy balance equation (Eq.1), although both effective and standard forcings are carried through in the MAGICC code. Note that this parameterization yields slightly faster transient climate responses compared to an approach where different climate sensitivities are applied for each individual forcing agent (cf.[[#Accounting for climate-state dependent feedbacks|Accounting for climate-state dependent feedbacks]] above).<br />
<br />
In MAGICC, forcings for some components differ by hemisphere and over land and ocean. Just as for the global sensitivity, this, in combination with different land/ocean feedback factors, results in MAGICC6 exhibiting efficacies different from unity for non-CO<sub>_2</sub> forcing agents. In other words, efficacies different from unity are in part a consequence of the geometric effect described above. MAGICC calculates these internal efficacies using reference year (default 2005) forcing patterns. After normalizing these forcing patterns to a global-mean of <math>\Delta Q_{2x}</math> (default 3.71 Wm<sup>-2</sup>), the internal efficacy can be determined as<br />
<br />
<math>E_{\rm int} = \frac{\Delta T_{\rm eff2x}}{\Delta T_{2x}}\label{eq_efficacies_internal}</math><span id="eq_A52"></span><div style="float: right; clear: right;">('''A52''')</div><br />
<br />
where <math>T_{\rm eff2x}</math> is the actual global-mean equilibrium temperature change resulting from a normalized forcing pattern and <math>\Delta T_{2x}</math> is the corresponding warming for 2x CO<sub>_2</sub> forcing, i.e., the climate sensitivity. For most forcing agents, these internal efficacies are very close to one, except for forcings with a strong land/ocean forcing contrast, such as aerosol forcings. For example, for direct aerosol forcing in the HadCM3 emulation (calibration III - see Table B3 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html) the efficacy is 1.14. By default, these internal efficacies are taken into account when applying prescribed efficacies, so that:<br />
<br />
<math>\Delta Q_e = \frac{E_a}{E_{\rm int}}\Delta Q_a \label{eq_efficacies_acc_for_intefficacies}</math><span id="eq_A53"></span><div style="float: right; clear: right;">('''A53''')</div><br />
<br />
===The upwelling-diffusion equations===<br />
<br />
The transient temperature change evolution is largely influenced by the climate system's inertia, which in turn depends on the nature of the heat uptake by the climate system. The transient energy balance equations can be written as:<br />
<br />
<math>f_{\rm NO}(\zeta_o \frac{d\Delta T_{\rm NO,1}}{dt}-\Delta Q_{\rm NO}+\lambda_o \alpha \Delta T_{\rm NO,1} + F_{N}) =k_{\rm LO}(\Delta T_{\rm NL} - \mu\alpha\Delta T_{\rm NO,1})+k_{NS}\alpha(\Delta T_{\rm SO,1} - \Delta T_{\rm NO,1})\label{eq_transient_linear_equations_NO}</math><span id="eq_A54"></span><div style="float: right; clear: right;">('''A54''')</div><br />
<br />
<br />
<math>f_{\rm NL}(\zeta_L \frac{d\Delta T_{\rm NL}}{dt} - \Delta Q_{\rm NL}+ \lambda_L \Delta T_{\rm NL}) =k_{\rm LO}(\mu\alpha\Delta T_{\rm NO,1}-\Delta T_{\rm NL})\label{eq_transient_linear_equations_NL}</math><span id="eq_A55"></span><div style="float: right; clear: right;">('''A55''')</div><br />
<br />
<br />
<math>f_{SO}(\zeta_o \frac{d\Delta T_{\rm SO,1}}{dt}-\Delta Q_{\rm SO}+ \lambda_o \alpha \Delta T_{\rm SO,1} + F_{S})=k_{\rm LO}(\Delta T_{\rm SL} - \mu\alpha\Delta T_{\rm SO,1})+k_{\rm NS}\alpha(\Delta T_{\rm NO,1} - \Delta T_{\rm SO,1})\label{eq_transient_linear_equations_SO}</math><span id="eq_A56"></span><div style="float: right; clear: right;">('''A56''')</div><br />
<br />
<br />
<math>f_{\rm SL}(\zeta_L \frac{d\Delta T_{\rm SL}}{dt} - \Delta Q_{\rm SL}+ \lambda_L \Delta T_{\rm SL}) =k_{\rm LO}(\mu\alpha\Delta T_{\rm SO,1}-\Delta T_{\rm SL})\label{eq_transient_linear_equations_SL}</math><span id="eq_A57"></span><div style="float: right; clear: right;">('''A57''')</div><br />
<br />
where the adjustment factor <math>\alpha</math> (default 1.2) determines - over ocean areas - the ratio of hemispheric changes in air (<math>\Delta T_{\rm xO}</math>) versus ocean mixed layer temperatures (<math>\Delta T_{\rm xO,1}</math>). Based on ECHAM1/LSG analysis ([[References#Raper_Cubasch_1996_Emulation_AOGCM_simplemodel|Raper and Cubasch, 1996]]), this sea-ice factor was first introduced by [[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2001)]] to account for the fact that the air temperature will exhibit additional warming, because the atmosphere feels warmer ocean surface temperatures where sea ice retreats. The bulk heat capacity of the mixed layer in each hemisphere x is <math>f_x\zeta_o=f_x\rho c h_m</math>, where <math>\rho</math> denotes the density of seawater (1.026<math>\times</math>10<sup>6</sup> g m<sup>-3</sup>), c is the specific heat capacity (0.9333 cal g<sup>-1</sup><sup><math>\circ</math></sup>C<sup>-1</sup>= 4.1856<math>\times</math>0.9333 Joule g<sup>-1</sup><sup><math>\circ</math></sup>C<sup>-1</sup>) and <math>h_m</math> is the mixed layer's thickness [m]. The bulk heat capacity of the land areas is <math>f_x\zeta_L</math>, here assumed to be zero. The net heat flux into the ocean below the mixed layer is denoted by <math>F_x</math>.<br />
<br />
Equation ([[#eq_A55|A55]]) can then be written as: <br />
<br />
<math>\Delta T_{\rm NL} = \frac{f_{\rm NL}\Delta Q_{\rm NL}+k_{\rm LO}\mu\alpha\Delta T_{\rm NO,1}}{f_{\rm NL}\lambda_L + k_{\rm LO}}\label{eq_transient_separating_TNL}</math><span id="eq_A58"></span><div style="float: right; clear: right;">('''A58''')</div><br />
<br />
Substituting <math>\Delta T_{\rm NL}</math> in Eq. ([[#eq_A55|A55]]) yields:<br />
<br />
<math>f_{\rm NO}(\zeta_o \frac{d\Delta T_{\rm NO,1}}{dt} - \Delta Q_{\rm NO} + \lambda_o \alpha\Delta T_{\rm NO,1} + F_N) = \frac{k_{\rm LO}}{\frac{k_{\rm LO}}{f_{\rm NL}}+\lambda_L}(\Delta Q_{\rm NL}-\lambda_L\mu\alpha \Delta T_{\rm NO,1})+ k_{\rm NS}\alpha(\Delta T_{\rm SO,1} - \Delta T_{\rm NO,1})\label{eq_transient_TNL_into_TNO}</math><span id="eq_A59"></span><div style="float: right; clear: right;">('''A59''')</div><br />
<br />
Provided we know the heat flux <math>F_N</math> into the ocean below the mixed layer, we could now derive <math>d\Delta T_{\rm NO,1}/dt</math>. The net heat flux <math>F_N</math> at the bottom of the mixed layer is determined by<br />
vertical heat diffusivity (diffusion coefficient <math>K_z</math> [cm<sup>2</sup>s<sup>-1</sup>=3155.76<sup>-1</sup>m<sup>2</sup>yr<sup>-1</sup>]), and upwelling and downwelling (upwelling velocity w [m yr<sup>-1</sup>]), both acting on the perturbations <math>\Delta T</math> from the initial temperature profile <math>T^0_{\rm NO,z}</math>. If the upwelling rate <math>w</math> varies over time, the change in upwelling velocity <math>\Delta w^t{=}(w^t-w^0)</math> compared to its initial state <math>w^0</math> is assumed to act on the initial temperature profile, so that:<br />
<br />
<math>F_N = \frac{K_z}{0.5h_d}\rho c (\Delta T_{\rm NO,1}-\Delta T_{\rm NO,2})- w \rho c (\Delta T_{\rm NO,2} - \beta \Delta T_{\rm NO,1})</math><br /><math>- \Delta w \rho c (T^0_{\rm NO,2}- T^0_{\rm NO,sink})\label{eq_transient<math>eatflux_bottom_mixedlayer}</math><span id="eq_A60"></span><div style="float: right; clear: right;">('''A60''')</div><br />
<br />
where <math>T^0_{\rm NO,z}</math> is the initial temperature for water in layer z or in the downwelling pipe (z="sink").<br />
<br />
Given that the top layer is assumed to be mixed, the gradient of the temperature perturbations is calculated by the difference of the perturbations divided by half the thickness <math>h_d</math> of the second layer (see Fig. [[#Fig-A2|A2]]). Substituting <math>F_N</math> in Eq.([[#eq_A59|A59]] with Eq.([[#eq_A60|A60]]) and transforming the equation to discrete time steps, yields:<br />
<br />
<br />
{| <br />
| <math>\frac{d\Delta T_{\rm NO,1}}{dt} \approx \frac{\Delta T_{\rm NO,1}^{t+1} - \Delta T_{\rm NO,1}^{t}}{\Delta t} =</math> || <span id="eq_A61"></span><div style="float: right; clear: right;">('''A61''')</div><br />
|- <br />
| <math>\frac{1}{\zeta_o}\Delta Q_{\rm NO}^t </math>|| <math>\textrm{:forcing} </math><br />
|- <br />
| <math>- \frac{\lambda_o \alpha}{\zeta_o}\Delta T_{\rm NO,1}^{t+1} </math>|| <math>\textrm{:feedback}</math><br />
|- <br />
| <math>-\frac{K_z}{0.5h_d h_m}(\Delta T_{\rm NO,1}^{t+1}-\Delta T_{\rm NO,2}^{t+1}) </math>|| <math>\textrm{:diffusion}</math><br />
|- <br />
| <math>+ \frac{w^{t}}{h_m}(\Delta T^{t+1}_{\rm NO,2}-\beta \Delta T^{t+1}_{\rm NO,1}) </math>|| <math>\textrm{:upwelling}</math><br />
|- <br />
| <math>+ \frac{\Delta w^{t}}{h_m}(T^{0}_{\rm NO,2}-T^{0}_{\rm NO,sink}) </math>|| <math>\textrm{:variable upwelling} </math><br />
|- <br />
| <math>+ \frac{k_{\rm LO}(\Delta Q^{t}_{\rm NL}-\lambda_L \mu\alpha\Delta T^{t+1}_{\rm NO,1})}{\zeta_o f_{\rm NO}(\frac{k_{\rm LO}}{f_{\rm NL}}+\lambda_L)} </math>|| <math>\textrm{:land forcing}</math><br />
|- <br />
| <math>+ \frac{k_{\rm NS}\alpha}{\zeta_o f_{\rm NO}}(\Delta T_{\rm SO,1}^{t}-\Delta T_{\rm NO,1}^{t}) </math>|| <math>\textrm{:inter-hemispheric ex.} </math><br />
|}<br />
<br />
For the layers below the mixed layer (2<math>\leq</math>z<math>\leq</math>n-1), the temperature updating is governed by diffusion (first two terms in Eq.[[#eq_A62|A62]] and upwelling (last two terms), so that:<br />
<br />
<math>\frac{\Delta T^{t+1}_{\rm NO,z}-\Delta T^{t}_{\rm NO,z}}{\Delta t}= \frac{K_z}{0.5(h_d+h_d')h_d}(\Delta T^{t+1}_{\rm NO,z-1}-\Delta T^{t+1}_{\rm NO,z})- \frac{K_z}{h_d^2}(\Delta T^{t+1}_{\rm NO,z}-\Delta T^{t+1}_{\rm NO,z+1})</math><br /><math>+ \frac{w^{t}}{h_d}(\Delta T^{t+1}_{\rm NO,z+1}-\Delta T^{t+1}_{\rm NO,z})+ \frac{\Delta w^{t}}{h_d}(T^0_{\rm NO,z+1}-T^0_{\rm NO,z})\label{eq_transient_discrete_NO_submixed}</math><span id="eq_A62"></span><div style="float: right; clear: right;">('''A62''')</div><br />
<br />
where <math>h_d'</math> is zero for the layer below the mixed layer (z=2) and <math>h_d</math> otherwise, <math>\Delta w^t</math> is the change from the initial upwelling rate.<br />
<br />
[[file:Fig-A2a.jpg|350px|thumb|left|'''Fig-A4''' The schematic oceanic area and initial temperature profiles in MAGICC'S ocean hemispheres. Diffusion-driven heat transport is modeled proportional to the vertical gradient of temperature, which is especially high below the mixed layer.]] <br />
<span id="upd_model_structure"></span><br />
<br />
For the bottom layer (z=n), the downwelling term has to be taken into account, so that:<br />
<br />
<math>\frac{\Delta T^{t+1}_{\rm NO,n}-\Delta T^{t}_{\rm NO,n}}{\Delta t}= \frac{K_z}{h_d^2}(\Delta T^{t+1}_{\rm NO,n-1}-\Delta T^{t+1}_{\rm NO,n})</math><br />
<br />
<math>+ \frac{w^{t}}{h_d}(\beta\Delta T^{t}_{\rm NO,1}-\Delta T^{t+1}_{\rm NO,n})+ \frac{\Delta w^{t}}{h_d}(T^0_{\rm NO,sink}-T^0_{\rm NO,n})\label{eq_transient_discrete_NO_bottom}</math><span id="eq_A63"></span><div style="float: right; clear: right;">('''A63''')</div><br />
<br />
<br />
Corresponding to the temperature calculations shown here for the Northern Hemisphere ocean (NO), the equivalent steps apply for the Southern Hemisphere ocean (SO). For simplicity, the equations described above are for the constant-depth area profile case, which MAGICC defaults to when the depth-dependency factor <math>\vartheta</math> is set to zero. The detailed code for the general case with <math>0{\leq}\vartheta{\leq}1</math> is given in the ([[#Implementation of upwelling-diffusion-entrainment equations|Implementation of upwelling-diffusion-entrainment equations]]) section.<br />
<br />
===Calculating heat uptake===<br />
<br />
Heat uptake by the climate system can be calculated in different ways. One method is to use the global energy balance (Eq.1). Using the effective sensitivity as in ([[Model Description#eq_1|Eq.1]]) the heat uptake <math>F^t</math> is estimated as:<br />
<br />
<math>{dH^t}{dt}=F^t = \Delta Q^t-(f_L \lambda_L \Delta T^t_{L} + f_O \lambda_O \Delta T^t_{O}) \label{eq<math>eatuptake_balance}</math><span id="eq_A64"></span><div style="float: right; clear: right;">('''A64''')</div><br />
<br />
For verification purposes MAGICC6 calculates heat uptake in two ways, both directly (as above) and by integrating heat content changes in each layer in the ocean (yielding identical results), given the assumed zero heat capacity of the atmosphere and land areas:<br />
<br />
<math>\Delta H^t = \sum^{n}_{i=1} \frac{1}{\rho c h_i}\frac{(f_{\rm NO}\Delta T^t_{\rm NO,i} + f_{\rm SO} \Delta T^t_{\rm SO,i})}{f_O}+\epsilon \label{eq<math>eatuptake_integrating}</math><span id="eq_A65"></span><div style="float: right; clear: right;">('''A65''')</div><br />
<br />
where <math>h_i</math> is the thickness of the layer, i.e., <math>h_m</math> for the mixed layer and <math>h_d</math> for the others and <math>\epsilon</math> is a small term to account for the heat content of the polar sinking water.<br />
<br />
===Depth-dependent ocean with entrainment===<br />
<br />
[[References#Harvey_Schneider_1985_PartII, Harvey_Schneider_1985_PartI|Harvey and Schneider (1985b,a)]] introduced the upwelling-diffusion model with entrainment from the polar sinking water by varying the upwelling velocity w with depth. Building on the work by [[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2001)]], MAGICC6 also includes the option of a depth-dependent ocean area profile. If the depth-dependency parameter <math>\vartheta</math> is set to 1 (default), a standard depth-dependent ocean area profile is assumed as in HadCM2 and used in [[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2001)]]}. A constant upwelling velocity is assumed and mass conservation is maintained by "entrainment" from the downwelling pipe. With ocean area decreasing with depth and constant upwelling velocity, the upwelling mass flux would also have to decrease with depth. To offset this, the amount of entrainment into layer z is assumed to be proportional to the decrease in area from the top to the bottom of each layer (cf. [[#Fig-A2a|Fig-A4]]). We differ from the model structures tested by<br />
[[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2001)]], by equating changes in the temperature of the entraining water to those in the downwelling pipe, namely a fraction <math>\beta</math> (default 0.2) of the mixed layer temperature <math>\Delta T_{x,1}^{t-1}</math> of the previous timestep in Hemisphere x. For a detailed description of the code, see the following Sect. [[#Implementation of upwelling-diffusion-entrainment equations|Implementation of upwelling-diffusion-entrainment equations]]. Simple upwelling-diffusion models can overestimate the ocean heat uptake for higher warming scenarios when applying parameter values calibrated to match heat uptake for lower warming scenarios (see e.g. Fig. 17b in<br />
[[References#Harvey_etal_1997_IPCC_IntroductionSimpleClimateModels|Harvey et al., 1997]]). To address this, MAGICC6 includes a warming-dependent vertical diffusivity gradient. The physical reasoning is that a strengthened<br />
thermal stratification and, hence, reduced vertical mixing leads to decreased heat uptake for higher warming. Thus, the effective vertical diffusivity at <math>K_{z,i}</math> between ocean layer i and i+1 is<br />
given by:<br />
<br />
<math>K_{z,i} = {\rm max}\,(K_{z,{\rm min}}(1 - d_i)\frac{dK_{\rm z}}{dT}(\Delta T_{H,1}^{t-1}-\Delta T_{H,n}^{t-1})+K_z) \label{eq_verticalDiffusivity<math>eatdependent}</math><span id="eq_A66"></span><div style="float: right; clear: right;">('''A66''')</div><br />
<br />
where <math>K_{z,{\rm min}}</math> is the minimum vertical diffusivity (default 0.1 cm<sup>2</sup> s<sup>-1</sup>); <math>d_i</math> is the relative depth of the layer boundary with zero at the bottom of the mixed layer and one for the top of the bottom layer; <math>\frac{dK_{\rm z}}{dT}</math> is a newly introduced ocean stratification coefficient specifying how the vertical diffusivity <math>K_{\rm z}</math> between the mixed layer 1 and layer 2 changes with a change in the temperature difference between the top/mixed and bottom ocean layer of the respective hemisphere at the previous timestep t-1 <math>(\Delta T_{H,1}^{t-1}{-}\Delta T_{H,n}^{t-1})</math>.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Radiative_Forcing&diff=38Radiative Forcing2013-06-17T15:10:52Z<p>Antonius Golly: </p>
<hr />
<div>*[[Model Description|model description]]<br />
**[[The Carbon Cycle| carbon cycle]]<br />
**[[Non-CO2 Concentrations | non-CO2 concentrations]]<br />
**[[Radiative Forcing | radiative forcing routines]]<br />
**[[Upwelling_diffusion_climate_model | climate model]]<br />
**[[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]]<br />
<br />
<br />
==Radiative forcing==<br />
<br />
The following section highlights the key parameterizations used for estimating the radiative forcing due to human-induced changes in greenhouse gas concentrations, tropospheric ozone and aerosols. The radiative forcing applied in MAGICC is in general the forcing at tropopause level after stratospheric temperature adjustment. Efficacies of the forcings, as discussed by [[References#Hansen_etal_2005_Efficacies|Hansen et al. (2005)]] and [[References#IPCC_AR4_Chapter10_Projections_Meehletal|Meehl et al. (2007)]] can be applied.<br />
<br />
===Carbon dioxide===<br />
<br />
Taking into account the "saturation" effect of CO<sub>2</sub> forcing, i.e., the decreasing forcing efficiency for a unit increases of CO<sub>2</sub> concentrations with higher background concentrations, the first IPCC Assessment ([[References#Shine_IPCC1990_Chapter2|Shine et al., 1990]]) presented the simplified expression of the form:<br />
<br />
<math>\label{eq_CO2_forcing} \Delta Q_{\rm CO_2}=\alpha_{\rm CO_2}{\rm ln} (\rm C/C_0)</math><span id="eq_A35"></span><div style="float: right; clear: right;">('''A35''')</div><br />
<br />
where <math>\Delta Q_{\rm CO_2}</math> is the adjusted radiative forcing by CO<sub>2</sub> (Wm<sup>-2</sup>) for a CO<sub>2</sub> concentration <math>C</math> (ppm) above the pre-industrial concentration <math>C</math><sub>0</sub> (278 ppm). This expression proved to be a good approximation, although the scaling parameter <math>\alpha_{\rm CO_2}</math> has since been updated to a best-estimate of 5.35 Wm<sup>-2</sup> (=<math>\frac{3.71}{ln(2)} </math>Wm<sup>-2</sup>)[[References#Myhre_etal_1998_newestimates_GHGforcing|Myhre et al. (1998)]], used as default in MAGICC. When applying AOGCM-specific CO<sub>2</sub> forcing, <math>\alpha_{\rm CO_2}</math> is set to: <br />
<br />
<math>\label{eq_CO2_forcing_dQ2x} \alpha_{\rm CO_2} = \frac{\Delta Q_{\rm 2\times}}{\rm ln(2)}</math><span id="eq_A36"></span><div style="float: right; clear: right;">('''A36''')</div><br />
<br />
===Methane and nitrous oxide===<br />
<br />
Methane and nitrous oxide have overlapping absorption bands so that higher concentrations of one gas will reduce the effective absorption by the other and vice versa. This is reflected in the standard simplified expression for methane and nitrous oxide forcing, <math>\Delta Q_{\rm CH4}</math> and <math>\Delta Q_{\rm N2O}</math>, respectively (see [[References#Ramaswamy_2001_IPPCWG1_RadiativeForcing|Ramaswamy et al., 2001]], [[References#Myhre_etal_1998_newestimates_GHGforcing|Myhre et al. 1998]]):<br />
<br />
<math>\label{eq_methane_forcing}\Delta Q_{\rm CH_4} = \alpha_{\rm CH_4}(\sqrt{\rm C_{\rm CH_4}}-\sqrt{\rm C_{\rm CH_4}^0}-f(\rm C_{\rm CH_4},{\rm C}_{\rm N_2O}^0)-f({\rm C}_{\rm CH_4}^0,{\rm C}_{\rm N_2O}^0)</math><span id="eq_A37"></span><div style="float: right; clear: right;">('''A37''')</div><br />
<br />
<br />
<math>\Delta Q_{\rm N_2O} = \alpha_{\rm N_2O}(\sqrt{{\rm C}_{\rm N_2O}}-\sqrt{{\rm C}_{\rm N_2O}^0})-f({\rm C}_{\rm CH_4}^0,{\rm C}_{\rm N_2O})-f({\rm C}_{\rm CH_4}^0,{\rm C}_{\rm N_2O}^0)</math><span id="eq_A38"></span><div style="float: right; clear: right;">('''A38''')</div><br />
<br />
where the overlap is captured by the function<br />
<br />
<math>\label{eq_methane_forcing_overlap}f(\rm M,N)=0.47{\rm ln}\,(1+0.6356(\frac{\rm MN}{10^6})^{0.75}+0.007\frac{\rm M}{10^3}(\frac{\rm MN}{10^6})^{1.52})</math><span id="eq_A39"></span><div style="float: right; clear: right;">('''A39''')</div><br />
<br />
with M and N being CH<sub>4</sub> and N<sub>2</sub>O concentrations in ppb. For methane, an additional forcing factor due to methane-induced enhancement of stratospheric water vapor content is included. This enhancement is assumed to be proportional to (default <math>\beta</math>=15 %) the ``pure´´ methane radiative forcing, i.e., without subtraction of N<sub>2</sub>O absorption band overlaps:<br />
<br />
<math>\Delta Q_{\rm CH_4}^{\rm stratoH2O} =\beta\alpha_{\rm CH_4}(\sqrt{\rm C_{\rm CH_4}}-\sqrt{\rm C_{\rm CH_4}^0}). </math><span id="eq_A40"></span><div style="float: right; clear: right;">('''A40''')</div><br />
<br />
===Tropospheric ozone=== <br />
<br />
From the tropospheric ozone precursor emissions and following the updated parameterizations of OxComp as given in footnote a of Table 4.11 in [[References#Ehhalt_Prather_2001_IPCC_Chemistry|Ehhalt et al. (2001)]], the change in hemispheric tropospheric ozone concentrations (in DU) is parameterized as: <br />
<br />
<math>\label{eq_tropospheric_ozone} \Delta (\rm trop O_3)={\rm S}_{\rm CH_4}^{O_3}\Delta ln(\rm CH_4)+ {\rm S}_{\rm NOx}^{\rm O_3} E_{\rm NOx} + {\rm S}_{\rm CO}^{\rm O_3} E_{\rm CO} + {\rm S}_{\rm VOC}^{\rm O_3} E_{\rm VOC}</math><span id="eq_A41"></span><div style="float: right; clear: right;">('''A41''')</div><br />
<br />
where <math>S_{\rm x}^{\rm O_3}</math> are the respective sensitivity coefficients of tropospheric ozone to methane concentrations and precursor emissions. The radiative forcing is then approximated by a linear abundance to forcing relationship so that <math>\Delta Q_{\rm trop O_3}=\alpha_{\rm trop O3} \Delta (\rm trop O_3)</math> with <math>\alpha_{\rm trop O3}</math> being the radiative efficiency factor (default 0.042).<br />
<br />
===Halogenated gases===<br />
<br />
The global-mean radiative forcing <math>\Delta Q_{t,i}</math> of halogenated gases is simply derived from their atmospheric concentrations C (see [[Non-CO2 Concentrations#|Non-CO2 concentrations]]) and radiative efficiencies <math>\varrho_i</math> [[References#Ehhalt_Prather_2001_IPCC_Chemistry|Ehhalt et al. (2001)]] table 4.11.<br />
<br />
<math>\Delta {Q_{t,i}} = \varrho_i (C_{t,i}-C_{0,i})\label{eq_halogas_RF}</math><span id="eq_A42"></span><div style="float: right; clear: right;">('''A42''')</div><br />
<br />
The land-ocean forcing contrast in each hemisphere for halogenated gases is assumed to follow the one [[References#Hansen_etal_2005_Efficacies|Hansen et al. (2005)]] estimated for CFC-11. The hemispheric forcing contrast is dependent on the lifetime of the gas. For short-lived gases (<math>{<}</math>1\,yr) the hemispheric forcing contrast is assumed to equal the time-variable hemispheric emission ratio. For longer lived gases (default <math>{>}</math>8\,yrs), the hemispheric forcing contrast is assumed to equal the one from CFC-11 with linear scaling in between these two approaches for gases with a medium lifetime.<br />
<br />
===Stratospheric ozone===<br />
<br />
Depletion of the stratospheric ozone layer causes a negative global-mean radiative forcing <math>\Delta Q_{t}</math>. The depletion and hence radiative forcing is assumed to be dependent on the equivalent effective stratospheric chlorine (EESC) concentrations as follows:<br />
<br />
<math>\Delta Q_{t} = \eta_1 (\eta_2 \times \Delta {\rm EESC}_{t})^{\eta_3} \label{eq_stratospheric_ozone} </math><span id="eq_A43"></span><div style="float: right; clear: right;">('''A43''')</div><br />
<br />
where <math>\eta_1</math> is a sensitivity scaling factor (default <math>-</math>4.49e-4 Wm<sup>-2</sup>), <math>\Delta {\rm EESC}_{t}</math> the EESC concentrations above 1980 levels (in ppb), the factor <math>\eta_2</math> equals <math>\frac{1}{100}</math> (ppb<math>^{-1}</math>) and <math>\eta_3</math> is the sensitivity exponent (default 1.7).<br />
<br />
EESC concentrations are derived from the modeled concentrations of 16 ozone depleting substances controlled under the Montreal Protocol, their respective chlorine and bromine atoms, fractional release factors and a bromine versus chlorine ozone depletion efficiency (default 45) ([[References#Daniel_1999_relativeImportance_Bromine_Chlorine|Daniel et al., 1999]]).<br />
<br />
<br />
===Tropospheric aerosols===<br />
\label{section_TropAerosolParameterization}<br />
<br />
The direct effect of aerosols is approximated by simple linear forcing-abundance relationships for sulfate, nitrate, black carbon and organic carbon. Time-variable hemispheric abundances of these short-lived aerosols are in turn approximated by their hemispheric emissions, justifiable because of their very short lifetimes. The ratio of direct forcing over land and ocean areas in each hemisphere is taken from [[References#Hansen_etal_2005_Efficacies|Hansen et al. (2005)]] (available at http://data.giss.nasa.gov/efficacy/). Specifying the direct radiative forcing patterns for one particular year, and knowing the<br />
hemispheric emissions in that year, allows us to define the future forcing as a function of future emissions.<br />
<br />
The indirect radiative forcing, formerly modeled as dependent on SO<math>_{\rm x}</math> abundances only [[References#Wigley_1991_ReducingFossilCO2IncreaseClimateChange|Wigley, 1991a]], is now estimated by taking into account time-series of sulfate, nitrate, black carbon and organic carbon optical thickness:<br />
<br />
<math>\label{eq_forcing_indirectAer} \Delta Q_{\rm Alb,i} = r\times {\rm P}_{\rm Alb,i}\times \log(\frac{\sum_g w_g {\rm N}_{g,i}}{\sum_g w_g {\rm N}_{g,i}^0})</math><span id="eq_A44"></span><div style="float: right; clear: right;">('''A44''')</div><br />
<br />
where <math>\Delta Q_{\rm Alb,i}</math> is the first indirect aerosol forcing in the four atmospheric boxes <math>i</math>, representing land and ocean areas in each hemisphere; P<math>_{\rm Alb}</math> is the four-element pattern of aerosol indirect effects related to albedo ([[References#Twomey_1977_albedo|HTwomey, 1977]]) in a reference year. The second indirect effect on cloud cover changes ([[References#Albrecht_1989_cloudcover_aerosols|Albrecht, 1989]]) is modeled equivalently -- using a reference year pattern P<math>_{\rm Cvr,i}</math>. The respective default patterns are derived from data displayed in Fig. 13 of [[References#Hansen_etal_2005_Efficacies|Hansen et al. (2005)]]. The scaling factor <math>r</math> allows one to specify a global-mean first or second indirect forcing for a specific reference year. The time-variable number concentrations of soluble aerosols N<math>_{g,i}</math> relative to their pre-industrial level in each hemisphere N<math>_{g,i}^0</math> are normed to unity in that reference year. This is done separately for sulfates, nitrates, black carbon and organic carbon. For the latter, the differential solubility from industrial (fossil fuel) and biomass burning sources is taken into account (default solubility ratio 0.6/0.8) ([[References#Hansen_etal_2005_Efficacies|Hansen et al., 2005]]). The default contribution shares w<math>_g</math> of the individual aerosol types g to the indirect aerosol effect were assigned to reflect the preliminary results by [[References#Hansen_etal_2005_Efficacies|Hansen et al. (2005)]], namely 36 % for sulfates, 36 % for organic carbon, 23 % for nitrates and 5 % for black carbon. Note, however, that these estimates of the importance of non-SOx aerosol contributions are very uncertain, not least because the solubility, e.g. for organic carbon and nitrates have large uncertainties. The number concentrations <math>N_{g,i}</math> are here approximated by historical optical thickness estimates (as provided on http://data.giss.nasa.gov/efficacy/ see as well Supplement) and extrapolated into the future by scaling with hemispheric emissions. The general logarithmic relation between number concentrations and forcing is based on the findings by [[References#Wigley_Raper_1992_ImplicationsWarmingIPCC_Nature|Wigley and Raper (1992)]]; [[References#Wigley_1991_ReducingFossilCO2IncreaseClimateChange|Wigley (1991a)]]; [[References#Gultepe_Isaac_1999_aerosols|Gultepe and Isaac(1999)]] and used in [[References#Hansen_etal_2005_Efficacies|Hansen et al. (2005)]]}.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Non-CO2_Concentrations&diff=37Non-CO2 Concentrations2013-06-17T15:10:08Z<p>Antonius Golly: </p>
<hr />
<div>*[[Model Description|model description]]<br />
**[[The Carbon Cycle| carbon cycle]]<br />
**[[Non-CO2 Concentrations | non-CO2 concentrations]]<br />
**[[Radiative Forcing | radiative forcing routines]]<br />
**[[Upwelling_diffusion_climate_model | climate model]]<br />
**[[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]]<br />
<br />
<br />
==Non-CO<sub>2</sub> concentrations==<br />
<br />
This section provides the formulas used to convert emissions to concentrations, while the [[#Radiative Forcing|Radiative Forcing]] section provides details on the derivation of radiative forcings.<br />
<br />
===Methane===<br />
<br />
Natural emissions of methane are inferred by balancing the budget for a user-defined historical period, e.g. from 1980-1990, so that<br />
<br />
<math>\label{eq_natural emissions}E^n_{\o} = \theta (\Delta C_{\o} - C_{\o '}/\tau_{\rm tot})-E^f_{\o} - E^b_{\o}</math><span id="eq_A28"></span><div style="float: right; clear: right;">('''A28''')</div><br />
<br />
where <math>E^n_{\o}</math>, <math>E^f_{\o}</math> and <math>E^b_{\o}</math> are the average natural, fossil and land use related emissions, respectively; <math>\theta</math> is the conversion factor between atmospheric concentrations and mass loadings. <math>C_{\o'}</math> (and <math>\Delta C_{\o}</math>) are the average (annual changes in) concentrations. The net atmospheric lifetime <math>\tau_{\rm tot}</math> in the case of methane consists of the atmospheric chemical lifetime and lifetimes that characterize the soil and other (e.g. stratospheric) sink components according to <br />
<br />
<math>\label{eq_methane lifetime} \frac{1}{\tau_{\rm tot}} = \frac{1}{\tau_{\rm tropos}} + \frac{1}{\tau_{\rm soil}} + \frac{1}{\tau_{\rm other}}</math><span id="eq_A29"></span><div style="float: right; clear: right;">('''A29''')</div><br />
<br />
The feedback of methane on tropospheric OH and its own lifetime follows the results of the OxComp work (tropospheric oxidant model comparison) (see[[References#Ehhalt_Prather_2001_IPCC_Chemistry| Ehhalt et al., 2001]] in particular Table 4.11, which provides simple parameterizations for simulating complex three-dimensional atmospheric chemistry models. As default, tropospheric OH abundances are assumed to decrease by 0.32 % for every 1 % increase in CH<math>_4</math>. The change in tropospheric OH abundances is thus modeled as:<br />
<br />
<math>\label{eq_troposphericOH} \noindent \Delta {\rm ln}\,({\rm trop} {\rm OH}) = { S_{\rm CH_4}^{\rm OH}}\, \Delta{{\rm ln}\,(\rm CH_4)}+ { S_{{\rm NO_x}}^{\rm OH}} {E_{{\rm NO_x}} + S_{\rm CO}^{\rm OH} E_{\rm CO}} + {\rm S_{\rm VOC}^{\rm OH} E_{\rm VOC}}</math><span id="eq_A30"></span><div style="float: right; clear: right;">('''A30''')</div><br />
<br />
where <math>S_x^{\rm OH}</math> is the sensitivity of tropospheric OH towards CH<math>_4</math>, NOx, CO and VOC, with default values of <math>-</math>0.32, +0.0042, <math>-</math>1.05e-4 and <math>-</math>3.15e-4, respectively. Increases in tropospheric OH abundances decrease the tropospheric lifetime <math>\tau '</math> of methane (default 9.6 yrs<sup>-1</sup>), which is approximated as a simple exponential relationship <br />
<br />
<math>\label{eq_tropos_methane lifetime} \tau_{\rm CH_4,tropos}' = \tau_{\rm CH_4,tropos}^0\, {\rm exp}\,^{\Delta {\rm ln}\,({\rm trop OH})}</math><span id="eq_A31"></span><div style="float: right; clear: right;">('''A31''')</div><br />
<br />
Approximating the temperature sensitivity of the net effect of tropospheric chemical reaction rates, the tropospheric lifetime of CH<math>_4</math> is adjusted:<br />
<br />
<math>\label{eq_tropos_methane lifetime_inclTemp} \tau_{\rm CH_4,tropos} = \frac{\tau_{\rm CH_4,tropos}^0}{\frac{\tau_{\rm CH_4,tropos}^0}{\tau_{\rm CH_4,tropos}'} + S_{\tau_{\rm CH_4}}\Delta T}</math><span id="eq_A32"></span><div style="float: right; clear: right;">('''A32''')</div><br />
<br />
where <math>S_{\tau_{\rm CH_4}}</math> is the temperature sensitivity coefficient (default <math>S_{\tau_{\rm CH_4}}</math>=3.16e-2<sup><math>^{\circ}</math></sup>C<sup>-1</sup>) and <math>\Delta T</math> is the temperature change above a user-definable year, e.g. 1990.<br />
<br />
===Nitrous oxide===<br />
<br />
As for methane, natural nitrous oxide emissions are estimated by a budget [[#A28|(A28)]]. For nitrous oxide however, the average concentrations <math>C_{\o'}</math>=<math>C_{\o-3}</math> are taken for a period shifted by 3 years to account for a three year delay of transport of tropospheric N<math>_2</math>O to the main stratospheric sink. The feedback of the atmospheric burden C<sub>N<math>_2</math>O</sub> of nitrous oxide on its own lifetime is approximated by:<br />
<br />
<math>\tau_{\rm N_2O} = \tau_{\rm N_2O}^0 (\frac{{\rm C}_{\rm N_2O}}{{\rm C}_{\rm N_2O}^0})^{S_{\tau_{\rm N_2O}}}\\ \label{eq_nitrous_lifetime}</math><span id="eq_A33"></span><div style="float: right; clear: right;">('''A33''')</div><br />
<br />
where <math>S_{\tau_{\rm N_2O}}</math> is the sensitivity coefficient (default <math>S_{\tau_{\rm N_2O}}</math>=<math>-</math>5e-2) and the superscript ``<sup><math>0</math></sup>´´ indicates a pre-industrial reference state.<br />
<br />
===Tropospheric aerosols===<br />
<br />
Due to their short atmospheric residence time, changes in hemispheric abundances of aerosols are approximated by changes in their hemispheric emissions. Historical emissions of tropospheric aerosols are extended into the future either by emissions scenarios (SO<math>_{\rm x}</math>, NO<math>_{\rm x}</math>, CO) or, if scenario data are not available, with proxy emissions, e.g. using CO as a proxy emission<br />
for OC and BC. As with many other emissions scenarios, the harmonized IPCC SRES scenarios do not provide black (BC) and organic carbon (OC) emissions. Hence, various ''ad-hoc'' scaling approaches have been applied, often scaling BC and OC synchronously [[References#Takemura_2006_MIROC_forcings|(Takemura et al., 2006)]], sometimes linearly with CO<math>_2</math> emissions. The MESSAGE emissions scenario modeling group is one of the few explicitly including BC and OC emissions in their multi-gas emissions scenarios [[References#Rao_etal_2005_blackcarbon_organiccarbon_emissions|(Rao et al, 2005; Rao and Riahi, 2006)]]. By analyzing MESSAGE scenarios, a scaling factor was derived for this study in relation to carbon monoxide emissions (CO), varying linearly in time to 0.4 by 2100 relative to current BC/CO or OC/CO emission ratios.<br />
<br />
===Halogenated gases===<br />
<br />
The derivation of concentrations of halogenated gases controlled under either the Kyoto or Montreal Protocol assumes time-variable lifetimes. The net atmospheric lifetime <math>\tau_i</math> of each halogenated gas is calculated by summing the inverse lifetimes related to stratospheric, OH-related and other sinks. Stratospheric lifetimes are assumed to decrease 15 % per degree of global mean surface temperature warming, due to an increased Brewer-Dobson circulation [[References#butchart_scaife2001_brewerDobson|(Butchart and Scaife, 2001)]]. Tropospheric OH-related losses are scaled by parameterized changes in OH-abundances, matching the respective changes in the lifetime of methane. The concentration <math>C_{t,i}</math> for the beginning of each year <math>t</math> is updated, using a central differencing formulation, according to:<br />
<br />
<math>C_{t+1,i}{=}\tau_i E_{t,i} \frac{\rho_{\rm atm}}{m_{\rm atm}\mu_i}(1-e^{\frac{-1}{\tau_i}})+C_{t,i}(1-e^{\frac{-1}{\tau_i}})\label{eq_halogas_conc}</math><span id="eq_A34"></span><div style="float: right; clear: right;">('''A34''')</div><br />
<br />
where <math>E_{t,i}</math> is the average emissions of gas <math>i</math> through year <math>t</math>, <math>C_{t,i}</math> the atmospheric concentration of gas <math>i</math> in year <math>t</math>, <math>\rho_{\rm atm}</math> the average density of air, <math>m_{\rm atm}</math> the total mass of the atmosphere [[References#Trenberth_etal1994_totalmassofatmosphere|(Trenberth and Guillemot, 1994)]], and <math>\mu_i</math> is the mass per mol of gas <math>i</math>. For hydrogenated halocarbons, the tropospheric OH-related lifetimes are assumed to vary in proportion to the changes in methane lifetime.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=The_Carbon_Cycle&diff=36The Carbon Cycle2013-06-17T15:09:24Z<p>Antonius Golly: </p>
<hr />
<div>*[[Model Description|model description]]<br />
**[[The Carbon Cycle| carbon cycle]]<br />
**[[Non-CO2 Concentrations | non-CO2 concentrations]]<br />
**[[Radiative Forcing | radiative forcing routines]]<br />
**[[Upwelling_diffusion_climate_model | climate model]]<br />
**[[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]]<br />
<br />
<br />
==The carbon cycle==<br />
<br />
Changes in atmospheric CO<sub>2</sub> concentration, C, are determined by CO<sub>2</sub> emissions from fossil and industrial sources (<math>E_{\rm foss}</math>), other directly human-induced CO<sub>2</sub> emissions from or removals to the terrestrial biosphere (<math>E_{\rm lu}</math>), the contribution from oxidized methane of fossil fuel origin (<math>E_{\rm fCH_4},</math>), the flux due to ocean carbon uptake (<math>F_{\rm ocn}</math>) and the net carbon uptake or release by the terrestrial biosphere (<math>F_{\rm terr}</math>) due to CO<sub>2</sub> fertilization and climate feedbacks. As in the C4MIP generation of carbon cycle models, no nitrogen or sulphur deposition effects on biospheric carbon uptake are included here [[References#Thornton_nitrogenCarbonCycle|Thornton et al., 2006]]. Hence, the budget <br />
Eq.[[#eq_A1|A1]] for a change in atmospheric CO<sub>2</sub> concentrations is:<br />
<br />
<math>\Delta C/\Delta t= E_{\rm foss} + E_{\rm lu} + E_{\rm fCH_4}- F_{\rm ocn} - F_{\rm terr}</math><span id="eq_A1"></span><div style="float: right; clear: right;">('''A1''')</div><br />
<br />
[[file:Fig-A2.jpg|350px|thumb|left|'''Fig-A2''' The terrestrial carbon cycle component in MAGICC with its carbon pools and carbon fluxes. <br />
For description of the pools and fluxes, including the treatment of <br />
temperature feedbacks and CO<sub>2</sub> fertilization, see Sect.[[#Terrestrial carbon cycle|Terrestrial carbon cycle]] ]] <br />
<span id="fig_terr_carboncycle"></span> <br />
<br />
===Terrestrial carbon cycle=== <br />
<br />
The terrestrial carbon cycle follows that in [[References#Wigley_1993_BalancingCarbonBudget|Wigley, 1993]], in turn is based on [[References#Harvey_1989_ManagingAtmCO2|Harvey, 1989]]. It is modeled with three boxes, one living plant box <math>P</math> (see Fig.[[#fig_terr_carboncycle|Terrestrial Carbon Cycle]]) and two dead biomass boxes, of which one is for detritus <math>H</math> and one for <br />
organic matter in soils <math>S</math>. The plant box comprises woody material, leaves/needles, grass, and roots, but does not include the rapid turnover part of living biomass, which can be assumed to have a zero lifetime on the timescales of interest here (dashed extension of plant box <math>P</math> in Fig.[[#fig_terr_carboncycle|Fig-A2]]. Thus, a fraction of gross primary product (GPP) cycles through the plant box directly back to the atmosphere due to autotrophic respiration and can be ignored (dashed arrows). Only the remaining part of GPP, namely the net primary production (NPP) is simulated. The NPP flux is channeled through the ``rapid turnover´´ part of the plant box and partitioned into carbon fluxes to the remainder plant box (default <math>g_P</math>=35%), detritus (<math>g_H</math>=60%) and soil box<br /> (<math>g_S</math>=1-<math>g_P</math>-<math>g_H</math>=5%).<br />
<br />
The plant box has two decay terms, litter production <math>L</math> and a part of gross deforestation <math>D_{\rm gross}^P</math>. Litter production is partitioned <br />
to both the detritus (<math>\phi_H</math>=98%) and soil box (<math>\phi_S</math>=1-<math>\phi_H</math>=2%). Thus, the mass balance for the plant box is: <br />
<br />
<math>\Delta P/\Delta t = g_P{\rm NPP} - R - L - D_{\rm gross}^P \label{eq_massbalance_P}</math><span id="eq_A2"></span><div style="float: right; clear: right;">('''A2''')</div><br />
<br />
The detritus box has sources from litter production (<math>\phi_HL</math>) and sinks to the atmosphere due to land use (<math>D_{\rm lu}^H</math>), non-land use related oxidation (<math>Q_A</math>), and a sink to the soil box (<math>Q_S</math>). The mass balance for the detritus box is thus<br />
<br />
<math> \Delta H/\Delta t = g_H{\rm NPP} + \phi_H L - Q_A - Q_S - D_{\rm lu}^H \label{eq_massbalance_H}</math><span id="eq_A3"></span><div style="float: right; clear: right;">('''A3''')</div><br />
<br />
The soil box has sources from litter production (<math>\phi_S</math>L), the detritus box (<math>Q_S</math>) and fluxes to the atmosphere due to land use <br />
