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modules/15_climate/box/equations.gms
+ 179
− 116
@@ -8,129 +8,192 @@
ta2ttot10(ta10, ttot)$((ttot.val lt ta10.val) AND (pm_ttot_val(ttot+1) gt ta10.val)AND (ttot.val ge 2005)) = Yes;
display ttot2ta10, ta2ttot10;
*** taken from box-model.inc ---------------------------
*** carbon cycle
* AL changed towards an IRF Model with 2 or 3 time scales
***---------------------------------------------------------------------------
*' Carbon Cycle. CO2 concentration is calculated using and Impulse-Response-Function Model with 3 time scales
***---------------------------------------------------------------------------
q15_cc(ta10)$(ord(ta10) ge 1)..
v15_conc(ta10,'CO2') =e= s15_c0 + ((s15_c2000-s15_c0)/(s15_ca0*s15_cq0+s15_ca1*s15_cq1+s15_ca2*s15_cq2+s15_ca3*s15_cq3))*
(s15_ca0*s15_cq0 + s15_ca1*s15_cq1*exp(-(ord(ta10)-1)/s15_ctau1) + s15_ca2*s15_cq2*exp(-(ord(ta10)-1)/s15_ctau2) + s15_ca3*s15_cq3*exp(-(ord(ta10)-1)/s15_ctau3))+
s15_cconvi*sum((tx)$(ord(tx)lt ord(ta10)),v15_emi(tx,'CO2')*p15_epsilon(ta10-ord(tx)));
*** N20 concentration (from ACC2)
q15_concN2OQ(ta10) $(Ord(ta10) GT 1) .. (v15_conc(ta10,'N2O')-v15_conc(ta10-1,'N2O'))/s15_DELTAT =E= 0.5*
((1/s15_CNVN2O*(v15_emi(ta10,'N2O')+ s15_NATN2O)-(1/s15_TAUN2O*(v15_conc(ta10,'N2O')/s15_CONN2O2000R)**(-s15_SENTAUN2O)*v15_conc(ta10,'N2O')))+
(1/s15_CNVN2O*(v15_emi(ta10-1,'N2O')+ s15_NATN2O)-(1/s15_TAUN2O*(v15_conc(ta10-1,'N2O')/s15_CONN2O2000R)**(-s15_SENTAUN2O)*v15_conc(ta10-1,'N2O'))));
*** end of stuff taken from box-model.inc ---------------------------
*** taken from box-model.inc ---------------------------
q15_concCH4Q(ta10) $(Ord(ta10) GT 1) .. (v15_conc(ta10,'CH4')-v15_conc(ta10-1,'CH4'))/s15_DELTAT =E= 0.5*
((1/s15_CNVCH4*(v15_emi(ta10,'CH4')+ s15_NATCH4)-
(p15_conroh(ta10)/s15_TAUCH4OH+1/s15_TAUCH4SS)*v15_conc(ta10,'CH4'))+
(1/s15_CNVCH4*(v15_emi(ta10-1,'CH4')+ s15_NATCH4)-
(p15_conroh(ta10-1)/s15_TAUCH4OH+1/s15_TAUCH4SS)*v15_conc(ta10-1,'CH4')));
*** CH4 radiative forcing (from ACC2)
q15_forcCH4Q(ta10) .. v15_forcComp(ta10,'CH4') =E= s15_RHOCH4*(SQRT(v15_conc(ta10,'CH4'))-SQRT(s15_CONCH4PRE))
-s15_OVERLFAC1*LOG(1+s15_OVERLFAC2*(v15_conc(ta10,'CH4')*s15_CONN2OPRE)**s15_OVERLEXP1+
s15_OVERLFAC3*v15_conc(ta10,'CH4')*(v15_conc(ta10,'CH4')*s15_CONN2OPRE)**s15_OVERLEXP2)
+s15_OVERLFAC1*LOG(1+s15_OVERLFAC2*(s15_CONCH4PRE*s15_CONN2OPRE)**s15_OVERLEXP1+
s15_OVERLFAC3*s15_CONCH4PRE*(s15_CONCH4PRE*s15_CONN2OPRE)**s15_OVERLEXP2);
*** N2O radiative forcing (from ACC2)
q15_forcN2OQ(ta10) .. v15_forcComp(ta10,'N2O') =E= s15_RHON2O*(SQRT(v15_conc(ta10,'N2O'))-SQRT(s15_CONN2OPRE))
-s15_OVERLFAC1*LOG(1+s15_OVERLFAC2*(s15_CONCH4PRE*v15_conc(ta10,'N2O'))**s15_OVERLEXP1+
s15_OVERLFAC3*s15_CONCH4PRE*(s15_CONCH4PRE*v15_conc(ta10,'N2O'))**s15_OVERLEXP2)
+s15_OVERLFAC1*LOG(1+s15_OVERLFAC2*(s15_CONCH4PRE*s15_CONN2OPRE)**s15_OVERLEXP1+
s15_OVERLFAC3*s15_CONCH4PRE*(s15_CONCH4PRE*s15_CONN2OPRE)**s15_OVERLEXP2);
*AL* changed towards the ACC2 approach to use the foghg
*** so2 radiative forcing module
q15_forcso2(ta10)..
