View source for Non-CO2 Concentrations

*[[Model Description|model description]]
**[[The Carbon Cycle| carbon cycle]]
**[[Non-CO2 Concentrations | non-CO2 concentrations]]
**[[Radiative Forcing | radiative forcing routines]]
**[[Upwelling_diffusion_climate_model | climate model]]
**[[Upwelling Diffusion Entrainment Implementation | upwelling-diffusion-entrainment implementation]]


==Non-CO<sub>2</sub> concentrations==

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.

===Methane===

Natural emissions of methane are inferred by balancing the budget for a user-defined historical period, e.g. from 1980-1990, so that

<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>

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 

<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>

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:

<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>

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 

<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>

Approximating the temperature sensitivity of the net effect of tropospheric chemical reaction rates, the tropospheric lifetime of CH<math>_4</math> is adjusted:

<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>

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.

===Nitrous oxide===

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:

<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>

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.

===Tropospheric aerosols===

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
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.

===Halogenated gases===

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:

<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>

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.