(<math>D_{\rm gross}^S</math>), and non-land use related oxidation (<math>U</math>). The mass balance for the soil box is thus <br />
<br />
<math> \Delta S/\Delta t = g_S{\rm NPP} +\phi_S L + Q_S - U - D_{\rm lu}^S \label{eq_massbalance_S}</math><span id="eq_A4"></span><div style="float: right; clear: right;">('''A4''')</div><br />
<br />
The decay rates (<math>L</math>, <math>Q</math> and <math>U</math>) of each pool are assumed to be proportional to pool's box masses <math>P</math>, <math>H</math> and <math>S</math>, respectively. The turnover times <math>\tau_P</math>, <math>\tau_H</math> and <math>\tau_S</math> are determined by the initial steady-state conditions for box sizes and fluxes.<br />
<br />
<math>L_0 = P_0/\tau^P_0</math><span id="eq_A5"></span><div style="float: right; clear: right;">('''A5''')</div><br />
<br />
<br />
<math>Q_0 = H_0/\tau^H_0</math><span id="eq_A6"></span><div style="float: right; clear: right;">('''A6''')</div><br />
<br />
<br />
<math>U_0 = S_0/\tau^S_0\label{eq_terrcc_turnovertimes}</math><span id="eq_A7"></span><div style="float: right; clear: right;">('''A7''')</div><br />
<br />
Constant relaxation times <math>\tau</math> ensure that the box masses will relax back to their initial sizes if perturbed by a one-off land use change-related carbon release or uptake -- assuming no changes in fertilization and temperature feedback terms. This relaxation acts as an effective regrowth term so that deforestation <math>\Sigma D_{\rm gross}{=}D_{\rm gross}^P + D_{\rm gross}^H + D_{\rm gross}^S</math> represents the gross land use emissions, related to net land use emissions <math>E_{\rm lu}</math> by regrowth <math>\Sigma G</math>=<math>G^P</math> + <math>G^H</math> + <math>G^S</math><br />
<br />
<math>\Sigma D_{\rm gross} - \Sigma {\rm G} = E_{\rm lu}</math><span id="eq_A8"></span><div style="float: right; clear: right;">('''A8''')</div><br />
<br />
<br />
<math>D_{\rm gross}^P - {\rm G}^P = d_P E_{\rm lu}</math><span id="eq_A9"></span><div style="float: right; clear: right;">('''A9''')</div><br />
<br />
<br />
<math>D_{\rm gross}^H - {\rm G}^H = d_H E_{\rm lu}</math><span id="eq_A10"></span><div style="float: right; clear: right;">('''A10''')</div><br />
<br />
<br />
<math>D_{\rm gross}^S - {\rm G}^S = d_S E_{\rm lu}\label{eq_grossandnet_deforestation}</math><span id="eq_A11"></span><div style="float: right; clear: right;">('''A11''')</div><br />
<br />
Gross land-use related emissions might be smaller (compared to a case where relaxation times are assumed constant) as some human land use activities, e.g.\ deforestation, can lead to persistent changes of the ecosystems over the time scales of interest, thereby preventing full regrowth to the initial state <math>P_0</math>, <math>H_0</math> or <math>S_0</math>. A factor <math>\psi</math> is used to denote the fraction of gross deforestation that does not regrow (0<math>{\leq}{\psi}{\leq}</math>1). Thus, the relaxation times <math>\tau</math> are made time-dependent according to the following equation:<br />
<br />
<math>\tau^P(t) = \left(P_0 - \psi\int_0^t d_PE_{\rm lu}(t')dt'\right)/L_0</math><span id="eq_A12"></span><div style="float: right; clear: right;">('''A12''')</div><br />
<br />
<br />
<math>\tau^H(t) = \left(H_0 - \psi\int_0^t d_HE_{\rm lu}(t')dt'\right)/Q_0</math><span id="eq_A13"></span><div style="float: right; clear: right;">('''A13''')</div><br />
<br />
<br />
<math>\tau^S(t) = \left(S_0 - \psi\int_0^t d_SE_{\rm lu}(t')dt'\right)/U_0 \label{eq_terrcc_turnovertimes_timedep}</math><span id="eq_A14"></span><div style="float: right; clear: right;">('''A14''')</div><br />
<br />
====Formulation for CO<sub>2</sub> fertilization====<br />
<br />
CO<sub>2</sub> fertilization indicates the enhancement in net primary production (NPP) due to elevated atmospheric CO<sub>2</sub> concentration. As described in [[References#Wigley_2000_balancingCarbonBudget|Wigley, 2000]], there are two common forms used in simple models to simulate the CO<sub>2</sub> fertilization effect: (a) the logarithmic form (fertilization parameter <math>\beta_m</math>=1) and (b) the rectangular hyperbolic or sigmoidal growth function (<math>\beta_m</math>=2) (see e.g. [[References#Gates_1985_globalbiosphericCCycle|Gates, 1985]]. The rectangular hyperbolic formulation provides more realistic results for both low and high concentrations so that NPP does not rise without limit as CO<sub>2</sub> concentrations increase. Previous MAGICC versions include both formulations, but used the second as default. The code now allows use of a linear combination of both formulations (1<math>{\leq}{\beta_m}{\leq}</math>2).<br />
<br />
The classic logarithmic fertilization formulation calculates the enhancement of NPP as being proportional to the logarithm of the change in CO<sub>2</sub> concentrations C above the preindustrial level <math>C_0</math>:<br />
<br />
<math>\beta_{\rm log}=1 + \beta_s \,{\rm ln}\,({\rm C/C}_0) \label{eq_CO2fertilization_logarithm}</math><span id="eq_A15"></span><div style="float: right; clear: right;">('''A15''')</div> <br />
<br />
The rectangular hyperbolic parameterization for fertilization is given by<br />
<br />
<math>N=\frac{{C-C}_b}{1+b({C-C}_b)}</math><br />
<br />
:<math>=\frac{{N_0}(1+b(C_0-C_b))({C}-{C_b})}{(C_0-C_b)(1+b({C-C}_b))}\label{eq_CO2fertilization_sigmoidal growth}</math><span id="eq_A16"></span><div style="float: right; clear: right;">('''A16''')</div><br />
<br />
where <math>N_0</math> is the net primary production and <math>C_0</math> the CO<sub>2</sub> concentrations at pre-industrial conditions, <math>C_b</math> the concentration value at which NPP is zero (default setting: <math>C_b</math>=31 ppm, see [[References#gifford_1993|Gifford, 1993]].<br />
<br />
For better comparability with models using the logarithmic formulation, following [[References#Wigley_2000_balancingCarbonBudget|Wigley, 2000]], the CO<sub>2</sub> fertilization factor <math>\beta_s</math> expresses the NPP enhancement due to a CO<sub>2</sub> increase from 340 ppm to 680 ppm, valid under both formulations. Thus, MAGICC first determines the NPP ratio <math>r</math> for a given <math>\beta_s</math> fertilization factor according to:<br />
<br />
<math>r=\frac{{N}(680)}{{N}(340)}=\frac{{N}_0(1+\beta_s \,{\rm ln}\,(680/{{C}}_0))}{{N}_0(1+\beta_s \,{\rm ln}\, (340/{C}_0))}\label{eq_CO2fertilization_340to640}</math><span id="eq_A17"></span><div style="float: right; clear: right;">('''A17''')</div><br />
<br />
Following from here, <math>b</math> in Eq. [[#eq_A16|A16]] is determined by<br />
<br />
<math>b=\frac{(680-{C}_b)-r(340-{C}_b)}{(r-1)(680-{C}_b)(340-{C}_b)}\label{eq_CO2fertilization_determining b}</math><span id="eq_A18"></span><div style="float: right; clear: right;">('''A18''')</div><br />
<br />
which can in turn be used in Eq. [[#eq_A16|A16]] to calculate the effective CO<sub>2</sub> fertilization factor <math>\beta _{\rm sig}</math> at time <math>t</math> as<br />
<br />
<math>\beta _{\rm sig}(t)=\frac{1/({C}_0 - {C}_b) + b}{1/({C}(t)- {C}_b) + b} \label{eq_CO2fertilization_factor_michaelismenton}</math><span id="eq_A19"></span><div style="float: right; clear: right;">('''A19''')</div><br />
<br />
MAGICC6 allows for an increased flexibility, as any linear combination between the two fertilization parameterizations can be chosen (1<math>{\leq}{\beta_m}{\leq}</math>2), so that the effective fertilization factor <math>\beta _{\rm eff}</math> is given by:<br />
<br />
<math>\beta _{\rm eff}(t)=(2-\beta_m)\beta_{\rm log}+(\beta_m-1)\beta_{\rm sig}\label{eq_CO2fertilization_factor_effective}</math><span id="eq_A20"></span><div style="float: right; clear: right;">('''A20''')</div><br />
<br />
The CO<sub>2</sub> fertilization effect affects NPP so that <math>\beta_{\rm eff}</math> = NPP - NPP<sub>0</sub>. MAGICC's terrestrial carbon cycle furthermore applies the fertilization factor to one of the heterotrophic respiration fluxes <math>R</math> that cycles through the detritus box, which makes up 18.5 % of the total heterotrophic respiration (<math>\sum {\rm R} {=} R+U_a+Q</math>) at the initial steady-state.<br />
<br />
====Temperature effect on respiration and decomposition====<br />
<br />
Global-mean temperature increase is taken as a proxy for climate-related impacts on the carbon cycle fluxes induced by regional temperature, cloudiness or precipitation regime changes. Those impacts are commonly referred to as ``climate feedbacks on the carbon cycle´´, or simply, ``carbon cycle feedbacks´´. Here, the terrestrial carbon fluxes NPP, and the heterotrophic respiration/decomposition fluxes <math>R</math>, <math>Q</math> and <math>U</math> are scaled assuming an exponential relationship,<br />
<br />
<math>F_{i}(t)= F_{i}'(t)\cdot {\rm exp}(\sigma_{i}\Delta T(t))\label{eq_CO2feedback_GPP}</math><span id="eq_A21"></span><div style="float: right; clear: right;">('''A21''')</div><br />
<br />
where <math>\Delta T(t)</math> is the temperature above a reference year level, e.g. for 1990 or 1900, and <math>F_i'</math> (<math>F_i</math>) stands for the (feedback-adjusted) fluxes ''NPP'', <math>R</math>, <math>Q</math> and <math>U</math>. The parameters <math>\sigma_i</math> (K<math>^{-1}</math>) are their respective sensitivities to temperature changes. In order to model the actual change in <math>Q</math> and <math>U</math>, the relaxation times <math>\tau</math> for the detritus and soil pool are adjusted, respectively. Land use CO<sub>2</sub> emissions in many emissions scenarios ([[References#Nakicenovic_etal_2000_IPCCSRES|e.g SRES, Nakicenovic and Swart, 2000]]) reflect the net directly human-induced emissions. At each time-step, the gross land use emissions are subtracted from the plant, detritus and soil carbon pools. The difference between net and gross land use emissions is the CO<sub>2</sub> uptake due to regrowth. Thus, a separation between directly human-induced (deforestation-related) emissions and indirectly human-induced effects (regrowth) on the carbon cycle is required. As both regrowth and the temperature sensitivity are modeled by adjusting the turnover times, a no-feedback case is computed separately, retrieving the regrowth, then calculating the feedback-case including the formerly calculated regrowth.<br />
<br />
===Ocean carbon cycle===<br />
<br />
For modeling the perturbation of ocean surface dissolved inorganic carbon, an efficient impulse response substitute for the 3D-GFDL model [[References#Sarmiento_etal_1992_perturbationCO2_ocean_general_circulation_model|Sarmiento et al. (1992)]] is incorporated into MAGICC. The applied analytical representation of the pulse response function is provided in Appendix A.2.2 of [[References#Joos_Bruno_etal_1996_efficient_accurate_carbonuptake|Joos et al. (1996)]]. <br />
<br />
The sea-to-air flux <math>F_{\rm ocn}</math> is determined by the partial pressure differential for CO<sub>2</sub> between the atmosphere C and surface layer of the ocean <math>\rho</math>CO<sub>2</sub><br />
<br />
<math>{\rm F}_{\rm ocn} = k (C-\rho {\rm CO}_2) \label{eq_fluxocean}</math><span id="eq_A22"></span><div style="float: right; clear: right;">('''A22''')</div><br />
<br />
where <math>k</math> is the global average gas exchange coefficient ([[References#Joos_Prentice_etal_2001_feedbacks_biosphere_IPCC|Joos et al., 2001]]). This exchange coefficient is here calibrated to the individual C<math>^4</math>MIP carbon cycle models (default value (7.66 yr<sup>-1</sup>). The perturbation in dissolved inorganic carbon in the surface ocean <math>\Delta\Sigma {\rm <br />
CO_2}(t)</math> at any point t in time is obtained from the convolution integral of the mixed layer impulse response function <math>r_s</math> and the net air-to-sea flux <math>F_{\rm ocn}</math>:<br />
<br />
<math>\label{eq_hilda_pertdissolvedinorgCO2}\Delta\Sigma {\rm CO_2}(t) &=& \frac{c}{hA}\{\int_{t_0}^{t} {F}_{\rm ocn}(t') r_s(t-t')dt')\}</math><span id="eq_A23"></span><div style="float: right; clear: right;">('''A23''')</div><br />
<br />
The impulse response function <math>r_s</math> is given for the time immediately after the impulse injection (<1 yr) by (see Appendix A.2.4 of [[References#Joos_Bruno_etal_1996_efficient_accurate_carbonuptake|Joos et al., 1996]]):<br />
<br />
<math>r_s(t)&=& 1.0 - 2.2617t + 14.002t^2-48.770t^3+82.986t^4-67.527t^5+21.037t^6 \label{eq_hilda_impulseresponse_below2years}</math><span id="eq_A24"></span><div style="float: right; clear: right;">('''A24''')</div><br />
<br />
and for t<math>{\geq}</math>1 year is given by:<br />
<br />
<math>r_s(t)= \sum_{i=1}^6 \gamma_i e^{-\tau_i t}\label{eq_oceancc_after_initialphase}</math><span id="eq_A25"></span><div style="float: right; clear: right;">('''A25''')</div><br />
<br />
with the partitioning <math>\gamma</math> and relaxation <math>\tau</math> coefficients:<br />
<br />
<math>\gamma=\left[\begin{array}{l}0.01481\\0.70367\\0.24966\\0.066485\\0.038344\\0.019439\end{array}\right]\tau=\left[\begin{array}{l}0\\1/0.70177\\1/2.3488\\1/15.281\\1/65.359\\1/347.55\end{array}\right] \label{eq_hilda_impulseresponse_after2years_coefficients}</math><span id="eq_A26"></span><div style="float: right; clear: right;">('''A26''')</div><br />
<br />
The relationship between the perturbation to dissolved inorganic carbon <math>\Delta\Sigma</math>CO<math>_2(t)</math> and ocean surface partial pressures <math>\Delta\rho</math>CO<sub>2</sub>(<math>T_0</math>) (expressed in ppm or <math>\mu</math>atm) at the preindustrial temperature level <math>T_0</math> is given by Eq.(A23) in [[References#Joos_Prentice_etal_2001_feedbacks_biosphere_IPCC|Joos et al. (1996)]]. Furthermore, the temperature sensitivity effect on CO<sub>2</sub> solubility and hence oceanic carbon uptake is parameterized with a simple exponential expression. The modeled partial pressure <math>\rho</math>CO<math>_2(t)</math> increases with sea surface temperatures according to:<br />
<br />
<math>\rho {\rm CO}_2(t) = [\rho {\rm CO}_2(t_0) + \Delta\rho {\rm CO}_2(T_0)]\, {\rm exp}(\alpha_T \Delta T)\label{eq_partialpressure_ocn}</math><span id="eq_A27"></span><div style="float: right; clear: right;">('''A27''')</div><br />
<br />
where <math>\alpha_T</math> (default <math>\alpha_T</math>=0.0423 K<sup>-1</sup>) is the sensitivity of the sea surface partial pressure to changes in temperature (<math>\Delta T</math>) away from the preindustrial level (see <br />
Eq.(A24) in [[References#Joos_Prentice_etal_2001_feedbacks_biosphere_IPCC|Joos et al. (1996)]], based on [[References#Takahashi_etal_1993_surfaceOceans_CO2|Takahashi et al. (1993)]]).</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Model_Description&diff=35Model Description2013-06-17T15:07:41Z<p>Antonius Golly: </p>
<hr />
<div>*[[Model Description|model description]]<br />
**[[The Carbon Cycle| carbon cycle]]<br />
**[[Non-CO2 Concentrations | non-CO2 concentrations]]<br />
**[[Radiative Forcing | radiative forcing routines]]<br />
**[[Upwelling_diffusion_climate_model | climate model]]<br />
**[[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]]<br />
<br />
<br />
==Model description==<br />
<br />
=== Overview ===<br />
<br />
The 'Model for the Assessment of Greenhouse Gas Induced Climate Change' (MAGICC) is a simple/reduced complexity climate model. MAGICC was originally developed by Tom Wigley (National Centre for Atmospheric Research, Boulder, US, and University of Adelaide, Australia) and Sarah Raper (Manchester Metropolitan University, UK) in the late 1980s and continuously developed since then. It has been one of the widely used climate models in various IPCC Assessment Reports. The latest version, MAGICC6, is co-developed by Malte Meinshausen (Potsdam Institute for Climate Impact Research, Germany, and the University of Melbourne, Australia). These pages provide an extensive model description, sourced from a 2011 publication in Atmospheric Chemistry & Physics [http://www.atmos-chem-phys.net/11/1417/2011/ (M. Meinshausen, S. Raper and T. Wigley, 2011)]. <br />
<br />
This Page provides a detailed description of MAGICC6 and its<br />
different modules (see [[#Fig_A1|Fig-A1]] below). A basic [[Model_Documentation|model description]] is given, while subsections describe MAGICC's <br />
[[The Carbon Cycle| carbon cycle]], the atmospheric-chemistry<br />
parameterizations and derivation of <br />
[[Non-CO2 Concentrations | non-CO<sub>2</sub> concentrations]], <br />
[[Radiative Forcing | radiative forcing routines]], and the climate module to get from<br />
radiative forcing to hemispheric (land and ocean, separately) to<br />
global-mean temperatures ([[Upwelling_diffusion_climate_model|climate model]]), as<br />
well as oceanic heat uptake. Finally, details are provided on the implementation scheme for the [[UDB Implementation | upwelling-diffusion-entrainment ocean]]<br />
climate module. A technical upgrade is that MAGICC6 has been re-coded in Fortran95,<br />
updated from previous Fortran77 versions. Nearly all of the MAGICC6 code is directly based on the earlier<br />
MAGICC versions programmed by Wigley and Raper <br />
([[References#Wigley_Raper_1987_ThermalExpansion_SeaWater_Nature| 1987]], [[References#Wigley_Raper_1992_ImplicationsWarmingIPCC_Nature | 1992]], [[References#Wigley_Raper_2001_Science_InterpretationHighProjections | 2001]]).<br />
<br />
[[File:OverviewGraph Fig1.png|frame|right|'''Fig-A1''' Schematic overview of MAGICC calculations showing the key steps<br />
from emissions to global and hemispheric climate responses.<br />
Black circled numbers denote the sections in the Appendix<br />
describing the respective algorithms used. Source: Fig A.1. in Meinshausen et al. 2011, ACP]]<span id="fig_A1"></span> <br />
<br />
===Basic model description===<br />
<br />
MAGICC has a hemispherically averaged upwelling-diffusion ocean coupled to an atmosphere layer and a globally averaged carbon cycle model. As with most other simple models, MAGICC evolved from a simple global average energy-balance equation. The energy balance equation for the perturbed climate system can be written as:<br />
<br />
<math>\Delta Q_G = \lambda_G \Delta T_G + \frac{d H}{d t}\label{eq_globalenergybalance}</math><span id="eq_1"></span><div style="float: right; clear: right;">('''1''')</div><br />
<br />
where <math>\Delta Q_G</math> is the global-mean radiative forcing at the top of the troposphere. This extra energy influx is partitioned into increased outgoing energy flux and heat content changes in the ocean <math>\frac{d H}{d t}</math>. The outgoing energy flux is dependent on the global-mean feedback factor, <math>\lambda_G</math>, and the surface temperature perturbation <math>\Delta T_G</math>.<br />
<br />
While MAGICC is designed to provide maximum flexibility in order to match different types of responses seen in more sophisticated models, the approach in MAGICC's model development has always been to derive the simple equations as much as possible from key physical and biological processes. In other words, MAGICC is as simple as possible, but as mechanistic as necessary. This process-based approach has a strong conceptual advantage in comparison to simple statistical fits that are more likely to quickly degrade in their skill when emulating scenarios outside the original calibration space of sophisticated models.<br />
<br />
The main improvements in MAGICC6 compared to the version used in the IPCC AR4 are briefly highlighted in this section (Note that there is an intermediate version, MAGICC 5.3, described in [[References#Wigley_etal_2009_UncertaintiesClimateStabilization|Wigley et al., 2009]]). The options introduced to account for variable climate sensitivities are described in Sect. [[#introduction of variable climate sensitivities|introduction of variable climate sensitivities]]. With the exception of the updated carbon cycle routines [[#updated carbon cycle|updated carbon cycle]], the MAGICC 4.2 and 5.3 parameterizations are covered as special cases of the 6.0 version, i.e., the IPCC AR4 version, for example, can be recovered by appropriate parameter settings.<br />
<br />
===Introduction of variable climate sensitivities===<br />
<br />
Climate sensitivity (<math>\Delta T_{2x}</math>) is a useful metric to compare models and is usually defined as the equilibrium global-mean warming after a doubling of CO<math>_2</math> concentrations. In the case of MAGICC, the equilibrium climate sensitivity is a primary model parameter that may be identified with the eventual global-mean warming that would occur if the CO<math>_2</math> concentrations were doubled from pre-industrial levels. Climate sensitivity is inversely related to the feedback factor <math>\lambda</math>:<br />
<br />
<math>\label{eq_climatesensitivity}\Delta T_{2x} = \frac{\Delta Q_{2x}}{\lambda}</math><span id="eq_2"></span><div style="float: right; clear: right;">('''2''')</div><br />
<br />
where <math>\Delta T_{2x}</math> is the climate sensitivity, and <math>\Delta Q_{2x}</math> the radiative forcing after a doubling of CO<math>_2</math> concentrations (see energy balance<br />
Eq. [[#eq_A45|A45]]).<br />
<br />
The (time- or state-dependent) effective climate sensitivity (<math>S^t</math>)([[References#Murphy_Mitchell_1995_SpatialTemporalResponse|Murphy and Mitchell, 1995]]) is defined using the transient energy balance Eq. ([[#eq_1|1]]) and can be diagnosed from model output for any part of a model run where radiative forcing and ocean heat uptake are both known and their sum is different from zero, so that:<br />
<br />
<math>\label{eq_effective_climatesensitivity} S^t = \frac{\Delta Q_{2x}}{\lambda^t} = \Delta Q_{2x} \frac{\Delta T_{G}^t}{\Delta Q^t - \frac{d H}{dt}|^t}</math><span id="eq_3"></span><div style="float: right; clear: right;">('''3''')</div><br />
<br />
where <math>\Delta Q_{2x}</m> is the model-specific forcing for doubled CO<math>_2</math> concentration, <math>\lambda_t</math> is the time-variable feedback factor, <math>\Delta Q^t</math> the radiative forcing, <math>\Delta T_{GL}^t</math> the global-mean temperature perturbation and <math>\frac{dH}{dt}|^t</math> the climate system's heat uptake at time <math>t</math>. By definition, the traditional (equilibrium) climate sensitivity (<math>\Delta T_{2x}</math>) is equal to the effective climate sensitivity <math>S^t</math> at equilibrium (<math>\frac{dH}{dt}|^t</math>=0) after doubled (pre-industrial) CO<math>_2</math> concentration.<br />
<br />
If there were only one globally homogenous, fast and constant feedback process, the diagnosed effective climate sensitivity would always equal the equilibrium climate sensitivity <math>\Delta T_{2x}</math>. However, many CMIP3 AOGCMs exhibit variable effective climate sensitivities, often increasing over time (e.g. models CCSM3, CNRM-CM3, GFDL-CM2.0, GFDL-CM2.1, GISS-EH - see Figs. (B1, B2, B3 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html). This is consistent with earlier results of increasing effective sensitivities found by ([[References#Senior_Mitchell_2000_TimeDependence_ClimateSensitivity|Senior and Mitchell (2000)]];[[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2000)]]) for the HadCM2 model. In addition, some models present significantly higher sensitivities for higher forcing scenarios (1pctto4x) than for lower forcing scenarios (1pctto2x) (e.g. ECHAM5/MPI-OM and GISS-ER, see [[#fig_increasing_ClimSens_CCSM3_ECHAM5|Fig.1 ]]<br />
<br />
In order to better emulate these time-variable effective climate sensitivities, this version of MAGICC incorporates two modifications: Firstly, an amended land-ocean heat exchange<br />
formulation allows effective climate sensitivities to increase on the path to equilibrium warming. In this formulation, changes in effective climate sensitivity arise from a geometrical effect: spatially non-homogenous feedbacks can lead to a time-variable effective global-mean climate sensitivity, if the spatial warming distributions change over time. Hence, by modifying land-ocean heat exchange in MAGICC, the spatial evolution of warming is altered, leading to changes in effective climate sensitivities ([[References#Raper_2004_GeometricalEffectClimsens|Raper, 2004]]) given that MAGICC has different equilibrium sensitivities over land and ocean. Secondly, the climate sensitivities, and hence the feedback parameters, can be made explicitly dependent on the current forcing at time <math>t</math>. Both amendments are detailed in the [[Upwelling_Diffusion_Entrainment_Implementation#Revised land-ocean heat formulation|Revised land-ocean heat formulation]], and [[Upwelling_Diffusion_Entrainment_Implementation#Accounting for climate-state dependent feedbacks|Accounting for climate-state dependent feedbacks]] sections. Although these two amendments both modify the same diagnostic, i.e., the time-variable effective sensitivities in MAGICC, they are distinct: the land-ocean heat exchange modification changes the shape of the effective climate sensitivity's time evolution to equilibrium, but keeps the equilibrium sensitivity unaffected. In contrast, making the sensitivity explicitly dependent on the forcing primarily affects the equilibrium sensitivity value.<br />
<br />
Note that time-varying effective sensitivities are not only empirically observed in AOGCMs, but they are necessary here in order for MAGICC to accurately emulate AOGCM results. Alternative parameterizations to emulate time-variable climate sensitivities are possible, e.g.~assuming a dependence on temperatures instead of forcing, or by implementing indirect radiative forcing effects that are most often regarded as feedbacks see Section 6.2 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html. However, this study chose to limit the degrees of freedom with respect to time-variable climate sensitivities given that a clear separation into three (or more) different parameterizations seemed unjustified based on the AOGCM data analyzed here.<br />
<br />
[[file:Fig-1.png|350px|thumb|The effective climate sensitivity diagnosed from low-pass filtered CCSM3 (a) and ECHAM5/MPI-OM (b) output for two idealized<br />
scenarios assuming an annual 1% increase in CO2 concentrations until twice pre-industrial values in year 70 (1pctto2×) or quadrupled concentration in year 140 (1pctto4×), with constant<br />
concentrations thereafter. Additionally, the reported slab ocean model equilibrium climate sensitivity (“slab”) and the sensitivity estimates by Forster and Taylor (2006) are shown (“F&T(06)”). ]] <br />
<span id="fig_increasing_ClimSens_CCSM3_ECHAM5"></span><br />
<br />
===Updated carbon cycle=== <br />
<br />
MAGICC's terrestrial carbon cycle model is a globally integrated box model, similar to that in [[References#Harvey_1989_ManagingAtmCO2|Harvey (1989)]] and [[References#Wigley_1993_BalancingCarbonBudget|Wigley (1993)]]. The MAGICC6 carbon cycle can emulate temperature-feedback effects on the heterotrophic respiration carbon fluxes. One improvement in MAGICC6 allows increased flexibility when accounting for CO<sub>2</sub> fertilization. This increase in flexibility allows a better fit to some of the more complex carbon cycle models reviewed in C<math>^4</math>MIP([[References#Friedlingstein_2006_climatecarbonInteraction_C4MIP|Friedlingstein, 2006]])(see [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]).<br />
<br />
Another update in MAGICC6 relates to the relaxation in carbon pools after a deforestation event. The gross CO<sub>2</sub> emissions related to deforestation and other land use activities are subtracted from the plant, detritus and soil carbon pools (see Fig. [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]]. While in previous versions only the regrowth in the plant carbon pool was taken into account to calculate the net deforestation, MAGICC6 now includes an effective relaxation/regrowth term for all three terrestrial carbon pools (see [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]).<br />
<br />
The original ocean carbon cycle model used a convolution representation ([[References#Wigley_1991_simpleInverseCarbonCycleModel|Wigley, 1991]]) to quantify the ocean-atmosphere CO<math>_2</math> flux. A similar representation is used here, but modified to account for nonlinearities. Specifically, the impulse response representation of the Princeton 3D GFDL model ([[References#Sarmiento_etal_1992_perturbationCO2_ocean_general_circulation_model|Sarmiento, 1992]]) is used to approximate the inorganic carbon perturbation in the mixed layer (for the impulse response representation see, [[References#Joos_Bruno_etal_1996_efficient_accurate_carbonuptake|Joos, 1991]]). The temperature sensitivity of the sea surface partial pressure is implemented based on [[References#Takahashi_etal_1993_surfaceOceans_CO2|Takahashi et al. (1993)]] as given in [[References#Joos_Prentice_etal_2001_feedbacks_biosphere_IPCC|Joos et al. (2001)]]. For details on the updated carbon cycle routines, see the [[The Carbon Cycle|The carbon cycle]].<br />
<br />
===Other additional capabilities compared to MAGICC4.2===<br />
<br />
Five additional amendments to the climate model have been implemented in MAGICC6 compared to the MAGICC4.2 version that has<br />
been used in IPCC AR4.<br />
<br />
====Aerosol indirect effects====<br />
<br />
It is now possible to account directly for contributions from black carbon, organic carbon and nitrate aerosols to indirect (i.e., cloud albedo) effects ([[References#Twomey_1977_albedo|Twomey, 1977]]). The first indirect effect, affecting cloud droplet size and the second indirect effect, affecting cloud cover and lifetime, can also be modeled separately. Following the convention in IPCC AR4 ([[References#Forster_Ramaswamy_etal_2007_IPCCAR4_Chapter2_radiativeForcing|Forster et al., 2007]]), the second indirect effect is modeled as a prescribed change in efficacy of the first indirect effect. See [[Non-CO2 Concentrations|Tropospheric aerosols]] for details.<br />
<br />
====Depth-variable ocean with entrainment====<br />
<br />
Building on the work by [[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2007)]], MAGICC6 includes the option of a depth-dependent ocean area profile with entrainment at each of the ocean levels (default, 50 levels) from the polar sinking water column. The default ocean area profile decreases from unity at the surface to, for example, 30<math>%</math>, 13<math>%</math> and 0<math>%</math> at depths of 4000, 4500 and 5000 m. Although comprehensive data on depth-dependent heat uptake profiles of the CMIP3 AOGCMs were not available for this study, this entrainment update provides more flexibility and allows for a better simulation of the characteristic depth-dependent heat uptake as observed in one analyzed AOGCM, namely HadCM2 ([[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al., 2000]]).<br />
<br />
====Vertical mixing depending on warming gradient====<br />
<br />
Simple models, including earlier versions of MAGICC, sometimes overestimated the ocean heat uptake for higher warming scenarios when applying parameter sets chosen to match heat uptake for lower warming scenarios, see e.g. Fig. 17b in [[References#Harvey_etal_1997_IPCC_IntroductionSimpleClimateModels|Harvey et al. (1997)]]. A strengthened thermal stratification and hence reduced vertical mixing might contribute to the lower heat uptake for higher warming cases. To model this effect, a warming-dependent vertical gradient of the thermal diffusivity is implemented here(see[[Upwelling diffusion climate model#Depth-dependent ocean with entrainment|Depth-dependent ocean with entrainment]]).<br />
<br />
====Forcing efficacies====<br />
<br />
Since the IPCC TAR, a number of studies have focussed on forcing efficacies, i.e., on the differences in surface temperature response due to a unit forcing by different radiative forcing agents with different geographical and vertical distributions ([[References#Joshi_etal_2003_improvedmetric_climatechange|Joshi et al., 1997]]). This version of MAGICC includes the option to apply different efficacy terms for the different forcings agents (see the [[Upwelling_Diffusion_Entrainment_Implementation#Depth-dependent ocean with entrainment|efficacies]] section for details and supplement pdf in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html for default values).<br />
<br />
====Radiative forcing patterns====<br />
<br />
Earlier versions of MAGICC used time-independent (but user-specifiable) ratios to distribute the global-mean forcing of tropospheric ozone and aerosols to the four atmospheric boxes, i.e., land and ocean in both hemispheres. This model structure and the simple 4-box forcing patterns are retained as it is able to capture a large fraction of the forcing agent characteristics of interest here. However, we now use patterns for each forcing individually, and allow for these patterns to vary over time. For example, the historical forcing pattern evolutions for tropospheric aerosols are based on results from [[References#Hansen_etal_2005_Efficacies|Hansen et al. (2005)]], which are interpolated to annual values and extrapolated into the future using hemispheric emissions. Additionally, MAGICC6 now incorporates forcing patterns for the long-lived greenhouse gases as well, although these patterns are assumed to be constant in time and scaled with global-mean radiative forcing (supplement pdf in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html for details on the default forcing patterns and time series).</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Model_Description&diff=34Model Description2013-06-17T14:44:30Z<p>Antonius Golly: /* Introduction of variable climate sensitivities */</p>
<hr />
<div>*[[Model Description|model description]]<br />
**[[The Carbon Cycle| carbon cycle]]<br />
**[[Non-CO2 Concentrations | non-CO2 concentrations]]<br />
**[[Radiative Forcing | radiative forcing routines]]<br />
**[[Upwelling_diffusion_climate_model | climate model]]<br />
**[[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]]<br />
<br />
<br />
==Model description==<br />
<br />
=== Overview ===<br />
<br />
The 'Model for the Assessment of Greenhouse Gas Induced Climate Change' (MAGICC) is a simple/reduced complexity climate model. MAGICC was originally developed by Tom Wigley (National Centre for Atmospheric Research, Boulder, US, and University of Adelaide, Australia) and Sarah Raper (Manchester Metropolitan University, UK) in the late 1980s and continuously developed since then. It has been one of the widely used climate models in various IPCC Assessment Reports. The latest version, MAGICC6, is co-developed by Malte Meinshausen (Potsdam Institute for Climate Impact Research, Germany, and the University of Melbourne, Australia). These pages provide an extensive model description, sourced from a 2011 publication in Atmospheric Chemistry & Physics [http://www.atmos-chem-phys.net/11/1417/2011/ (M. Meinshausen, S. Raper and T. Wigley, 2011)]. <br />
<br />
This Page provides a detailed description of MAGICC6 and its<br />
different modules (see [[#Fig_A1|Fig-A1]] below). A basic [[Model_Documentation|model description]] is given, while subsections describe MAGICC's <br />
[[The Carbon Cycle| carbon cycle]], the atmospheric-chemistry<br />
parameterizations and derivation of <br />
[[Non-CO2 Concentrations | non-CO<sub>2</sub> concentrations]], <br />
[[Radiative Forcing | radiative forcing routines]], and the climate module to get from<br />
radiative forcing to hemispheric (land and ocean, separately) to<br />
global-mean temperatures ([[Upwelling_diffusion_climate_model|climate model]]), as<br />
well as oceanic heat uptake. Finally, details are provided on the implementation scheme for the [[UDB Implementation | upwelling-diffusion-entrainment ocean]]<br />
climate module. A technical upgrade is that MAGICC6 has been re-coded in Fortran95,<br />
updated from previous Fortran77 versions. Nearly all of the MAGICC6 code is directly based on the earlier<br />
MAGICC versions programmed by Wigley and Raper <br />
([[References#Wigley_Raper_1987_ThermalExpansion_SeaWater_Nature| 1987]], [[References#Wigley_Raper_1992_ImplicationsWarmingIPCC_Nature | 1992]], [[References#Wigley_Raper_2001_Science_InterpretationHighProjections | 2001]]).<br />
<br />
[[File:OverviewGraph Fig1.png|frame|right|'''Fig-A1''' Schematic overview of MAGICC calculations showing the key steps<br />
from emissions to global and hemispheric climate responses.<br />
Black circled numbers denote the sections in the Appendix<br />
describing the respective algorithms used. Source: Fig A.1. in Meinshausen et al. 2011, ACP]]<span id="fig_A1"></span> <br />
<br />
===Basic model description===<br />
<br />
MAGICC has a hemispherically averaged upwelling-diffusion ocean coupled to an atmosphere layer and a globally averaged carbon cycle model. As with most other simple models, MAGICC evolved from a simple global average energy-balance equation. The energy balance equation for the perturbed climate system can be written as:<br />
<br />
<m>\Delta Q_G = \lambda_G \Delta T_G + \frac{d H}{d t}\label{eq_globalenergybalance}</m><span id="eq_1"></span><div style="float: right; clear: right;">('''1''')</div><br />
<br />
where <m>\Delta Q_G</m> is the global-mean radiative forcing at the top of the troposphere. This extra energy influx is partitioned into increased outgoing energy flux and heat content changes in the ocean <m>\frac{d H}{d t}</m>. The outgoing energy flux is dependent on the global-mean feedback factor, <m>\lambda_G</m>, and the surface temperature perturbation <m>\Delta T_G</m>.<br />
<br />
While MAGICC is designed to provide maximum flexibility in order to match different types of responses seen in more sophisticated models, the approach in MAGICC's model development has always been to derive the simple equations as much as possible from key physical and biological processes. In other words, MAGICC is as simple as possible, but as mechanistic as necessary. This process-based approach has a strong conceptual advantage in comparison to simple statistical fits that are more likely to quickly degrade in their skill when emulating scenarios outside the original calibration space of sophisticated models.<br />
<br />
The main improvements in MAGICC6 compared to the version used in the IPCC AR4 are briefly highlighted in this section (Note that there is an intermediate version, MAGICC 5.3, described in [[References#Wigley_etal_2009_UncertaintiesClimateStabilization|Wigley et al., 2009]]). The options introduced to account for variable climate sensitivities are described in Sect. [[#introduction of variable climate sensitivities|introduction of variable climate sensitivities]]. With the exception of the updated carbon cycle routines [[#updated carbon cycle|updated carbon cycle]], the MAGICC 4.2 and 5.3 parameterizations are covered as special cases of the 6.0 version, i.e., the IPCC AR4 version, for example, can be recovered by appropriate parameter settings.<br />
<br />
===Introduction of variable climate sensitivities===<br />
<br />
Climate sensitivity (<m>\Delta T_{2x}</m>) is a useful metric to compare models and is usually defined as the equilibrium global-mean warming after a doubling of CO<m>_2</m> concentrations. In the case of MAGICC, the equilibrium climate sensitivity is a primary model parameter that may be identified with the eventual global-mean warming that would occur if the CO<m>_2</m> concentrations were doubled from pre-industrial levels. Climate sensitivity is inversely related to the feedback factor <m>\lambda</m>:<br />
<br />
<m>\label{eq_climatesensitivity}\Delta T_{2x} = \frac{\Delta Q_{2x}}{\lambda}</m><span id="eq_2"></span><div style="float: right; clear: right;">('''2''')</div><br />
<br />
where <m>\Delta T_{2x}</m> is the climate sensitivity, and <m>\Delta Q_{2x}</m> the radiative forcing after a doubling of CO<m>_2</m> concentrations (see energy balance<br />
Eq. [[#eq_A45|A45]]).<br />
<br />
The (time- or state-dependent) effective climate sensitivity (<m>S^t</m>)([[References#Murphy_Mitchell_1995_SpatialTemporalResponse|Murphy and Mitchell, 1995]]) is defined using the transient energy balance Eq. ([[#eq_1|1]]) and can be diagnosed from model output for any part of a model run where radiative forcing and ocean heat uptake are both known and their sum is different from zero, so that:<br />
<br />
<m>\label{eq_effective_climatesensitivity} S^t = \frac{\Delta Q_{2x}}{\lambda^t} = \Delta Q_{2x} \frac{\Delta T_{G}^t}{\Delta Q^t - \frac{d H}{dt}|^t}</m><span id="eq_3"></span><div style="float: right; clear: right;">('''3''')</div><br />
<br />
where <m>\Delta Q_{2x}</m> is the model-specific forcing for doubled CO<m>_2</m> concentration, <m>\lambda_t</m> is the time-variable feedback factor, <m>\Delta Q^t</m> the radiative forcing, <m>\Delta T_{GL}^t</m> the global-mean temperature perturbation and <m>\frac{dH}{dt}|^t</m> the climate system's heat uptake at time <m>t</m>. By definition, the traditional (equilibrium) climate sensitivity (<m>\Delta T_{2x}</m>) is equal to the effective climate sensitivity <m>S^t</m> at equilibrium (<m>\frac{dH}{dt}|^t</m>=0) after doubled (pre-industrial) CO<m>_2</m> concentration.<br />
<br />