v15_forcComp(ta10,'SO2') =e= s15_dso1990 * v15_emi(ta10,'SO2') / s15_so1990 +
s15_iso1990 * log(1 + v15_emi(ta10,'SO2')/s15_enatso2) /
log(1 + s15_so1990/s15_enatso2) ;
v15_conc(ta10,'CO2')
=e=
s15_c0 + ((s15_c2000-s15_c0)/(s15_ca0*s15_cq0+s15_ca1*s15_cq1+s15_ca2*s15_cq2+s15_ca3*s15_cq3))
* (s15_ca0*s15_cq0 + s15_ca1*s15_cq1*exp(-(ord(ta10)-1)/s15_ctau1) + s15_ca2*s15_cq2*exp(-(ord(ta10)-1)/s15_ctau2) + s15_ca3*s15_cq3*exp(-(ord(ta10)-1)/s15_ctau3))
+ s15_cconvi * sum((tx)$(ord(tx)lt ord(ta10)),v15_emi(tx,'CO2')*p15_epsilon(ta10-ord(tx)));
***---------------------------------------------------------------------------
*' CH4 concentration
***---------------------------------------------------------------------------
q15_concCH4Q(ta10)$(Ord(ta10) GT 1)..
(v15_conc(ta10,'CH4')-v15_conc(ta10-1,'CH4'))/s15_DELTAT
=e=
0.5 * (
(1/s15_CNVCH4 * (v15_emi(ta10,'CH4')+ s15_NATCH4) - (p15_conroh(ta10) / s15_TAUCH4OH + 1 / s15_TAUCH4SS) * v15_conc(ta10,'CH4'))
+ (1/s15_CNVCH4*(v15_emi(ta10-1,'CH4') + s15_NATCH4) - (p15_conroh(ta10-1) / s15_TAUCH4OH + 1 / s15_TAUCH4SS) * v15_conc(ta10-1,'CH4'))
);
***---------------------------------------------------------------------------
*' N20 concentration (from ACC2)
***---------------------------------------------------------------------------
q15_concN2OQ(ta10)$(Ord(ta10) GT 1)..
(v15_conc(ta10,'N2O')-v15_conc(ta10-1,'N2O'))/s15_DELTAT
=e=
0.5 * (
(1/s15_CNVN2O * (v15_emi(ta10,'N2O')+ s15_NATN2O) - (1/s15_TAUN2O*(v15_conc(ta10,'N2O')/s15_CONN2O2000R)**(-s15_SENTAUN2O)*v15_conc(ta10,'N2O')))
+ (1/s15_CNVN2O * (v15_emi(ta10-1,'N2O') + s15_NATN2O) - (1/s15_TAUN2O*(v15_conc(ta10-1,'N2O')/s15_CONN2O2000R)**(-s15_SENTAUN2O)*v15_conc(ta10-1,'N2O')))
);
***---------------------------------------------------------------------------
*' CO2 radiative forcing
***---------------------------------------------------------------------------
q15_forcco2(ta10)..
v15_forcComp(ta10,'CO2')
=e=
s15_fcodb * log(v15_conc(ta10,'CO2')/s15_c0) / log(2) ;
***---------------------------------------------------------------------------
*' CH4 radiative forcing (from ACC2)
***---------------------------------------------------------------------------
q15_forcCH4Q(ta10)..
v15_forcComp(ta10,'CH4')
=e=
s15_RHOCH4 * (SQRT(v15_conc(ta10,'CH4')) - SQRT(s15_CONCH4PRE))
- s15_OVERLFAC1 * LOG(1 + s15_OVERLFAC2 *(v15_conc(ta10,'CH4') * s15_CONN2OPRE)**s15_OVERLEXP1
+ s15_OVERLFAC3 * v15_conc(ta10,'CH4') * (v15_conc(ta10,'CH4')*s15_CONN2OPRE)**s15_OVERLEXP2
)
+ s15_OVERLFAC1 * LOG(1 + s15_OVERLFAC2 * (s15_CONCH4PRE*s15_CONN2OPRE)**s15_OVERLEXP1
+ s15_OVERLFAC3 * s15_CONCH4PRE * (s15_CONCH4PRE*s15_CONN2OPRE)**s15_OVERLEXP2
);
***---------------------------------------------------------------------------
*' N2O radiative forcing (from ACC2)
***---------------------------------------------------------------------------
q15_forcN2OQ(ta10)..
v15_forcComp(ta10,'N2O')
=e=
s15_RHON2O * (SQRT(v15_conc(ta10,'N2O'))-SQRT(s15_CONN2OPRE))
- s15_OVERLFAC1 * LOG(1 + s15_OVERLFAC2 * (s15_CONCH4PRE*v15_conc(ta10,'N2O'))**s15_OVERLEXP1
+ s15_OVERLFAC3 * s15_CONCH4PRE * (s15_CONCH4PRE*v15_conc(ta10,'N2O'))**s15_OVERLEXP2
)
+ s15_OVERLFAC1 * LOG(1 + s15_OVERLFAC2 * (s15_CONCH4PRE*s15_CONN2OPRE)**s15_OVERLEXP1
+ s15_OVERLFAC3 * s15_CONCH4PRE * (s15_CONCH4PRE*s15_CONN2OPRE)**s15_OVERLEXP2
);
***---------------------------------------------------------------------------
*' SO2 radiative forcing
***---------------------------------------------------------------------------
q15_forcso2(ta10)..
v15_forcComp(ta10,'SO2')
=e=
s15_dso1990 * v15_emi(ta10,'SO2') / s15_so1990
+ s15_iso1990 * log(1 + v15_emi(ta10,'SO2')/s15_enatso2) / log(1 + s15_so1990/s15_enatso2) ;
*** BC and OC from fossil fuels forcing
q15_forcbc(ta10)..
v15_forcComp(ta10,'BC') =e= (v15_emi(ta10,'BC') / s15_bc2005) * p15_oghgf_ffbc('2005');
***---------------------------------------------------------------------------
*' BC and OC from fossil fuels radiative forcing; scales linear with emissions.
***---------------------------------------------------------------------------
q15_forcbc(ta10)..
v15_forcComp(ta10,'BC')
=e=
(v15_emi(ta10,'BC') / s15_bc2005) * p15_oghgf_ffbc('2005');
q15_forcoc(ta10)..
v15_forcComp(ta10,'OC') =e= (v15_emi(ta10,'OC') / s15_oc2005) * p15_oghgf_ffoc('2005');
*** co2 radiative forcing module
q15_forcco2(ta10)..
v15_forcComp(ta10,'CO2') =e= s15_fcodb * log(v15_conc(ta10,'CO2')/s15_c0) / log(2) ;
*** total radiative forcing (foghg given exogenously)
q15_forctotal(ta10)..
v15_forcComp(ta10,'TTL') =e= v15_forcComp(ta10,'CO2') +
v15_forcComp(ta10,'SO2') +
v15_forcComp(ta10,'CH4') +
v15_forcComp(ta10,'N2O') +
v15_forcComp(ta10,'BC') +
v15_forcComp(ta10,'OC') +
v15_forcComp(ta10,'oghg_nokyo') +
v15_forcComp(ta10,'oghg_kyo');
q15_forcoc(ta10)..
v15_forcComp(ta10,'OC')
=e=
(v15_emi(ta10,'OC') / s15_oc2005) * p15_oghgf_ffoc('2005');
***---------------------------------------------------------------------------
*' Total radiative forcing (foghg given exogenously)
***---------------------------------------------------------------------------
q15_forctotal(ta10)..