If there were only one globally homogenous, fast and constant feedback process, the diagnosed effective climate sensitivity would always equal the equilibrium climate sensitivity <m>\Delta T_{2x}</m>. However, many CMIP3 AOGCMs exhibit variable effective climate sensitivities, often increasing over time (e.g. models CCSM3, CNRM-CM3, GFDL-CM2.0, GFDL-CM2.1, GISS-EH - see Figs. (B1, B2, B3 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html). This is consistent with earlier results of increasing effective sensitivities found by ([[References#Senior_Mitchell_2000_TimeDependence_ClimateSensitivity|Senior and Mitchell (2000)]];[[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2000)]]) for the HadCM2 model. In addition, some models present significantly higher sensitivities for higher forcing scenarios (1pctto4x) than for lower forcing scenarios (1pctto2x) (e.g. ECHAM5/MPI-OM and GISS-ER, see [[#fig_increasing_ClimSens_CCSM3_ECHAM5|Fig.1 ]]<br />
<br />
In order to better emulate these time-variable effective climate sensitivities, this version of MAGICC incorporates two modifications: Firstly, an amended land-ocean heat exchange<br />
formulation allows effective climate sensitivities to increase on the path to equilibrium warming. In this formulation, changes in effective climate sensitivity arise from a geometrical effect: spatially non-homogenous feedbacks can lead to a time-variable effective global-mean climate sensitivity, if the spatial warming distributions change over time. Hence, by modifying land-ocean heat exchange in MAGICC, the spatial evolution of warming is altered, leading to changes in effective climate sensitivities ([[References#Raper_2004_GeometricalEffectClimsens|Raper, 2004]]) given that MAGICC has different equilibrium sensitivities over land and ocean. Secondly, the climate sensitivities, and hence the feedback parameters, can be made explicitly dependent on the current forcing at time <m>t</m>. Both amendments are detailed in the [[Upwelling_Diffusion_Entrainment_Implementation#Revised land-ocean heat formulation|Revised land-ocean heat formulation]], and [[Upwelling_Diffusion_Entrainment_Implementation#Accounting for climate-state dependent feedbacks|Accounting for climate-state dependent feedbacks]] sections. Although these two amendments both modify the same diagnostic, i.e., the time-variable effective sensitivities in MAGICC, they are distinct: the land-ocean heat exchange modification changes the shape of the effective climate sensitivity's time evolution to equilibrium, but keeps the equilibrium sensitivity unaffected. In contrast, making the sensitivity explicitly dependent on the forcing primarily affects the equilibrium sensitivity value.<br />
<br />
Note that time-varying effective sensitivities are not only empirically observed in AOGCMs, but they are necessary here in order for MAGICC to accurately emulate AOGCM results. Alternative parameterizations to emulate time-variable climate sensitivities are possible, e.g.~assuming a dependence on temperatures instead of forcing, or by implementing indirect radiative forcing effects that are most often regarded as feedbacks see Section 6.2 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html. However, this study chose to limit the degrees of freedom with respect to time-variable climate sensitivities given that a clear separation into three (or more) different parameterizations seemed unjustified based on the AOGCM data analyzed here.<br />
<br />
[[file:Fig-1.png|350px|thumb|The effective climate sensitivity diagnosed from low-pass filtered CCSM3 (a) and ECHAM5/MPI-OM (b) output for two idealized<br />
scenarios assuming an annual 1% increase in CO2 concentrations until twice pre-industrial values in year 70 (1pctto2×) or quadrupled concentration in year 140 (1pctto4×), with constant<br />
concentrations thereafter. Additionally, the reported slab ocean model equilibrium climate sensitivity (“slab”) and the sensitivity estimates by Forster and Taylor (2006) are shown (“F&T(06)”). ]] <br />
<span id="fig_increasing_ClimSens_CCSM3_ECHAM5"></span><br />
<br />
===Updated carbon cycle=== <br />
<br />
MAGICC's terrestrial carbon cycle model is a globally integrated box model, similar to that in [[References#Harvey_1989_ManagingAtmCO2|Harvey (1989)]] and [[References#Wigley_1993_BalancingCarbonBudget|Wigley (1993)]]. The MAGICC6 carbon cycle can emulate temperature-feedback effects on the heterotrophic respiration carbon fluxes. One improvement in MAGICC6 allows increased flexibility when accounting for CO<sub>2</sub> fertilization. This increase in flexibility allows a better fit to some of the more complex carbon cycle models reviewed in C<m>^4</m>MIP([[References#Friedlingstein_2006_climatecarbonInteraction_C4MIP|Friedlingstein, 2006]])(see [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]).<br />
<br />
Another update in MAGICC6 relates to the relaxation in carbon pools after a deforestation event. The gross CO<sub>2</sub> emissions related to deforestation and other land use activities are subtracted from the plant, detritus and soil carbon pools (see Fig. [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]]. While in previous versions only the regrowth in the plant carbon pool was taken into account to calculate the net deforestation, MAGICC6 now includes an effective relaxation/regrowth term for all three terrestrial carbon pools (see [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]).<br />
<br />
The original ocean carbon cycle model used a convolution representation ([[References#Wigley_1991_simpleInverseCarbonCycleModel|Wigley, 1991]]) to quantify the ocean-atmosphere CO<m>_2</m> flux. A similar representation is used here, but modified to account for nonlinearities. Specifically, the impulse response representation of the Princeton 3D GFDL model ([[References#Sarmiento_etal_1992_perturbationCO2_ocean_general_circulation_model|Sarmiento, 1992]]) is used to approximate the inorganic carbon perturbation in the mixed layer (for the impulse response representation see, [[References#Joos_Bruno_etal_1996_efficient_accurate_carbonuptake|Joos, 1991]]). The temperature sensitivity of the sea surface partial pressure is implemented based on [[References#Takahashi_etal_1993_surfaceOceans_CO2|Takahashi et al. (1993)]] as given in [[References#Joos_Prentice_etal_2001_feedbacks_biosphere_IPCC|Joos et al. (2001)]]. For details on the updated carbon cycle routines, see the [[The Carbon Cycle|The carbon cycle]].<br />
<br />
===Other additional capabilities compared to MAGICC4.2===<br />
<br />
Five additional amendments to the climate model have been implemented in MAGICC6 compared to the MAGICC4.2 version that has<br />
been used in IPCC AR4.<br />
<br />
====Aerosol indirect effects====<br />
<br />
It is now possible to account directly for contributions from black carbon, organic carbon and nitrate aerosols to indirect (i.e., cloud albedo) effects ([[References#Twomey_1977_albedo|Twomey, 1977]]). The first indirect effect, affecting cloud droplet size and the second indirect effect, affecting cloud cover and lifetime, can also be modeled separately. Following the convention in IPCC AR4 ([[References#Forster_Ramaswamy_etal_2007_IPCCAR4_Chapter2_radiativeForcing|Forster et al., 2007]]), the second indirect effect is modeled as a prescribed change in efficacy of the first indirect effect. See [[Non-CO2 Concentrations|Tropospheric aerosols]] for details.<br />
<br />
====Depth-variable ocean with entrainment====<br />
<br />
Building on the work by [[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2007)]], MAGICC6 includes the option of a depth-dependent ocean area profile with entrainment at each of the ocean levels (default, 50 levels) from the polar sinking water column. The default ocean area profile decreases from unity at the surface to, for example, 30<m>%</m>, 13<m>%</m> and 0<m>%</m> at depths of 4000, 4500 and 5000 m. Although comprehensive data on depth-dependent heat uptake profiles of the CMIP3 AOGCMs were not available for this study, this entrainment update provides more flexibility and allows for a better simulation of the characteristic depth-dependent heat uptake as observed in one analyzed AOGCM, namely HadCM2 ([[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al., 2000]]).<br />
<br />
====Vertical mixing depending on warming gradient====<br />
<br />
Simple models, including earlier versions of MAGICC, sometimes overestimated the ocean heat uptake for higher warming scenarios when applying parameter sets chosen to match heat uptake for lower warming scenarios, see e.g. Fig. 17b in [[References#Harvey_etal_1997_IPCC_IntroductionSimpleClimateModels|Harvey et al. (1997)]]. A strengthened thermal stratification and hence reduced vertical mixing might contribute to the lower heat uptake for higher warming cases. To model this effect, a warming-dependent vertical gradient of the thermal diffusivity is implemented here(see[[Upwelling diffusion climate model#Depth-dependent ocean with entrainment|Depth-dependent ocean with entrainment]]).<br />
<br />
====Forcing efficacies====<br />
<br />
Since the IPCC TAR, a number of studies have focussed on forcing efficacies, i.e., on the differences in surface temperature response due to a unit forcing by different radiative forcing agents with different geographical and vertical distributions ([[References#Joshi_etal_2003_improvedmetric_climatechange|Joshi et al., 1997]]). This version of MAGICC includes the option to apply different efficacy terms for the different forcings agents (see the [[Upwelling_Diffusion_Entrainment_Implementation#Depth-dependent ocean with entrainment|efficacies]] section for details and supplement pdf in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html for default values).<br />
<br />
====Radiative forcing patterns====<br />
<br />
Earlier versions of MAGICC used time-independent (but user-specifiable) ratios to distribute the global-mean forcing of tropospheric ozone and aerosols to the four atmospheric boxes, i.e., land and ocean in both hemispheres. This model structure and the simple 4-box forcing patterns are retained as it is able to capture a large fraction of the forcing agent characteristics of interest here. However, we now use patterns for each forcing individually, and allow for these patterns to vary over time. For example, the historical forcing pattern evolutions for tropospheric aerosols are based on results from [[References#Hansen_etal_2005_Efficacies|Hansen et al. (2005)]], which are interpolated to annual values and extrapolated into the future using hemispheric emissions. Additionally, MAGICC6 now incorporates forcing patterns for the long-lived greenhouse gases as well, although these patterns are assumed to be constant in time and scaled with global-mean radiative forcing (supplement pdf in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html for details on the default forcing patterns and time series).</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=File:Fig-1.png&diff=33File:Fig-1.png2013-06-17T14:42:21Z<p>Antonius Golly: </p>
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<div></div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Upwelling_Diffusion_Entrainment_Implementation&diff=23Upwelling Diffusion Entrainment Implementation2013-06-17T11:31:38Z<p>Antonius Golly: Created page with "*model description ** carbon cycle ** non-CO2 concentrations **[[Radiative Forcing | radiative forcing r..."</p>
<hr />
<div>*[[Model Description|model description]]<br />
**[[The Carbon Cycle| carbon cycle]]<br />
**[[Non-CO2 Concentrations | non-CO2 concentrations]]<br />
**[[Radiative Forcing | radiative forcing routines]]<br />
**[[Upwelling_diffusion_climate_model | climate model]]<br />
**[[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]]<br />
<br />
<br />
==Implementation of upwelling-diffusion-entrainment equations==<br />
<br />
This section details how the equations governing the upwelling-diffusion-entrainment (UDE) ocean (Eqs. [[#eq_62|A62]], [[#eq_63|A63]]) are implemented and modified by entrainment terms and depth-dependent ocean area (see Fig. [[#Fig-A2a|A2]]). These equations represent the core of the UDE model and build on the initial work by ([[References#Hoffert_1980_Role_DeapSea, Harvey_Schneider_1985_PartII, Harvey_Schneider_1985_PartI|Hoffert et al. (1980)]].<br />
<br />
The entrainment is here modeled so that the upwelling velocity in the main column is the same in each layer. Thus, the three area correction factors, <m>\theta_z^{\rm top}</m>, <m>\theta_z^{b}</m> and<br />
<m>\theta_z^{\rm dif}</m>, applied below are:<br />
<br />
<m>\theta_z^{\rm top} = \frac{A_z}{(A_{z+1}+A_z)/2}</m><br />
<br />
<m>\theta_z^{b} = \frac{A_{z+1}}{(A_{z+1}+A_z)/2} </m><br />
<br />
<m>\theta_z^{\rm dif} = \frac{A_{z+1}-A_{z}}{(A_{z+1}+A_z)/2}\label{eq_areacorrection_thetatop}</m><span id="eq_A67"></span><div style="float: right; clear: right;">('''A67''')</div><br />
<br />
<br />
where <m>A_z</m> is the area at the top of layer z or bottom of layer z-1 and the denominator is thus an approximation for the mean area of each ocean layer.<br />
<br />
For the mixed layer, all terms in Eq. ([[#eq_62|A62]]) involving <m>\Delta T^{t+1}_{\rm NO,1}</m> are collected on the left hand side in variable <m>A(1)</m>. All terms involving <m>\Delta T^{t+1}_{\rm NO,2}</m> are collected in variable <m>B(1)</m> on the left hand side. All other terms are held in variable <m>D(1)</m> on the right hand side, so that the<br />
equation reads:<br />
<br />
{| <br />
| <m>\Delta T_{\rm NO,1}^{t+1} = -\frac{B(1)}{A(1)}\Delta T_{\rm NO,2}^{t+1} + \frac{D(1)}{A(1)} \label{eq_udebm_coding_ALL1}</m> || || <span id="eq_A68"></span><div style="float: right; clear: right;">('''A68''')</div><br />
|- <br />
| with || || <br />
|- <br />
| <m>A(1) = 1.0+\theta_1^{\rm top}\Delta t\frac{ \lambda_O\alpha}{\zeta_o}</m> || :feedback over ocean || <span id="eq_A69"></span><div style="float: right; clear: right;">('''A69''')</div><br />
|- <br />
| <m>+\theta_1^{b}\Delta t\frac{ K_z}{0.5h_m h_d}</m> || :diffusion to layer 2 || <br />
|- <br />
| <m>+\theta_1^{b}\Delta t\frac{ w^t \beta}{h_m}</m> || :downwelling || <br />
|- <br />
| <m>+\theta_1^{\rm top}\Delta t\frac{ k_{\rm LO}\lambda_L\mu\alpha }{\zeta_o f_{\rm NO} (\frac{k_{\rm LO}}{f_{\rm NL}} + \lambda_L)}</m> || :feedback over land || <br />
|- <br />
| <m>B(1) = -\theta_1^{b}\Delta t\frac{ K_z}{0.5h_m h_d}</m> || :diffusion from layer 2 || <span id="eq_A70"></span><div style="float: right; clear: right;">('''A70''')</div><br />
|- <br />
| <m>-\theta_1^{b}\Delta t\frac{ w^t}{h_m}</m> || :upwelling from layer 2 || <br />
|- <br />
| <m>D(1) = \Delta T_{\rm NO,1}^{t}</m> || :previous temp || <span id="eq_A71"></span><div style="float: right; clear: right;">('''A71''')</div><br />
|- <br />
| <m>+ \theta_1^{\rm top}\Delta t\frac{1}{\zeta_o}DeltaQ_{NO}</m> || : forcing ocean || <br />
|- <br />
| <m>+ \theta_1^{\rm top}\Delta t\frac{\alpha k_{NS}}{\zeta_o f_{NO}}(\Delta T^t_{\rm SO,1}-\Delta T^t_{NO,1})</m> || :inter-hemis. exch. || <br />
|- <br />
| <m>+ \theta_1^{\rm top}\Delta t\frac{ k_{LO}\Delta Q_{NL}}{\zeta_o f_{NO} (\frac{k_{LO}}{f_{NL}} + \lambda_L)} </m> || : land forcing || <br />
|- <br />
| <m>+ \theta_1^{b}\Delta t\frac{\Delta w^t}{h_m}(T^0_{\rm NO,2}-T^0_{NO,sink})</m> || : variable upwelling || <br />
|}<br />
<br />
For the interior layers (2<m>{\leq}</m>z<m>{\leq}</m><m>n</m>), i.e., all layers except the top mixed layer and the bottom layer, the terms are re-ordered, so that <m>A(z)</m> comprises the terms for <m>\Delta T^{t+1}_{\rm NO,z-1}</m>, <m>B(z)</m> the terms for <m>\Delta T^{t+1}_{\rm NO,z}</m>, <m>C(z)</m> the terms for <m>\Delta T^{t+1}_{\rm NO,z+1}</m> and <m>D(z)</m> the remaining terms, according to:<br />
<br />
<br />
<br />
{| <br />
| <m>\Delta T_{\rm NO,z-1}^{t+1} = -\frac{B(z)}{A(z)}\Delta T_{\rm NO,z}^{t+1} - \frac{C(z)}{A(z)}\Delta T_{\rm NO,z+1}^{t+1} + \frac{D(z)}{A(z)}</m> || || <span id="eq_A72"></span><div style="float: right; clear: right;">('''A72''')</div><br />
|- <br />
| with || || <br />
|- <br />
| <m>A(z) = - \theta_z^{top}\Delta t\frac{K_z}{0.5(h_d+h_d')h_d}</m>|| : diffusion from layer above || <span id="eq_A73"></span><div style="float: right; clear: right;">('''A73''')</div><br />
|- <br />
| <m>B(z) = 1.0 + \theta_z^{b}\Delta t\frac{K_z}{h_d^2}</m> || :diffusion to layer below || <br />
|- <br />
| <m>+\theta_z^{top}\Delta t\frac{K_z}{0.5(h_d+h_d')h_d}</m> || :diffusion to layer above || <br />
|- <br />
| <m>+\theta_z^{top}\Delta t\frac{ w^t}{h_d}</m> || :upwelling to layer above || <span id="eq_A74"></span><div style="float: right; clear: right;">('''A74''')</div><br />
|- <br />
| <m>C(z) = - \theta_z^{b}\Delta t\frac{K_z}{h_d^2}</m> || :diffusion from layer below || <br />
|- <br />
| <m>-\theta_z^{b}\Delta t\frac{ w^t}{h_d}</m> || :upwelling from layer below || <span id="eq_A75"></span><div style="float: right; clear: right;">('''A75''')</div><br />
|- <br />
| <m>D(z) = \Delta T_{\rm NO,z}^{t}</m> || :previous temp || <br />
|- <br />
| <m>+\Delta t\frac{\Delta w^t}{h_d} (\theta_z^{b}T^{0}_{\rm NO,z+1}-\theta_z^{top}T^{0}_{\rm NO,z})</m> || :variable upwelling || <br />
|- <br />
| <m>+\theta_z^{\rm dif}\Delta t\frac{ w^t}{h_d}\beta\Delta T_{\rm NO,1}^{t-1}</m> || :entrainment || <br />
|- <br />
| <m>+\theta_z^{\rm dif}\Delta t\frac{\Delta w^t}{h_d} T^{0}_{\rm NO,sink}</m> || :variable entrainment || <span id="eq_A76"></span><div style="float: right; clear: right;">('''A76''')</div><br />
|}<br />
<br />
where <m>h_d'</m> is zero for the layer below the mixed layer and <m>h_d</m> otherwise. For the bottom layer, the respective sum factor <m>A(n)</m> for <m>\Delta T^{t+1}_{\rm NO,n-1}</m>, <m>B(n)</m> for <m>\Delta T^{t+1}_{\rm NO,n}</m> and <m>D(n)</m> for the remaining terms is:<br />
<br />
{|<br />
| <m>\Delta T_{{\rm NO},n-1}^{t+1} = -\frac{B(n)}{A(n)}\Delta T_{{\rm NO},n}^{t+1} + \frac{D(n)}{A(n)}</m> || || <span id="eq_A77"></span><div style="float: right; clear: right;">('''A77''')</div><br />
|- <br />
| with || || <br />
|- <br />
| <m>A(n) = - \theta_{n}^{\rm top}\Delta t\frac{K_z}{h_d^2}</m> || :diffusion from layer n-1 || <span id="eq_A78"></span><div style="float: right; clear: right;">('''A78''')</div><br />
|- <br />
| <m>B(n) = 1.0 + \theta_{n}^{\rm top}\Delta t\frac{K_z}{h_d^2}</m> || :diffusion to layer n-1 || <span id="eq_A79"></span><div style="float: right; clear: right;">('''A79''')</div><br />
|- <br />
| <m>+\theta_{n}^{\rm top}\Delta t\frac{ w^t}{h_d}</m> || :upwelling to layer n-1 || <br />
|- <br />
| <m>D(n) = \Delta T_{{\rm NO},n}^{t}</m> || :previous temp || <span id="eq_A80"></span><div style="float: right; clear: right;">('''A80''')</div><br />
|- <br />
| <m>+\theta_{n}^{\rm top}\Delta t\frac{w^t}{h_d} \beta\Delta T^{t-1}_{\rm NO,1}</m> || :downwelling from top layer || <br />
|- <br />
| <m>-\theta_{n}^{\rm top}\Delta t\frac{\Delta w^t}{h_d} T^{0}_{{\rm NO},n}</m> || :variable upwelling || <br />
|- <br />
| <m>+\theta_{n}^{\rm top}\Delta t\frac{\Delta w^t}{h_d} T^{0}_{\rm NO,sink}</m> || :variable downweilling || <br />
|}<br />
<br />
With these Eqs. ([[#eq_68|A68]]-[[#eq_80|A80]]), the ocean temperatures can be solved consecutively from the bottom to the top layer at each time step.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Upwelling_diffusion_climate_model&diff=22Upwelling diffusion climate model2013-06-17T11:29:09Z<p>Antonius Golly: Created page with "*model description ** carbon cycle ** non-CO2 concentrations **[[Radiative Forcing | radiative forcing r..."</p>
<hr />
<div>*[[Model Description|model description]]<br />
**[[The Carbon Cycle| carbon cycle]]<br />
**[[Non-CO2 Concentrations | non-CO2 concentrations]]<br />
**[[Radiative Forcing | radiative forcing routines]]<br />
**[[Upwelling_diffusion_climate_model | climate model]]<br />
**[[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]]<br />
<br />
<br />
==From forcing to temperatures: the upwelling-diffusion climate model==<br />
<br />
In the early stages, MAGICC's climate module evolved from the simple climate model introduced by [[References#Hoffert_1980_Role_DeapSea|Hoffert et al. (1980)]]. MAGICC's atmosphere has four boxes with zero heat capacity, one over land and one over ocean for each hemisphere. The atmospheric boxes over the ocean are coupled to the mixed layer of the ocean hemispheres, with a set of n-1 vertical layers below (see [[#upd_model_structure|Fig-A3]]). The heat exchange between the oceanic layers is driven by vertical diffusion and advection. In the previous model versions, the ocean area profile is uniform with<br />
depth and the corresponding downwelling is modeled as a stream of polar sinking water from the top mixed layer to the bottom layer. In this study, an updated upwelling-diffusion-entrainment (UDE) ocean model is implemented with a depth-dependent ocean area (from HadCM2). For simplicity, the following equations govern the uniform area upwelling-diffusion version of the model. The [[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]] section provides details on the UDE algorithms.<br />
<br />
[[file:Fig-A1.jpg|330px|thumb|left|'''Fig-A3''' The schematic structure of MAGICC's upwelling-diffusion energy balance module with land and ocean boxes in eache hemisphere. The processes for heat transport in the ocean are deepw-watwe formation, upwelling diffusion, and heat exchange between the hemispheres. Not shown is the entrainment and the vertically depth-dependent area of the ocean layers (see [[Fig-A2a|fig.A2]] and text)]] <br />
<span id="upd_model_structure"></span> <br />
<br />
===Partitioning of feedbacks===<br />
<br />
In order to improve the comparability between MAGICC and AOGCMs, and following earlier versions of MAGICC, we use different feedback parameters over land and ocean. This requires an adjustable land to<br />
ocean warming ratio in equilibrium based on AOGCM results. Given that in equilibrium the oceanic heat uptake is zero, the global energy balance equation can be written as:<br />
<br />
<m>C\Delta Q_G=\lambda_G\Delta T_G=f_{L}\lambda_L \Delta T_{L} + f_{O}\lambda_O \Delta T_{O}\label{eq_globalenergybalance_equilibrium}</m><span id="eq_A45"></span><div style="float: right; clear: right;">('''A45''')</div><br />
<br />
where <m>\Delta Q_G</m>, <m>\lambda_G</m> and <m>\Delta T_G</m> are the global-mean forcing, feedback, and temperature change, respectively. The right hand side uses the area fractions <m>f</m>, feedbacks <m>\lambda</m>, and mean temperature changes, <m>\Delta T</m> for ocean (<m>O</m>) and land (<m>L</m>). As in earlier versions of MAGICC, the non-linear set of equations that determines <m>\lambda_O</m> and <m>\lambda_L</m> for a given set of equilibrium land-ocean warming ratio <m>RLO</m>=<m>\Delta T_L/ \Delta T_O</m>), global-mean feedback <m>\lambda_G</m>, heat exchange and enhancement factors (<m>k</m>, <m>\mu</m>), is solved by an iterative procedure involving the set of linear Eqs. ([[#A46|A46]]-[[#A49|A49]]), seeking the solution for <m>\lambda_L</m> closest to <m>\lambda_G</m>. The procedure in version 6 has been modified slightly to take into account the time-constant radiative forcing pattern by CO<sub>2</sub> for the four boxes with hemispheric land/ocean regions, if prescribed.<br />
<br />
<br />
Following [[References#Wigley_Schlesinger_1985_AnalyticalSolutionsTemperature|Wigley and Schlesinger (1985)]], it is assumed that the atmosphere is in equilibrium with the underlying ocean mixed layer, so that the energy balance equation for the Northern Hemispheric ocean (NO) is:<br />
<br />
{| <br />
| <m>&f_{\rm NO}\lambda_{O}\Delta T_{\rm NO} =</m> || <m>\textrm{:infrared outgoing flux}</m><br />
|- <br />
| <m>f_{\rm NO}\Delta Q_{\rm NO}</m> || <m>\textrm{:forcing}</m> <br />
|-<br />
| <m>+ k_{\rm LO}(\Delta T_{\rm NL} - \mu \Delta T_{\rm NO})</m> || <m>\textrm{:land-ocean heat exchange}</m><br />
|- <br />
| <m>+ k_{\rm NS}\alpha(\Delta T_{\rm SO} - \Delta T_{\rm NO})</m> || <m>\textrm{:hemispheric heat exch.}</m> <br />
|}<span id="eq_A46"></span><div style="float: right; clear: right;">('''A46''')</div><br />
<br />
<br />
where <m>\Delta T_{\rm NO}</m> is the surface temperature change over the Northern Hemisphere ocean, <m>\Delta Q_{\rm NO}</m> the radiative forcing over that region, <m>f_{\rm NO}</m> the northern ocean's area fraction of the earth surface, <m>k_{\rm LO}</m> the land-ocean heat exchange coefficient [Wm<sup>-2</sup><sup><m>^\circ</m></sup>C<sup>-1</sup>], a heat transport enhancement factor <m>\mu</m> allowing for asymmetric heat exchange between land and ocean (1<m>\leq</m><m>\mu</m> (see Sect. [[#Revised land-ocean heat exchange formation|Revised land-ocean heat exchange formation]] below), <m>k_{\rm NS}</m> is the hemispheric heat exchange coefficient in the mixed layer. Following [[References#Raper_Cubasch_1996_Emulation_AOGCM_simplemodel|Raper and Cubasch (1996))]] <m>\alpha</m> is a sea-ice related adjustment factor to relate upper ocean temperature change to surface air temperature change (see [[#Revised land-ocean heat exchange formation|Revised land-ocean heat exchange formation]]). Correspondingly, the equilibrium energy balance equations for the Northern Hemisphere land (NL), Southern Hemisphere ocean (SO) and Southern Hemisphere land (SL) are:<br />
<br />
<br />
<br />
<m>f_{\rm NL}\lambda_{L}\Delta T_{\rm NL} &=& f_{\rm NL}\Delta Q_{\rm NL}+ k_{\rm LO}(\mu \Delta T_{\rm NO} - \Delta T_{\rm NL})\label{eq_fourboxequations_NL}</m><span id="eq_A47"></span><div style="float: right; clear: right;">('''A47''')</div><br />
<br />
<br />
<m>f_{\rm SO}\lambda_{O}\Delta T_{\rm SO} &=& f_{\rm SO}\Delta Q_{\rm SO}+ k_{\rm LO}(\Delta T_{\rm SL} - \mu \Delta T_{\rm SO})+ k_{\rm NS}\alpha(\Delta T_{\rm NO} - \Delta T_{\rm SO})\label{eq_fourboxequations_SO}</m><span id="eq_A48"></span><div style="float: right; clear: right;">('''A48''')</div><br />
<br />
<br />
<m>f_{\rm SL}\lambda_{L}\Delta T_{\rm SL} &=& f_{SL}\Delta Q_{SL}+ k_{\rm LO}(\mu \Delta T_{\rm SO} - \Delta T_{\rm SL})\label{eq_fourboxequations_SL}</m><span id="eq_A49"></span><div style="float: right; clear: right;">('''A49''')</div><br />
<br />
As detailed below ([[#Accounting for climate-state dependent feedbacks|Accounting for climate-state dependent feedbacks]]), if the sensitivity factor <m>\xi</m> is set different from zero (see Eq.[[#A51|A51]]), it is possible to make the feedback factors <m>\lambda</m> in the energy balance equation dependent on the total radiative forcing. This forcing dependence of the feedback factors and the heat exchange enhancement factors are newly introduced in this version of MAGICC. The following two sections ([[#Revised land-ocean heat exchange formation|Revised land-ocean heat exchange formation]] and [[#Accounting for climate-state dependent feedbacks|Accounting for climate-state dependent feedbacks]]) are intended to provide both the motivation and details of these new parameterizations.<br />
<br />
===Revised land-ocean heat exchange formulation===<br />
<br />
This section highlights a "geometric" effect that can cause effective climate sensitivities to change over time. The global-mean sensitivity may increase simply due to decreasing land-ocean warming ratios, given that climate feedbacks over land and ocean areas are different. To control the relative temperature changes over ocean and land, a heat transport enhancement factor <m>\mu</m> is introduced. Enhancing the ocean-to-land heat transport (<m>\mu{\geq}</m>1) has the benefit that the simple climate model can better simulate some characteristic AOGCM responses. In the idealized forcing runs, AOGCMs often show a transient land-ocean warming ratio that slightly decreases over time, but stays above unity, combined with an increasing effective climate sensitivity in some models (see bottom rows in Fig. B1, B2, and B3 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html). The higher land than ocean warming (RLO<m>{>}</m>1) could be achieved by a smaller feedback (greater climate sensitivity) over land compared to the ocean boxes. However, as the land-ocean warming ratio decreases over time (due to less and less ocean heat uptake towards equilibrium), so would the effective global-mean climate sensitivity in previous model versions. The method used here, to allow both a RLO above unity and a non-decreasing effective climate sensitivity, assumes that ocean temperature perturbations influence the heat exchange more than land temperature changes. This asymmetric heat exchange formulation is then given by:<br />
<br />
<m>{\rm HX}_{\rm LO}=k_{\rm LO}(\Delta T_{L} - \mu \Delta T_{O})\label{eq<m>eatxchange}</m><span id="eq_A50"></span><div style="float: right; clear: right;">('''A50''')</div><br />
<br />
where <m>HX_{\rm LO}</m> is the land-ocean heat exchange (positive in direction land to ocean), <m>\mu</m> is the ocean-to-land enhancement factor and <m>\Delta T_L</m> and <m>\Delta T_O</m> are the temperature<br />
perturbations for the land and ocean region, respectively (cf. Eq. [[#eq_A46|A46]] ff.). Typical values for <m>\mu</m> range between 1 and 1.4 as estimated from calibrating the CMIP3 ensemble.<br />
<br />
===Accounting for climate-state dependent feedbacks===<br />
<br />
Some AOGCM runs indicate higher effective climate sensitivities for higher forcings and/or temperatures. For example, the ECHAM5/MPI-OM model shows an effective climate sensitivity of approximately 3.5<sup><m>\circ</m></sup>C after stabilization at twice pre-industrial CO<sub>2</sub> concentrations and 4<sup><m>\circ</m></sup>C for stabilization at quadrupled pre-industrial CO<sub>2</sub> concentrations (see [[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al., 2001]], [[References#Hansen_etal_2005_Efficacies|Hansen et al., 2005]]). Given that the transient land-ocean warming ratio is the same for the 1pctto2x and 1pctto4x runs ( see Fig. B1.last row in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html), the 'geometric' effect discussed in the Sect. [[#Revised land-ocean heat exchange formation|Revised land-ocean heat exchange formation]] would not explain this increase in climate sensitivity. An alternative explanation could be that climate feedbacks are climate-state dependent. The assumption in the standard energy balance with a constant global feedback (<m>\lambda</m>), with its attendant requirement that the outgoing energy flux scales proportionally with temperature change, may be an oversimplification. For example, the slow feedback due to retreating ice-sheets can lead to changes in the diagnosed effective sensitivities in AOGCMs (see e.g. [[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al., 2001]]) over long time-scales. [[References#Hansen_etal_2005_Efficacies|Hansen et al., 2005]] show that the 100-year climate response in the GISS model is more sensitive to higher forcings than to lower or negative forcings. Hansen et al.~(2005) express this effect by increasing efficacies for increasing radiative forcing. Table 1 in [[References#Hansen_etal_2005_Efficacies|Hansen et al., 2005]] suggests a gradient of roughly 1 % increase in efficacy for each additional Wm<sup>-2</sup> (OLS-regression of Ea versus Fa across the full range of CO<sub>2</sub> experiments), although some intervals (e.g. from 1.25 to 1.5<m>\times</m>CO<sub>2</sub>) show a slightly higher sensitivity of efficacy to forcing, i.e., 3% per Wm<sup>-2</sup>.<br />
<br />
Rather than making the efficacies dependent on forcing, an alternative is to make the climate sensitivity dependent on the forcing level. This distinction, on whether to modify forcing or sensitivity, is not important when the climate system is at or close to equilibrium. However, if the efficacies of the forcing, instead of the feedback parameters are allowed to vary with forcing, the transient climate response after a change in forcing will be slightly faster. In this MAGICC version, if a forcing dependency of the sensitivity is assumed, the land and ocean feedback parameters<br />
<m>\lambda_L</m> and <m>\lambda_O</m> are scaled as<br />
<br />
<m>\lambda =\frac{\Delta Q_{2x}}{\frac{\Delta Q_{2x}}{\lambda_{2x}}+\xi(\Delta Q- \Delta Q_{2x})} \label{eq_feedback_dependency_forcing}</m><span id="eq_A51"></span><div style="float: right; clear: right;">('''A51''')</div><br />
<br />
where <m>\lambda_{2x}</m> is the feedback parameter (=<m>\frac{\Delta Q_{2x}}{\Delta T_{2x}}</m>) at the forcing level for twice pre-industrial CO<sub>_2</sub> concentrations. The sensitivity factor <m>\xi</m> (KW<sup>-1</sup>m<sup>2</sup>) scales the climate sensitivity in proportion to the difference of forcing away from the model-specific "twice pre-industrial CO<m>_2</m> forcing level" (<m>\Delta Q{-} \Delta Q_{2x}</m>). The 1% increase in efficacy for each additional unit forcing in Hansen's findings translates into a feedback sensitivity factor <m>\xi</m> of 0.03 KW<sup>-1</sup>m<sup>2</sup>> (assuming a climate sensitivity <m\Delta T_{2x}</m>} of 3<sup><m>\circ</m></sup>C. Note that this scaling convention ([[#eq_51|A51]]) ensures that climate sensitivities are comparable for the equilibrium warming that corresponds to twice preindustrial CO<sub>_2</sub> concentration levels (see Table. 3 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html).<br />
<br />
===Efficacies===<br />
<br />
Efficacy is defined as the ratio of global-mean temperature response for a particular radiative forcing divided by the global-mean temperature response for the same amount of global-mean radiative forcing induced by CO<sub>_2</sub> (see Sect. 2.8.5 in [[References#Forster_Ramaswamy_etal_2007_IPCCAR4_Chapter2_radiativeForcing|Forster et al., 2005]]). In most cases, the efficacies are different for different forcing agents because of the geographical and vertical distributions of the forcing ([[References#Boer_Yu_2003_ClimateSensitivityResponse|Boer and Yu, 2003]];[[References#Joshi_etal_2003_improvedmetric_climatechange|Joshi et al., 2003]];[[References#Hansen_etal_2005_Efficacies|Hansen et al., 2005]]). The effective radiative forcing (<m>\Delta Q_e</m>) is the product of the standard climate forcing (<m>\Delta Q_a</m>), calculated after thermal adjustment of the stratosphere, and the efficacy (E<m>_a</m>). It is the effective forcings that are used in the energy balance equation (Eq.1), although both effective and standard forcings are carried through in the MAGICC code. Note that this parameterization yields slightly faster transient climate responses compared to an approach where different climate sensitivities are applied for each individual forcing agent (cf.[[#Accounting for climate-state dependent feedbacks|Accounting for climate-state dependent feedbacks]] above).<br />
<br />
In MAGICC, forcings for some components differ by hemisphere and over land and ocean. Just as for the global sensitivity, this, in combination with different land/ocean feedback factors, results in MAGICC6 exhibiting efficacies different from unity for non-CO<sub>_2</sub> forcing agents. In other words, efficacies different from unity are in part a consequence of the geometric effect described above. MAGICC calculates these internal efficacies using reference year (default 2005) forcing patterns. After normalizing these forcing patterns to a global-mean of <m>\Delta Q_{2x}</m> (default 3.71 Wm<sup>-2</sup>), the internal efficacy can be determined as<br />
<br />
<m>E_{\rm int} = \frac{\Delta T_{\rm eff2x}}{\Delta T_{2x}}\label{eq_efficacies_internal}</m><span id="eq_A52"></span><div style="float: right; clear: right;">('''A52''')</div><br />
<br />
where <m>T_{\rm eff2x}</m> is the actual global-mean equilibrium temperature change resulting from a normalized forcing pattern and <m>\Delta T_{2x}</m> is the corresponding warming for 2x CO<sub>_2</sub> forcing, i.e., the climate sensitivity. For most forcing agents, these internal efficacies are very close to one, except for forcings with a strong land/ocean forcing contrast, such as aerosol forcings. For example, for direct aerosol forcing in the HadCM3 emulation (calibration III - see Table B3 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html) the efficacy is 1.14. By default, these internal efficacies are taken into account when applying prescribed efficacies, so that:<br />
<br />
<m>\Delta Q_e = \frac{E_a}{E_{\rm int}}\Delta Q_a \label{eq_efficacies_acc_for_intefficacies}</m><span id="eq_A53"></span><div style="float: right; clear: right;">('''A53''')</div><br />
<br />
===The upwelling-diffusion equations===<br />
<br />
The transient temperature change evolution is largely influenced by the climate system's inertia, which in turn depends on the nature of the heat uptake by the climate system. The transient energy balance equations can be written as:<br />
<br />
<m>f_{\rm NO}(\zeta_o \frac{d\Delta T_{\rm NO,1}}{dt}-\Delta Q_{\rm NO}+\lambda_o \alpha \Delta T_{\rm NO,1} + F_{N}) =k_{\rm LO}(\Delta T_{\rm NL} - \mu\alpha\Delta T_{\rm NO,1})+k_{NS}\alpha(\Delta T_{\rm SO,1} - \Delta T_{\rm NO,1})\label{eq_transient_linear_equations_NO}</m><span id="eq_A54"></span><div style="float: right; clear: right;">('''A54''')</div><br />
<br />
<br />
<m>f_{\rm NL}(\zeta_L \frac{d\Delta T_{\rm NL}}{dt} - \Delta Q_{\rm NL}+ \lambda_L \Delta T_{\rm NL}) =k_{\rm LO}(\mu\alpha\Delta T_{\rm NO,1}-\Delta T_{\rm NL})\label{eq_transient_linear_equations_NL}</m><span id="eq_A55"></span><div style="float: right; clear: right;">('''A55''')</div><br />
<br />
<br />
<m>f_{SO}(\zeta_o \frac{d\Delta T_{\rm SO,1}}{dt}-\Delta Q_{\rm SO}+ \lambda_o \alpha \Delta T_{\rm SO,1} + F_{S})=k_{\rm LO}(\Delta T_{\rm SL} - \mu\alpha\Delta T_{\rm SO,1})+k_{\rm NS}\alpha(\Delta T_{\rm NO,1} - \Delta T_{\rm SO,1})\label{eq_transient_linear_equations_SO}</m><span id="eq_A56"></span><div style="float: right; clear: right;">('''A56''')</div><br />
<br />
<br />
<m>f_{\rm SL}(\zeta_L \frac{d\Delta T_{\rm SL}}{dt} - \Delta Q_{\rm SL}+ \lambda_L \Delta T_{\rm SL}) =k_{\rm LO}(\mu\alpha\Delta T_{\rm SO,1}-\Delta T_{\rm SL})\label{eq_transient_linear_equations_SL}</m><span id="eq_A57"></span><div style="float: right; clear: right;">('''A57''')</div><br />
<br />
where the adjustment factor <m>\alpha</m> (default 1.2) determines - over ocean areas - the ratio of hemispheric changes in air (<m>\Delta T_{\rm xO}</m>) versus ocean mixed layer temperatures (<m>\Delta T_{\rm xO,1}</m>). Based on ECHAM1/LSG analysis ([[References#Raper_Cubasch_1996_Emulation_AOGCM_simplemodel|Raper and Cubasch, 1996]]), this sea-ice factor was first introduced by [[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2001)]] to account for the fact that the air temperature will exhibit additional warming, because the atmosphere feels warmer ocean surface temperatures where sea ice retreats. The bulk heat capacity of the mixed layer in each hemisphere x is <m>f_x\zeta_o=f_x\rho c h_m</m>, where <m>\rho</m> denotes the density of seawater (1.026<m>\times</m>10<sup>6</sup> g m<sup>-3</sup>), c is the specific heat capacity (0.9333 cal g<sup>-1</sup><sup><m>\circ</m></sup>C<sup>-1</sup>= 4.1856<m>\times</m>0.9333 Joule g<sup>-1</sup><sup><m>\circ</m></sup>C<sup>-1</sup>) and <m>h_m</m> is the mixed layer's thickness [m]. The bulk heat capacity of the land areas is <m>f_x\zeta_L</m>, here assumed to be zero. The net heat flux into the ocean below the mixed layer is denoted by <m>F_x</m>.<br />
<br />
Equation ([[#eq_A55|A55]]) can then be written as: <br />
<br />
<m>\Delta T_{\rm NL} = \frac{f_{\rm NL}\Delta Q_{\rm NL}+k_{\rm LO}\mu\alpha\Delta T_{\rm NO,1}}{f_{\rm NL}\lambda_L + k_{\rm LO}}\label{eq_transient_separating_TNL}</m><span id="eq_A58"></span><div style="float: right; clear: right;">('''A58''')</div><br />
<br />
Substituting <m>\Delta T_{\rm NL}</m> in Eq. ([[#eq_A55|A55]]) yields:<br />
<br />
<m>f_{\rm NO}(\zeta_o \frac{d\Delta T_{\rm NO,1}}{dt} - \Delta Q_{\rm NO} + \lambda_o \alpha\Delta T_{\rm NO,1} + F_N) = \frac{k_{\rm LO}}{\frac{k_{\rm LO}}{f_{\rm NL}}+\lambda_L}(\Delta Q_{\rm NL}-\lambda_L\mu\alpha \Delta T_{\rm NO,1})+ k_{\rm NS}\alpha(\Delta T_{\rm SO,1} - \Delta T_{\rm NO,1})\label{eq_transient_TNL_into_TNO}</m><span id="eq_A59"></span><div style="float: right; clear: right;">('''A59''')</div><br />
<br />
Provided we know the heat flux <m>F_N</m> into the ocean below the mixed layer, we could now derive <m>d\Delta T_{\rm NO,1}/dt</m>. The net heat flux <m>F_N</m> at the bottom of the mixed layer is determined by<br />
vertical heat diffusivity (diffusion coefficient <m>K_z</m> [cm<sup>2</sup>s<sup>-1</sup>=3155.76<sup>-1</sup>m<sup>2</sup>yr<sup>-1</sup>]), and upwelling and downwelling (upwelling velocity w [m yr<sup>-1</sup>]), both acting on the perturbations <m>\Delta T</m> from the initial temperature profile <m>T^0_{\rm NO,z}</m>. If the upwelling rate <m>w</m> varies over time, the change in upwelling velocity <m>\Delta w^t{=}(w^t-w^0)</m> compared to its initial state <m>w^0</m> is assumed to act on the initial temperature profile, so that:<br />
<br />
<m>F_N = \frac{K_z}{0.5h_d}\rho c (\Delta T_{\rm NO,1}-\Delta T_{\rm NO,2})- w \rho c (\Delta T_{\rm NO,2} - \beta \Delta T_{\rm NO,1})</m><br /><m>- \Delta w \rho c (T^0_{\rm NO,2}- T^0_{\rm NO,sink})\label{eq_transient<m>eatflux_bottom_mixedlayer}</m><span id="eq_A60"></span><div style="float: right; clear: right;">('''A60''')</div><br />
<br />
where <m>T^0_{\rm NO,z}</m> is the initial temperature for water in layer z or in the downwelling pipe (z="sink").<br />
<br />
Given that the top layer is assumed to be mixed, the gradient of the temperature perturbations is calculated by the difference of the perturbations divided by half the thickness <m>h_d</m> of the second layer (see Fig. [[#Fig-A2|A2]]). Substituting <m>F_N</m> in Eq.([[#eq_A59|A59]] with Eq.([[#eq_A60|A60]]) and transforming the equation to discrete time steps, yields:<br />
<br />
<br />
{| <br />
| <m>\frac{d\Delta T_{\rm NO,1}}{dt} \approx \frac{\Delta T_{\rm NO,1}^{t+1} - \Delta T_{\rm NO,1}^{t}}{\Delta t} =</m> || <span id="eq_A61"></span><div style="float: right; clear: right;">('''A61''')</div><br />
|- <br />
| <m>\frac{1}{\zeta_o}\Delta Q_{\rm NO}^t </m>|| <m>\textrm{:forcing} </m><br />
|- <br />
| <m>- \frac{\lambda_o \alpha}{\zeta_o}\Delta T_{\rm NO,1}^{t+1} </m>|| <m>\textrm{:feedback}</m><br />
|- <br />
| <m>-\frac{K_z}{0.5h_d h_m}(\Delta T_{\rm NO,1}^{t+1}-\Delta T_{\rm NO,2}^{t+1}) </m>|| <m>\textrm{:diffusion}</m><br />
|- <br />
| <m>+ \frac{w^{t}}{h_m}(\Delta T^{t+1}_{\rm NO,2}-\beta \Delta T^{t+1}_{\rm NO,1}) </m>|| <m>\textrm{:upwelling}</m><br />
|- <br />
| <m>+ \frac{\Delta w^{t}}{h_m}(T^{0}_{\rm NO,2}-T^{0}_{\rm NO,sink}) </m>|| <m>\textrm{:variable upwelling} </m><br />
|- <br />
| <m>+ \frac{k_{\rm LO}(\Delta Q^{t}_{\rm NL}-\lambda_L \mu\alpha\Delta T^{t+1}_{\rm NO,1})}{\zeta_o f_{\rm NO}(\frac{k_{\rm LO}}{f_{\rm NL}}+\lambda_L)} </m>|| <m>\textrm{:land forcing}</m><br />
|- <br />
| <m>+ \frac{k_{\rm NS}\alpha}{\zeta_o f_{\rm NO}}(\Delta T_{\rm SO,1}^{t}-\Delta T_{\rm NO,1}^{t}) </m>|| <m>\textrm{:inter-hemispheric ex.} </m><br />
|}<br />
<br />
For the layers below the mixed layer (2<m>\leq</m>z<m>\leq</m>n-1), the temperature updating is governed by diffusion (first two terms in Eq.[[#eq_A62|A62]] and upwelling (last two terms), so that:<br />
<br />
<m>\frac{\Delta T^{t+1}_{\rm NO,z}-\Delta T^{t}_{\rm NO,z}}{\Delta t}= \frac{K_z}{0.5(h_d+h_d')h_d}(\Delta T^{t+1}_{\rm NO,z-1}-\Delta T^{t+1}_{\rm NO,z})- \frac{K_z}{h_d^2}(\Delta T^{t+1}_{\rm NO,z}-\Delta T^{t+1}_{\rm NO,z+1})</m><br /><m>+ \frac{w^{t}}{h_d}(\Delta T^{t+1}_{\rm NO,z+1}-\Delta T^{t+1}_{\rm NO,z})+ \frac{\Delta w^{t}}{h_d}(T^0_{\rm NO,z+1}-T^0_{\rm NO,z})\label{eq_transient_discrete_NO_submixed}</m><span id="eq_A62"></span><div style="float: right; clear: right;">('''A62''')</div><br />
<br />
where <m>h_d'</m> is zero for the layer below the mixed layer (z=2) and <m>h_d</m> otherwise, <m>\Delta w^t</m> is the change from the initial upwelling rate.<br />
<br />
[[file:Fig-A2a.jpg|350px|thumb|left|'''Fig-A4''' The schematic oceanic area and initial temperature profiles in MAGICC'S ocean hemispheres. Diffusion-driven heat transport is modeled proportional to the vertical gradient of temperature, which is especially high below the mixed layer.]] <br />
<span id="upd_model_structure"></span><br />
<br />
For the bottom layer (z=n), the downwelling term has to be taken into account, so that:<br />
<br />
<m>\frac{\Delta T^{t+1}_{\rm NO,n}-\Delta T^{t}_{\rm NO,n}}{\Delta t}= \frac{K_z}{h_d^2}(\Delta T^{t+1}_{\rm NO,n-1}-\Delta T^{t+1}_{\rm NO,n})</m><br />
<br />
<m>+ \frac{w^{t}}{h_d}(\beta\Delta T^{t}_{\rm NO,1}-\Delta T^{t+1}_{\rm NO,n})+ \frac{\Delta w^{t}}{h_d}(T^0_{\rm NO,sink}-T^0_{\rm NO,n})\label{eq_transient_discrete_NO_bottom}</m><span id="eq_A63"></span><div style="float: right; clear: right;">('''A63''')</div><br />
<br />
<br />
Corresponding to the temperature calculations shown here for the Northern Hemisphere ocean (NO), the equivalent steps apply for the Southern Hemisphere ocean (SO). For simplicity, the equations described above are for the constant-depth area profile case, which MAGICC defaults to when the depth-dependency factor <m>\vartheta</m> is set to zero. The detailed code for the general case with <m>0{\leq}\vartheta{\leq}1</m> is given in the ([[#Implementation of upwelling-diffusion-entrainment equations|Implementation of upwelling-diffusion-entrainment equations]]) section.<br />
<br />
===Calculating heat uptake===<br />
<br />
Heat uptake by the climate system can be calculated in different ways. One method is to use the global energy balance (Eq.1). Using the effective sensitivity as in ([[Model Description#eq_1|Eq.1]]) the heat uptake <m>F^t</m> is estimated as:<br />
<br />
<m>{dH^t}{dt}=F^t = \Delta Q^t-(f_L \lambda_L \Delta T^t_{L} + f_O \lambda_O \Delta T^t_{O}) \label{eq<m>eatuptake_balance}</m><span id="eq_A64"></span><div style="float: right; clear: right;">('''A64''')</div><br />
<br />
For verification purposes MAGICC6 calculates heat uptake in two ways, both directly (as above) and by integrating heat content changes in each layer in the ocean (yielding identical results), given the assumed zero heat capacity of the atmosphere and land areas:<br />
<br />
<m>\Delta H^t = \sum^{n}_{i=1} \frac{1}{\rho c h_i}\frac{(f_{\rm NO}\Delta T^t_{\rm NO,i} + f_{\rm SO} \Delta T^t_{\rm SO,i})}{f_O}+\epsilon \label{eq<m>eatuptake_integrating}</m><span id="eq_A65"></span><div style="float: right; clear: right;">('''A65''')</div><br />
<br />
where <m>h_i</m> is the thickness of the layer, i.e., <m>h_m</m> for the mixed layer and <m>h_d</m> for the others and <m>\epsilon</m> is a small term to account for the heat content of the polar sinking water.<br />
<br />
===Depth-dependent ocean with entrainment===<br />
<br />
[[References#Harvey_Schneider_1985_PartII, Harvey_Schneider_1985_PartI|Harvey and Schneider (1985b,a)]] introduced the upwelling-diffusion model with entrainment from the polar sinking water by varying the upwelling velocity w with depth. Building on the work by [[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2001)]], MAGICC6 also includes the option of a depth-dependent ocean area profile. If the depth-dependency parameter <m>\vartheta</m> is set to 1 (default), a standard depth-dependent ocean area profile is assumed as in HadCM2 and used in [[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2001)]]}. A constant upwelling velocity is assumed and mass conservation is maintained by "entrainment" from the downwelling pipe. With ocean area decreasing with depth and constant upwelling velocity, the upwelling mass flux would also have to decrease with depth. To offset this, the amount of entrainment into layer z is assumed to be proportional to the decrease in area from the top to the bottom of each layer (cf. [[#Fig-A2a|Fig-A4]]). We differ from the model structures tested by<br />
[[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2001)]], by equating changes in the temperature of the entraining water to those in the downwelling pipe, namely a fraction <m>\beta</m> (default 0.2) of the mixed layer temperature <m>\Delta T_{x,1}^{t-1}</m> of the previous timestep in Hemisphere x. For a detailed description of the code, see the following Sect. [[#Implementation of upwelling-diffusion-entrainment equations|Implementation of upwelling-diffusion-entrainment equations]]. Simple upwelling-diffusion models can overestimate the ocean heat uptake for higher warming scenarios when applying parameter values calibrated to match heat uptake for lower warming scenarios (see e.g. Fig. 17b in<br />
[[References#Harvey_etal_1997_IPCC_IntroductionSimpleClimateModels|Harvey et al., 1997]]). To address this, MAGICC6 includes a warming-dependent vertical diffusivity gradient. The physical reasoning is that a strengthened<br />
thermal stratification and, hence, reduced vertical mixing leads to decreased heat uptake for higher warming. Thus, the effective vertical diffusivity at <m>K_{z,i}</m> between ocean layer i and i+1 is<br />
given by:<br />
<br />
<m>K_{z,i} = {\rm max}\,(K_{z,{\rm min}}(1 - d_i)\frac{dK_{\rm z}}{dT}(\Delta T_{H,1}^{t-1}-\Delta T_{H,n}^{t-1})+K_z) \label{eq_verticalDiffusivity<m>eatdependent}</m><span id="eq_A66"></span><div style="float: right; clear: right;">('''A66''')</div><br />
<br />
where <m>K_{z,{\rm min}}</m> is the minimum vertical diffusivity (default 0.1 cm<sup>2</sup> s<sup>-1</sup>); <m>d_i</m> is the relative depth of the layer boundary with zero at the bottom of the mixed layer and one for the top of the bottom layer; <m>\frac{dK_{\rm z}}{dT}</m> is a newly introduced ocean stratification coefficient specifying how the vertical diffusivity <m>K_{\rm z}</m> between the mixed layer 1 and layer 2 changes with a change in the temperature difference between the top/mixed and bottom ocean layer of the respective hemisphere at the previous timestep t-1 <m>(\Delta T_{H,1}^{t-1}{-}\Delta T_{H,n}^{t-1})</m>.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=The_Carbon_Cycle&diff=21The Carbon Cycle2013-06-17T11:15:23Z<p>Antonius Golly: Created page with "*model description ** carbon cycle ** non-CO2 concentrations **[[Radiative Forcing | radiative forcing r..."</p>
<hr />
<div>*[[Model Description|model description]]<br />
**[[The Carbon Cycle| carbon cycle]]<br />
**[[Non-CO2 Concentrations | non-CO2 concentrations]]<br />
**[[Radiative Forcing | radiative forcing routines]]<br />
**[[Upwelling_diffusion_climate_model | climate model]]<br />
**[[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]]<br />
<br />
<br />
==The carbon cycle==<br />
<br />
Changes in atmospheric CO<sub>2</sub> concentration, C, are determined by CO<sub>2</sub> emissions from fossil and industrial sources (<m>E_{\rm foss}</m>), other directly human-induced CO<sub>2</sub> emissions from or removals to the terrestrial biosphere (<m>E_{\rm lu}</m>), the contribution from oxidized methane of fossil fuel origin (<m>E_{\rm fCH_4},</m>), the flux due to ocean carbon uptake (<m>F_{\rm ocn}</m>) and the net carbon uptake or release by the terrestrial biosphere (<m>F_{\rm terr}</m>) due to CO<sub>2</sub> fertilization and climate feedbacks. As in the C4MIP generation of carbon cycle models, no nitrogen or sulphur deposition effects on biospheric carbon uptake are included here [[References#Thornton_nitrogenCarbonCycle|Thornton et al., 2006]]. Hence, the budget <br />
Eq.[[#eq_A1|A1]] for a change in atmospheric CO<sub>2</sub> concentrations is:<br />
<br />
<m>\Delta C/\Delta t= E_{\rm foss} + E_{\rm lu} + E_{\rm fCH_4}- F_{\rm ocn} - F_{\rm terr}</m><span id="eq_A1"></span><div style="float: right; clear: right;">('''A1''')</div><br />
<br />
[[file:Fig-A2.jpg|350px|thumb|left|'''Fig-A2''' The terrestrial carbon cycle component in MAGICC with its carbon pools and carbon fluxes. <br />
For description of the pools and fluxes, including the treatment of <br />
temperature feedbacks and CO<sub>2</sub> fertilization, see Sect.[[#Terrestrial carbon cycle|Terrestrial carbon cycle]] ]] <br />
<span id="fig_terr_carboncycle"></span> <br />
<br />
===Terrestrial carbon cycle=== <br />
<br />
The terrestrial carbon cycle follows that in [[References#Wigley_1993_BalancingCarbonBudget|Wigley, 1993]], in turn is based on [[References#Harvey_1989_ManagingAtmCO2|Harvey, 1989]]. It is modeled with three boxes, one living plant box <m>P</m> (see Fig.[[#fig_terr_carboncycle|Terrestrial Carbon Cycle]]) and two dead biomass boxes, of which one is for detritus <m>H</m> and one for <br />
organic matter in soils <m>S</m>. The plant box comprises woody material, leaves/needles, grass, and roots, but does not include the rapid turnover part of living biomass, which can be assumed to have a zero lifetime on the timescales of interest here (dashed extension of plant box <m>P</m> in Fig.[[#fig_terr_carboncycle|Fig-A2]]. Thus, a fraction of gross primary product (GPP) cycles through the plant box directly back to the atmosphere due to autotrophic respiration and can be ignored (dashed arrows). Only the remaining part of GPP, namely the net primary production (NPP) is simulated. The NPP flux is channeled through the ``rapid turnover´´ part of the plant box and partitioned into carbon fluxes to the remainder plant box (default <m>g_P</m>=35%), detritus (<m>g_H</m>=60%) and soil box<br /> (<m>g_S</m>=1-<m>g_P</m>-<m>g_H</m>=5%).<br />
<br />
The plant box has two decay terms, litter production <m>L</m> and a part of gross deforestation <m>D_{\rm gross}^P</m>. Litter production is partitioned <br />
to both the detritus (<m>\phi_H</m>=98%) and soil box (<m>\phi_S</m>=1-<m>\phi_H</m>=2%). Thus, the mass balance for the plant box is: <br />
<br />
<m>\Delta P/\Delta t = g_P{\rm NPP} - R - L - D_{\rm gross}^P \label{eq_massbalance_P}</m><span id="eq_A2"></span><div style="float: right; clear: right;">('''A2''')</div><br />
<br />
The detritus box has sources from litter production (<m>\phi_HL</m>) and sinks to the atmosphere due to land use (<m>D_{\rm lu}^H</m>), non-land use related oxidation (<m>Q_A</m>), and a sink to the soil box (<m>Q_S</m>). The mass balance for the detritus box is thus<br />
<br />
<m> \Delta H/\Delta t = g_H{\rm NPP} + \phi_H L - Q_A - Q_S - D_{\rm lu}^H \label{eq_massbalance_H}</m><span id="eq_A3"></span><div style="float: right; clear: right;">('''A3''')</div><br />
<br />
The soil box has sources from litter production (<m>\phi_S</m>L), the detritus box (<m>Q_S</m>) and fluxes to the atmosphere due to land use <br />
(<m>D_{\rm gross}^S</m>), and non-land use related oxidation (<m>U</m>). The mass balance for the soil box is thus <br />
<br />
<m> \Delta S/\Delta t = g_S{\rm NPP} +\phi_S L + Q_S - U - D_{\rm lu}^S \label{eq_massbalance_S}</m><span id="eq_A4"></span><div style="float: right; clear: right;">('''A4''')</div><br />
<br />
The decay rates (<m>L</m>, <m>Q</m> and <m>U</m>) of each pool are assumed to be proportional to pool's box masses <m>P</m>, <m>H</m> and <m>S</m>, respectively. The turnover times <m>\tau_P</m>, <m>\tau_H</m> and <m>\tau_S</m> are determined by the initial steady-state conditions for box sizes and fluxes.<br />
<br />
<m>L_0 = P_0/\tau^P_0</m><span id="eq_A5"></span><div style="float: right; clear: right;">('''A5''')</div><br />
<br />
<br />
<m>Q_0 = H_0/\tau^H_0</m><span id="eq_A6"></span><div style="float: right; clear: right;">('''A6''')</div><br />
<br />
<br />
<m>U_0 = S_0/\tau^S_0\label{eq_terrcc_turnovertimes}</m><span id="eq_A7"></span><div style="float: right; clear: right;">('''A7''')</div><br />
<br />
Constant relaxation times <m>\tau</m> ensure that the box masses will relax back to their initial sizes if perturbed by a one-off land use change-related carbon release or uptake -- assuming no changes in fertilization and temperature feedback terms. This relaxation acts as an effective regrowth term so that deforestation <m>\Sigma D_{\rm gross}{=}D_{\rm gross}^P + D_{\rm gross}^H + D_{\rm gross}^S</m> represents the gross land use emissions, related to net land use emissions <m>E_{\rm lu}</m> by regrowth <m>\Sigma G</m>=<m>G^P</m> + <m>G^H</m> + <m>G^S</m><br />
<br />
<m>\Sigma D_{\rm gross} - \Sigma {\rm G} = E_{\rm lu}</m><span id="eq_A8"></span><div style="float: right; clear: right;">('''A8''')</div><br />
<br />
<br />
<m>D_{\rm gross}^P - {\rm G}^P = d_P E_{\rm lu}</m><span id="eq_A9"></span><div style="float: right; clear: right;">('''A9''')</div><br />
<br />
<br />
<m>D_{\rm gross}^H - {\rm G}^H = d_H E_{\rm lu}</m><span id="eq_A10"></span><div style="float: right; clear: right;">('''A10''')</div><br />
<br />
<br />
<m>D_{\rm gross}^S - {\rm G}^S = d_S E_{\rm lu}\label{eq_grossandnet_deforestation}</m><span id="eq_A11"></span><div style="float: right; clear: right;">('''A11''')</div><br />
<br />
Gross land-use related emissions might be smaller (compared to a case where relaxation times are assumed constant) as some human land use activities, e.g.\ deforestation, can lead to persistent changes of the ecosystems over the time scales of interest, thereby preventing full regrowth to the initial state <m>P_0</m>, <m>H_0</m> or <m>S_0</m>. A factor <m>\psi</m> is used to denote the fraction of gross deforestation that does not regrow (0<m>{\leq}{\psi}{\leq}</m>1). Thus, the relaxation times <m>\tau</m> are made time-dependent according to the following equation:<br />
<br />
<m>\tau^P(t) = \left(P_0 - \psi\int_0^t d_PE_{\rm lu}(t')dt'\right)/L_0</m><span id="eq_A12"></span><div style="float: right; clear: right;">('''A12''')</div><br />
<br />
<br />
<m>\tau^H(t) = \left(H_0 - \psi\int_0^t d_HE_{\rm lu}(t')dt'\right)/Q_0</m><span id="eq_A13"></span><div style="float: right; clear: right;">('''A13''')</div><br />
<br />
<br />
<m>\tau^S(t) = \left(S_0 - \psi\int_0^t d_SE_{\rm lu}(t')dt'\right)/U_0 \label{eq_terrcc_turnovertimes_timedep}</m><span id="eq_A14"></span><div style="float: right; clear: right;">('''A14''')</div><br />
<br />
====Formulation for CO<sub>2</sub> fertilization====<br />
<br />
CO<sub>2</sub> fertilization indicates the enhancement in net primary production (NPP) due to elevated atmospheric CO<sub>2</sub> concentration. As described in [[References#Wigley_2000_balancingCarbonBudget|Wigley, 2000]], there are two common forms used in simple models to simulate the CO<sub>2</sub> fertilization effect: (a) the logarithmic form (fertilization parameter <m>\beta_m</m>=1) and (b) the rectangular hyperbolic or sigmoidal growth function (<m>\beta_m</m>=2) (see e.g. [[References#Gates_1985_globalbiosphericCCycle|Gates, 1985]]. The rectangular hyperbolic formulation provides more realistic results for both low and high concentrations so that NPP does not rise without limit as CO<sub>2</sub> concentrations increase. Previous MAGICC versions include both formulations, but used the second as default. The code now allows use of a linear combination of both formulations (1<m>{\leq}{\beta_m}{\leq}</m>2).<br />
<br />
The classic logarithmic fertilization formulation calculates the enhancement of NPP as being proportional to the logarithm of the change in CO<sub>2</sub> concentrations C above the preindustrial level <m>C_0</m>:<br />
<br />
<m>\beta_{\rm log}=1 + \beta_s \,{\rm ln}\,({\rm C/C}_0) \label{eq_CO2fertilization_logarithm}</m><span id="eq_A15"></span><div style="float: right; clear: right;">('''A15''')</div> <br />
<br />
The rectangular hyperbolic parameterization for fertilization is given by<br />
<br />
<m>N=\frac{{C-C}_b}{1+b({C-C}_b)}</m><br />
<br />
:<m>=\frac{{N_0}(1+b(C_0-C_b))({C}-{C_b})}{(C_0-C_b)(1+b({C-C}_b))}\label{eq_CO2fertilization_sigmoidal growth}</m><span id="eq_A16"></span><div style="float: right; clear: right;">('''A16''')</div><br />
<br />
where <m>N_0</m> is the net primary production and <m>C_0</m> the CO<sub>2</sub> concentrations at pre-industrial conditions, <m>C_b</m> the concentration value at which NPP is zero (default setting: <m>C_b</m>=31 ppm, see [[References#gifford_1993|Gifford, 1993]].<br />
<br />
For better comparability with models using the logarithmic formulation, following [[References#Wigley_2000_balancingCarbonBudget|Wigley, 2000]], the CO<sub>2</sub> fertilization factor <m>\beta_s</m> expresses the NPP enhancement due to a CO<sub>2</sub> increase from 340 ppm to 680 ppm, valid under both formulations. Thus, MAGICC first determines the NPP ratio <m>r</m> for a given <m>\beta_s</m> fertilization factor according to:<br />
<br />
<m>r=\frac{{N}(680)}{{N}(340)}=\frac{{N}_0(1+\beta_s \,{\rm ln}\,(680/{{C}}_0))}{{N}_0(1+\beta_s \,{\rm ln}\, (340/{C}_0))}\label{eq_CO2fertilization_340to640}</m><span id="eq_A17"></span><div style="float: right; clear: right;">('''A17''')</div><br />
<br />
Following from here, <m>b</m> in Eq. [[#eq_A16|A16]] is determined by<br />
<br />
<m>b=\frac{(680-{C}_b)-r(340-{C}_b)}{(r-1)(680-{C}_b)(340-{C}_b)}\label{eq_CO2fertilization_determining b}</m><span id="eq_A18"></span><div style="float: right; clear: right;">('''A18''')</div><br />
<br />
which can in turn be used in Eq. [[#eq_A16|A16]] to calculate the effective CO<sub>2</sub> fertilization factor <m>\beta _{\rm sig}</m> at time <m>t</m> as<br />
<br />
<m>\beta _{\rm sig}(t)=\frac{1/({C}_0 - {C}_b) + b}{1/({C}(t)- {C}_b) + b} \label{eq_CO2fertilization_factor_michaelismenton}</m><span id="eq_A19"></span><div style="float: right; clear: right;">('''A19''')</div><br />
<br />
MAGICC6 allows for an increased flexibility, as any linear combination between the two fertilization parameterizations can be chosen (1<m>{\leq}{\beta_m}{\leq}</m>2), so that the effective fertilization factor <m>\beta _{\rm eff}</m> is given by:<br />
<br />
<m>\beta _{\rm eff}(t)=(2-\beta_m)\beta_{\rm log}+(\beta_m-1)\beta_{\rm sig}\label{eq_CO2fertilization_factor_effective}</m><span id="eq_A20"></span><div style="float: right; clear: right;">('''A20''')</div><br />
<br />
The CO<sub>2</sub> fertilization effect affects NPP so that <m>\beta_{\rm eff}</m> = NPP - NPP<sub>0</sub>. MAGICC's terrestrial carbon cycle furthermore applies the fertilization factor to one of the heterotrophic respiration fluxes <m>R</m> that cycles through the detritus box, which makes up 18.5 % of the total heterotrophic respiration (<m>\sum {\rm R} {=} R+U_a+Q</m>) at the initial steady-state.<br />
<br />
====Temperature effect on respiration and decomposition====<br />
<br />
Global-mean temperature increase is taken as a proxy for climate-related impacts on the carbon cycle fluxes induced by regional temperature, cloudiness or precipitation regime changes. Those impacts are commonly referred to as ``climate feedbacks on the carbon cycle´´, or simply, ``carbon cycle feedbacks´´. Here, the terrestrial carbon fluxes NPP, and the heterotrophic respiration/decomposition fluxes <m>R</m>, <m>Q</m> and <m>U</m> are scaled assuming an exponential relationship,<br />
<br />
<m>F_{i}(t)= F_{i}'(t)\cdot {\rm exp}(\sigma_{i}\Delta T(t))\label{eq_CO2feedback_GPP}</m><span id="eq_A21"></span><div style="float: right; clear: right;">('''A21''')</div><br />
<br />
where <m>\Delta T(t)</m> is the temperature above a reference year level, e.g. for 1990 or 1900, and <m>F_i'</m> (<m>F_i</m>) stands for the (feedback-adjusted) fluxes ''NPP'', <m>R</m>, <m>Q</m> and <m>U</m>. The parameters <m>\sigma_i</m> (K<m>^{-1}</m>) are their respective sensitivities to temperature changes. In order to model the actual change in <m>Q</m> and <m>U</m>, the relaxation times <m>\tau</m> for the detritus and soil pool are adjusted, respectively. Land use CO<sub>2</sub> emissions in many emissions scenarios ([[References#Nakicenovic_etal_2000_IPCCSRES|e.g SRES, Nakicenovic and Swart, 2000]]) reflect the net directly human-induced emissions. At each time-step, the gross land use emissions are subtracted from the plant, detritus and soil carbon pools. The difference between net and gross land use emissions is the CO<sub>2</sub> uptake due to regrowth. Thus, a separation between directly human-induced (deforestation-related) emissions and indirectly human-induced effects (regrowth) on the carbon cycle is required. As both regrowth and the temperature sensitivity are modeled by adjusting the turnover times, a no-feedback case is computed separately, retrieving the regrowth, then calculating the feedback-case including the formerly calculated regrowth.<br />
<br />
===Ocean carbon cycle===<br />
<br />
For modeling the perturbation of ocean surface dissolved inorganic carbon, an efficient impulse response substitute for the 3D-GFDL model [[References#Sarmiento_etal_1992_perturbationCO2_ocean_general_circulation_model|Sarmiento et al. (1992)]] is incorporated into MAGICC. The applied analytical representation of the pulse response function is provided in Appendix A.2.2 of [[References#Joos_Bruno_etal_1996_efficient_accurate_carbonuptake|Joos et al. (1996)]]. <br />
<br />
The sea-to-air flux <m>F_{\rm ocn}</m> is determined by the partial pressure differential for CO<sub>2</sub> between the atmosphere C and surface layer of the ocean <m>\rho</m>CO<sub>2</sub><br />
<br />
<m>{\rm F}_{\rm ocn} = k (C-\rho {\rm CO}_2) \label{eq_fluxocean}</m><span id="eq_A22"></span><div style="float: right; clear: right;">('''A22''')</div><br />
<br />
where <m>k</m> is the global average gas exchange coefficient ([[References#Joos_Prentice_etal_2001_feedbacks_biosphere_IPCC|Joos et al., 2001]]). This exchange coefficient is here calibrated to the individual C<m>^4</m>MIP carbon cycle models (default value (7.66 yr<sup>-1</sup>). The perturbation in dissolved inorganic carbon in the surface ocean <m>\Delta\Sigma {\rm <br />
CO_2}(t)</m> at any point t in time is obtained from the convolution integral of the mixed layer impulse response function <m>r_s</m> and the net air-to-sea flux <m>F_{\rm ocn}</m>:<br />
<br />
<m>\label{eq_hilda_pertdissolvedinorgCO2}\Delta\Sigma {\rm CO_2}(t) &=& \frac{c}{hA}\{\int_{t_0}^{t} {F}_{\rm ocn}(t') r_s(t-t')dt')\}</m><span id="eq_A23"></span><div style="float: right; clear: right;">('''A23''')</div><br />
<br />
The impulse response function <m>r_s</m> is given for the time immediately after the impulse injection (<1 yr) by (see Appendix A.2.4 of [[References#Joos_Bruno_etal_1996_efficient_accurate_carbonuptake|Joos et al., 1996]]):<br />
<br />
<m>r_s(t)&=& 1.0 - 2.2617t + 14.002t^2-48.770t^3+82.986t^4-67.527t^5+21.037t^6 \label{eq_hilda_impulseresponse_below2years}</m><span id="eq_A24"></span><div style="float: right; clear: right;">('''A24''')</div><br />
<br />
and for t<m>{\geq}</m>1 year is given by:<br />
<br />
<m>r_s(t)= \sum_{i=1}^6 \gamma_i e^{-\tau_i t}\label{eq_oceancc_after_initialphase}</m><span id="eq_A25"></span><div style="float: right; clear: right;">('''A25''')</div><br />
<br />
with the partitioning <m>\gamma</m> and relaxation <m>\tau</m> coefficients:<br />
<br />
<m>\gamma=\left[\begin{array}{l}0.01481\\0.70367\\0.24966\\0.066485\\0.038344\\0.019439\end{array}\right]\tau=\left[\begin{array}{l}0\\1/0.70177\\1/2.3488\\1/15.281\\1/65.359\\1/347.55\end{array}\right] \label{eq_hilda_impulseresponse_after2years_coefficients}</m><span id="eq_A26"></span><div style="float: right; clear: right;">('''A26''')</div><br />
<br />
The relationship between the perturbation to dissolved inorganic carbon <m>\Delta\Sigma</m>CO<m>_2(t)</m> and ocean surface partial pressures <m>\Delta\rho</m>CO<sub>2</sub>(<m>T_0</m>) (expressed in ppm or <m>\mu</m>atm) at the preindustrial temperature level <m>T_0</m> is given by Eq.(A23) in [[References#Joos_Prentice_etal_2001_feedbacks_biosphere_IPCC|Joos et al. (1996)]]. Furthermore, the temperature sensitivity effect on CO<sub>2</sub> solubility and hence oceanic carbon uptake is parameterized with a simple exponential expression. The modeled partial pressure <m>\rho</m>CO<m>_2(t)</m> increases with sea surface temperatures according to:<br />
<br />
<m>\rho {\rm CO}_2(t) = [\rho {\rm CO}_2(t_0) + \Delta\rho {\rm CO}_2(T_0)]\, {\rm exp}(\alpha_T \Delta T)\label{eq_partialpressure_ocn}</m><span id="eq_A27"></span><div style="float: right; clear: right;">('''A27''')</div><br />
<br />
where <m>\alpha_T</m> (default <m>\alpha_T</m>=0.0423 K<sup>-1</sup>) is the sensitivity of the sea surface partial pressure to changes in temperature (<m>\Delta T</m>) away from the preindustrial level (see <br />
Eq.(A24) in [[References#Joos_Prentice_etal_2001_feedbacks_biosphere_IPCC|Joos et al. (1996)]], based on [[References#Takahashi_etal_1993_surfaceOceans_CO2|Takahashi et al. (1993)]]).</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=References_Model_Description&diff=20References Model Description2013-06-17T11:15:02Z<p>Antonius Golly: Created page with "This page lists the references relevant for the MAGICC6 model description. <!--Albrecht(1989)--><span id="Albrecht_1989_cloudcover_aerosols"></span> Albrecht, B.A.: Aeroso..."</p>
<hr />
<div>This page lists the references relevant for the MAGICC6 model description. <br />
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<hr />
<div>This page lists the references relevant for the MAGICC6 model description. <br />
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climate sensitivity in GCMs, J. Climate, 21, 5076--5090, 2008.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Radiative_Forcing&diff=18Radiative Forcing2013-06-17T10:21:39Z<p>Antonius Golly: Created page with "*model description ** carbon cycle ** non-CO2 concentrations **[[Radiative Forcing | radiative forcing r..."</p>
<hr />
<div>*[[Model Description|model description]]<br />
**[[The Carbon Cycle| carbon cycle]]<br />
**[[Non-CO2 Concentrations | non-CO2 concentrations]]<br />
**[[Radiative Forcing | radiative forcing routines]]<br />
**[[Upwelling_diffusion_climate_model | climate model]]<br />
**[[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]]<br />
<br />
<br />
==Radiative forcing==<br />
<br />
The following section highlights the key parameterizations used for estimating the radiative forcing due to human-induced changes in greenhouse gas concentrations, tropospheric ozone and aerosols. The radiative forcing applied in MAGICC is in general the forcing at tropopause level after stratospheric temperature adjustment. Efficacies of the forcings, as discussed by [[References#Hansen_etal_2005_Efficacies|Hansen et al. (2005)]] and [[References#IPCC_AR4_Chapter10_Projections_Meehletal|Meehl et al. (2007)]] can be applied.<br />
<br />
===Carbon dioxide===<br />
<br />
Taking into account the "saturation" effect of CO<sub>2</sub> forcing, i.e., the decreasing forcing efficiency for a unit increases of CO<sub>2</sub> concentrations with higher background concentrations, the first IPCC Assessment ([[References#Shine_IPCC1990_Chapter2|Shine et al., 1990]]) presented the simplified expression of the form:<br />
<br />
<m>\label{eq_CO2_forcing} \Delta Q_{\rm CO_2}=\alpha_{\rm CO_2}{\rm ln} (\rm C/C_0)</m><span id="eq_A35"></span><div style="float: right; clear: right;">('''A35''')</div><br />
<br />
where <m>\Delta Q_{\rm CO_2}</m> is the adjusted radiative forcing by CO<sub>2</sub> (Wm<sup>-2</sup>) for a CO<sub>2</sub> concentration <m>C</m> (ppm) above the pre-industrial concentration <m>C</m><sub>0</sub> (278 ppm). This expression proved to be a good approximation, although the scaling parameter <m>\alpha_{\rm CO_2}</m> has since been updated to a best-estimate of 5.35 Wm<sup>-2</sup> (=<m>\frac{3.71}{ln(2)} </m>Wm<sup>-2</sup>)[[References#Myhre_etal_1998_newestimates_GHGforcing|Myhre et al. (1998)]], used as default in MAGICC. When applying AOGCM-specific CO<sub>2</sub> forcing, <m>\alpha_{\rm CO_2}</m> is set to: <br />
<br />
<m>\label{eq_CO2_forcing_dQ2x} \alpha_{\rm CO_2} = \frac{\Delta Q_{\rm 2\times}}{\rm ln(2)}</m><span id="eq_A36"></span><div style="float: right; clear: right;">('''A36''')</div><br />
<br />
===Methane and nitrous oxide===<br />
<br />
Methane and nitrous oxide have overlapping absorption bands so that higher concentrations of one gas will reduce the effective absorption by the other and vice versa. This is reflected in the standard simplified expression for methane and nitrous oxide forcing, <m>\Delta Q_{\rm CH4}</m> and <m>\Delta Q_{\rm N2O}</m>, respectively (see [[References#Ramaswamy_2001_IPPCWG1_RadiativeForcing|Ramaswamy et al., 2001]], [[References#Myhre_etal_1998_newestimates_GHGforcing|Myhre et al. 1998]]):<br />
<br />
<m>\label{eq_methane_forcing}\Delta Q_{\rm CH_4} = \alpha_{\rm CH_4}(\sqrt{\rm C_{\rm CH_4}}-\sqrt{\rm C_{\rm CH_4}^0}-f(\rm C_{\rm CH_4},{\rm C}_{\rm N_2O}^0)-f({\rm C}_{\rm CH_4}^0,{\rm C}_{\rm N_2O}^0)</m><span id="eq_A37"></span><div style="float: right; clear: right;">('''A37''')</div><br />
<br />
<br />
<m>\Delta Q_{\rm N_2O} = \alpha_{\rm N_2O}(\sqrt{{\rm C}_{\rm N_2O}}-\sqrt{{\rm C}_{\rm N_2O}^0})-f({\rm C}_{\rm CH_4}^0,{\rm C}_{\rm N_2O})-f({\rm C}_{\rm CH_4}^0,{\rm C}_{\rm N_2O}^0)</m><span id="eq_A38"></span><div style="float: right; clear: right;">('''A38''')</div><br />
<br />
where the overlap is captured by the function<br />
<br />
<m>\label{eq_methane_forcing_overlap}f(\rm M,N)=0.47{\rm ln}\,(1+0.6356(\frac{\rm MN}{10^6})^{0.75}+0.007\frac{\rm M}{10^3}(\frac{\rm MN}{10^6})^{1.52})</m><span id="eq_A39"></span><div style="float: right; clear: right;">('''A39''')</div><br />
<br />
with M and N being CH<sub>4</sub> and N<sub>2</sub>O concentrations in ppb. For methane, an additional forcing factor due to methane-induced enhancement of stratospheric water vapor content is included. This enhancement is assumed to be proportional to (default <m>\beta</m>=15 %) the ``pure´´ methane radiative forcing, i.e., without subtraction of N<sub>2</sub>O absorption band overlaps:<br />
<br />
<m>\Delta Q_{\rm CH_4}^{\rm stratoH2O} =\beta\alpha_{\rm CH_4}(\sqrt{\rm C_{\rm CH_4}}-\sqrt{\rm C_{\rm CH_4}^0}). </m><span id="eq_A40"></span><div style="float: right; clear: right;">('''A40''')</div><br />
<br />
===Tropospheric ozone=== <br />
<br />
From the tropospheric ozone precursor emissions and following the updated parameterizations of OxComp as given in footnote a of Table 4.11 in [[References#Ehhalt_Prather_2001_IPCC_Chemistry|Ehhalt et al. (2001)]], the change in hemispheric tropospheric ozone concentrations (in DU) is parameterized as: <br />
<br />
<m>\label{eq_tropospheric_ozone} \Delta (\rm trop O_3)={\rm S}_{\rm CH_4}^{O_3}\Delta ln(\rm CH_4)+ {\rm S}_{\rm NOx}^{\rm O_3} E_{\rm NOx} + {\rm S}_{\rm CO}^{\rm O_3} E_{\rm CO} + {\rm S}_{\rm VOC}^{\rm O_3} E_{\rm VOC}</m><span id="eq_A41"></span><div style="float: right; clear: right;">('''A41''')</div><br />
<br />
where <m>S_{\rm x}^{\rm O_3}</m> are the respective sensitivity coefficients of tropospheric ozone to methane concentrations and precursor emissions. The radiative forcing is then approximated by a linear abundance to forcing relationship so that <m>\Delta Q_{\rm trop O_3}=\alpha_{\rm trop O3} \Delta (\rm trop O_3)</m> with <m>\alpha_{\rm trop O3}</m> being the radiative efficiency factor (default 0.042).<br />
<br />
===Halogenated gases===<br />
<br />
The global-mean radiative forcing <m>\Delta Q_{t,i}</m> of halogenated gases is simply derived from their atmospheric concentrations C (see [[Non-CO2 Concentrations#|Non-CO2 concentrations]]) and radiative efficiencies <m>\varrho_i</m> [[References#Ehhalt_Prather_2001_IPCC_Chemistry|Ehhalt et al. (2001)]] table 4.11.<br />
<br />
<m>\Delta {Q_{t,i}} = \varrho_i (C_{t,i}-C_{0,i})\label{eq_halogas_RF}</m><span id="eq_A42"></span><div style="float: right; clear: right;">('''A42''')</div><br />
<br />
The land-ocean forcing contrast in each hemisphere for halogenated gases is assumed to follow the one [[References#Hansen_etal_2005_Efficacies|Hansen et al. (2005)]] estimated for CFC-11. The hemispheric forcing contrast is dependent on the lifetime of the gas. For short-lived gases (<m>{<}</m>1\,yr) the hemispheric forcing contrast is assumed to equal the time-variable hemispheric emission ratio. For longer lived gases (default <m>{>}</m>8\,yrs), the hemispheric forcing contrast is assumed to equal the one from CFC-11 with linear scaling in between these two approaches for gases with a medium lifetime.<br />
<br />
===Stratospheric ozone===<br />
<br />
Depletion of the stratospheric ozone layer causes a negative global-mean radiative forcing <m>\Delta Q_{t}</m>. The depletion and hence radiative forcing is assumed to be dependent on the equivalent effective stratospheric chlorine (EESC) concentrations as follows:<br />
<br />
<m>\Delta Q_{t} = \eta_1 (\eta_2 \times \Delta {\rm EESC}_{t})^{\eta_3} \label{eq_stratospheric_ozone} </m><span id="eq_A43"></span><div style="float: right; clear: right;">('''A43''')</div><br />
<br />
where <m>\eta_1</m> is a sensitivity scaling factor (default <m>-</m>4.49e-4 Wm<sup>-2</sup>), <m>\Delta {\rm EESC}_{t}</m> the EESC concentrations above 1980 levels (in ppb), the factor <m>\eta_2</m> equals <m>\frac{1}{100}</m> (ppb<m>^{-1}</m>) and <m>\eta_3</m> is the sensitivity exponent (default 1.7).<br />
<br />
EESC concentrations are derived from the modeled concentrations of 16 ozone depleting substances controlled under the Montreal Protocol, their respective chlorine and bromine atoms, fractional release factors and a bromine versus chlorine ozone depletion efficiency (default 45) ([[References#Daniel_1999_relativeImportance_Bromine_Chlorine|Daniel et al., 1999]]).<br />
<br />
<br />
===Tropospheric aerosols===<br />
\label{section_TropAerosolParameterization}<br />
<br />
The direct effect of aerosols is approximated by simple linear forcing-abundance relationships for sulfate, nitrate, black carbon and organic carbon. Time-variable hemispheric abundances of these short-lived aerosols are in turn approximated by their hemispheric emissions, justifiable because of their very short lifetimes. The ratio of direct forcing over land and ocean areas in each hemisphere is taken from [[References#Hansen_etal_2005_Efficacies|Hansen et al. (2005)]] (available at http://data.giss.nasa.gov/efficacy/). Specifying the direct radiative forcing patterns for one particular year, and knowing the<br />
hemispheric emissions in that year, allows us to define the future forcing as a function of future emissions.<br />
<br />
The indirect radiative forcing, formerly modeled as dependent on SO<m>_{\rm x}</m> abundances only [[References#Wigley_1991_ReducingFossilCO2IncreaseClimateChange|Wigley, 1991a]], is now estimated by taking into account time-series of sulfate, nitrate, black carbon and organic carbon optical thickness:<br />
<br />
<m>\label{eq_forcing_indirectAer} \Delta Q_{\rm Alb,i} = r\times {\rm P}_{\rm Alb,i}\times \log(\frac{\sum_g w_g {\rm N}_{g,i}}{\sum_g w_g {\rm N}_{g,i}^0})</m><span id="eq_A44"></span><div style="float: right; clear: right;">('''A44''')</div><br />
<br />
where <m>\Delta Q_{\rm Alb,i}</m> is the first indirect aerosol forcing in the four atmospheric boxes <m>i</m>, representing land and ocean areas in each hemisphere; P<m>_{\rm Alb}</m> is the four-element pattern of aerosol indirect effects related to albedo ([[References#Twomey_1977_albedo|HTwomey, 1977]]) in a reference year. The second indirect effect on cloud cover changes ([[References#Albrecht_1989_cloudcover_aerosols|Albrecht, 1989]]) is modeled equivalently -- using a reference year pattern P<m>_{\rm Cvr,i}</m>. The respective default patterns are derived from data displayed in Fig. 13 of [[References#Hansen_etal_2005_Efficacies|Hansen et al. (2005)]]. The scaling factor <m>r</m> allows one to specify a global-mean first or second indirect forcing for a specific reference year. The time-variable number concentrations of soluble aerosols N<m>_{g,i}</m> relative to their pre-industrial level in each hemisphere N<m>_{g,i}^0</m> are normed to unity in that reference year. This is done separately for sulfates, nitrates, black carbon and organic carbon. For the latter, the differential solubility from industrial (fossil fuel) and biomass burning sources is taken into account (default solubility ratio 0.6/0.8) ([[References#Hansen_etal_2005_Efficacies|Hansen et al., 2005]]). The default contribution shares w<m>_g</m> of the individual aerosol types g to the indirect aerosol effect were assigned to reflect the preliminary results by [[References#Hansen_etal_2005_Efficacies|Hansen et al. (2005)]], namely 36 % for sulfates, 36 % for organic carbon, 23 % for nitrates and 5 % for black carbon. Note, however, that these estimates of the importance of non-SOx aerosol contributions are very uncertain, not least because the solubility, e.g. for organic carbon and nitrates have large uncertainties. The number concentrations <m>N_{g,i}</m> are here approximated by historical optical thickness estimates (as provided on http://data.giss.nasa.gov/efficacy/ see as well Supplement) and extrapolated into the future by scaling with hemispheric emissions. The general logarithmic relation between number concentrations and forcing is based on the findings by [[References#Wigley_Raper_1992_ImplicationsWarmingIPCC_Nature|Wigley and Raper (1992)]]; [[References#Wigley_1991_ReducingFossilCO2IncreaseClimateChange|Wigley (1991a)]]; [[References#Gultepe_Isaac_1999_aerosols|Gultepe and Isaac(1999)]] and used in [[References#Hansen_etal_2005_Efficacies|Hansen et al. (2005)]]}.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Online_Help&diff=17Online Help2013-06-17T10:21:22Z<p>Antonius Golly: Created page with "With the [http://live.magicc.org live.magicc.org] interface for running MAGICC6 on our servers, you have a simple 3-step process to generate your own climate scenario output. ..."</p>
<hr />
<div>With the [http://live.magicc.org live.magicc.org] interface for running MAGICC6 on our servers, you have a simple 3-step process to generate your own climate scenario output. Below, we provide a little bit of help with the choices you have during this three step process; <br />
<br />
== Step 1: Choosing Emissions == <br />
<br />
I notice that there isn't any quetsion also I notice the scene involves 3 different kinds of balls tennis ball, soccer ball, and baseball. I notice that you use ounces also there is a balance where the balls are getting weighed on. I also notice that a soccer ball weighs the most then baseball and then tennis ballI wonder why there isn't a quetsion. I also wonder how you can find an equation or an answer.<br />
<br />
Wonrdfuel explanation of facts available here.<br />
<br />
=== Upload your own emission scenario ===<br />
You have the option to upload your own MAGICC emission scenario as an ASCII file. You can either provide only globally aggregate emissions or regional emissions. If you want to put your own emission data into such a scenario input file, see this page of [[Creating_MAGICC_Scenario_Files | how to create your own .SCEN file ]].<br />
<br />
== Step 2: Select Model Settings == <br />
You can run MAGICC in two distinct modes, a "standard" one and a "probabilistic" one. <br />
<br />
Nothing wrong with beeing a geek but then that's just me. Sometimes you get bednard with a certain clique that is not who you really are, just because you happen to be smart, shy, and scrawny So, I think the most important thing you can do in the summer is to get to know yourself better. Who are you really? Don't think about what other people say or who you feel are cool in school. Figure out what you truly want to do, what music you truly love to listen to regardless of what the cool people are listening to, what you like wearing, what you want to be when you grow up, etc. etc. Then when you are confident in who you are, then you can find cool clothes, shoes, sunglasses, wrist watch, necklace, backpack, etc. that matches your style and not just a mimic of everybody else. Brand name or clothing style is not really what makes somebody cool , it is the way the guy wears the clothes that is the secret ingredient and that's attitude/self-confidence. Of course it matters that the clothes you wear compliment your skin-tone, eye-color, body-shape. But, a lot of times, that's instinctive. When you wear something and look at yourself in the mirror and feel icky, then chances are, it is not a pleasing combination.About the muscles that has nothing to do with being cool . You should exercise/workout to be healthy. And you'll need muscles for strength not to look cool . What people will see is the health emanating from you which is perceived as youth and longevity . You know, like those skinny girls out there, they think being skinny is cool but then they go to extremes and then they just look sickly like Lindsey Lohan at one time And one more tip (from a girl who was the most popular girl in school) what people really dig is not how you look but how you make others feel when they're around you. If you look drop dead gorgeous but you make everybody feel like dirt when they're around you, then they'll just find something to hate about you.Good Luck!<br />
<br />
=== Selecting "Probabilistic" run mode === <br />
If you choose the "probabilistic" setting, your selected emission scenarios will be run multiple times by MAGICC, each time with a slightly different parameter setting. The results will not be single temperature or CO<sub>2</sub> concentration outcomes for each scenario, but actually uncertainty distributions.<br />
<br />
Note: Since probabilistic runs will require the climate model to be run 171 or even 600 times for each scenario, some patience is required. Normally, finishing a probabilistic run will take just a couple of minutes, maybe up to 10min. You will be provided with distributions of key climate outputs for every decade, but not for every year, as under the "standard" runs.<br />
<br />
==== Choose the "multi-model ensemble" probabilistic run mode ====<br />
<br />
If you select this option, we will run your emission scenarios 171 times, with all combinations of 19 AOGCM calibrations and 9 carbon cycle model calibrations. These AOGCMs and carbon cycle models are from the IPCC Fourth Assessment Report and belong to the so-called "CMIP3" and "C4MIP" intercomparisons. If you assume that all those 19 AOGCMs and 9 carbon cycle models are equally likely and sampling the full uncertainty space (and there are good reasons, by the way, not to make that assumption), then you can interpret your outcome as a probabilistic distribution of expected future climate change. Otherwise, simply call it what it is: a "multi-model ensemble" without assigning this statistical property to it. <br />
<br />
It's spooky how clveer some ppl are. Thanks!<br />
<br />
Что-то красивой темы ни одной не нашел) Остаюсь пока на своей;;;;; Цвета(setq default-frame-alist ( ;;(cursor-color . Firebrick ) (cursor-color . White ) (cursor-type . box) ;;(foreground-color . White ) ;;(background-color . DarkSlateGray ) (foreground-color . White ) (background-color . Black ) (vertical-scroll-bars . right)))p.s.: Интересный блог, только оформление ужасное (размер шрифтов замого контента мал), и комментарии рекомендую через DISQUS сделать.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Online_Emission_Scenarios&diff=16Online Emission Scenarios2013-06-17T10:21:01Z<p>Antonius Golly: Created page with "When running MAGICC6 via [http://live.magicc.org live.magicc.org], you can select a number of emission scenarios. Here, we provide a short description of those, ordered by the..."</p>
<hr />
<div>When running MAGICC6 via [http://live.magicc.org live.magicc.org], you can select a number of emission scenarios. Here, we provide a short description of those, ordered by their (often somewhat cryptic) name. <br />
<br />
== RCP scenarios == <br />
<br />
The RCP scenarios are the newest set of scenarios that are used for intercomparison purposes in the global climate science community. The four RCP scenarios are: <br />
* RCP3-PD (which as well goes by the name RCP2.6): This scenario is a strong mitigation scenario. Global emissions peak before 2020 and roughly reduce to halved global emission levels by 2050. This scenario has the best chance of, for example, staying below 2C global warming. None of the other scenarios has a reasonable chance of doing that. The name "PD" results from Peak & Decline, because the radiative under this scenario is likely to peak and then decline. Substantial net negative CO2 emissions are for example implied after the 2070s. <br />
* RCP45: This is a medium-low pathway. This scenario roughly results in a CO2 concentrations of 550ppm by the end of the century and a forcing of approximately 4.5 W/m2. It is comparable to the former SRES B1 scenario, which was the lowest of the 6 Illustrative SRES Marker scenarios used previously in IPCC (see below). <br />
* RCP60: This scenario can be considered a medium-high pathway. This scenario has initially (in the first two, three decades of the 21st century) rather low emissions, but then increases and stabilizes at around 6 W/m2 by the time of 2150. <br />
* RCP85: This is one of the highest emission scenarios around. It implies CO2 concentrations of approximately 2000 ppm by 2250. The opposite of any mitigation scenario, rather a "burn-coal-as-much-as-you-can" world, and likely not a very pleasant world in terms of the climate impacts. <br />
<br />
For more information: See the special issue of Climatic Change: <br />
van Vuuren, D., J. Edmonds, M. Kainuma, K. Riahi, A. Thomson, K. Hibbard, G. Hurtt, T. Kram, V. Krey, J.-F. Lamarque, T. Masui, M. Meinshausen, N. Nakicenovic, S. Smith and S. Rose (2011). "The representative concentration pathways: an overview." Climatic Change 109(1): 5-31, DOI:10.1007/s10584-011-0148-z, [http://www.springerlink.com/content/f296645337804p75/ freely available online]<br />
<br />
==SRES scenarios == <br />
These SRES scenarios were the standard scenarios in climate system science for more than a decade. They are still in use and a vast body of literature anchors their results onto one of these 6 Illustrative Marker scenarios. <br />
<br />
To be continued.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Non-CO2_Concentrations&diff=15Non-CO2 Concentrations2013-06-17T10:20:45Z<p>Antonius Golly: Created page with "*model description ** carbon cycle ** non-CO2 concentrations **[[Radiative Forcing | radiative forcing r..."</p>
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<div>*[[Model Description|model description]]<br />
**[[The Carbon Cycle| carbon cycle]]<br />
**[[Non-CO2 Concentrations | non-CO2 concentrations]]<br />
**[[Radiative Forcing | radiative forcing routines]]<br />
**[[Upwelling_diffusion_climate_model | climate model]]<br />
**[[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]]<br />
<br />
<br />
==Non-CO<sub>2</sub> concentrations==<br />
<br />
This section provides the formulas used to convert emissions to concentrations, while the [[#Radiative Forcing|Radiative Forcing]] section provides details on the derivation of radiative forcings.<br />
<br />
===Methane===<br />
<br />
Natural emissions of methane are inferred by balancing the budget for a user-defined historical period, e.g. from 1980-1990, so that<br />
<br />
<m>\label{eq_natural emissions}E^n_{\o} = \theta (\Delta C_{\o} - C_{\o '}/\tau_{\rm tot})-E^f_{\o} - E^b_{\o}</m><span id="eq_A28"></span><div style="float: right; clear: right;">('''A28''')</div><br />
<br />
where <m>E^n_{\o}</m>, <m>E^f_{\o}</m> and <m>E^b_{\o}</m> are the average natural, fossil and land use related emissions, respectively; <m>\theta</m> is the conversion factor between atmospheric concentrations and mass loadings. <m>C_{\o'}</m> (and <m>\Delta C_{\o}</m>) are the average (annual changes in) concentrations. The net atmospheric lifetime <m>\tau_{\rm tot}</m> in the case of methane consists of the atmospheric chemical lifetime and lifetimes that characterize the soil and other (e.g. stratospheric) sink components according to <br />
<br />
<m>\label{eq_methane lifetime} \frac{1}{\tau_{\rm tot}} = \frac{1}{\tau_{\rm tropos}} + \frac{1}{\tau_{\rm soil}} + \frac{1}{\tau_{\rm other}}</m><span id="eq_A29"></span><div style="float: right; clear: right;">('''A29''')</div><br />
<br />
The feedback of methane on tropospheric OH and its own lifetime follows the results of the OxComp work (tropospheric oxidant model comparison) (see[[References#Ehhalt_Prather_2001_IPCC_Chemistry| Ehhalt et al., 2001]] in particular Table 4.11, which provides simple parameterizations for simulating complex three-dimensional atmospheric chemistry models. As default, tropospheric OH abundances are assumed to decrease by 0.32 % for every 1 % increase in CH<m>_4</m>. The change in tropospheric OH abundances is thus modeled as:<br />
<br />
<m>\label{eq_troposphericOH} \noindent \Delta {\rm ln}\,({\rm trop} {\rm OH}) = { S_{\rm CH_4}^{\rm OH}}\, \Delta{{\rm ln}\,(\rm CH_4)}+ { S_{{\rm NO_x}}^{\rm OH}} {E_{{\rm NO_x}} + S_{\rm CO}^{\rm OH} E_{\rm CO}} + {\rm S_{\rm VOC}^{\rm OH} E_{\rm VOC}}</m><span id="eq_A30"></span><div style="float: right; clear: right;">('''A30''')</div><br />
<br />
where <m>S_x^{\rm OH}</m> is the sensitivity of tropospheric OH towards CH<m>_4</m>, NOx, CO and VOC, with default values of <m>-</m>0.32, +0.0042, <m>-</m>1.05e-4 and <m>-</m>3.15e-4, respectively. Increases in tropospheric OH abundances decrease the tropospheric lifetime <m>\tau '</m> of methane (default 9.6 yrs<sup>-1</sup>), which is approximated as a simple exponential relationship <br />
<br />
<m>\label{eq_tropos_methane lifetime} \tau_{\rm CH_4,tropos}' = \tau_{\rm CH_4,tropos}^0\, {\rm exp}\,^{\Delta {\rm ln}\,({\rm trop OH})}</m><span id="eq_A31"></span><div style="float: right; clear: right;">('''A31''')</div><br />
<br />
Approximating the temperature sensitivity of the net effect of tropospheric chemical reaction rates, the tropospheric lifetime of CH<m>_4</m> is adjusted:<br />
<br />
<m>\label{eq_tropos_methane lifetime_inclTemp} \tau_{\rm CH_4,tropos} = \frac{\tau_{\rm CH_4,tropos}^0}{\frac{\tau_{\rm CH_4,tropos}^0}{\tau_{\rm CH_4,tropos}'} + S_{\tau_{\rm CH_4}}\Delta T}</m><span id="eq_A32"></span><div style="float: right; clear: right;">('''A32''')</div><br />
<br />
where <m>S_{\tau_{\rm CH_4}}</m> is the temperature sensitivity coefficient (default <m>S_{\tau_{\rm CH_4}}</m>=3.16e-2<sup><m>^{\circ}</m></sup>C<sup>-1</sup>) and <m>\Delta T</m> is the temperature change above a user-definable year, e.g. 1990.<br />
<br />
===Nitrous oxide===<br />
<br />
As for methane, natural nitrous oxide emissions are estimated by a budget [[#A28|(A28)]]. For nitrous oxide however, the average concentrations <m>C_{\o'}</m>=<m>C_{\o-3}</m> are taken for a period shifted by 3 years to account for a three year delay of transport of tropospheric N<m>_2</m>O to the main stratospheric sink. The feedback of the atmospheric burden C<sub>N<m>_2</m>O</sub> of nitrous oxide on its own lifetime is approximated by:<br />
<br />
<m>\tau_{\rm N_2O} = \tau_{\rm N_2O}^0 (\frac{{\rm C}_{\rm N_2O}}{{\rm C}_{\rm N_2O}^0})^{S_{\tau_{\rm N_2O}}}\\ \label{eq_nitrous_lifetime}</m><span id="eq_A33"></span><div style="float: right; clear: right;">('''A33''')</div><br />
<br />
where <m>S_{\tau_{\rm N_2O}}</m> is the sensitivity coefficient (default <m>S_{\tau_{\rm N_2O}}</m>=<m>-</m>5e-2) and the superscript ``<sup><m>0</m></sup>´´ indicates a pre-industrial reference state.<br />
<br />
===Tropospheric aerosols===<br />
<br />
Due to their short atmospheric residence time, changes in hemispheric abundances of aerosols are approximated by changes in their hemispheric emissions. Historical emissions of tropospheric aerosols are extended into the future either by emissions scenarios (SO<m>_{\rm x}</m>, NO<m>_{\rm x}</m>, CO) or, if scenario data are not available, with proxy emissions, e.g. using CO as a proxy emission<br />
for OC and BC. As with many other emissions scenarios, the harmonized IPCC SRES scenarios do not provide black (BC) and organic carbon (OC) emissions. Hence, various ''ad-hoc'' scaling approaches have been applied, often scaling BC and OC synchronously [[References#Takemura_2006_MIROC_forcings|(Takemura et al., 2006)]], sometimes linearly with CO<m>_2</m> emissions. The MESSAGE emissions scenario modeling group is one of the few explicitly including BC and OC emissions in their multi-gas emissions scenarios [[References#Rao_etal_2005_blackcarbon_organiccarbon_emissions|(Rao et al, 2005; Rao and Riahi, 2006)]]. By analyzing MESSAGE scenarios, a scaling factor was derived for this study in relation to carbon monoxide emissions (CO), varying linearly in time to 0.4 by 2100 relative to current BC/CO or OC/CO emission ratios.<br />
<br />
===Halogenated gases===<br />
<br />
The derivation of concentrations of halogenated gases controlled under either the Kyoto or Montreal Protocol assumes time-variable lifetimes. The net atmospheric lifetime <m>\tau_i</m> of each halogenated gas is calculated by summing the inverse lifetimes related to stratospheric, OH-related and other sinks. Stratospheric lifetimes are assumed to decrease 15 % per degree of global mean surface temperature warming, due to an increased Brewer-Dobson circulation [[References#butchart_scaife2001_brewerDobson|(Butchart and Scaife, 2001)]]. Tropospheric OH-related losses are scaled by parameterized changes in OH-abundances, matching the respective changes in the lifetime of methane. The concentration <m>C_{t,i}</m> for the beginning of each year <m>t</m> is updated, using a central differencing formulation, according to:<br />
<br />
<m>C_{t+1,i}{=}\tau_i E_{t,i} \frac{\rho_{\rm atm}}{m_{\rm atm}\mu_i}(1-e^{\frac{-1}{\tau_i}})+C_{t,i}(1-e^{\frac{-1}{\tau_i}})\label{eq_halogas_conc}</m><span id="eq_A34"></span><div style="float: right; clear: right;">('''A34''')</div><br />
<br />
where <m>E_{t,i}</m> is the average emissions of gas <m>i</m> through year <m>t</m>, <m>C_{t,i}</m> the atmospheric concentration of gas <m>i</m> in year <m>t</m>, <m>\rho_{\rm atm}</m> the average density of air, <m>m_{\rm atm}</m> the total mass of the atmosphere [[References#Trenberth_etal1994_totalmassofatmosphere|(Trenberth and Guillemot, 1994)]], and <m>\mu_i</m> is the mass per mol of gas <m>i</m>. For hydrogenated halocarbons, the tropospheric OH-related lifetimes are assumed to vary in proportion to the changes in methane lifetime.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Model_Documentation&diff=14Model Documentation2013-06-17T10:20:29Z<p>Antonius Golly: Created page with "==Model description== ===model description=== MAGICC has a hemispherically averaged upwelling-diffusion ocean coupled to an atmosphere layer and a globally averaged carbon c..."</p>
<hr />
<div>==Model description==<br />
<br />
===model description===<br />
<br />
MAGICC has a hemispherically averaged upwelling-diffusion ocean coupled to an atmosphere layer and a globally averaged carbon cycle model. As with most other simple models, MAGICC evolved from a simple global average energy-balance equation. The energy balance equation for the perturbed climate system can be written as:<br />
<br />
<m>\Delta Q_G = \lambda_G \Delta T_G + \frac{d H}{d t}\label{eq_globalenergybalance}</m><span id="eq_1"></span><div style="float: right; clear: right;">('''1''')</div><br />
<br />
where <m>\Delta Q_G</m> is the global-mean radiative forcing at the top of the troposphere. This extra energy influx is partitioned into increased outgoing energy flux and heat content changes in the ocean <m>\frac{d H}{d t}</m>. The outgoing energy flux is dependent on the global-mean feedback factor, <m>\lambda_G</m>, and the surface temperature perturbation <m>\Delta T_G</m>.<br />
<br />
While MAGICC is designed to provide maximum flexibility in order to match different types of responses seen in more sophisticated models, the approach in MAGICC's model development has always been to derive the simple equations as much as possible from key physical and biological processes. In other words, MAGICC is as simple as possible, but as mechanistic as necessary. This process-based approach has a strong conceptual advantage in comparison to simple statistical fits that are more likely to quickly degrade in their skill when emulating scenarios outside the original calibration space of sophisticated models.<br />
<br />
The main improvements in MAGICC6 compared to the version used in the IPCC AR4 are briefly highlighted in this section (Note that there is an intermediate version, MAGICC 5.3, described in [[References#Wigley_etal_2009_UncertaintiesClimateStabilization|Wigley et al., 2009]]). The options introduced to account for variable climate sensitivities are described in Sect. [[#introduction of variable climate sensitivities|introduction of variable climate sensitivities]]. With the exception of the updated carbon cycle routines [[#updated carbon cycle|updated carbon cycle]], the MAGICC 4.2 and 5.3 parameterizations are covered as special cases of the 6.0 version, i.e., the IPCC AR4 version, for example, can be recovered by appropriate parameter settings.<br />
<br />
===Introduction of variable climate sensitivities===<br />
<br />
Climate sensitivity ({<m>\Delta T_{2x}</m>}) is a useful metric to compare models and is usually defined as the equilibrium global-mean warming after a doubling of CO<m>_2</m> concentrations. In the case of MAGICC, the equilibrium climate sensitivity is a primary model parameter that may be identified with the eventual global-mean warming that would occur if the CO<m>_2</m> concentrations were doubled from pre-industrial levels. Climate sensitivity is inversely related to the feedback factor <m>\lambda</m>:<br />
<br />
<m>\label{eq_climatesensitivity}\Delta T_{2x} = \frac{\Delta Q_{2x}}{\lambda}</m><span id="eq_2"></span><div style="float: right; clear: right;">('''2''')</div><br />
<br />
where \emph{<m>\Delta T_{2x}</m>} is the climate sensitivity, and \emph{<m>\Delta Q_{2x}</m>} the radiative forcing after a doubling of CO<m>_2</m> concentrations (see energy balance<br />
Eq. [[#eq_A45|A45]]).<br />
<br />
The (time- or state-dependent) effective climate sensitivity (<m>S^t</m>)([[References#Murphy_Mitchell_1995_SpatialTemporalResponse|Murphy and Mitchell, 1995]]) is defined using the transient energy balance Eq. ([[#eq_1|1]]) and can be diagnosed from model output for any part of a model run where radiative forcing and ocean heat uptake are both known and their sum is different from zero, so that:<br />
<br />
<m>\label{eq_effective_climatesensitivity} S^t = \frac{\Delta Q_{2x}}{\lambda^t} = \Delta Q_{2x} \frac{\Delta T_{G}^t}{\Delta Q^t - \frac{d H}{dt}|^t}</m><span id="eq_3"></span><div style="float: right; clear: right;">('''3''')</div><br />
<br />
where \emph{<m>\Delta Q_{2x}</m>} is the model-specific forcing for doubled CO<m>_2</m> concentration, <m>\lambda_t</m> is the time-variable feedback factor, <m>\Delta Q^t</m> the radiative forcing, <m>\Delta T_{GL}^t</m> the global-mean temperature perturbation and <m>\frac{dH}{dt}|^t</m> the climate system's heat uptake at time \emph{t}. By definition, the traditional (equilibrium) climate sensitivity (\emph{<m>\Delta T_{2x}</m>}) is equal to the effective climate sensitivity <m>S^t</m> at equilibrium (<m>\frac{dH}{dt}|^t</m>{=}0) after doubled (pre-industrial) CO<m>_2</m> concentration.<br />
<br />
If there were only one globally homogenous, fast and constant feedback process, the diagnosed effective climate sensitivity would always equal the equilibrium climate sensitivity $\Delta T_{2x}$. However, many CMIP3 AOGCMs exhibit variable effective climate sensitivities, often increasing over time (e.g. models CCSM3, CNRM-CM3, GFDL-CM2.0, GFDL-CM2.1, GISS-EH - see<br />
Figs. (B1, B2, B3 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html). This is consistent with earlier results of increasing effective sensitivities found by<br />
([[References#Senior_Mitchell_2000_TimeDependence_ClimateSensitivity|Senior and Mitchell (2000)]];[[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2000)]]) for the HadCM2 model. In addition, some models present significantly higher sensitivities for higher forcing scenarios (1pctto4x) than for lower forcing scenarios (1pctto2x) (e.g. ECHAM5/MPI-OM and GISS-ER, see Fig. [[#fig_increasing_ClimSens_CCSM3_ECHAM5|Fig.1 ]]<br />
<br />
In order to better emulate these time-variable effective climate sensitivities, this version of MAGICC incorporates two modifications: Firstly, an amended land-ocean heat exchange<br />
formulation allows effective climate sensitivities to increase on the path to equilibrium warming. In this formulation, changes in effective climate sensitivity arise from a geometrical effect: spatially non-homogenous feedbacks can lead to a time-variable effective global-mean climate sensitivity, if the spatial warming distributions change over time. Hence, by modifying land-ocean heat exchange in MAGICC, the spatial evolution of warming is altered, leading to changes in effective climate sensitivities ([[References#Raper_2004_GeometricalEffectClimsens|Raper, 2004]]) given that MAGICC has different equilibrium sensitivities over land and ocean. Secondly, the climate sensitivities, and hence the feedback parameters, can be made explicitly dependent on the current forcing at time \emph{t}. Both amendments are detailed in [[Upwelling_diffusion_climate_model#Revised land-ocean heat formulation]][[Upwelling_diffusion_climate_model#Accounting for climate-state dependent feedbacks]]. Although these two amendments both modify the same diagnostic, i.e., the time-variable effective sensitivities in MAGICC, they are distinct: the land-ocean heat exchange modification changes the shape of the effective climate sensitivity's time evolution to equilibrium, but keeps the equilibrium sensitivity unaffected. In contrast, making the sensitivity explicitly dependent on the forcing primarily affects the equilibrium sensitivity value.<br />
<br />
Note that time-varying effective sensitivities are not only empirically observed in AOGCMs, but they are necessary here in order for MAGICC to accurately emulate AOGCM results. Alternative parameterizations to emulate time-variable climate sensitivities are possible, e.g.~assuming a dependence on temperatures instead of forcing, or by implementing indirect radiative forcing effects that are most often regarded as feedbacks see Section 6.2 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html. However, this study chose to limit the degrees of freedom with respect to time-variable climate sensitivities given that a clear separation into three (or more) different parameterizations seemed unjustified based on the AOGCM data analyzed here.<br />
<br />
[[file:Fig-1.jpg|350px|thumb|The effective climate sensitivity diagnosed from low-pass filtered CCSM3 (a) and ECHAM5/MPI-OM (b) output for two idealized<br />
scenarios assuming an annual 1% increase in CO2 concentrations until twice pre-industrial values in year 70 (1pctto2×) or quadrupled concentration in year 140 (1pctto4×), with constant<br />
concentrations thereafter. Additionally, the reported slab ocean model equilibrium climate sensitivity (“slab”) and the sensitivity estimates by Forster and Taylor (2006) are shown (“F&T(06)”). ]] <br />
<span id="fig_increasing_ClimSens_CCSM3_ECHAM5"></span> <br />
<br />
===Updated carbon cycle=== <br />
<br />
MAGICC's terrestrial carbon cycle model is a globally integrated box model, similar to that in [[References#Harvey_1989_ManagingAtmCO2|Harvey (1989)]] and [[References#Wigley_1993_BalancingCarbonBudget|Wigley (1993)]]. The MAGICC6 carbon cycle can emulate temperature-feedback effects on the heterotrophic respiration carbon fluxes. One improvement in MAGICC6 allows increased flexibility when accounting for CO$_2$ fertilization. This increase in flexibility allows a better fit to some of the more complex carbon cycle models reviewed in C<m>^4</m>MIP([[Friedlingstein_2006_climatecarbonInteraction_C4MIP|Friedlingstein, 2006]])(see [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]).<br />
<br />
Another update in MAGICC6 relates to the relaxation in carbon pools after a deforestation event. The gross CO<m_2</m> emissions related to deforestation and other land use activities are subtracted from the plant, detritus and soil carbon pools (see Fig. [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]]. While in previous versions only the regrowth in the plant carbon pool was taken into account to calculate the net deforestation, MAGICC6 now includes an effective relaxation/regrowth term for all three terrestrial carbon pools (see [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]).<br />
<br />
The original ocean carbon cycle model used a convolution representation ([[References#Wigley_1991_simpleInverseCarbonCycleModel|Wigley, 1991]]) to quantify the ocean-atmosphere CO<m>_2</m> flux. A similar representation is used here, but modified to account for nonlinearities. Specifically, the impulse response representation of the Princeton 3D GFDL model ([[References#Sarmiento_etal_1992_perturbationCO2_ocean_general_circulation_model|Sarmiento, 1992]]) is used to approximate the inorganic carbon perturbation in the mixed layer (for the impulse response representation see, [[References#Joos_Bruno_etal_1996_efficient_accurate_carbonuptake|Joos, 1991]]). The temperature sensitivity of the sea surface partial pressure is implemented based on [[References#Takahashi_etal_1993_surfaceOceans_CO2|Takahashi et al. (1993)]] as given in [[References#Joos_Prentice_etal_2001_feedbacks_biosphere_IPCC|Joos et al. (2001)]]. For details on the updated carbon cycle routines, see the [[The Carbon Cycle|The carbon cycle]].<br />
<br />
===Other additional capabilities compared to MAGICC4.2===<br />
<br />
Five additional amendments to the climate model have been implemented in MAGICC6 compared to the MAGICC4.2 version that has<br />
been used in IPCC AR4.<br />
<br />
====Aerosol indirect effects====<br />
<br />
It is now possible to account directly for contributions from black carbon, organic carbon and nitrate aerosols to indirect (i.e., cloud albedo) effects ([[References#Twomey_1977_albedo|Twomey, 1977]]). The first indirect effect, affecting cloud droplet size and the second indirect effect, affecting cloud cover and lifetime, can also be modeled separately. Following the convention in IPCC AR4 ([[References#Forster_Ramaswamy_etal_2007_IPCCAR4_Chapter2_radiativeForcing|Forster et al., 2007]]), the second indirect effect is modeled as a prescribed change in efficacy of the first indirect effect. See [[Non-CO2 Concentrations|Tropospheric aerosols]] for details.<br />
<br />
===Depth-variable ocean with entrainment===<br />
<br />
Building on the work by [[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2007)]], MAGICC6 includes the option of a depth-dependent ocean area profile with entrainment at each of the ocean levels (default, 50 levels) from the polar sinking water column. The default ocean area profile decreases from unity at the surface to, for example, 30<m>%</m>, 13<m>%</m> and 0<m>%</m> at depths of 4000, 4500 and 5000 m. Although comprehensive data on depth-dependent heat uptake profiles of the CMIP3 AOGCMs were not available for this study, this entrainment update provides more flexibility and allows for a better simulation of the characteristic depth-dependent heat uptake as observed in one analyzed AOGCM, namely HadCM2 ([[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al., 2000]])<br />
<br />
===Vertical mixing depending on warming gradient===<br />
<br />
Simple models, including earlier versions of MAGICC, sometimes overestimated the ocean heat uptake for higher warming scenarios when applying parameter sets chosen to match heat uptake for lower warming scenarios, see e.g. Fig. 17b in [[Harvey_etal_1997_IPCC_IntroductionSimpleClimateModels|Harvey et al. (1997)]]. A strengthened thermal stratification and hence reduced vertical mixing might contribute to the lower heat uptake for higher warming cases. To model this effect, a warming-dependent vertical gradient of the thermal diffusivity is implemented here(see[[Upwelling diffusion climate model#Depth-dependent ocean with entrainment|Depth-dependent ocean with entrainment]]).<br />
<br />
===Forcing efficacies===<br />
<br />
Since the IPCC TAR, a number of studies have focussed on forcing efficacies, i.e., on the differences in surface temperature response due to a unit forcing by different radiative forcing agents with different geographical and vertical distributions ([[Joshi_etal_2003_improvedmetric_climatechange|Joshi et al., 1997]]). This version of MAGICC includes the option to apply different efficacy terms for the different forcings agents (see [[Upwelling diffusion climate model#Depth-dependent ocean with entrainment|Efficacies]] for details and supplement pdf in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html for default values).<br />
<br />
===Radiative forcing patterns===<br />
<br />
Earlier versions of MAGICC used time-independent (but user-specifiable) ratios to distribute the global-mean forcing of tropospheric ozone and aerosols to the four atmospheric boxes, i.e., land and ocean in both hemispheres. This model structure and the simple 4-box forcing patterns are retained as it is able to capture a large fraction of the forcing agent characteristics of interest here. However, we now use patterns for each forcing individually, and allow for these patterns to vary over time. For example, the historical forcing pattern evolutions for tropospheric aerosols are based on results from [[Hansen_etal_2005_Efficacies|Hansen et al. (2005)]], which are interpolated to annual values and extrapolated into the future using hemispheric emissions. Additionally, MAGICC6 now incorporates forcing patterns for the long-lived greenhouse gases as well, although these patterns are assumed to be constant in time and scaled with global-mean radiative forcing (supplement pdf in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html for details on the default forcing patterns and time series).</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Model_Description&diff=13Model Description2013-06-17T10:20:16Z<p>Antonius Golly: Created page with "*model description ** carbon cycle ** non-CO2 concentrations **[[Radiative Forcing | radiative forcing r..."</p>
<hr />
<div>*[[Model Description|model description]]<br />
**[[The Carbon Cycle| carbon cycle]]<br />
**[[Non-CO2 Concentrations | non-CO2 concentrations]]<br />
**[[Radiative Forcing | radiative forcing routines]]<br />
**[[Upwelling_diffusion_climate_model | climate model]]<br />
**[[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]]<br />
<br />
<br />
==Model description==<br />
<br />
=== Overview ===<br />
<br />
The 'Model for the Assessment of Greenhouse Gas Induced Climate Change' (MAGICC) is a simple/reduced complexity climate model. MAGICC was originally developed by Tom Wigley (National Centre for Atmospheric Research, Boulder, US, and University of Adelaide, Australia) and Sarah Raper (Manchester Metropolitan University, UK) in the late 1980s and continuously developed since then. It has been one of the widely used climate models in various IPCC Assessment Reports. The latest version, MAGICC6, is co-developed by Malte Meinshausen (Potsdam Institute for Climate Impact Research, Germany, and the University of Melbourne, Australia). These pages provide an extensive model description, sourced from a 2011 publication in Atmospheric Chemistry & Physics [http://www.atmos-chem-phys.net/11/1417/2011/ (M. Meinshausen, S. Raper and T. Wigley, 2011)]. <br />
<br />
This Page provides a detailed description of MAGICC6 and its<br />
different modules (see [[#Fig_A1|Fig-A1]] below). A basic [[Model_Documentation|model description]] is given, while subsections describe MAGICC's <br />
[[The Carbon Cycle| carbon cycle]], the atmospheric-chemistry<br />
parameterizations and derivation of <br />
[[Non-CO2 Concentrations | non-CO<sub>2</sub> concentrations]], <br />
[[Radiative Forcing | radiative forcing routines]], and the climate module to get from<br />
radiative forcing to hemispheric (land and ocean, separately) to<br />
global-mean temperatures ([[Upwelling_diffusion_climate_model|climate model]]), as<br />
well as oceanic heat uptake. Finally, details are provided on the implementation scheme for the [[UDB Implementation | upwelling-diffusion-entrainment ocean]]<br />
climate module. A technical upgrade is that MAGICC6 has been re-coded in Fortran95,<br />
updated from previous Fortran77 versions. Nearly all of the MAGICC6 code is directly based on the earlier<br />
MAGICC versions programmed by Wigley and Raper <br />
([[References#Wigley_Raper_1987_ThermalExpansion_SeaWater_Nature| 1987]], [[References#Wigley_Raper_1992_ImplicationsWarmingIPCC_Nature | 1992]], [[References#Wigley_Raper_2001_Science_InterpretationHighProjections | 2001]]).<br />
<br />
[[File:OverviewGraph Fig1.png|frame|right|'''Fig-A1''' Schematic overview of MAGICC calculations showing the key steps<br />
from emissions to global and hemispheric climate responses.<br />
Black circled numbers denote the sections in the Appendix<br />
describing the respective algorithms used. Source: Fig A.1. in Meinshausen et al. 2011, ACP]]<span id="fig_A1"></span> <br />
<br />
===Basic model description===<br />
<br />
MAGICC has a hemispherically averaged upwelling-diffusion ocean coupled to an atmosphere layer and a globally averaged carbon cycle model. As with most other simple models, MAGICC evolved from a simple global average energy-balance equation. The energy balance equation for the perturbed climate system can be written as:<br />
<br />
<m>\Delta Q_G = \lambda_G \Delta T_G + \frac{d H}{d t}\label{eq_globalenergybalance}</m><span id="eq_1"></span><div style="float: right; clear: right;">('''1''')</div><br />
<br />
where <m>\Delta Q_G</m> is the global-mean radiative forcing at the top of the troposphere. This extra energy influx is partitioned into increased outgoing energy flux and heat content changes in the ocean <m>\frac{d H}{d t}</m>. The outgoing energy flux is dependent on the global-mean feedback factor, <m>\lambda_G</m>, and the surface temperature perturbation <m>\Delta T_G</m>.<br />
<br />
While MAGICC is designed to provide maximum flexibility in order to match different types of responses seen in more sophisticated models, the approach in MAGICC's model development has always been to derive the simple equations as much as possible from key physical and biological processes. In other words, MAGICC is as simple as possible, but as mechanistic as necessary. This process-based approach has a strong conceptual advantage in comparison to simple statistical fits that are more likely to quickly degrade in their skill when emulating scenarios outside the original calibration space of sophisticated models.<br />
<br />
The main improvements in MAGICC6 compared to the version used in the IPCC AR4 are briefly highlighted in this section (Note that there is an intermediate version, MAGICC 5.3, described in [[References#Wigley_etal_2009_UncertaintiesClimateStabilization|Wigley et al., 2009]]). The options introduced to account for variable climate sensitivities are described in Sect. [[#introduction of variable climate sensitivities|introduction of variable climate sensitivities]]. With the exception of the updated carbon cycle routines [[#updated carbon cycle|updated carbon cycle]], the MAGICC 4.2 and 5.3 parameterizations are covered as special cases of the 6.0 version, i.e., the IPCC AR4 version, for example, can be recovered by appropriate parameter settings.<br />
<br />
===Introduction of variable climate sensitivities===<br />
<br />
Climate sensitivity (<m>\Delta T_{2x}</m>) is a useful metric to compare models and is usually defined as the equilibrium global-mean warming after a doubling of CO<m>_2</m> concentrations. In the case of MAGICC, the equilibrium climate sensitivity is a primary model parameter that may be identified with the eventual global-mean warming that would occur if the CO<m>_2</m> concentrations were doubled from pre-industrial levels. Climate sensitivity is inversely related to the feedback factor <m>\lambda</m>:<br />
<br />
<m>\label{eq_climatesensitivity}\Delta T_{2x} = \frac{\Delta Q_{2x}}{\lambda}</m><span id="eq_2"></span><div style="float: right; clear: right;">('''2''')</div><br />
<br />
where <m>\Delta T_{2x}</m> is the climate sensitivity, and <m>\Delta Q_{2x}</m> the radiative forcing after a doubling of CO<m>_2</m> concentrations (see energy balance<br />
Eq. [[#eq_A45|A45]]).<br />
<br />
The (time- or state-dependent) effective climate sensitivity (<m>S^t</m>)([[References#Murphy_Mitchell_1995_SpatialTemporalResponse|Murphy and Mitchell, 1995]]) is defined using the transient energy balance Eq. ([[#eq_1|1]]) and can be diagnosed from model output for any part of a model run where radiative forcing and ocean heat uptake are both known and their sum is different from zero, so that:<br />
<br />
<m>\label{eq_effective_climatesensitivity} S^t = \frac{\Delta Q_{2x}}{\lambda^t} = \Delta Q_{2x} \frac{\Delta T_{G}^t}{\Delta Q^t - \frac{d H}{dt}|^t}</m><span id="eq_3"></span><div style="float: right; clear: right;">('''3''')</div><br />
<br />
where <m>\Delta Q_{2x}</m> is the model-specific forcing for doubled CO<m>_2</m> concentration, <m>\lambda_t</m> is the time-variable feedback factor, <m>\Delta Q^t</m> the radiative forcing, <m>\Delta T_{GL}^t</m> the global-mean temperature perturbation and <m>\frac{dH}{dt}|^t</m> the climate system's heat uptake at time <m>t</m>. By definition, the traditional (equilibrium) climate sensitivity (<m>\Delta T_{2x}</m>) is equal to the effective climate sensitivity <m>S^t</m> at equilibrium (<m>\frac{dH}{dt}|^t</m>=0) after doubled (pre-industrial) CO<m>_2</m> concentration.<br />
<br />
If there were only one globally homogenous, fast and constant feedback process, the diagnosed effective climate sensitivity would always equal the equilibrium climate sensitivity <m>\Delta T_{2x}</m>. However, many CMIP3 AOGCMs exhibit variable effective climate sensitivities, often increasing over time (e.g. models CCSM3, CNRM-CM3, GFDL-CM2.0, GFDL-CM2.1, GISS-EH - see Figs. (B1, B2, B3 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html). This is consistent with earlier results of increasing effective sensitivities found by ([[References#Senior_Mitchell_2000_TimeDependence_ClimateSensitivity|Senior and Mitchell (2000)]];[[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2000)]]) for the HadCM2 model. In addition, some models present significantly higher sensitivities for higher forcing scenarios (1pctto4x) than for lower forcing scenarios (1pctto2x) (e.g. ECHAM5/MPI-OM and GISS-ER, see [[#fig_increasing_ClimSens_CCSM3_ECHAM5|Fig.1 ]]<br />
<br />
In order to better emulate these time-variable effective climate sensitivities, this version of MAGICC incorporates two modifications: Firstly, an amended land-ocean heat exchange<br />
formulation allows effective climate sensitivities to increase on the path to equilibrium warming. In this formulation, changes in effective climate sensitivity arise from a geometrical effect: spatially non-homogenous feedbacks can lead to a time-variable effective global-mean climate sensitivity, if the spatial warming distributions change over time. Hence, by modifying land-ocean heat exchange in MAGICC, the spatial evolution of warming is altered, leading to changes in effective climate sensitivities ([[References#Raper_2004_GeometricalEffectClimsens|Raper, 2004]]) given that MAGICC has different equilibrium sensitivities over land and ocean. Secondly, the climate sensitivities, and hence the feedback parameters, can be made explicitly dependent on the current forcing at time <m>t</m>. Both amendments are detailed in the [[Upwelling_Diffusion_Entrainment_Implementation#Revised land-ocean heat formulation|Revised land-ocean heat formulation]], and [[Upwelling_Diffusion_Entrainment_Implementation#Accounting for climate-state dependent feedbacks|Accounting for climate-state dependent feedbacks]] sections. Although these two amendments both modify the same diagnostic, i.e., the time-variable effective sensitivities in MAGICC, they are distinct: the land-ocean heat exchange modification changes the shape of the effective climate sensitivity's time evolution to equilibrium, but keeps the equilibrium sensitivity unaffected. In contrast, making the sensitivity explicitly dependent on the forcing primarily affects the equilibrium sensitivity value.<br />
<br />
Note that time-varying effective sensitivities are not only empirically observed in AOGCMs, but they are necessary here in order for MAGICC to accurately emulate AOGCM results. Alternative parameterizations to emulate time-variable climate sensitivities are possible, e.g.~assuming a dependence on temperatures instead of forcing, or by implementing indirect radiative forcing effects that are most often regarded as feedbacks see Section 6.2 in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html. However, this study chose to limit the degrees of freedom with respect to time-variable climate sensitivities given that a clear separation into three (or more) different parameterizations seemed unjustified based on the AOGCM data analyzed here.<br />
<br />
[[file:Fig-1.jpg|350px|thumb|The effective climate sensitivity diagnosed from low-pass filtered CCSM3 (a) and ECHAM5/MPI-OM (b) output for two idealized<br />
scenarios assuming an annual 1% increase in CO2 concentrations until twice pre-industrial values in year 70 (1pctto2×) or quadrupled concentration in year 140 (1pctto4×), with constant<br />
concentrations thereafter. Additionally, the reported slab ocean model equilibrium climate sensitivity (“slab”) and the sensitivity estimates by Forster and Taylor (2006) are shown (“F&T(06)”). ]] <br />
<span id="fig_increasing_ClimSens_CCSM3_ECHAM5"></span> <br />
<br />
===Updated carbon cycle=== <br />
<br />
MAGICC's terrestrial carbon cycle model is a globally integrated box model, similar to that in [[References#Harvey_1989_ManagingAtmCO2|Harvey (1989)]] and [[References#Wigley_1993_BalancingCarbonBudget|Wigley (1993)]]. The MAGICC6 carbon cycle can emulate temperature-feedback effects on the heterotrophic respiration carbon fluxes. One improvement in MAGICC6 allows increased flexibility when accounting for CO<sub>2</sub> fertilization. This increase in flexibility allows a better fit to some of the more complex carbon cycle models reviewed in C<m>^4</m>MIP([[References#Friedlingstein_2006_climatecarbonInteraction_C4MIP|Friedlingstein, 2006]])(see [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]).<br />
<br />
Another update in MAGICC6 relates to the relaxation in carbon pools after a deforestation event. The gross CO<sub>2</sub> emissions related to deforestation and other land use activities are subtracted from the plant, detritus and soil carbon pools (see Fig. [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]]. While in previous versions only the regrowth in the plant carbon pool was taken into account to calculate the net deforestation, MAGICC6 now includes an effective relaxation/regrowth term for all three terrestrial carbon pools (see [[The Carbon Cycle#terrestrial carbon cycle|terrestrial carbon cycle]]).<br />
<br />
The original ocean carbon cycle model used a convolution representation ([[References#Wigley_1991_simpleInverseCarbonCycleModel|Wigley, 1991]]) to quantify the ocean-atmosphere CO<m>_2</m> flux. A similar representation is used here, but modified to account for nonlinearities. Specifically, the impulse response representation of the Princeton 3D GFDL model ([[References#Sarmiento_etal_1992_perturbationCO2_ocean_general_circulation_model|Sarmiento, 1992]]) is used to approximate the inorganic carbon perturbation in the mixed layer (for the impulse response representation see, [[References#Joos_Bruno_etal_1996_efficient_accurate_carbonuptake|Joos, 1991]]). The temperature sensitivity of the sea surface partial pressure is implemented based on [[References#Takahashi_etal_1993_surfaceOceans_CO2|Takahashi et al. (1993)]] as given in [[References#Joos_Prentice_etal_2001_feedbacks_biosphere_IPCC|Joos et al. (2001)]]. For details on the updated carbon cycle routines, see the [[The Carbon Cycle|The carbon cycle]].<br />
<br />
===Other additional capabilities compared to MAGICC4.2===<br />
<br />
Five additional amendments to the climate model have been implemented in MAGICC6 compared to the MAGICC4.2 version that has<br />
been used in IPCC AR4.<br />
<br />
====Aerosol indirect effects====<br />
<br />
It is now possible to account directly for contributions from black carbon, organic carbon and nitrate aerosols to indirect (i.e., cloud albedo) effects ([[References#Twomey_1977_albedo|Twomey, 1977]]). The first indirect effect, affecting cloud droplet size and the second indirect effect, affecting cloud cover and lifetime, can also be modeled separately. Following the convention in IPCC AR4 ([[References#Forster_Ramaswamy_etal_2007_IPCCAR4_Chapter2_radiativeForcing|Forster et al., 2007]]), the second indirect effect is modeled as a prescribed change in efficacy of the first indirect effect. See [[Non-CO2 Concentrations|Tropospheric aerosols]] for details.<br />
<br />
====Depth-variable ocean with entrainment====<br />
<br />
Building on the work by [[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al. (2007)]], MAGICC6 includes the option of a depth-dependent ocean area profile with entrainment at each of the ocean levels (default, 50 levels) from the polar sinking water column. The default ocean area profile decreases from unity at the surface to, for example, 30<m>%</m>, 13<m>%</m> and 0<m>%</m> at depths of 4000, 4500 and 5000 m. Although comprehensive data on depth-dependent heat uptake profiles of the CMIP3 AOGCMs were not available for this study, this entrainment update provides more flexibility and allows for a better simulation of the characteristic depth-dependent heat uptake as observed in one analyzed AOGCM, namely HadCM2 ([[References#Raper_Gregory_Osborn_2001_diagnosingAOGCMresults|Raper et al., 2000]]).<br />
<br />
====Vertical mixing depending on warming gradient====<br />
<br />
Simple models, including earlier versions of MAGICC, sometimes overestimated the ocean heat uptake for higher warming scenarios when applying parameter sets chosen to match heat uptake for lower warming scenarios, see e.g. Fig. 17b in [[References#Harvey_etal_1997_IPCC_IntroductionSimpleClimateModels|Harvey et al. (1997)]]. A strengthened thermal stratification and hence reduced vertical mixing might contribute to the lower heat uptake for higher warming cases. To model this effect, a warming-dependent vertical gradient of the thermal diffusivity is implemented here(see[[Upwelling diffusion climate model#Depth-dependent ocean with entrainment|Depth-dependent ocean with entrainment]]).<br />
<br />
====Forcing efficacies====<br />
<br />
Since the IPCC TAR, a number of studies have focussed on forcing efficacies, i.e., on the differences in surface temperature response due to a unit forcing by different radiative forcing agents with different geographical and vertical distributions ([[References#Joshi_etal_2003_improvedmetric_climatechange|Joshi et al., 1997]]). This version of MAGICC includes the option to apply different efficacy terms for the different forcings agents (see the [[Upwelling_Diffusion_Entrainment_Implementation#Depth-dependent ocean with entrainment|efficacies]] section for details and supplement pdf in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html for default values).<br />
<br />
====Radiative forcing patterns====<br />
<br />
Earlier versions of MAGICC used time-independent (but user-specifiable) ratios to distribute the global-mean forcing of tropospheric ozone and aerosols to the four atmospheric boxes, i.e., land and ocean in both hemispheres. This model structure and the simple 4-box forcing patterns are retained as it is able to capture a large fraction of the forcing agent characteristics of interest here. However, we now use patterns for each forcing individually, and allow for these patterns to vary over time. For example, the historical forcing pattern evolutions for tropospheric aerosols are based on results from [[References#Hansen_etal_2005_Efficacies|Hansen et al. (2005)]], which are interpolated to annual values and extrapolated into the future using hemispheric emissions. Additionally, MAGICC6 now incorporates forcing patterns for the long-lived greenhouse gases as well, although these patterns are assumed to be constant in time and scaled with global-mean radiative forcing (supplement pdf in http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html for details on the default forcing patterns and time series).</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Manual_MAGICC6_Executable&diff=12Manual MAGICC6 Executable2013-06-17T10:19:58Z<p>Antonius Golly: Created page with "This page provides a short user manual and FAQ for how to run the MAGICC6 Windows executable, which you can download from [http://www.magicc.org/download www.magicc.org/downlo..."</p>
<hr />
<div>This page provides a short user manual and FAQ for how to run the MAGICC6 Windows executable, which you can download from [http://www.magicc.org/download www.magicc.org/download]. Note that probably the easiest way to do your own runs with MAGICC6 is the web-interface to the MAGICC version that we have running on our servers, accessible via [http://live.magicc.org live.magicc.org]. <br />
<br />
== Installation == <br />
<br />
# Download the zipped MAGICC6 version from [http://www.magicc.org/download www.magicc.org/download].<br />
# Unzip in a directory of your choice, e.g. into D:/MAGICC6/<br />
# The executable "magicc6.exe", all its input data files (".IN") and configuration settings ("*.CFG") files are now in this MAGICC6 folder and ready to use. No further steps necessary. <br />
<br />
== Quick User Guide == <br />
Suppose you wanted to run MAGICC6 for the RCP85 scenario and with default RCP climate and carbon cycle settings. <br />
<br />
The only file you need to change then is MAGTUNE_SIMPLE.CFG file. <br />
* Set FILE_EMISSIONSCENARIO = "RCP85". This defines the emission scenario that shall be run, like RCP85.SCEN in this case. See your MAGICC installation folder for all the scenarios that are available. Scenario files in MAGICC 6.0 always end with .SCEN.<br />
* Set FILE_TUNINGMODEL = "C4MIP_BERN". This defines the C4MIP carbon cycle emulation - it will cause MAGICC to read out the parameters in the file MAGTUNE_C4MIP_BERN.CFG and overwrite any carbon cycle parameter settings with these values. (These are the default values used in the RCP creation process).<br />
* Set FILE_TUNINGMODEL_2 = "FULLTUNE_MEDIUM_CMIP3_ECS3". This defines the emulated climate response of MAGICC6, which in this case is the average of the AOGCM CMIP3 tunings. This setting will cause MAGICC to read out the parameters in the file MAGTUNE_FULLTUNE_MEDIUM_CMIP3_ECS3.CFG and overwrite respective parameter settings in MAGCFG_USER.CFG.<br />
<br />
<br />
By default, MAGICC will produce a large bunch of output files, ending with .OUT (which takes some time..). If you want to restrict that, then change the OUT_XXXX parameters in the MAGCFG_USER.CFG file. Keep the OUT_PARAMETERS parameters set to 1, as this will produce a PARAMETERS.OUT file, which will tell you, what the exact model setting was for your run. <br />
<br />
The easiest way to view the output is probably if you import the ASCII output files (ending with *.OUT) into a spreadsheet program, like MS Excel.<br />
<br />
== Expert User Guide == <br />
If you want, you can change any of the more than 400 input parameters to MAGICC. Please be advised though, that in most cases a non-sensible input will produce a non-sensible output. And sometimes, even sensible inputs bring the model to its knees... Anyway, you should know what you are doing or be in a very playful mood - and do not blame MAGICC6 for the outcome, if you choose to change any of these extra parameters. <br />
<br />
Simply go into the file MAGCFG_USER.CFG and change the values for any of the parameters in there... Some description of what the parameters are meant to be doing are in MAGICC_DEFAULTALL_69.CFG. It would be best, though, if you do not change that MAGICC_DEFAULTALL_69.CFG file.<br />
<br />
== Feedback == <br />
We greatly appreciate your feedback. It helps us most, if you file a feedback via [http://www.magicc.org/feedback www.magicc.org/feedback]. Please note though, that we generally won't be able to provide user support as those people who pay us in our working time, generally prefer us to do other stuff... But be assured that we truly honor your feedback.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=MAGICC6_User_FAQ&diff=11MAGICC6 User FAQ2013-06-17T10:19:38Z<p>Antonius Golly: Created page with "This page provides you with some of the common questions that you might come across, when using MAGICC6, either via our [http://live.magicc.org webinterface] or when using the..."</p>
<hr />
<div>This page provides you with some of the common questions that you might come across, when using MAGICC6, either via our [http://live.magicc.org webinterface] or when using the [http://www.magicc.org/download downloadable Windows executable]. <br />
<br />
== General Questions == <br />
<br />
=== Is MAGICC6 the best climate model ever? ===<br />
Certainly not. MAGICC6 is a reduced-complexity climate model that attempts to synthesize current scientific understanding about many different gas-cycles, including the carbon cycle, climate feedbacks and radiative forcing. The strength of MAGICC is that it is sufficiently flexible to be able to closely emulate the large and complex climate models, sufficiently physically based to allow credible interpolations and indicative extrapolation near the calibration range. Furthermore, MAGICC6 is fast. That is an advantage, particularly for producing probabilistic projections for new emission scenarios, a process that is computationally unfeasible with the complex climate models. Thus, with due respect, if the question is whether MAGICC6 is the best method around to synthesize a whole range of climate and carbon cycle knowledge for probabilistic projections over the 21st century and beyond, we are inclined to say "yes". MAGICC6 thereby only complements, rather than aiming to replace, any complex climate models (simply because MAGICC6 is closely calibrated towards these "big brothers").<br><br><br />
<br />
=== I am teaching a class on climate. How can I use MAGICC? ===<br />
Probably the best method is to use our online web-interface [http://live.magicc.org live.magicc.org]<br />
<br />
== Questions related to live.magicc.org ==<br />
=== Which version does liveMAGICC use? ===<br />
liveMAGICC currently uses MAGICC. <br />
<br><br><br />
<br />
=== How do I use liveMAGICC? ===<br />
Well, that's easy. <br />
<br />
When you're entering liveMAGICC you will see '''Tab 1 - Emissions''' where you can select one or more emission scenarios. Click '''NEXT''' to get to '''Tab 2 - Model Settings''' where you are able to tune the climate and carbon cycle settings for MAGICC (optional). Switch to '''Tab 3 - Climate''' to actually run MAGICC and view the results of the desired settings made on Tab 1 and Tab 2.<br />
<br />
Find a step-by-step online Help for the use of liveMAGICC under [[Online Help]].<br />
<br><br><br />
<br />
=== How can I navigate through the tabs of liveMagicc? ===<br />
You can navigate through the tabs by clicking the '''NEXT''' and '''BACK''' buttons or by clicking the '''Nutshells''' acting as tab titles. There is no difference between those two ways.<br />
<br />
'''Tab 3 - Climate''' acts slightly different to the first two tabs. While you are switching between the forms on '''Tab 1 - Emissions''' and '''Tab 2 - Model Settings''', clicking '''Tab 3 - Climate''' will result in a server request and will run Magicc on our server. Be sure that you made the desired settings on Tab 1 and 2 once you switch to '''Tab 3 - Climate''' since this will force the website to queue the task in the task list. <br />
<br><br><br />
<br />
=== What is in Tab 1 - Emissions? ===<br />
On the left is a list of scenarios available to run Magicc with. You can customize this list <span style="color:red;">(not yet implemented)</span> or it may be customized for you by your supervisor, teacher or class leader. You are also allowed to upload your own scenario files (SCEN-files) <span style="color:red;">(not yet implemented)</span>. <br />
<br />
Once you select one or more scenarios in the select box on the left the chart on the right will be refreshed and show the scenario pathway(s). You can navigate through the different emission variables by selecting an emission variable on top of the emission chart.<br />
<br><br><br />
<br />
===What is in Tab 2 - Model Settings?===<br />
In this tab one can change the run mode on the left and all model settings. There are two run modes, '''Standard''' and '''Probabilistic'''. In Standard mode one can specify climate parameters and carbon cycle settings on the right. In probabilistic mode one can choose from the probabilistic modes '''Multi-model-ensemble emulations (171)''' and '''Probabilistic / historical constrained (600)'''. See ?? for detailed information.<br />
<br><br><br />
<br />
=== What is in Tab 3 - Climate?===<br />
'''Tab 3 - Climate''' shows the results of the individually created Magicc runs. Note that the Magicc runs will be processed once you switch to that tab. On the left you can see your personal run list. The items are attached either to a checkbox or a spinning wheel, depending on their status. A currently processing run has a blue spinning wheel. A queued run (not yet processed run) has a grey spinning wheel. All runs in the queue will be processed in sequence. Depending on the runmode it takes seconds (single run mode) to minutes (bulk run mode) to process a run. For probabilistic runs a feedback of the process is displayed (e.g "Magicc run 34 of 171"). The checkbox marks runs as completely processed. A horizontal line in the run list divides standard runs (single runs) from probabilistic runs (bulk runs). The checkboxes allow for plotting. Checking and unchecking will refresh the climate chart on the right. You can compare as many runs as you desire. To change the plotted climate variable choose from the list on top of the chart. <br />
<br><br><br />
<br />
=== How do I know what the different emission scenarios actually mean? ===<br />
<br><br><br />
<br />
=== Are all the emission scenarios "business-as-usual" scenarios? ===<br />
<br><br><br />
<br />
=== If I select an emissions variable like "Fossil CO2" on Tab 1 - Emissions will I get different climate results ? ===<br />
The selection of a emission path variable in the emission chart has no effect to the Magicc run. The emission chart is just for your information. <br />
<br><br><br />
<br />
=== Can I run multiple emission scenarios at the same time? ===<br />
You can do multiple selection of emission scenarios in the '''scenario select''' box on '''Tab 1 - Emissions'''. The procedure is dependent to your OS / browser. For Windows users: hold CTRL while selecting scenarios with the mouse or hold SHIFT to select a range of scenarios.<br />
<br />
The multiple scenario selection will result in several tasks in ''Tab 3 - Climate'' that are queued to the users task list. Magicc will process them in sequence.<br />
<br />
'''Note''' that multiple selection of scenarios is also available in Bulk Run Mode. This may result in a long term processing queue.<br />
<br><br><br />
<br />
=== How can I select multiple climate or carbon cycle settings? === <br />
Choose a desired climate or carbon cycle setting and switch to '''Tab 3 - Climate'''. The run will be queued. Now return to '''Tab 2 - Model Settings''' and choose another desired climate or carbon cycle setting. You can repeat these steps as often as desired. If you choose an already-processed setting accidentally Magicc will not process that setting again. You get a message in the console (What is the console?) that the configuration has been skipped.<br />
<br><br><br />
<br />
=== How can I compare the same emission scenario for two different climate settings? ===<br />
Choose a desired climate or carbon cycle setting and switch to '''Tab 3 - Climate'''. The run will be queued. Now return to '''Tab 2 - Model Settings''' and choose another desired climate or carbon cycle setting. You can repeat these steps as often as desired. <br />
<br><br><br />
<br />
=== How can I change only the climate sensitivity or other parameters? ===<br />
Return to '''Tab 2 - Model Settings''' and change only desired parameters. Once you switch to '''Tab 3 - Climate''' the forms of Tab 1 and Tab 2 will be evaluated and only if changes were made Magicc will be executed.<br />
<br><br><br />
<br />
=== Why is the carbon cycle setting important when I want to know about the climate ? ===<br />
<br><br><br />
<br />
=== What do all these acronyms CMIP3, C4MIP etc. mean? ===<br />
<br><br><br />
<br />
=== Why can I select from a range of other climate models? ===<br />
<br><br><br />
<br />
=== Why can't I select another climate model when doing probabilistic runs? ===<br />
<br><br><br />
<br />
=== What does probabilistic projection mean? ===<br />
<br><br><br />
<br />
=== Where can I see my outputs? ===<br />
You can see your outputs on '''Tab 3 - Climate'''. On the left you will see your individual run list. Checkboxes indicate the already processed runs. By checking / unchecking the checkboxes you select the runs that will be plotted in the chart on the right.<br />
<br><br><br />
<br />
=== Can I plot different variables in the same plot? ===<br />
No, that is not possible because different climate variables require different y-axes and units. The variable list is therefore a single select box.<br />
<br><br><br />
<br />
=== Can I download the data that live.magicc.org created? ===<br />
This feature is scheduled on high priority. Please, stay tuned to [http://live.magicc.org live.magicc.org].<br />
<br><br><br />
<br />
=== How can I run create GHG concentrations according to the RCP default settings ? ===<br />
<br><br><br />
<br />
=== How can I share my results with another user? ===<br />
This feature is scheduled on high priority. Please, stay tuned to [http://live.magicc.org live.magicc.org].<br />
<br><br><br />
<br />
=== Why would I want to sign up with a User Account on live.magicc.org? === <br />
This allows you to resume a session as well as share your results with other users (This feature is scheduled on high priority. Please, stay tuned to our [http://live.magicc.org live.magicc.org]).<br />
<br><br><br />
<br />
=== What are the system requirements for participating in live.magicc.org? === <br />
You need a browser that is able to display our website. We tested our website for IE6, FF4, Opera7. To report a bug for your browser, please see the bug report section(??). You will need JavaScript. <br />
<br />
There are no requirements for your processor or any of your hardware since liveMagicc runs on our server.<br />
<br><br><br />
<br />
=== How much does it cost? ===<br />
The service is free to use. If you make any use of this work, please cite:<br />
<br />
Meinshausen, M., S. C. B. Raper and T. M. L. Wigley (2011). "Emulating coupled atmosphere-ocean and carbon cycle models with a simpler model, MAGICC6: Part I – Model Description and Calibration." Atmospheric Chemistry and Physics 11: 1417-1456. doi:[http://dx.doi.org/10.5194/acp-11-1417-2011 10.5194/acp-11-1417-2011]<br />
<br><br><br />
<br />
=== How can I save the graphs that I create? ===<br />
This feature is scheduled on high priority. Please, stay tuned to [http://live.magicc.org live.magicc.org]. <br />
<br><br><br />
<br />
== Questions related to Windows executable ==</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=MAGICC_team&diff=10MAGICC team2013-06-17T10:19:09Z<p>Antonius Golly: </p>
<hr />
<div>==Background==<br />
<br />
MAGICC has a history of over 20 years and was brought to life by Tom Wigley and Sarah Raper, largely during their time at the Climate Research Unit at the University of Norwich. A lot of recent development has as well taken place by Tom Wigley at the National Centre for Atmospheric Research in Boulder, USA. Malte Meinshausen joined and co-developed the most recent MAGICC version. Furthermore, numerous collaborators and users help to expand the code, report bugs and thereby provide an invaluable contribution to the ongoing development of MAGICC. Particular thanks go as well to the international model intercomparison efforts of various kinds, which provide the vital database for parameterizing and calibrating various climate change, gas cycle and carbon cycle uncertainties. Without those, the MAGICC model, or any other reduced-complexity modelling approach, would miss the data for calibration and therefore its basis to estimate future climate change and its uncertainties. <br />
<br />
== The MAGICC Developers == <br />
<br />
[[File:Tom_Wigley_small.jpg|100px|thumb|right|Dr. Tom Wigley]] Dr. Tom Wigley - is senior scientist in the Climate and Global Dynamics Division at [http://www.cgd.ucar.edu/cas/ NCAR ] in Boulder, USA and has been named a fellow of the American Association for the Advancement of Science (AAAS) for his major contributions to climate and carbon-cycle modeling and to climate data analysis. He is now part time again at the University of Adelaide, Australia, where he received his doctorate as a mathematical physicist. Tom is one of the world's foremost experts on climate change and one of the most highly cited scientists in the discipline. <br />
<br />
<br />
[[File:Sarah_Raper_small.jpg|100px|thumb|right|Dr. Sarah Raper]] Dr. Sarah Raper - is Senior Research Fellow at the [http://www.cate.mmu.ac.uk/ Centre for Air Transport and the Environment at Manchester Metropolitan University]. Sarah is a climate modeller, specializing in mountain glaciers, sea level rise, emulation of AOGCM climate models and, of course, the co-development of MAGICC. Sarah has an extensive involvement in the Intergovernmental Panel on Climate Change (IPCC), having been a lead author of the projections chapter of the IPCC 3rd and 4th Assessment Reports. [http://www.cate.mmu.ac.uk/staffpage.asp?chg2=staff&chg=who&id=197 Sarah's home page].<br />
<br />
<br />
[[File:Malte_Meinshausen_small.jpg|100px|thumb|right|Dr. Malte Meinshausen]] Dr. Malte Meinshausen - is Honorary Senior Research Fellow at the School of Earth Sciences, University of Melbourne and Senior Researcher at the Potsdam Institiute for Climate Impact Research, Germany. Earlier he was a Post-Doc at the National Center for Atmospheric Research in Boulder, Colorado. He has been contributing author to various chapters in the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR4). [http://www.pik-potsdam.de/members/mmalte Malte's home page]. <br />
<br />
== Acknowledgements and key contributors == <br />
Many people helped in various ways in the development of MAGICC over the past 20 years, namely M. Salmon, M. Schlesinger, M. Hulme, T. Osborn, S. McGinnis and many more. We would like to warmly thank all those contributors and collaborators for making MAGICC possible. A special thanks to Dan Sandiford for making this WIKI possible.<br />
<br />
== The web-interface to MAGICC6 on live.magicc.org == <br />
As a recent development, MAGICC6 was equipped with a web-interface, accessible via [http://live.magicc.org live.magicc.org]. The programmer behind this effort is Antonius Golly, member of the PIK Research Group [http://www.primap.org PRIMAP].</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=MAGICC_team&diff=9MAGICC team2013-06-17T10:18:47Z<p>Antonius Golly: Created page with "==Background== MAGICC has a history of over 20 years and was brought to life by Tom Wigley and Sarah Raper, largely during their time at the Climate Research Unit at the Univ..."</p>
<hr />
<div>==Background==<br />
<br />
MAGICC has a history of over 20 years and was brought to life by Tom Wigley and Sarah Raper, largely during their time at the Climate Research Unit at the University of Norwich. A lot of recent development has as well taken place by Tom Wigley at the National Centre for Atmospheric Research in Boulder, USA. Malte Meinshausen joined and co-developed the most recent MAGICC version. Furthermore, numerous collaborators and users help to expand the code, report bugs and thereby provide an invaluable contribution to the ongoing development of MAGICC. Particular thanks go as well to the international model intercomparison efforts of various kinds, which provide the vital database for parameterizing and calibrating various climate change, gas cycle and carbon cycle uncertainties. Without those, the MAGICC model, or any other reduced-complexity modelling approach, would miss the data for calibration and therefore its basis to estimate future climate change and its uncertainties.<br />
<br />
== The MAGICC Developers == <br />
<br />
[[File:Tom_Wigley_small.jpg|100px|thumb|right|Dr. Tom Wigley]] Dr. Tom Wigley - is senior scientist in the Climate and Global Dynamics Division at NCAR in Boulder, USA and has been named a fellow of the American Association for the Advancement of Science (AAAS) for his major contributions to climate and carbon-cycle modeling and to climate data analysis. He is now part time again at the University of Adelaide, Australia, where he received his doctorate as a mathematical physicist. Tom is one of the world's foremost experts on climate change and one of the most highly cited scientists in the discipline.<br />
<br />
<br />
[[File:Sarah_Raper_small.jpg|100px|thumb|right|Dr. Sarah Raper]] Dr. Sarah Raper - is Senior Research Fellow at the Centre for Air Transport and the Environment at Manchester Metropolitan University. Sarah is a climate modeller, specializing in mountain glaciers, sea level rise, emulation of AOGCM climate models and, of course, the co-development of MAGICC. Sarah has an extensive involvement in the Intergovernmental Panel on Climate Change (IPCC), having been a lead author of the projections chapter of the IPCC 3rd and 4th Assessment Reports.<br />
<br />
<br />
[[File:Malte_Meinshausen_small.jpg|100px|thumb|right|Dr. Malte Meinshausen]] Dr. Malte Meinshausen - is Honorary Senior Research Fellow at the School of Earth Sciences, University of Melbourne and Senior Researcher at the Potsdam Institiute for Climate Impact Research, Germany. Earlier he was a Post-Doc at the National Center for Atmospheric Research in Boulder, Colorado. He has been contributing author to various chapters in the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR4).<br />
<br />
== Acknowledgements and key contributors == <br />
Many people helped in various ways in the development of MAGICC over the past 20 years, namely M. Salmon, M. Schlesinger, M. Hulme, T. Osborn, S. McGinnis and many more. We would like to warmly thank all those contributors and collaborators for making MAGICC possible. A special thanks to Dan Sandiford for making this WIKI possible.<br />
<br />
== The web-interface to MAGICC6 on live.magicc.org == <br />
As a recent development, MAGICC6 was equipped with a web-interface, accessible via live.magicc.org. The programmer behind this effort is Antonius Golly, member of the PIK Research Group PRIMAP.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=MAGICC_projects&diff=8MAGICC projects2013-06-17T10:18:25Z<p>Antonius Golly: Created page with "Out of the dozens of scientific publications that used MAGICC, this page provides you with a small sample of those. They are listed in chronological order. # '''1992: T. M..."</p>
<hr />
<div>Out of the dozens of scientific publications that used MAGICC, this page provides you with a small sample of those. They are listed in chronological order. <br />
<br />
<br />
<br />
# '''1992: T. M. L. Wigley and S. C. B. Raper "Implications for climate and sea level of revised IPCC emissions scenarios", Nature, 357 293-300''' Abstract: A new set of greenhouse gas emissions scenarios has been produced by the Intergovernmental Panel on Climate Change (IPCC). Incorporating these into models that also include the effects of C02 fertilization, feedback from stratospheric ozone depletion and the radiative effects of sulphate aerosols yields new projections for radiative forcing of climate and for changes in global-mean temperature and sea level. Changes in temperature and sea level are predicted to be less severe than those estimated previously, but are still far beyond the limits of natural variability.<br />
# '''1993: T. M. L. Wigley "Balancing the Carbon Budget - Implications for Projections of Future Carbon-Dioxide Concentration Changes", Tellus Series B-Chemical and Physical Meteorology, 45 (5), 409-425''' Abstract: A carbon cycle model is described incorporating CO2 fertilization feedback and a convolution ocean model that allows the atmosphere-to-ocean flux to be varied. The main parameters controlling the model's behaviour are a fertilization feedback parameter (r) and an ocean flux scaling factor (characterized by the mean carbon flux into the ocean over the 1980s, F(1980s)). Since the model's 1980s-mean net land-use-change flux (D(n)(1980s)) is a unique function of r and F(1980s), the model's behaviour can also be characterized by specifying D(n)(1980s) (instead of r) and F(1980s). The history of past land-use fluxes, D(n)(t), is derived by inverse modelling for a range of values of F(1980s) (1.0-3.0 GtC/yr) and D(n)(1980s) (0.6-2.6 GtC/yr). Even with this flexibility, the resultant D(n)(t) differs markedly from the observationally-based record of Houghton, particularly before 1950. The inverse calculations are used to determine the history of the so-called ''missing sink'', as implied directly by the model and by the observationally-based record of D(n)(t), for a range of ocean uptake efficiencies as defined by F(1980s). Projections of future CO2 concentration changes are made for the 6 emissions scenarios recently produced by the Intergovernmental Panel on Climate Change (IS92a-f). The ability to specify F(1980s) and D.(1980s) allows one to account for the missing sink in a variety of ways, and to account for uncertainties in the amount of missing carbon. This leads to a range of projections and provides some insights into the uncertainties surrounding these projections.<br />
# '''1995: T. M. L. Wigley "Global Mean Temperature and Sea-Level Consequences of Greenhouse-Gas Concentration Stabilization", Geophysical Research Letters, 22 (1), 45-48''' Abstract: The Intergovernmental Panel on Climate Change (IPCC) has defined a set of scenarios for future CO2 concentrations stabilizing at levels of 350 to 750 ppmv. Using models previously employed by IPCC, the implied global-mean temperature and sea level changes are calculated out to 2500. While uncertainties are large, the results show that even with concerted efforts to stabilize concentrations of greenhouse gases, substantial temperature and sea level increases can be expected to occur over the next century. Increases ia sea level are likely to continue for many centuries after concentration stabilization because of the extremely long time scales associated with the deep ocean (which influences thermal expansion) and with the large ice sheets of Greenland and Antarctica.<br />
# '''1996: S. C. B. Raper and U. Cubasch "Emulation of the results from a coupled general circulation model using a simple climate model", Geophysical Research Letters, 23 (10), 1107-1110''' Abstract: An upwelling diffusion (UD) model has been fitted to the results of a globally coupled ocean atmosphere general circulation model (O/AGCM). In order to adequately simulate the results of the O/AGCM, the differential heating over land and ocean, the change of the upwelling rate with rising mixed-layer temperature and the climate adjustment of the O/AGCM evident in the control simulation had to be taken into account. Comparisons using the results of four O/AGCM perturbation experiments show that the timing of the adjustment in the O/AGCM control run differs from that in the perturbed runs. The UD model simulates the global mean temperature evolution, as calculated by the O/AGCM reasonably well. However, when time dependent upwelling is included, the UD model substantially overestimates the thermal expansion compared to this O/AGCM. Possible reasons for this overestimation have been identified.<br />
# '''1996: S. C. B. Raper, T. M. L. Wigley and R. A. Warrick "Global Sea-level Rise: Past and Future", Sea-Level Rise and Coastal Subsidence: Causes, Consequences and Strategies, 11-45 '''<br />
# '''1997: T. M. L. Wigley "Implications of recent CO2 emission-limitation proposals for stabilization of atmospheric concentrations", Nature, 390 267-270''' <br />
# '''1998: T. M. L. Wigley "The Kyoto Protocol: CO2, CH4 and climate implications", Geophysical Research Letters, 25 (13), 2285-2288''' Abstract: Kyoto Protocol implications for CO2, temperature and sea level are examined. Three scenarios for post-Kyoto emissions reductions are considered. In all cases, the longterm consequences are small. The limitations specified under the Protocol are interpreted in terms of both CO2 and CH4 emissions reductions and a new emissions comparison index, the Forcing Equivalence Index (FEI), is introduced. The use of GWPs to assess CO2-equivalence is assessed.<br />
# '''2000: M. Hulme, T. Wigley, E. Barrow, S. Raper, A. Centella, S. Smith and A. Chipanshi "Using a Climate Scenario Generator for Vulnerability and Adaptaion Assessments: MAGICC and SCENGEN Version 2.4 Workbook", 52, [http://www.atmosphere.mpg.de/documents/ACCENT/Edition02a/Texts%20Material/english/ClimateSensitivityWorkbook2.pdf available online]''' <br />
# '''2001: S. C. B. Raper, J. M. Gregory and T. J. Osborn "Use of an upwelling-diffusion energy balance climate model to simulate and diagnose A/OGCM results", Climate Dynamics, 17 (8), 601-613''' Abstract: We demonstrate that a hemispherically averaged upwelling- diffusion energy-balance climate model (UD/EBM) can emulate the surface air temperature change and sea-level rise due to thermal expansion, predicted by the HadCM2 coupled atmosphere- ocean general circulation model, for various scenarios of anthropogenic radiative forcing over 1860-2100. A climate sensitivity of 2.6 degreesC is assumed, and a representation of the effect of sea-ice retreat on surface air temperature is required. In an extended experiment, with CO2 concentration held constant at twice the control run value, the HadCM2 effective climate sensitivity is found to increase from about 2.0 degreesC at the beginning of the integration to 3.85 degreesC after 900 years. The sea-level rise by this time is almost 1.0 m and the rate of rise fairly steady, implying that the final equilibrium value (the 'commitment') is large. The base UD/EBM can fit the 900-year simulation of surface temperature change and thermal expansion provided that the time-dependent climate sensitivity is specified, but the vertical profile of warming in the ocean is not well reproduced. The main discrepancy is the relatively large mid- depth warming in the HadCM2 ocean, that can be emulated by (1) diagnosing depth-dependent diffusivities that increase through time; (2) diagnosing depth-dependent diffusivities for a pure- diffusion (zero upwelling) model; or (3) diagnosing higher depth-dependent diffusivities that are applied to temperature pertubarions only. The latter two models can be run to equilibrium, and with a climate sensitivity of 3.85 degreesC, they give sea-level rise commitments of 1.7 m and 1.3 m, respectively.<br />
# '''2001: T. M. L. Wigley and S. C. B. Raper "Interpretation of high projections for global-mean warming", Science, 293 (5529), 451-454''' Abstract: The Intergovernmental Panel on Climate Change (IPCC) has recently released its Third Assessment Report (TAR), in which new projections are given for global-mean warming in the absence of policies to limit climate change. The full warming range over 1990 to 2100, 1.4 degrees to 5.8 degreesC, is substantially higher than the range given previously in the IPCC Second Assessment Report. Here we interpret the new warming range in probabilistic terms, accounting for uncertainties in emissions, the climate sensitivity, the carbon cycle, ocean mixing, and aerosol forcing. We show that the probabilities of warming values at both the high and Low ends of the TAR range are very Low. In the absence of climate- mitigation policies, the 90% probability interval for 1990 to 2100 warming is 1.7 degrees to 4.9 degreesC.<br />
# '''2002: S. C. B. Raper, J. M. Gregory and R. J. Stouffer "The Role of Climate Sensitivity and Ocean Heat Uptake on AOGCM Transient Temperature Response", Journal of Climate, 15 124-130''' Abstract: The role of climate sensitivity and ocean heat uptake in determining the range of climate model response is investigated in the second phase of the Coupled Model Intercomparison Project (CMIP2) AOGCM results. The fraction of equilibrium warming that is realized at any one time is less in those models with higher climate sensitivity, leading to a reduction in the temperature response range at the time of CO2 doubling [transient climate response (TCR) range]. The range is reduced by a further 15% because of an apparent relationship between climate sensitivity and the efficiency of ocean heat uptake. Some possible physical causes for this relationship are suggested.<br />
# '''2002: T. M. L. Wigley and S. C. B. Raper "Reasons for larger warming projections in the IPCC Third Assessment Report", Journal of Climate, 15 (20), 2945-2952''' Abstract: Projections of future warming in the Intergovernmental Panel on Climate Change (IPCC) Third Assessment Report (TAR) are substantially larger than those in the Second Assessment Report (SAR). The reasons for these differences are documented and quantified. Differences are divided into differences in the emissions scenarios and differences in the science (gas cycle, forcing, and climate models). The main source of emissions-related differences in warming is aerosol forcing, primarily due to large differences in SO2 emissions between the SAR and TAR scenarios. For any given emissions scenario, concentration projections based on SAR and TAR science are similar, except for methane at high emissions levels where TAR science leads to substantially lower concentrations. The new (TAR) science leads to slightly lower total forcing and slightly larger warming. At the low end of the warming range the effects of the new science and the new emissions scenarios are roughly equal. At the high end, TAR science has a smaller effect and the main reason for larger TAR warming is the use of a different high-end emissions scenario, primarily changes in SO2 emissions.<br />
# '''2004: S. C. B. Raper "Interpretation of Model Results that Show Changes in the Effective Climate Sensitivity with Time", IPCC Workshop on Climate Sensitivity, 131-133'''<br />
# '''2005: T. M. L. Wigley "The climate change commitment", Science, 307 (5716), 1766-1769''' Abstract: Even if atmospheric composition were fixed today, global-mean temperature and sea level rise would continue due to oceanic thermal inertia. These constant-composition (CC) commitments and their uncertainties are quantified. Constant-emissions (CE) commitments are also considered. The CC warming commitment could exceed 1 degrees C. The CE warming commitment is 2 degrees to 6 degrees C by the year 2400. For sea level rise, the CC commitment is 10 centimeters per century (extreme range approximately 1 to 30 centimeters per century) and the CE commitment is 25 centimeters per century (7 to 50 centimeters per century). Avoiding these changes requires, eventually, a reduction in emissions to substantially below present levels. For sea level rise, a substantial long-term commitment may be impossible to avoid.<br />
# '''2005: T. M. L. Wigley and S. C. B. Raper "Extended scenarios for glacier melt due to anthropogenic forcing", Geophysical Research Letters, 32 (5)''' Abstract: The IPCC Third Assessment Report (TAR) developed a formula for the global meltwater contribution to sea level rise from Glaciers and Small Ice Caps (GSICs) that is applicable out to 2100. We show that, if applied to times beyond 2100 (as is necessary to assess sea level rise for concentration-stabilization scenarios), the formula imposes an unrealistic upper bound on GSIC melt. A modification is introduced that allows the formula to be extended beyond 2100 with asymptotic melt equal to the initially available ice volume (V-0). The modification has a negligible effect on the original TAR formulation out to 2100 and provides support for the IPCC method over this time period. We examine the sensitivity of GSIC melt to uncertainties in V0 and mass balance sensitivity, and give results for a range of CO2 concentration stabilization cases. Approximately 73-94% of GSIC ice is lost by 2400.<br />
# '''2005: Wigley, T. M. L. "The climate change commitment." Science 307(5716): 1766-1769. [http://www.sciencemag.org/content/307/5716/1766.abstract available online]''' Abstract: Even if atmospheric composition were fixed today, global-mean temperature and sea level rise would continue due to oceanic thermal inertia. These constant-composition (CC) commitments and their uncertainties are quantified. Constant-emissions (CE) commitments are also considered. The CC warming commitment could exceed 1°C. The CE warming commitment is 2° to 6°C by the year 2400. For sea level rise, the CC commitment is 10 centimeters per century (extreme range approximately 1 to 30 centimeters per century) and the CE commitment is 25 centimeters per century (7 to 50 centimeters per century). Avoiding these changes requires, eventually, a reduction in emissions to substantially below present levels. For sea level rise, a substantial long-term commitment may be impossible to avoid. <br />
# '''2006: T. J. Osborn, S. C. B. Raper and K. R. Briffa "Simulated climate change during the last 1000 years: comparing the ECHO-G general circulation model with the MAGICC simple climate model. ", Climate Dynamics, 27 185-197, doi:10.1007/s00382-006-0129-5 [http://www.springerlink.com/content/5712246147878214/ available online]''' Abstract: An intercomparison of eight climate simulations, each driven with estimated natural and anthropogenic forcings for the last millennium, indicates that the so-called “Erik” simulation of the ECHO-G coupled ocean-atmosphere climate model exhibits atypical behaviour. The ECHO-G simulation has a much stronger cooling trend from 1000 to 1700 and a higher rate of warming since 1800 than the other simulations, with the result that the overall amplitude of millennial-scale temperature variations in the ECHO-G simulation is much greater than in the other models. The MAGICC (Model for the Assessment of Greenhouse-gas-Induced Climate Change) simple climate model is used to investigate possible causes of this atypical behaviour. It is shown that disequilibrium in the initial conditions probably contributes spuriously to the cooling trend in the early centuries of the simulation, and that the omission of tropospheric sulphate aerosol forcing is the likely explanation for the anomalously large recent warming. The simple climate model results are used to adjust the ECHO-G Erik simulation to mitigate these effects, which brings the simulation into better agreement with the other seven models considered here and greatly reduces the overall range of temperature variations during the last millennium simulated by ECHO-G. Smaller inter-model differences remain which can probably be explained by a combination of the particular forcing histories and model sensitivities of each experiment. These have not been investigated here, though we have diagnosed the effective climate sensitivity of ECHO-G to be 2.39±0.11 K for a doubling of CO2.<br />
# '''2007: T. M. L. Wigley, R. Richels and J. Edmonds "Overshoot pathways to CO2 stabilization in a multi-gas context", Human Induced Climate Change: An Interdisciplinary Assessment, 84-92''' <br />
# '''2009: M. Meinshausen, N. Meinshausen, W. Hare, S. C. B. Raper, K. Frieler, R. Knutti, D. J. Frame and M. R. Allen "Greenhouse-gas emission targets for limiting global warming to 2°C", Nature, 458 (7242), 1158''' Abstract: More than 100 countries have adopted a global warming limit of 2?°C or below (relative to pre-industrial levels) as a guiding principle for mitigation efforts to reduce climate change risks, impacts and damages1, 2. However, the greenhouse gas (GHG) emissions corresponding to a specified maximum warming are poorly known owing to uncertainties in the carbon cycle and the climate response. Here we provide a comprehensive probabilistic analysis aimed at quantifying GHG emission budgets for the 2000–50 period that would limit warming throughout the twenty-first century to below 2?°C, based on a combination of published distributions of climate system properties and observational constraints. We show that, for the chosen class of emission scenarios, both cumulative emissions up to 2050 and emission levels in 2050 are robust indicators of the probability that twenty-first century warming will not exceed 2?°C relative to pre-industrial temperatures. Limiting cumulative CO2 emissions over 2000–50 to 1,000?Gt CO2 yields a 25% probability of warming exceeding 2?°C—and a limit of 1,440 Gt CO2 yields a 50% probability—given a representative estimate of the distribution of climate system properties. As known 2000–06 CO2 emissions3 were ~234?Gt CO2, less than half the proven economically recoverable oil, gas and coal reserves4, 5, 6 can still be emitted up to 2050 to achieve such a goal. Recent G8 Communiqués7 envisage halved global GHG emissions by 2050, for which we estimate a 12–45% probability of exceeding 2?°C—assuming 1990 as emission base year and a range of published climate sensitivity distributions. Emissions levels in 2020 are a less robust indicator, but for the scenarios considered, the probability of exceeding 2?°C rises to 53–87% if global GHG emissions are still more than 25% above 2000 levels in 2020.<br />
# '''2010: J. Rogelj, C. Chen, J. Nabel, K. Macey, W. Hare, M. Schaeffer, K. Markmann, N. Hohne, K. K. Andersen and M. Meinshausen "Analysis of the Copenhagen Accord pledges and its global climatic impacts-a snapshot of dissonant ambitions", Environmental Research Letters, 5 (3)''' Abstract: This analysis of the Copenhagen Accord evaluates emission reduction pledges by individual countries against the Accord's climate-related objectives. Probabilistic estimates of the climatic consequences for a set of resulting multi-gas scenarios over the 21st century are calculated with a reduced complexity climate model, yielding global temperature increase and atmospheric CO2 and CO2-equivalent concentrations. Provisions for banked surplus emission allowances and credits from land use, land-use change and forestry are assessed and are shown to have the potential to lead to significant deterioration of the ambition levels implied by the pledges in 2020. This analysis demonstrates that the Copenhagen Accord and the pledges made under it represent a set of dissonant ambitions. The ambition level of the current pledges for 2020 and the lack of commonly agreed goals for 2050 place in peril the Accord's own ambition: to limit global warming to below 2 degrees C, and even more so for 1.5 degrees C, which is referenced in the Accord in association with potentially strengthening the long-term temperature goal in 2015. Due to the limited level of ambition by 2020, the ability to limit emissions afterwards to pathways consistent with either the 2 or 1.5 degrees C goal is likely to become less feasible.<br />
# '''2010: A. Reisinger, M. Meinshausen, M. Manning and G. Bodeker "Uncertainties of global warming metrics: CO2 and CH4", Geophys. Res. Lett., 37 (14), L14707, 10.1029/2010gl043803''' Abstract: We present a comprehensive evaluation of uncertainties in the Global Warming Potential (GWP) and Global Temperature Change Potential (GTP) of CH4, using a simple climate model calibrated to AOGCMs and coupled climate-carbon cycle models assessed in the IPCC Fourth Assessment Report (AR4). In addition, we estimate uncertainties in these metrics probabilistically by using a method that does not rely on AOGCMs but instead builds on historical constraints and uncertainty estimates of current radiative forcings. While our mean and median GWPs and GTPs estimates are consistent with previous studies, our analysis suggests that uncertainty ranges for GWPs are almost twice as large as estimated in the AR4. Relative uncertainties for GTPs are larger than for GWPs, nearly twice as high for a time horizon of 100 years. Given this uncertainty, our results imply the possibility for substantial future adjustments in best-estimate values of GWPs and in particular GTPs.<br />
# '''2011: A. Hof, C. Hope, J. Lowe, M. Mastrandrea, M. Meinshausen and D. van Vuuren "The benefits of climate change mitigation in integrated assessment models: the role of the carbon cycle and climate component", Climatic Change, 1-21, 10.1007/s10584-011-0363-7 (online first)''' Abstract: Integrated Assessment Models (IAMs) are an important tool to compare the costs and benefits of different climate policies. Recently, attention has been given to the effect of different discounting methods and damage estimates on the results of IAMs. One aspect to which little attention has been paid is how the representation of the climate system may affect the estimated benefits of mitigation action. In that respect, we analyse several well-known IAMs, including the newest versions of FUND, DICE and PAGE. Given the role of IAMs in integrating information from different disciplines, they should ideally represent both best estimates and the ranges of anticipated climate system and carbon cycle behaviour (as e.g. synthesised in the IPCC Assessment reports). We show that in the longer term, beyond 2100, most IAM parameterisations of the carbon cycle imply lower CO 2 concentrations compared to a model that captures IPCC AR4 knowledge more closely, e.g. the carbon-cycle climate model MAGICC6. With regard to the climate component, some IAMs lead to much lower benefits of mitigation than MAGICC6. The most important reason for the underestimation of the benefits of mitigation is the failure in capturing climate dynamics correctly, which implies this could be a potential development area to focus on.<br />
# '''2011: M. Meinshausen, S. C. B. Raper and T. M. L. Wigley "Emulating coupled atmosphere-ocean and carbon cycle models with a simpler model, MAGICC6: Part I – Model Description and Calibration", Atmospheric Chemistry and Physics 11 1417-1456, [http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html available online]''' Abstract: Current scientific knowledge on the future response of the climate system to human-induced perturbations is comprehensively captured by various model intercomparison efforts. In the preparation of the Fourth Assessment Report (AR4) of the Intergovernmental Panel on Climate Change (IPCC), intercomparisons were organized for atmosphere-ocean general circulation models (AOGCMs) and carbon cycle models, named "CMIP3" and "C4MIP", respectively. Despite their tremendous value for the scientific community and policy makers alike, there are some difficulties in interpreting the results. For example, radiative forcings were not standardized across the various AOGCM integrations and carbon cycle runs, and, in some models, key forcings were omitted. Furthermore, the AOGCM analysis of plausible emissions pathways was restricted to only three SRES scenarios. This study attempts to address these issues. We present an updated version of MAGICC, the simple carbon cycle-climate model used in past IPCC Assessment Reports with enhanced representation of time-varying climate sensitivities, carbon cycle feedbacks, aerosol forcings and ocean heat uptake characteristics. This new version, MAGICC6, is successfully calibrated against the higher complexity AOGCMs and carbon cycle models. Parameterizations of MAGICC6 are provided. The mean of the emulations presented here using MAGICC6 deviates from the mean AOGCM responses by only 2.2% on average for the SRES scenarios. This enhanced emulation skill in comparison to previous calibrations is primarily due to: making a "like-with-like comparison" using AOGCM-specific subsets of forcings; employing a new calibration procedure; as well as the fact that the updated simple climate model can now successfully emulate some of the climate-state dependent effective climate sensitivities of AOGCMs. The diagnosed effective climate sensitivity at the time of CO2 doubling for the AOGCMs is on average 2.88 °C, about 0.33 °C cooler than the mean of the reported slab ocean climate sensitivities. In the companion paper (Part 2) of this study, we examine the combined climate system and carbon cycle emulations for the complete range of IPCC SRES emissions scenarios and the new RCP pathways.<br />
# '''2011: M. Meinshausen, S. Smith, K. Calvin, J. Daniel, M. Kainuma, J. F. Lamarque, K. Matsumoto, S. Montzka, S. Raper, K. Riahi, A. Thomson, G. Velders and D. P. van Vuuren "The RCP greenhouse gas concentrations and their extensions from 1765 to 2300", Climatic Change, 109 (1), 213-241, 10.1007/s10584-011-0156-z [http://www.springerlink.com/content/96n71712n613752g/ available online].''' Abstract: We present the greenhouse gas concentrations for the Representative Concentration Pathways (RCPs) and their extensions beyond 2100, the Extended Concentration Pathways (ECPs). These projections include all major anthropogenic greenhouse gases and are a result of a multi-year effort to produce new scenarios for climate change research. We combine a suite of atmospheric concentration observations and emissions estimates for greenhouse gases (GHGs) through the historical period (1750–2005) with harmonized emissions projected by four different Integrated Assessment Models for 2005–2100. As concentrations are somewhat dependent on the future climate itself (due to climate feedbacks in the carbon and other gas cycles), we emulate median response characteristics of models assessed in the IPCC Fourth Assessment Report using the reduced-complexity carbon cycle climate model MAGICC6. Projected ‘best-estimate’ global-mean surface temperature increases (using inter alia a climate sensitivity of 3°C) range from 1.5°C by 2100 for the lowest of the four RCPs, called both RCP3-PD and RCP2.6, to 4.5°C for the highest one, RCP8.5, relative to pre-industrial levels. Beyond 2100, we present the ECPs that are simple extensions of the RCPs, based on the assumption of either smoothly stabilizing concentrations or constant emissions: For example, the lower RCP2.6 pathway represents a strong mitigation scenario and is extended by assuming constant emissions after 2100 (including net negative CO 2 emissions), leading to CO 2 concentrations returning to 360 ppm by 2300. We also present the GHG concentrations for one supplementary extension, which illustrates the stringent emissions implications of attempting to go back to ECP4.5 concentration levels by 2250 after emissions during the 21 st century followed the higher RCP6 scenario. Corresponding radiative forcing values are presented for the RCP and ECPs.<br />
# '''2011: M. Meinshausen, T. M. L. Wigley and S. C. B. Raper "Emulating atmosphere-ocean and carbon cycle models with a simpler model, MAGICC6: Part 2– Applications", Atmospheric Chemistry and Physics 11 1457-1471, [http://www.atmos-chem-phys.net/11/1457/2011/acp-11-1457-2011.html available online].''' Abstract: Intercomparisons of coupled atmosphere-ocean general circulation models (AOGCMs) and carbon cycle models are important for galvanizing our current scientific knowledge to project future climate. Interpreting such intercomparisons faces major challenges, not least because different models have been forced with different sets of forcing agents. Here, we show how an emulation approach with MAGICC6 can address such problems. In a companion paper (Meinshausen et al., 2011a), we show how the lower complexity carbon cycle-climate model MAGICC6 can be calibrated to emulate, with considerable accuracy, globally aggregated characteristics of these more complex models. Building on that, we examine here the Coupled Model Intercomparison Project's Phase 3 results (CMIP3). If forcing agents missed by individual AOGCMs in CMIP3 are considered, this reduces ensemble average temperature change from pre-industrial times to 2100 under SRES A1B by 0.4 °C. Differences in the results from the 1980 to 1999 base period (as reported in IPCC AR4) to 2100 are negligible, however, although there are some differences in the trajectories over the 21st century. In a second part of this study, we consider the new RCP scenarios that are to be investigated under the forthcoming CMIP5 intercomparison for the IPCC Fifth Assessment Report. For the highest scenario, RCP8.5, relative to pre-industrial levels, we project a median warming of around 4.6 °C by 2100 and more than 7 °C by 2300. For the lowest RCP scenario, RCP3-PD, the corresponding warming is around 1.5 °C by 2100, decreasing to around 1.1 °C by 2300 based on our AOGCM and carbon cycle model emulations. Implied cumulative CO2 emissions over the 21st century for RCP8.5 and RCP3-PD are 1881 GtC (1697 to 2034 GtC, 80% uncertainty range) and 381 GtC (334 to 488 GtC), when prescribing CO2 concentrations and accounting for uncertainty in the carbon cycle. Lastly, we assess the reasons why a previous MAGICC version (4.2) used in IPCC AR4 gave roughly 10% larger warmings over the 21st century compared to the CMIP3 average. We find that forcing differences and the use of slightly too high climate sensitivities inferred from idealized high-forcing runs were the major reasons for this difference.<br />
# '''2011: A. Reisinger, M. Meinshausen, M. Manning and G. Bodeker "Future changes in global warming potentials under representative concentration pathways", Environmental Research Letters, 6 (2), 024020''' Abstract: Global warming potentials (GWPs) are the metrics currently used to compare emissions of different greenhouse gases under the United Nations Framework Convention on Climate Change. Future changes in greenhouse gas concentrations will alter GWPs because the radiative efficiencies of marginal changes in CO 2 , CH 4 and N 2 O depend on their background concentrations, the removal of CO 2 is influenced by climate–carbon cycle feedbacks, and atmospheric residence times of CH 4 and N 2 O also depend on ambient temperature and other environmental changes. We calculated the currently foreseeable future changes in the absolute GWP of CO 2 , which acts as the denominator for the calculation of all GWPs, and specifically the GWPs of CH 4 and N 2 O, along four representative concentration pathways (RCPs) up to the year 2100. We find that the absolute GWP of CO 2 decreases under all RCPs, although for longer time horizons this decrease is smaller than for short time horizons due to increased climate–carbon cycle feedbacks. The 100-year GWP of CH 4 would increase up to 20% under the lowest RCP by 2100 but would decrease by up to 10% by mid-century under the highest RCP. The 100-year GWP of N 2 O would increase by more than 30% by 2100 under the highest RCP but would vary by less than 10% under other scenarios. These changes are not negligible but are mostly smaller than the changes that would result from choosing a different time horizon for GWPs, or from choosing altogether different metrics for comparing greenhouse gas emissions, such as global temperature change potentials.<br />
# '''2011: T. Wigley "Coal to gas: the influence of methane leakage", Climatic Change, 108 (3), 601-608, 10.1007/s10584-011-0217-3''' Abstract: Carbon dioxide (CO 2 ) emissions from fossil fuel combustion may be reduced by using natural gas rather than coal to produce energy. Gas produces approximately half the amount of CO 2 per unit of primary energy compared with coal. Here we consider a scenario where a fraction of coal usage is replaced by natural gas (i.e., methane, CH 4 ) over a given time period, and where a percentage of the gas production is assumed to leak into the atmosphere. The additional CH 4 from leakage adds to the radiative forcing of the climate system, offsetting the reduction in CO 2 forcing that accompanies the transition from coal to gas. We also consider the effects of: methane leakage from coal mining; changes in radiative forcing due to changes in the emissions of sulfur dioxide and carbonaceous aerosols; and differences in the efficiency of electricity production between coal- and gas-fired power generation. On balance, these factors more than offset the reduction in warming due to reduced CO 2 emissions. When gas replaces coal there is additional warming out to 2,050 with an assumed leakage rate of 0%, and out to 2,140 if the leakage rate is as high as 10%. The overall effects on global-mean temperature over the 21st century, however, are small.<br />
# '''2011: J. Rogelj, W. Hare, J. Lowe, D. P. van Vuuren, K. Riahi, B. Matthews, T. Hanaoka, K. Jiang and M. Meinshausen "Emission pathways consistent with a 2 degree C global temperature limit", Nature Clim. Change, 1 (8), 413-418, http://www.nature.com/nclimate/journal/v1/n8/abs/nclimate1258.html''' Abstract: In recent years, international climate policy has increasingly focused on limiting temperature rise, as opposed to achieving greenhouse-gas-concentration-related objectives. The agreements reached at the United Nations Framework Convention on Climate Change conference in Cancun in 2010 recognize that countries should take urgent action to limit the increase in global average temperature to less than 2?°C relative to pre-industrial levels1. If this is to be achieved, policymakers need robust information about the amounts of future greenhouse-gas emissions that are consistent with such temperature limits. This, in turn, requires an understanding of both the technical and economic implications of reducing emissions and the processes that link emissions to temperature. Here we consider both of these aspects by reanalysing a large set of published emission scenarios from integrated assessment models in a risk-based climate modelling framework. We find that in the set of scenarios with a ‘likely’ (greater than 66%) chance of staying below 2?°C, emissions peak between 2010 and 2020 and fall to a median level of 44?Gt of CO2 equivalent in 2020 (compared with estimated median emissions across the scenario set of 48?Gt of CO2 equivalent in 2010). Our analysis confirms that if the mechanisms needed to enable an early peak in global emissions followed by steep reductions are not put in place, there is a significant risk that the 2?°C target will not be achieved.<br />
# '''2012: J. Rogelj, M. Meinshausen and R. Knutti "Global warming under old and new scenarios using IPCC climate sensitivity range estimates", Nature Clim. Change, advance online publication http://www.nature.com/nclimate/journal/vaop/ncurrent/abs/nclimate1385.html''' Abstract: Climate projections for the fourth assessment report1 (AR4) of the Intergovernmental Panel on Climate Change (IPCC) were based on scenarios from the Special Report on Emissions Scenarios2 (SRES) and simulations of the third phase of the Coupled Model Intercomparison Project3 (CMIP3). Since then, a new set of four scenarios (the representative concentration pathways or RCPs) was designed4. Climate projections in the IPCC fifth assessment report (AR5) will be based on the fifth phase of the Coupled Model Intercomparison Project5 (CMIP5), which incorporates the latest versions of climate models and focuses on RCPs. This implies that by AR5 both models and scenarios will have changed, making a comparison with earlier literature challenging. To facilitate this comparison, we provide probabilistic climate projections of both SRES scenarios and RCPs in a single consistent framework. These estimates are based on a model set-up that probabilistically takes into account the overall consensus understanding of climate sensitivity uncertainty, synthesizes the understanding of climate system and carbon-cycle behaviour, and is at the same time constrained by the observed historical warming.<br />
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PS: If you would like to see any additional publications listed of yourself or others, which make use of MAGICC, please add them here (either register via link above, or send us an [mailto:add_publications@magicc.org email]</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=For_IAM_Modellers&diff=7For IAM Modellers2013-06-17T10:18:04Z<p>Antonius Golly: Created page with "If you are a scientific modeller, for example involved in maintaining or building an Integrated Assessment Model (IAM), why not use MAGICC6 as your climate core? MAGICC is use..."</p>
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<div>If you are a scientific modeller, for example involved in maintaining or building an Integrated Assessment Model (IAM), why not use MAGICC6 as your climate core? MAGICC is used by a number of leading IAM models, including the [http://themasites.pbl.nl/en/themasites/image/index.html IMAGE Group] at PBL Netherlands, the [http://www.iiasa.ac.at/Research/ENE/model/message.html MESSAGE model] at IIASA, the [http://www.globalchange.umd.edu/models/gcam/ GCAM model] by the Joint Climate Change Research Institute at the Pacific Northwest National Laboratory and University of Maryland, and multiple others. Another reason, why you might want to use MAGICC is because it was, for example, used to create the benchmark [http://www.pik-potsdam.de/~mmalte/rcps/ GHG concentrations] in the creation process of the [http://www.iiasa.ac.at/web-apps/tnt/RcpDb/ Representative Concentration Pathways] (RCPs). <br />
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==How to obtain your MAGICC version? == <br />
There are four options of how you can include MAGICC as your climate core: <br />
* You can use the [http://www.cgd.ucar.edu/cas/wigley/magicc/ MAGICC/SCENGEN 5.3] software. This provides you with the additional benefit of having a scenario pattern generator bundled into it. The software package comes with a graphical user interface, but can be run as well as executable with ASCII configuration files. <br />
* Similarly, you can download the [[Download MAGICC6|Windows executable of MAGICC6]], in case your modelling environment is running on Windows machines. This does not include a graphical user interface as version 5.3 (nor does it include SCENGEN), but you can set all of the model parameters via ASCII files ...<br />
* As part of a collaboration & license agreement, you obtain the source code from us to integrate them in your Linux etc environment. <br />
* And of course, you can use the web-interface [http://live.magicc.org live.magicc.org] to run MAGICC6 on our servers. This provides you with the additional benefit of probabilistic runs over the whole 21st century. The online interface provides as well a great way for checking your results against our current MAGICC version. <br />
<br />
== Collaboration & License Agreements ==<br />
In regard to the collaboration & license agreements, please contact Malte Meinshausen (malte.meinshausen@pik-potsdam.de). A short license agreement will have to be agreed upon and off you go, your IAM model can use a comprehensive range of gas cycles, climate feedbacks, and ESM or carbon cycle model calibrations in order to perform your experiments and sensitivity studies. All we ask for is a citation and that you share you experiences and development steps back to the central MAGICC development line. Of course, we, i.e. the developer team [[Team#Tom Wigley|Tom Wigley]], [[Team#Sarah Raper|Sarah Raper]] and [[Team#Malte Meinshausen|Malte Meinshausen]], do not mind to be offered co-authorship on publications, if our continued time investments helped you to produce nice results. Please understand though, that unless it is a joint research or publication project, our limited time (i.e. 24h a day) will generally not permit us to provide additional support. The User FAQs and Forum should help you though to get up and running.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Download_MAGICC6&diff=6Download MAGICC62013-06-17T10:17:46Z<p>Antonius Golly: Created page with "Given that MAGICC6 is used in many model intercomparison excercises and as the default model for the creation of the new [http://www.iiasa.ac.at/web-apps/tnt/RcpDb RCP scenari..."</p>
<hr />
<div>Given that MAGICC6 is used in many model intercomparison excercises and as the default model for the creation of the new [http://www.iiasa.ac.at/web-apps/tnt/RcpDb RCP scenarios], we provide you with a compiled version (for Windows machines) of MAGICC6. If you are an IAM modeller, there are [[For IAM Modellers|specific solutions for IAM Modellers]] to obtain MAGICC, if Windows is not for you. <br />
<br />
<br />
== Download == <br />
At magicc.org you will find a [http://www.magicc.org/download short registration form] to download your MAGICC6 version. It only takes a minute to complete and we will use the contact information to update you on any new version, if you wish. (Alternatively, download the [http://www.cgd.ucar.edu/cas/wigley/magicc/ MAGICC/SCENGEN 5.3] package). <br />
<br />
== The default RCP settings ==<br />
You can, if you wish, change all the parameter values for the set of more than 400 input parameters that MAGICC has. However, we recommend you run MAGICC6 using the RCP default settings. These default settings were used to produce the GHG concentrations for the new RCP scenarios and are described here: <br />
<br />
* Meinshausen, M., S. Smith, K. Calvin, J. Daniel, M. Kainuma, J. F. Lamarque, K. Matsumoto, S. Montzka, S. Raper, K. Riahi, A. Thomson, G. Velders and D. P. van Vuuren (2011). "The RCP greenhouse gas concentrations and their extensions from 1765 to 2300." Climatic Change 109(1): 213-241. [http://www.springerlink.com/content/96n71712n613752g/ freely available online] <br />
<br />
Regarding the CMIP4 and CMIP3 calibrations that were used for creating the RCP default settings, please find more information here: <br />
<br />
* Meinshausen, M., S. C. B. Raper and T. M. L. Wigley (2011). "Emulating coupled atmosphere-ocean and carbon cycle models with a simpler model, MAGICC6: Part I – Model Description and Calibration." Atmospheric Chemistry and Physics 11: 1417-1456. [http://www.atmos-chem-phys.net/11/1417/2011/acp-11-1417-2011.html freely available online]<br />
<br />
Thus, using the RCP default settings, you will get exactly the same version that we designed to perform the runs for the GHG concentrations in the RCP scenario process. This means that if you have a comparable set of input emissions, you could create your own GHG concentration trajectories, as if they would have been part of the RCP scenario process. This should be useful for a wide range of scientific research endeavors. Please note though, that unless we are involved in a joint research or publication project, we usually do not have the time answering user requests. In other words, the version comes as a "take-it-as-it-is" kind of package. <br />
<br />
==Citation ==</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Creating_MAGICC_Scenario_Files&diff=5Creating MAGICC Scenario Files2013-06-17T10:17:20Z<p>Antonius Golly: Created page with "= How to create your own emission scenario file for MAGICC6? = This is a quick recipe of how you can put your data into a ASCII fileformat that will work with MAGICC. Example..."</p>
<hr />
<div>= How to create your own emission scenario file for MAGICC6? =<br />
<br />
This is a quick recipe of how you can put your data into a ASCII fileformat that will work with MAGICC. Example files of the RCP scenarios can be downloaded from [http://www.pik-potsdam.de/~mmalte/rcps/ the RCP concentration calculations site] [only links labled "MAGICC"], e.g. [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP3PD.SCEN RCP3-PD] (sometimes as well called RCP2.6), [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP45.SCEN RCP45], [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP6.SCEN RCP6], or [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP85.SCEN RCP85]. Suitable scenario files have always the extension *.SCEN.<br />
<br />
== What ingredients do you need? ==<br />
<br />
1. In order to create an emission scenario file, you need the emission scenario data. Specifically, you need: <br />
* Fossil / Industrial carbon dioxide CO2 emissions in units GtC/yr (to convert from GtCO2/yr to GtC/yr, multiply by '12/44')<br />
* Landuse carbon dioxide CO2 emissions in units GtC/yr<br />
* Methane CH4 emissions in units MtCH4/yr<br />
* Nitrous oxide N2O emissions in units MtN/yr (note that to convert from MtN2O/yr to MtN/yr, multiply by '28/(28+16)')<br />
* Sulphate dioxide SO2 emissions in units MtS/yr<br />
* Carbon monoxide CO emissions in units MtCO/yr<br />
* Non-Methane Volatile Organic compounds NMVOC in units Mt/yr<br />
* Nitrogen Oxides NOx in units MtN/yr<br />
* Black Carbon BC in units Mt/yr<br />
* Organic Carbon OC in units Mt/yr <br />
* Ammonium NH3 in MtN/yr <br />
* Perfluorocarbons PFCs in the units kt/yr, namely CF4, C2F6, C6F14 <br />
* Hydrofluorocarbons HFCs in the units kt/yr, namely HFC23, HFC32, HFC43-10, HFC125, HFC134a, HFC143a, HFC227ea, HFC245fa <br />
* Sulfur hexafluoride SF6 in units kt/yr<br />
<br />
2. You need all these emission trajectories on the same points in time. MAGICC assumes linear interpolation between any years that are not provided. Thus, your time axis could either be 2000, 2005, 2050 and 2100, or, annual values or any other sequence of years as long as they monotonically increase. Note that historical emissions files are overwritten from the startpoint onwards, i.e. with the startpoint being your first year of your emission scenario, i.e. 2000 or 1990 or 2005. <br />
<br />
3. Optionally, you can prescribe all this data regionally. This has the advantage that MAGICC does not have to make guesses on what the regional distribution of your emissions are over time. The regional split up follows the five RCP regions, i.e. OECD, REF, ASIA, MAF and LAM, (where MAF and LAM are together the former ALM region of the SRES scenarios), as defined [http://www.iiasa.ac.at/web-apps/tnt/RcpDb/dsd?Action=htmlpage&page=about#regiondefs here]. In addition, you should specify emissions from international transport (i.e. the sum of aviation and shipping emissions) separately as the sixth region. Note that if you provide regional data, MAGICC expects the order of these data blocks to be GLOBAL, OECD, REF, ASIA, MAF, LAM, BUNKERS. And yes, globally aggregate emissions should be provided as well (although they will be ignored, if MAGICC is told to use the regional data..). <br />
<br />
== How do I format my scenario data? == <br />
<br />
Now that you have all your data, you have to take into account some formatting requirements of your ASCII .SCEN file. <br />
* Your file ending should be ".SCEN" and it should be an ASCII file under DOS standard. <br />
* The first line in your ASCII file consists of only one integer, ("20" in the example below), which specifies the number of prescribed years of your emission trajectory. For example, if your emission scenario is specified for the years, 2000, 2005, 2050 and 2100, then "4" is the number you should put into the top left corner of your ASCII file. <br />
* The second line consists of only one integer. Simplified speaking, this integer stands for whether you provide global data or regional data. The options are: <br />
** 11 - Global/World data only. <br />
** 21 - Global/World data plus the four SRES regions OECD90, REF, ASIA and ALM. See regional definition [http://www.ipcc.ch/ipccreports/sres/emission/index.php?idp=149 here]. <br />
** 31 - Global/World data plus the five RCP regions OECD, REF, ASIA, MAF and LAM. <br />
** 41 - Global/World data plus the five RCP regions OECD, REF, ASIA, MAF and LAM and international transport "BUNKERS". <br />
* The third line specifies the scenario name. Usually identical to the filename. <br />
* The fourth and fifth line are there for describing your scenario. <br />
* The sixth line is empty. <br />
* The seventh line contains WORLD as the regional definition for the first datablock. <br />
* The eights line contains first the YEARS column header and then the headers with the list of gases (note, column order is not variable, but fixed as shown in the example below). <br />
* The ninth line contains the units (only for the viewer as MAGICC expects the data to be in units as specified above). <br />
* The tenth line is the first data line. Note that the field width has to be 11 for every data column - with the years being integers and the other emissions being floating point numbers with four digits after the dot, as MAGICC uses the Fortran command READ(FILE_ID , '(I11 , 24F11.4)') to read in these datablock lines. <br />
* There are X data lines in total (including line 10), with X being the integer read in in the first line. <br />
* Afterwards, there are TWO empty lines as separator <br />
* Then, if regional flag is not set to 11, the header for the next regional block comes, i.e. "OECD". <br />
* Then there is one line with column headers (i.e. years and gas names) <br />
* Then there is one line with Units <br />
* Then comes the next data block and so on.. <br />
* After the last data block, two empty lines are again provided as separator. <br />
* Below these two empty lines, additional comments can be inserted, which will be ignored by MAGICC. <br />
<br />
<br />
<br />
== Example file ==<br />
<br />
This is how the header and first dataline of an emission scenario .SCEN file should look like. In this example, an array of 20 annual datapoints has been provided (hence first integer in line 1 being "20"), and the data is provided with regional detail of the RCP regions (plus bunkers) (hence "41" in second line, see description above). For full examples, see these files [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP3PD.SCEN RCP3-PD] (sometimes as well called RCP2.6), [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP45.SCEN RCP45], [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP6.SCEN RCP6], or [http://www.pik-potsdam.de/~mmalte/rcps/data/RCP85.SCEN RCP85]. <br />
<br />
<pre><br />
20<br />
41<br />
RCP3PD<br />
HARMONISED, EXTENDED FINAL RCP3-PD (Peak&Decline) Emission scenario for MAGICC6<br />
DATE: 26/11/2009 11:29:06; MAGICC-VERSION: 6.3.09, 25 November 2009<br />
<br />
WORLD<br />
YEARS FossilCO2 OtherCO2 CH4 N2O SOx CO NMVOC NOx BC OC NH3 CF4 C2F6 C6F14 HFC23 HFC32 HFC43-10 HFC125 HFC134a HFC143a HFC227ea HFC245fa SF6<br />
Yrs GtC GtC MtCH4 MtN2O-N MtS MtCO Mt MtN Mt Mt MtN kt kt kt kt kt kt kt kt kt kt kt kt<br />
2000 6.7350 1.1488 300.2070 7.4567 53.8413 1068.0009 210.6230 38.1623 7.8048 35.5434 40.0185 12.0000 2.3750 0.4624 10.3949 4.0000 0.0000 8.5381 75.0394 6.2341 1.9510 17.9257 5.5382 <br />
2001 6.8960 1.1320 303.4093 7.5029 54.4192 1066.7447 211.5938 38.2888 7.8946 35.7143 40.3916 11.9250 2.4344 0.4651 10.4328 5.3987 0.6470 9.0301 84.0409 7.4947 1.6450 19.7183 5.6990 <br />
2002 6.9490 1.2317 306.5787 7.5487 54.9960 1065.4692 212.5632 38.4153 7.9841 35.8846 40.7647 11.8480 2.4915 0.4058 10.4708 6.7974 1.2941 9.8853 94.7162 8.7389 2.5080 21.5109 5.8596 <br />
2003 7.2860 1.2256 309.7165 7.5942 55.5716 1064.1742 213.5311 38.5418 8.0734 36.0543 41.1377 11.7692 2.5464 0.3939 10.5083 8.1961 1.9411 12.0788 101.4157 9.9776 3.3410 23.3034 6.0202 <br />
2004 7.6720 1.2428 312.8241 7.6394 56.1461 1062.8596 214.4977 38.6683 8.1624 36.2233 41.5107 11.6885 2.5990 0.4062 10.5455 9.5948 2.5881 12.5074 113.9297 11.2136 4.2690 25.0960 6.1806<br />
<br />
...<br />
</pre><br />
<br />
Then, simply upload your scenario file on live.magicc.org and calculate climate effects following your own emission scenario.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Climate_Model_Description&diff=4Climate Model Description2013-06-17T10:16:54Z<p>Antonius Golly: Created page with "\subsection{From forcing to temperatures: the \\upwelling-diffusion climate model} \label{section_climatemodule} In the early stages, MAGICC's climate module evolved from the..."</p>
<hr />
<div>\subsection{From forcing to temperatures: the \\upwelling-diffusion climate model}<br />
\label{section_climatemodule}<br />
<br />
In the early stages, MAGICC's climate module evolved from the simple<br />
climate model introduced by \citet{Hoffert_1980_Role_DeapSea}.<br />
MAGICC's atmosphere has four boxes with zero heat capacity, one over<br />
land and one over ocean for each hemisphere. The atmospheric boxes<br />
over the ocean are coupled to the mixed layer of the ocean<br />
hemispheres, with a set of n-1 vertical layers below (see<br />
Fig.~\ref{fig_udebm_structure}). The heat exchange between the<br />
oceanic layers is driven by vertical diffusion and advection. In the<br />
previous model versions, the ocean area profile is uniform with<br />
depth and the corresponding downwelling is modeled as a stream of<br />
polar sinking water from the top mixed layer to the bottom layer. In<br />
this study, an updated upwelling-diffusion-entrainment (UDE) ocean<br />
model is implemented with a depth-dependent ocean area (from<br />
HadCM2). For simplicity, the following equations govern the uniform<br />
area upwelling-diffusion version of the model.<br />
Section~\ref{section_Appendix_implementation_UDE} provides details on the<br />
UDE algorithms.<br />
<br />
<br />
<br />
<br />
<br />
<br />
\subsubsection{Partitioning of feedbacks}<br />
<br />
In order to improve the comparability between MAGICC and AOGCMs, and<br />
following earlier versions of MAGICC, we use different feedback<br />
parameters over land and ocean. This requires an adjustable land to<br />
ocean warming ratio in equilibrium based on AOGCM results. Given<br />
that in equilibrium the oceanic heat uptake is zero, the global<br />
energy balance equation can be written as:<br />
<br />
\begin{eqnarray}<br />
\Delta Q_G=\lambda_G\Delta T_G=f_{L}\lambda_L \Delta T_{L} +<br />
f_{O}\lambda_O \Delta T_{O}<br />
\label{eq_globalenergybalance_equilibrium}<br />
\end{eqnarray}<br />
where $\Delta Q_G$, $\lambda_G$ and $\Delta T_G$ are the global-mean<br />
forcing, feedback, and temperature change, respectively. The right<br />
hand side uses the area fractions $f$, feedbacks $\lambda$, and mean<br />
temperature changes, $\Delta T$ for ocean ($O$) and land ($L$). As<br />
in earlier versions of MAGICC, the non-linear set of equations that<br />
determines $\lambda_O$ and $\lambda_L$ for a given set of<br />
equilibrium land-ocean warming ratio $RLO$ (=$\Delta T_L/\Delta<br />
T_O$), global-mean feedback $\lambda_G$, heat exchange and<br />
enhancement factors ($k$, $\mu$), is solved by an iterative<br />
procedure involving the set of linear<br />
Eqs.~(\ref{eq_fourboxequations_NO}--\ref{eq_fourboxequations_SL}),<br />
seeking the solution for $\lambda_L$ closest to $\lambda_G$. The<br />
procedure in version 6 has been modified slightly to take into<br />
account the time-constant radiative forcing pattern by CO$_2$ for<br />
the four boxes with hemispheric land/ocean regions, if prescribed.<br />
<br />
%f9<br />
\begin{figure}[t]\vspace*{2mm}<br />
\centering\includegraphics[width=8.3cm]<br />
{acpd-2007-0584-PartI-f09}<br />
\caption{The schematic structure of MAGICC's upwelling-diffusion energy balance module with<br />
land and ocean boxes in each hemisphere. The processes for heat transport in the ocean are<br />
deep-water formation, upwelling, diffusion, and heat exchange between the hemispheres. Not shown<br />
is the entrainment and the vertically depth-dependent area of the ocean layers<br />
(see Fig.~\ref{fig_udebm_tempprofile} and text).}<br />
\label{fig_udebm_structure}\end{figure}<br />
<br />
<br />
<br />
<br />
Following<br />
\citet{Wigley_Schlesinger_1985_AnalyticalSolutionsTemperature}, it<br />
is assumed that the atmosphere is in equilibrium with the underlying<br />
ocean mixed layer, so that the energy balance equation for the<br />
Northern Hemispheric ocean (NO) is:<br />
\begin{eqnarray}<br />
&f_{\rm NO}\lambda_{O}\Delta T_{\rm NO} =<br />
& \textrm{:infrared~outgoing~flux}\nonumber \\<br />
&f_{\rm NO}\Delta Q_{\rm NO} & \textrm{:forcing} \nonumber \\<br />
&+ k_{\rm LO}(\Delta T_{\rm NL} - \mu \Delta T_{\rm NO}) & \textrm{:land-ocean~heat~exchange} \nonumber \\<br />
&+ k_{\rm NS}\alpha(\Delta T_{\rm SO} - \Delta T_{\rm NO}) & \textrm{:hemispheric<br />
heat exch.}\label{eq_fourboxequations_NO}<br />
\end{eqnarray}<br />
where $\Delta T_{\rm NO}$ is the surface temperature change over the<br />
Northern Hemisphere ocean, $\Delta Q_{\rm NO}$ the radiative forcing<br />
over that region, $f_{\rm NO}$ the northern ocean's area fraction of<br />
the earth surface, $k_{\rm LO}$ the land-ocean heat exchange<br />
coefficient [W\,m{$^{-2}$}$^\circ$C$^{-1}$], a heat transport<br />
enhancement factor $\mu$ allowing for asymmetric heat exchange<br />
between land and ocean (1${\leq}\mu$ -- see<br />
Sect.~\ref{section_heatxchange_formulation} below), $k_{\rm NS}$ is<br />
the hemispheric heat exchange coefficient in the mixed layer.<br />
Following \citet{Raper_Cubasch_1996_Emulation_AOGCM_simplemodel}<br />
$\alpha$ is a sea-ice related adjustment factor to relate upper<br />
ocean temperature change to surface air temperature change (see<br />
Sect.~\ref{section_UD_equations}). Correspondingly, the equilibrium<br />
energy balance equations for the Northern Hemisphere land (NL),<br />
Southern Hemisphere ocean (SO) and Southern Hemisphere land (SL)<br />
are:<br />
<br />
\begin{eqnarray}<br />
f_{\rm NL}\lambda_{L}\Delta T_{\rm NL} &=& f_{\rm NL}\Delta Q_{\rm NL} \nonumber \\<br />
&&+ k_{\rm LO}(\mu \Delta T_{\rm NO} - \Delta T_{\rm NL})\label{eq_fourboxequations_NL}\\<br />
f_{\rm SO}\lambda_{O}\Delta T_{\rm SO} &=& f_{\rm SO}\Delta Q_{\rm SO} \nonumber \\<br />
&&+ k_{\rm LO}(\Delta T_{\rm SL} - \mu \Delta T_{\rm SO}) \nonumber \\<br />
&&+ k_{\rm NS}\alpha(\Delta T_{\rm NO} - \Delta T_{\rm SO})\label{eq_fourboxequations_SO}\\<br />
f_{\rm SL}\lambda_{L}\Delta T_{\rm SL} &=& f_{SL}\Delta Q_{SL} \nonumber \\<br />
&&+ k_{\rm LO}(\mu \Delta T_{\rm SO} - \Delta T_{\rm SL})\label{eq_fourboxequations_SL}<br />
\end{eqnarray}<br />
<br />
As detailed below (Sect.~\ref{section_feedback_depending_forcings}),<br />
if the sensitivity factor $\xi$ is set different from zero (see<br />
Eq.~\ref{eq_feedback_dependency_forcing}), it is possible to make<br />
the feedback factors $\lambda$ in the energy balance equation<br />
dependent on the total radiative forcing. This forcing dependence of<br />
the feedback factors and the heat exchange enhancement factors are<br />
newly introduced in this version of MAGICC. The following two<br />
sections.~(\ref{section_heatxchange_formulation} and<br />
\ref{section_heatxchange_formulation}) are intended to provide both<br />
the motivation and details of these new parameterizations.<br />
<br />
<br />
\subsubsection{Revised land-ocean heat exchange formulation}<br />
\label{section_heatxchange_formulation}<br />
<br />
<br />
This section highlights a ``geometric'' effect<br />
that can cause effective climate sensitivities to<br />
change over time. The global-mean sensitivity may increase simply<br />
due to decreasing land-ocean warming ratios, given that climate<br />
feedbacks over land and ocean areas are different. To control the<br />
relative temperature changes over ocean and land, a heat transport<br />
enhancement factor $\mu$ is introduced. Enhancing the ocean-to-land<br />
heat transport ($\mu{\geq}$1) has the benefit that the simple<br />
climate model can better simulate some characteristic AOGCM<br />
responses. In the idealized forcing runs, AOGCMs often show a<br />
transient land-ocean warming ratio that slightly decreases over<br />
time, but stays above unity, combined with an increasing effective<br />
climate sensitivity in some models (see bottom rows in<br />
Fig.~\ref{fig_AOGCMcalibration_part1of3}, \ref{fig_AOGCMcalibration_part2of3},<br />
and \ref{fig_AOGCMcalibration_part3of3}).<br />
The higher land than ocean warming (RLO${>}$1) could be achieved by<br />
a smaller feedback (greater climate sensitivity)<br />
over land compared to the ocean boxes. However, as the land-ocean warming ratio<br />
decreases over time (due to less and less ocean heat uptake towards equilibrium),<br />
so would the effective global-mean climate sensitivity in previous model versions.<br />
The method used here, to allow both a RLO above unity and a<br />
non-decreasing effective climate sensitivity, assumes that<br />
ocean temperature perturbations influence the heat<br />
exchange more than land temperature changes. This asymmetric heat<br />
exchange formulation is then given by:<br />
<br />
\begin{equation}<br />
{\rm HX}_{\rm LO}=k_{\rm LO}(\Delta T_{L} - \mu \Delta T_{O})<br />
\label{eq_heatxchange}<br />
\end{equation}<br />
where HX$_{\rm LO}$ is the land-ocean heat exchange (positive in<br />
direction land to ocean), $\mu$ is the ocean-to-land enhancement<br />
factor and $\Delta T_L$ and $\Delta T_O$ are the temperature<br />
perturbations for the land and ocean region, respectively<br />
(cf.~Eq.~\ref{eq_fourboxequations_NO} ff.). Typical values for $\mu$<br />
range between 1 and 1.4 as estimated from calibrating the CMIP3<br />
ensemble (see Table~\ref{table_AOGCM_calibrationvaluesIII}).<br />
<br />
<br />
\subsubsection{Accounting for climate-state dependent feedbacks}<br />
\label{section_feedback_depending_forcings}<br />
<br />
Some AOGCM runs indicate higher effective climate sensitivities for<br />
higher forcings and/or temperatures. For example, the ECHAM5/MPI-OM<br />
model shows an effective climate sensitivity of approximately<br />
3.5$^\circ$C after stabilization at twice pre-industrial CO$_2$<br />
concentrations and 4$^\circ$C for stabilization at quadrupled<br />
pre-industrial CO$_2$ concentrations (see<br />
Fig.~\ref{fig_increasing_ClimSens_CCSM3_ECHAM5}b -- \citealp[see as<br />
well ][]{Raper_Gregory_Osborn_2001_diagnosingAOGCMresults,<br />
Hansen_etal_2005_Efficacies}). Given that the transient land-ocean<br />
warming ratio is the same for the 1pctto2$\times$ and 1pctto4$\times$ runs (see<br />
Fig.~\ref{fig_AOGCMcalibration_part1of3} last row), the 'geometric'<br />
effect discussed in the Sect.~\ref{section_heatxchange_formulation}<br />
would not explain this increase in climate sensitivity. An<br />
alternative explanation could be that climate feedbacks are<br />
climate-state dependent. The assumption in the standard energy<br />
balance Eq.~(\ref{eq_globalenergybalance}) with a constant global<br />
feedback ($\lambda$), with its attendant requirement that the<br />
outgoing energy flux scales proportionally with temperature change,<br />
may be an oversimplification. For example, the slow feedback due to<br />
retreating ice-sheets can lead to changes in the diagnosed effective<br />
sensitivities in AOGCMs (see<br />
e.g.~\citealp{Raper_Gregory_Osborn_2001_diagnosingAOGCMresults})<br />
over long time-scales. \citet{Hansen_etal_2005_Efficacies} show that<br />
the 100-year climate response in the GISS model is more sensitive to<br />
higher forcings than to lower or negative forcings. Hansen et<br />
al.~(2005) express this effect by increasing efficacies for<br />
increasing radiative forcing. Table~1 in<br />
\citet{Hansen_etal_2005_Efficacies} suggests a gradient of roughly<br />
1\% increase in efficacy for each additional Wm$^{-2}$<br />
(OLS-regression of $E_a$ versus $F_a$ across the full range of CO$_2$<br />
experiments), although some intervals (e.g.~from 1.25 to<br />
1.5$\times$CO$_2$) show a slightly higher sensitivity of efficacy to<br />
forcing, i.e., 3\% per Wm$^{-2}$.<br />
<br />
Rather than making the efficacies dependent on forcing, an<br />
alternative is to make the climate sensitivity dependent on the<br />
forcing level. This distinction, on whether to modify forcing or<br />
sensitivity, is not important when the climate system is at or close<br />
to equilibrium. However, if the efficacies of the forcing, instead<br />
of the feedback parameters are allowed to vary with forcing, the<br />
transient climate response after a change in forcing will be<br />
slightly faster. In this MAGICC version, if a forcing dependency of<br />
the sensitivity is assumed, the land and ocean feedback parameters<br />
$\lambda_L$ and $\lambda_O$ are scaled as<br />
<br />
\begin{equation} \lambda =<br />
\frac{\Delta Q_{\rm 2\times}}{\frac{\Delta Q_{\rm 2\times}}{\lambda_{\rm 2\times}}+\xi(\Delta<br />
Q- \Delta Q_{\rm 2\times})} \label{eq_feedback_dependency_forcing}<br />
\end{equation}<br />
where $\lambda_{\rm 2\times}$ is the feedback parameter (=$\frac{\Delta<br />
Q_{\rm 2\times}}{\Delta T_{\rm 2\times}}$) at the forcing level for twice<br />
pre-industrial CO$_2$ concentrations. The sensitivity factor $\xi$<br />
(KW$^{-1}$\,m$^{2}$) scales the climate sensitivity in proportion to<br />
the difference of forcing away from the model-specific ``twice<br />
pre-industrial CO$_2$ forcing level'' ($\Delta Q{-} \Delta Q_{\rm 2\times}$).<br />
The 1\% increase in efficacy for each additional unit forcing in<br />
Hansen's findings translates into a feedback sensitivity factor<br />
$\xi$ of 0.03\,KW$^{-1}$\,m$^{2}$ (assuming a climate sensitivity<br />
\emph{$\Delta T_{\rm 2\times}$} of 3\,$^\circ$C). Note that this scaling<br />
convention (Eq.~\ref{eq_feedback_dependency_forcing}) ensures that<br />
climate sensitivities are comparable for the equilibrium warming<br />
that corresponds to twice preindustrial CO$_2$ concentration levels<br />
(see Table~\ref{table_AOGCM_climsenscomparison}).<br />
<br />
<br />
\subsubsection{Efficacies}<br />
\label{section_efficacies}<br />
<br />
Efficacy is defined as the ratio of<br />
global-mean temperature response for a particular radiative forcing<br />
divided by the global-mean temperature response for the same amount<br />
of global-mean radiative forcing induced by CO$_2$ \citep[see<br />
Sect.~2.8.5 in][]{Forster_Ramaswamy_etal_2007_IPCCAR4_Chapter2_radiativeForcing}.<br />
In most cases, the efficacies are different for different forcing<br />
agents because of the geographical and vertical distributions of the<br />
forcing<br />
\citep{Boer_Yu_2003_ClimateSensitivityResponse, Joshi_etal_2003_improvedmetric_climatechange, Hansen_etal_2005_Efficacies}. The effective radiative forcing<br />
($\Delta Q_e$) is the product of the standard climate forcing<br />
($\Delta Q_a$), calculated after thermal adjustment of the<br />
stratosphere, and the efficacy (E$_a$). It is the effective forcings<br />
that are used in the energy balance equation<br />
(Eq.~\ref{eq_globalenergybalance}), although both effective and<br />
standard forcings are carried through in the MAGICC code. Note that<br />
this parameterization yields slightly faster transient climate<br />
responses compared to an approach where different climate<br />
sensitivities are applied for each individual forcing agent<br />
(cf.~Sect.~\ref{section_feedback_depending_forcings} above).<br />
<br />
In MAGICC, forcings for some components differ by hemisphere and<br />
over land and ocean. Just as for the global sensitivity, this, in<br />
combination with different land/ocean feedback factors, results in<br />
MAGICC6 exhibiting efficacies different from unity for non-CO$_2$<br />
forcing agents. In other words, efficacies different from unity are<br />
in part a consequence of the geometric effect described above.<br />
MAGICC calculates these internal efficacies using reference year<br />
(default 2005) forcing patterns. After normalizing these forcing<br />
patterns to a global-mean of \emph{$\Delta Q_{\rm 2\times}$} (default<br />
3.71\,Wm$^{-2}$), the internal efficacy can be determined as<br />
<br />
\begin{equation}<br />
E_{\rm int} = \frac{\Delta T_{\rm eff2\times}}{\Delta T_{\rm 2\times}},<br />
\label{eq_efficacies_internal}<br />
\end{equation}<br />
where $T_{\rm eff2\times}$ is the actual global-mean equilibrium<br />
temperature change resulting from a normalized forcing pattern and<br />
\emph{$\Delta T_{\rm 2\times}$} is the corresponding warming for 2$\times$ CO$_2$<br />
forcing, i.e., the climate sensitivity. For most forcing agents,<br />
these internal efficacies are very close to one, except for forcings<br />
with a strong land/ocean forcing contrast, such as aerosol forcings.<br />
For example, for direct aerosol forcing in the HadCM3 emulation<br />
(calibration III -- see Table~\ref{tableB3})<br />
the efficacy is 1.14. By default, these internal efficacies are taken into<br />
account when applying prescribed efficacies, so that:<br />
<br />
\begin{equation} \Delta Q_e = \frac{E_a}{E_{\rm int}}\Delta Q_a<br />
\label{eq_efficacies_acc_for_intefficacies}<br />
\end{equation}<br />
<br />
\newpage<br />
<br />
\subsubsection{The upwelling-diffusion equations}<br />
\label{section_UD_equations}<br />
<br />
The transient temperature change<br />
evolution is largely influenced by the climate system's inertia,<br />
which in turn depends on the nature of the heat uptake by the<br />
climate system. The transient energy balance equations can be<br />
written as:<br />
<br />
\begin{eqnarray}<br />
f_{\rm NO}(\zeta_o \frac{d\Delta T_{\rm NO,1}}{dt}-\Delta Q_{\rm<br />
NO}+<br />
\lambda_o \alpha \Delta T_{\rm NO,1} + F_{N}) =\nonumber\\<br />
k_{\rm LO}(\Delta T_{\rm NL} - \mu\alpha\Delta T_{\rm NO,1})+k_{NS}<br />
\alpha(\Delta T_{\rm SO,1} - \Delta T_{\rm NO,1})\label{eq_transient_linear_equations_NO}\\<br />
f_{\rm NL}(\zeta_L \frac{d\Delta T_{\rm NL}}{dt} - \Delta Q_{\rm NL}<br />
+ \lambda_L \Delta T_{\rm NL}) =\nonumber\\<br />
k_{\rm LO}(\mu\alpha\Delta T_{\rm NO,1}-\Delta T_{\rm NL})\label{eq_transient_linear_equations_NL}\\<br />
f_{SO}(\zeta_o \frac{d\Delta T_{\rm SO,1}}{dt}-\Delta Q_{\rm SO}+<br />
\lambda_o \alpha \Delta T_{\rm SO,1} + F_{S}) =\nonumber\\<br />
k_{\rm LO}(\Delta T_{\rm SL} - \mu\alpha\Delta T_{\rm SO,1})+k_{\rm NS}<br />
\alpha(\Delta T_{\rm NO,1} - \Delta T_{\rm SO,1})\label{eq_transient_linear_equations_SO}\\<br />
f_{\rm SL}(\zeta_L \frac{d\Delta T_{\rm SL}}{dt} - \Delta Q_{\rm SL}<br />
+ \lambda_L \Delta T_{\rm SL}) =\nonumber\\<br />
k_{\rm LO}(\mu\alpha\Delta T_{\rm SO,1}-\Delta T_{\rm<br />
SL})\label{eq_transient_linear_equations_SL}<br />
\end{eqnarray}<br />
where the adjustment factor $\alpha$ (default 1.2) determines --<br />
over ocean areas -- the ratio of hemispheric changes in air ($\Delta<br />
T_{\rm xO}$) versus ocean mixed layer temperatures ($\Delta T_{\rm<br />
xO,1}$). Based on ECHAM1/LSG analysis<br />
\citep{Raper_Cubasch_1996_Emulation_AOGCM_simplemodel}, this sea-ice<br />
factor was first introduced by<br />
\citet{Raper_Gregory_Osborn_2001_diagnosingAOGCMresults} to account<br />
for the fact that the air temperature will exhibit additional<br />
warming, because the atmosphere feels warmer ocean surface<br />
temperatures where sea ice retreats. The bulk heat capacity of the<br />
mixed layer in each hemisphere $x$ is $f_x\zeta_o{=}f_x\rho c h_m$,<br />
where $\rho$ denotes the density of seawater<br />
(1.026$\times$10$^6$\,g\,m$^{-3}$), c is the specific heat capacity<br />
(0.9333\,cal\,g$^{-1}$$^\circ$C$^{-1}${=}4.1856$\times$0.9333\,Joule\,g$^{-1}$$^\circ$C$^{-1}$)<br />
and $h_m$ is the mixed layer's thickness [m]. The bulk heat capacity<br />
of the land areas is $f_x\zeta_L$, here assumed to be zero. The net<br />
heat flux into the ocean below the mixed layer is denoted by $F_x$.<br />
<br />
Equation~(\ref{eq_transient_linear_equations_NL}) can then be<br />
written as:<br />
\begin{eqnarray}<br />
\Delta T_{\rm NL} = \frac{f_{\rm NL}\Delta Q_{\rm NL}+k_{\rm<br />
LO}\mu\alpha\Delta T_{\rm NO,1}}{f_{\rm NL}\lambda_L + k_{\rm LO}}<br />
\label{eq_transient_separating_TNL}<br />
\end{eqnarray}<br />
Substituting $\Delta T_{\rm NL}$ in<br />
Eq.~(\ref{eq_transient_linear_equations_NO}) yields:<br />
\begin{eqnarray}<br />
f_{\rm NO}(\zeta_o \frac{d\Delta T_{\rm NO,1}}{dt} -<br />
\Delta Q_{\rm NO} + \lambda_o \alpha\Delta T_{\rm NO,1} + F_N) = \nonumber \\<br />
\frac{k_{\rm LO}}{\frac{k_{\rm LO}}{f_{\rm NL}}+\lambda_L}(\Delta<br />
Q_{\rm NL}-\lambda_L\mu\alpha \Delta<br />
T_{\rm NO,1})\nonumber\\<br />
+ k_{\rm NS}\alpha(\Delta T_{\rm SO,1} - \Delta T_{\rm NO,1})<br />
\label{eq_transient_TNL_into_TNO}<br />
\end{eqnarray}<br />
Provided we know the heat flux $F_N$ into the ocean below the mixed<br />
layer, we could now derive $d\Delta T_{\rm NO,1}/dt$. The net heat<br />
flux $F_N$ at the bottom of the mixed layer is determined by<br />
vertical heat diffusivity (diffusion coefficient $K_z$<br />
[cm$^2$\,s$^{-1}${=}$3155.76^{-1}$\,m$^2$\,yr$^{-1}$]), and<br />
upwelling and downwelling (upwelling velocity $w$ [m yr$^{-1}$]), both<br />
acting on the perturbations $\Delta T$ from the initial temperature<br />
profile $T^0_{\rm NO,z}$. If the upwelling rate $w$ varies over<br />
time, the change in upwelling velocity $\Delta w^t{=}(w^t-w^0)$<br />
compared to its initial state $w^0$ is assumed to act on the initial<br />
temperature profile, so that:<br />
\begin{eqnarray}<br />
F_N = \frac{K_z}{0.5h_d}\rho c (\Delta T_{\rm NO,1}-\Delta T_{\rm NO,2}) \nonumber \\<br />
- w \rho c (\Delta T_{\rm NO,2} - \beta \Delta T_{\rm NO,1})\nonumber \\<br />
- \Delta w \rho c (T^0_{\rm NO,2}- T^0_{\rm NO,sink})<br />
\label{eq_transient_heatflux_bottom_mixedlayer}<br />
\end{eqnarray}<br />
where $T^0_{\rm NO,z}$ is the initial temperature for water in layer<br />
$z$ or in the downwelling pipe ($z$\,{=}\,``sink'').<br />
<br />
Given that the top layer is assumed to be mixed, the gradient of the<br />
temperature perturbations is calculated by the difference of the<br />
perturbations divided by half the thickness $h_d$ of the second<br />
layer (see Fig.~\ref{fig_udebm_tempprofile}). Substituting $F_N$ in<br />
Eq.~(\ref{eq_transient_TNL_into_TNO}) with<br />
Eq.~(\ref{eq_transient_heatflux_bottom_mixedlayer}) and transforming<br />
the equation to discrete time steps, yields:<br />
\begin{eqnarray}<br />
\frac{d\Delta T_{\rm NO,1}}{dt} \approx \frac{\Delta<br />
T_{\rm NO,1}^{t+1} - \Delta T_{\rm NO,1}^{t}}{\Delta t} =& \\<br />
\frac{1}{\zeta_o}\Delta Q_{\rm NO}^t & \textrm{:forcing} \nonumber \\<br />
- \frac{\lambda_o \alpha}{\zeta_o}\Delta T_{\rm NO,1}^{t+1} &<br />
\textrm{:feedback}\nonumber \\<br />
-\frac{K_z}{0.5h_d h_m}(\Delta T_{\rm NO,1}^{t+1}-\Delta T_{\rm NO,2}^{t+1}) & \textrm{:diffusion} \nonumber \\<br />
+ \frac{w^{t}}{h_m}(\Delta T^{t+1}_{\rm NO,2}-\beta \Delta T^{t+1}_{\rm NO,1}) & \textrm{:upwelling} \nonumber \\<br />
+ \frac{\Delta w^{t}}{h_m}(T^{0}_{\rm NO,2}-T^{0}_{\rm NO,sink}) &<br />
\textrm{:variable upwelling} \nonumber \\<br />
+ \frac{k_{\rm LO}(\Delta Q^{t}_{\rm NL}-\lambda_L \mu\alpha\Delta<br />
T^{t+1}_{\rm NO,1})}{\zeta_o f_{\rm NO}(\frac{k_{\rm LO}}{f_{\rm<br />
NL}}+\lambda_L)} & \textrm{:land forcing} \nonumber \\<br />
\nonumber + \frac{k_{\rm NS}\alpha}{\zeta_o f_{\rm NO}}(\Delta T_{\rm<br />
SO,1}^{t}-\Delta T_{\rm NO,1}^{t}) & \textrm{:inter-hemispheric ex.}<br />
\label{eq_transient_discrete_NO_mixed}<br />
\end{eqnarray}<br />
For the layers below the mixed layer (2$\leq$z$\leq$n--1), the<br />
temperature updating is governed<br />
by diffusion (first two<br />
terms in Eq.~\ref{eq_transient_discrete_NO_submixed}) and upwelling<br />
(last two terms), so that:<br />
\begin{eqnarray}<br />
\frac{\Delta T^{t+1}_{{\rm NO},z}-\Delta T^{t}_{{\rm NO},z}}{\Delta t}= \nonumber \\<br />
\frac{K_z}{0.5(h_d+h_d')h_d}(\Delta T^{t+1}_{{\rm NO},z-1}-\Delta T^{t+1}_{{\rm NO},z}) \nonumber \\<br />
- \frac{K_z}{h_d^2}(\Delta T^{t+1}_{\rm NO,z}-\Delta T^{t+1}_{{\rm NO},z+1})\nonumber \\<br />
+ \frac{w^{t}}{h_d}(\Delta T^{t+1}_{{\rm NO},z+1}-\Delta T^{t+1}_{{\rm NO},z}) \nonumber \\<br />
+ \frac{\Delta w^{t}}{h_d}(T^0_{{\rm NO},z+1}-T^0_{{\rm NO},z})<br />
\label{eq_transient_discrete_NO_submixed}<br />
\end{eqnarray}<br />
where $h_d'$ is zero for the layer below the mixed layer ($z${=}2) and<br />
$h_d$ otherwise, $\Delta w^t$ is the change from the initial<br />
upwelling rate.<br />
<br />
<br />
<br />
For the bottom layer ($z = n$), the downwelling term has to be taken<br />
into account, so that:<br />
\begin{eqnarray}<br />
\frac{\Delta T^{t+1}_{{\rm NO},n}-\Delta T^{t}_{{\rm NO},n}}{\Delta t}=<br />
\frac{K_z}{h_d^2}(\Delta T^{t+1}_{{\rm NO,n}-1}-\Delta T^{t+1}_{{\rm NO},n}) \nonumber \\<br />
+ \frac{w^{t}}{h_d}(\beta\Delta T^{t}_{\rm NO,1}-\Delta T^{t+1}_{{\rm NO},n}) \nonumber \\<br />
+ \frac{\Delta w^{t}}{h_d}(T^0_{\rm NO,sink}-T^0_{{\rm NO},n})<br />
\label{eq_transient_discrete_NO_bottom}<br />
\end{eqnarray}<br />
<br />
Corresponding to the temperature calculations shown here for the<br />
Northern Hemisphere ocean (NO), the equivalent steps apply for the<br />
Southern Hemisphere ocean (SO). For simplicity, the equations<br />
described above are for the constant-depth area profile case, which<br />
MAGICC defaults to when the depth-dependency factor $\vartheta$ is<br />
set to zero. The detailed code for the general case with<br />
$0{\leq}\vartheta{\leq}1$ is given in<br />
Sect.~\ref{section_Appendix_implementation_UDE}.<br />
<br />
\subsubsection{Calculating heat uptake}<br />
\label{section_Appendix_HeatUptake}<br />
<br />
Heat uptake by the climate system can be calculated in different<br />
ways. One method is to use the global energy balance<br />
(Eq.~\ref{eq_globalenergybalance}). Using the effective sensitivity<br />
as in Eq.~(\ref{eq_globalenergybalance_equilibrium}) the heat uptake<br />
$F^t$ is estimated as:<br />
\begin{eqnarray}<br />
\frac{dH^t}{dt}=F^t = \Delta Q^t-(f_L \lambda_L \Delta T^t_{L} + f_O<br />
\lambda_O \Delta T^t_{O}) \label{eq_heatuptake_balance}<br />
\end{eqnarray}<br />
<br />
%f10<br />
\begin{figure}[t]\vspace*{2mm}<br />
\centering\includegraphics[width=8.3cm]{acpd-2007-0584-PartI-f10}<br />
\caption{The schematic oceanic area and initial temperature profiles in MAGICC's ocean hemispheres.<br />
Diffusion driven heat transport is modeled proportional to the vertical gradient of temperature,<br />
which is especially high below the mixed layer. } \label{fig_udebm_tempprofile}\end{figure}<br />
<br />
<br />
For verification purposes MAGICC6 calculates heat uptake in two<br />
ways, both directly (as above) and by integrating heat content<br />
changes in each layer in the ocean (yielding identical results),<br />
given the assumed zero heat capacity of the atmosphere and land<br />
areas:<br />
\begin{eqnarray}<br />
\Delta H^t = \sum^{n}_{i=1} \frac{1}{\rho c h_i}\frac{(f_{\rm NO}<br />
\Delta T^t_{\rm NO,i} + f_{\rm SO} \Delta T^t_{\rm<br />
SO,i})}{f_O}+\epsilon \label{eq_heatuptake_integrating}<br />
\end{eqnarray}<br />
where $h_i$ is the thickness of the layer, i.e., $h_m$ for the mixed<br />
layer and $h_d$ for the others and $\epsilon$ is a small term to<br />
account for the heat content of the polar sinking water.<br />
<br />
<br />
<br />
\subsubsection{Depth-dependent ocean with entrainment}<br />
\label{section_depthdependency_ocean}<br />
<br />
\citet{Harvey_Schneider_1985_PartII, Harvey_Schneider_1985_PartI}<br />
introduced the upwelling-diffusion model with entrainment from the<br />
polar sinking water by varying the upwelling velocity $w$ with depth.<br />
Building on the work by<br />
\citet{Raper_Gregory_Osborn_2001_diagnosingAOGCMresults}, MAGICC6<br />
also includes the option of a depth-dependent ocean area profile. If<br />
the depth-dependency parameter $\vartheta$ is set to 1 (default), a<br />
standard depth-dependent ocean area profile is assumed as in HadCM2<br />
and used in<br />
\citet{Raper_Gregory_Osborn_2001_diagnosingAOGCMresults}. A constant<br />
upwelling velocity is assumed and mass conservation is maintained by<br />
``entrainment'' from the downwelling pipe. With ocean area decreasing<br />
with depth and constant upwelling velocity, the upwelling mass flux<br />
would also have to decrease with depth. To offset this, the amount<br />
of entrainment into layer $z$ is assumed to be proportional to the<br />
decrease in area from the top to the bottom of each layer (cf.\<br />
Fig.~\ref{fig_udebm_tempprofile}). We differ from the model<br />
structures tested by<br />
\citet{Raper_Gregory_Osborn_2001_diagnosingAOGCMresults}, by<br />
equating changes in the temperature of the entraining water to those<br />
in the downwelling pipe, namely a fraction $\beta$ (default 0.2) of<br />
the mixed layer temperature $\Delta T_{x,1}^{t-1}$ of the previous<br />
timestep in Hemisphere $x$. For a detailed description of the code,<br />
see the following Sect.~\ref{section_Appendix_implementation_UDE}.<br />
Simple upwelling-diffusion models can overestimate the ocean heat<br />
uptake for higher warming scenarios when applying parameter values<br />
calibrated to match heat uptake for lower warming scenarios (see<br />
e.g.~Fig.~17b in<br />
\citealp{Harvey_etal_1997_IPCC_IntroductionSimpleClimateModels}). To<br />
address this, MAGICC6 includes a warming-dependent vertical<br />
diffusivity gradient. The physical reasoning is that a strengthened<br />
thermal stratification and, hence, reduced vertical mixing leads to<br />
decreased heat uptake for higher warming. Thus, the effective<br />
vertical diffusivity at $K_{z,i}$ between ocean layer $i$ and $i$+1 is<br />
given by:<br />
\begin{eqnarray}<br />
K_{z,i} = {\rm max}\,(K_{z,{\rm min}}(1 - d_i)\frac{dK_{\rm<br />
z}}{dT}(\Delta T_{H,1}^{t-1}-\Delta T_{H,n}^{t-1})+K_z)<br />
\label{eq_verticalDiffusivity_heatdependent}<br />
\end{eqnarray}<br />
where $K_{z,{\rm min}}$ is the minimum vertical diffusivity (default<br />
0.1\,cm$^2$\,s$^{-1}$); $d_i$ is the relative depth of the layer<br />
boundary with zero at the bottom of the mixed layer and one for the<br />
top of the bottom layer; $\frac{dK_{\rm z}}{dT}$ is a newly<br />
introduced ocean stratification coefficient specifying how the<br />
vertical diffusivity $K_{\rm z}$ between the mixed layer 1 and layer<br />
2 changes with a change in the temperature difference between the<br />
top/mixed and bottom ocean layer of the respective hemisphere at the<br />
previous timestep $t-$1 $(\Delta T_{H,1}^{t-1}{-}\Delta<br />
T_{H,n}^{t-1})$.<br />
<br />
<br />
<br />
\subsection{Implementation of upwelling-diffusion-entrainment\\<br />
equations} \label{section_Appendix_implementation_UDE}<br />
<br />
This section details how the equations governing the<br />
upwelling-diffusion-entrainment (UDE) ocean<br />
(Eqs.~\ref{eq_transient_discrete_NO_mixed}, \ref{eq_transient_discrete_NO_submixed}, \ref{eq_transient_discrete_NO_bottom})<br />
are implemented and modified by entrainment terms and depth-dependent ocean area (see<br />
Fig.~\ref{fig_udebm_tempprofile}). These equations represent the<br />
core of the UDE model and build on the initial work by<br />
\citet{Hoffert_1980_Role_DeapSea, Harvey_Schneider_1985_PartII, Harvey_Schneider_1985_PartI}.<br />
<br />
The entrainment is here modeled so that the upwelling velocity in<br />
the main column is the same in each layer. Thus, the three area<br />
correction factors, $\theta_z^{\rm top}$, $\theta_z^{b}$ and<br />
$\theta_z^{\rm dif}$, applied below are:<br />
<br />
\begin{eqnarray}<br />
\theta_z^{\rm top} = \frac{A_z}{(A_{z+1}+A_z)/2}\nonumber\\<br />
\theta_z^{b} = \frac{A_{z+1}}{(A_{z+1}+A_z)/2} \nonumber\\<br />
\theta_z^{\rm dif} = \frac{A_{z+1}-A_{z}}{(A_{z+1}+A_z)/2} \nonumber\\<br />
\label{eq_areacorrection_thetatop}<br />
\end{eqnarray}<br />
where $A_z$ is the area at the top of layer $z$ or bottom of layer $z-1$<br />
and the denominator is thus an approximation for the mean area of<br />
each ocean layer.<br />
<br />
For the mixed layer, all terms in<br />
Eq.~(\ref{eq_transient_discrete_NO_mixed}) involving $\Delta<br />
T^{t+1}_{\rm NO,1}$ are collected on the left hand side in variable<br />
$A(1)$. All terms involving $\Delta T^{t+1}_{\rm NO,2}$ are<br />
collected in variable $B(1)$ on the left hand side. All other terms<br />
are held in variable $D(1)$ on the right hand side, so that the<br />
equation reads:<br />
<br />
\begin{eqnarray}<br />
\Delta T_{\rm NO,1}^{t+1} = -\frac{B(1)}{A(1)}\Delta T_{\rm<br />
NO,2}^{t+1} + \frac{D(1)}{A(1)} \label{eq_udebm_coding_ALL1}<br />
\end{eqnarray}<br />
with<br />
\begin{equation}\label{eq_udebm_coding_A1}<br />
A(1) = 1.0+\theta_1^{\rm top}\Delta t\frac{ \lambda_O\alpha}{\zeta_o} \quad \textrm{:feedback over ocean}<br />
\end{equation}<br />
\[+\theta_1^{b}\Delta t\frac{ K_z}{0.5h_m h_d} \quad \textrm{:diffusion to layer 2}<br />
\]<br />
\[+\theta_1^{b}\Delta t\frac{ w^t \beta}{h_m} \quad \textrm{:downwelling} \]<br />
\[+\theta_1^{\rm top}\Delta t\frac{ k_{\rm LO}\lambda_L\mu\alpha }{\zeta_o f_{\rm NO}<br />
(\frac{k_{\rm LO}}{f_{\rm NL}} + \lambda_L)} \quad \textrm{:feedback over<br />
land}\]<br />
\begin{equation}\label{eq_udebm_coding_B1}B(1) = -\theta_1^{b}\Delta t\frac{ K_z}{0.5h_m h_d} \quad \textrm{:diffusion from layer 2}<br />
\end{equation}<br />
\[-\theta_1^{b}\Delta t\frac{ w^t}{h_m} \quad \textrm{:upwelling from layer<br />
2}\]<br />
\begin{equation}\label{eq_udebm_coding_D1}D(1) = \Delta T_{\rm NO,1}^{t} \quad \textrm{:previous temp} \end{equation}<br />
\[+ \theta_1^{\rm top}\Delta t\frac{1}{\zeta_o}\Delta Q_{NO} \quad \textrm{:forcing ocean}<br />
\]<br />
\[+ \theta_1^{\rm top}\Delta t\frac{\alpha k_{NS}}{\zeta_o f_{NO}}(\Delta T^t_{\rm SO,1}-\Delta T^t_{NO,1}) \quad \textrm{:inter-hemis.<br />
exch.}\]<br />
\[+ \theta_1^{\rm top}\Delta t\frac{ k_{LO}\Delta Q_{NL}}{\zeta_o f_{NO} (\frac{k_{LO}}{f_{NL}} + \lambda_L)} \quad \textrm{:land<br />
forcing}\]<br />
\[+ \theta_1^{b}\Delta t\frac{\Delta w^t}{h_m}(T^0_{\rm NO,2}-<br />
T^0_{NO,sink}) \quad \textrm{:variable upwelling}\]<br />
<br />
<br />
<br />
For the interior layers (2${\leq}z{\leq}n$), i.e., all layers<br />
except the top mixed layer and the bottom layer, the terms are<br />
re-ordered, so that A(z) comprises the terms for $\Delta<br />
T^{t+1}_{\rm NO,z-1}$, $B(z)$ the terms for $\Delta T^{t+1}_{\rm<br />
NO,z}$, C(z) the terms for $\Delta T^{t+1}_{\rm NO,z+1}$ and $D(z)$<br />
the remaining terms, according to:<br />
<br />
\begin{equation}<br />
\Delta T_{\rm NO,z-1}^{t+1} = -\frac{B(z)}{A(z)}\Delta T_{\rm<br />
NO,z}^{t+1} - \frac{C(z)}{A(z)}\Delta T_{\rm NO,z+1}^{t+1} +<br />
\frac{D(z)}{A(z)} \label{eq_udebm_coding_ALLmiddle}<br />
\end{equation}<br />
with<br />
\begin{equation}<br />
\scalebox{.84}[.84]{\lefteqn{A(z) = - \theta_z^{top}\Delta t\frac{K_z}{0.5(h_d+h_d')h_d} \quad \textrm{:diffusion from layer above}<br />
\label{eq_udebm_coding_Amiddle}}}<br />
\end{equation}<br />
\[B(z) = 1.0 + \theta_z^{b}\Delta t\frac{K_z}{h_d^2} \quad \textrm{:diffusion to layer below}<br />
\nonumber\]<br />
\[+\theta_z^{top}\Delta t\frac{K_z}{0.5(h_d+h_d')h_d} \quad \textrm{:diffusion to layer above}<br />
\]<br />
\begin{equation}<br />
+\theta_z^{top}\Delta t\frac{ w^t}{h_d} \quad \textrm{:upwelling to layer above} \label{eq_udebm_coding_Bmiddle}<br />
\end{equation}<br />
\[C(z) = - \theta_z^{b}\Delta t\frac{K_z}{h_d^2} \quad \textrm{:diffusion from layer<br />
below}\]<br />
\begin{equation}<br />
-\theta_z^{b}\Delta t\frac{ w^t}{h_d} \quad \textrm{:upwelling from layer below} \label{eq_udebm_coding_Cmiddle}\\<br />
\end{equation}<br />
\[D(z) = \Delta T_{\rm NO,z}^{t} \quad \textrm{:previous temp}\]<br />
\[+\Delta t\frac{\Delta w^t}{h_d} (\theta_z^{b}T^{0}_{\rm<br />
NO,z+1}-\theta_z^{top}T^{0}_{\rm NO,z}) \quad \textrm{:variable upwelling}\]<br />
\[+\theta_z^{\rm dif}\Delta t\frac{ w^t}{h_d}\beta\Delta T_{\rm<br />
NO,1}^{t-1}\quad \textrm{:entrainment}\]<br />
\begin{equation}<br />
+\theta_z^{\rm dif}\Delta t\frac{\Delta w^t}{h_d} T^{0}_{\rm<br />
NO,sink} \quad \textrm{:variable entrainment}<br />
\label{eq_udebm_coding_Dmiddle}<br />
\end{equation}<br />
where $h_d'$ is zero for the layer below the mixed layer and $h_d$<br />
otherwise. For the bottom layer, the respective sum factor $A(n)$ for<br />
$\Delta T^{t+1}_{\rm NO,n-1}$, $B(n)$ for $\Delta T^{t+1}_{\rm NO,n}$<br />
and $D(n)$ for the remaining terms is:<br />
<br />
<br />
<br />
\begin{eqnarray}<br />
\Delta T_{{\rm NO},n-1}^{t+1} = -\frac{B(n)}{A(n)}\Delta T_{{\rm<br />
NO},n}^{t+1} + \frac{D(n)}{A(n)} \label{eq_udebm_coding_Alln}<br />
\end{eqnarray}<br />
with<br />
\begin{equation}<br />
A(n) = - \theta_{n}^{\rm top}\Delta t\frac{K_z}{h_d^2}<br />
\quad \textrm{:diffusion from layer n-1} \label{eq_udebm_coding_An}<br />
\end{equation}<br />
\begin{equation}\label{eq_udebm_coding_Bn}<br />
B(n) = 1.0 + \theta_{n}^{\rm top}\Delta t\frac{K_z}{h_d^2}<br />
\quad \textrm{:diffusion to layer n-1}\end{equation}<br />
\[+\theta_{n}^{\rm top}\Delta t\frac{ w^t}{h_d} \quad<br />
\textrm{:upwelling to layer n-1} \]<br />
\begin{equation}\label{eq_udebm_coding_Dn}D(n) = \Delta T_{{\rm NO},n}^{t} \quad \textrm{:previous temp} \end{equation}<br />
\[+\theta_{n}^{\rm top}\Delta t\frac{w^t}{h_d} \beta\Delta<br />
T^{t-1}_{\rm NO,1} \quad \textrm{:downwelling from top layer} \]<br />
\[-\theta_{n}^{\rm top}\Delta t\frac{\Delta w^t}{h_d}<br />
T^{0}_{{\rm NO},n} \quad \textrm{:variable upwelling}\]<br />
\[+\theta_{n}^{\rm top}\Delta t\frac{\Delta w^t}{h_d} T^{0}_{\rm<br />
NO,sink} \quad \textrm{:variable downwelling}<br />
\]<br />
<br />
With these Eqs.~(\ref{eq_udebm_coding_ALL1}--\ref{eq_udebm_coding_Dn}), the<br />
ocean temperatures can be solved consecutively from the bottom to<br />
the top layer at each time step.</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Bug_Report&diff=3Bug Report2013-06-17T10:16:27Z<p>Antonius Golly: Created page with "We moved this section to the liveMAGICC website. You can now find the bug tracker under: [http://live.magicc.org/bugtracker live.magicc.org/bugtracker]."</p>
<hr />
<div>We moved this section to the liveMAGICC website. You can now find the bug tracker under: [http://live.magicc.org/bugtracker live.magicc.org/bugtracker].</div>Antonius Gollyhttp://wiki.magicc.org/index.php?title=Main_Page&diff=2Main Page2013-06-17T10:15:59Z<p>Antonius Golly: </p>
<hr />
<div>Welcome to the MAGICC Wiki. Here, we provide you with model descriptions, FAQs, user instructions and more ... all around the latest version of the "Model for the Assessment of Greenhouse Gas Induced Climate Change", i.e. MAGICC. <br />
<br />
<br />
[[File:MAGICC_logo_small.jpg|right]]<br />
<br />
<br />
[[Model_Description|Model Description]] - See what is behind MAGICC, a complete scientific description of datasets and parameterisations used in MAGICC6. <br />
<br />
[[Online_Help|Access MAGICC6 online]] - Help files and instructions for using our online interface [http://live.magicc.org live.magicc.org] for running MAGICC6 on our servers. <br />
<br />
[[Download MAGICC6|Download MAGICC6]] - Download and installation instructions for MAGICC6 executable.<br />
<br />
[[MAGICC6 User FAQ|Frequently Asked Questions]] - Find answers to the frequently asked questions regarding the Magicc6 model.<br />
<br />
[[For IAM Modellers|For IAM Modellers]] - Find information if you like to include MAGICC in an Integrated Assessment Model.<br />
<br />
[[MAGICC_projects|MAGICC Projects]] - See a list of publications that have made various uses of MAGICC in the past. <br />
<br />
[[MAGICC_team|MAGICC Team]] - Meet the MAGICC Development Team, Tom Wigley, Sarah Raper and Malte Meinshausen.</div>Antonius Golly