v15_forcComp(ta10,'TTL')
=e=
hv15_forcComp(ta10,'CO2')
+ v15_forcComp(ta10,'SO2')
+ v15_forcComp(ta10,'CH4')
+ v15_forcComp(ta10,'N2O')
+ v15_forcComp(ta10,'BC')
+ v15_forcComp(ta10,'OC')
+ v15_forcComp(ta10,'oghg_nokyo')
+ v15_forcComp(ta10,'oghg_kyo');
*GL: Total forcing of Kyoto gases - required for formulation of policy targets
q15_forc_kyo(ta10)..
v15_forcKyo(ta10) =e= v15_forcComp(ta10,'CO2') +
v15_forcComp(ta10,'CH4') +
v15_forcComp(ta10,'N2O') +
v15_forcComp(ta10,'oghg_kyo');
*JeS* rcp forcing
q15_forc_rcp(ta10)..
v15_forcRcp(ta10) =e= v15_forcComp(ta10,'CO2') +
v15_forcComp(ta10,'CH4') +
v15_forcComp(ta10,'N2O') +
v15_forcComp(ta10,'oghg_kyo') +
v15_forcComp(ta10,'SO2') +
v15_forcComp(ta10,'BC') +
v15_forcComp(ta10,'OC') +
v15_forcComp(ta10,'oghg_nokyo_rcp');
***---------------------------------------------------------------------------
*' Total radiative forcing of Kyoto gases
***---------------------------------------------------------------------------
q15_forc_kyo(ta10)..
v15_forcKyo(ta10)
=e=
v15_forcComp(ta10,'CO2')
+ v15_forcComp(ta10,'CH4')
+ v15_forcComp(ta10,'N2O')
+ v15_forcComp(ta10,'oghg_kyo');
***---------------------------------------------------------------------------
*' RCP forcing
***---------------------------------------------------------------------------
q15_forc_rcp(ta10)..
v15_forcRcp(ta10)
=e=
v15_forcComp(ta10,'CO2')
+ v15_forcComp(ta10,'CH4')
+ v15_forcComp(ta10,'N2O')
+ v15_forcComp(ta10,'oghg_kyo')
+ v15_forcComp(ta10,'SO2')
+ v15_forcComp(ta10,'BC')
+ v15_forcComp(ta10,'OC')
+ v15_forcComp(ta10,'oghg_nokyo_rcp');
*** new temperature equations
q15_clisys1(ta10) $(Ord(ta10) > 1) .. (v15_tempFast(ta10)-v15_tempFast(ta10-1))/s15_deltat_box =E= 0.5/s15_RPCTT1*
((s15_RPCTA1*v15_forcComp(ta10,'TTL')/3.7-v15_tempFast(ta10))+
(s15_RPCTA1*v15_forcComp(ta10-1,'TTL')/3.7-v15_tempFast(ta10-1)));
q15_clisys2(ta10) $(Ord(ta10) > 1) .. (v15_tempSlow(ta10)-v15_tempSlow(ta10-1))/s15_deltat_box =E= 0.5/s15_RPCTT2*
((s15_RPCTA2*v15_forcComp(ta10,'TTL')/3.7-v15_tempSlow(ta10))+
(s15_RPCTA2*v15_forcComp(ta10-1,'TTL')/3.7-v15_tempSlow(ta10-1)));
q15_clisys(ta10) .. v15_temp(ta10) =E= v15_tempFast(ta10) + v15_tempSlow(ta10);
q15_clisys01(ta10) $(ord(ta10)=1)..
v15_tempFast(ta10) =e= s15_RPCTA1 * s15_temp2000/s15_tsens;
q15_clisys02(ta10) $(ord(ta10)=1)..
v15_tempSlow(ta10) =e= s15_RPCTA2 * s15_temp2000/s15_tsens;
*JeS* forcing overshoot for damage function
***---------------------------------------------------------------------------
*' Temperature equations, consisting of a fast and a slow response function
***---------------------------------------------------------------------------
q15_clisys01(ta10)$(ord(ta10)=1)..
v15_tempFast(ta10)
=e=
s15_RPCTA1 * s15_temp2000 / s15_tsens;
q15_clisys02(ta10)$(ord(ta10)=1)..
v15_tempSlow(ta10)
=e=
s15_RPCTA2 * s15_temp2000 / s15_tsens;
q15_clisys1(ta10)$(Ord(ta10) > 1)..
(v15_tempFast(ta10) - v15_tempFast(ta10-1)) / s15_deltat_box
=e=
0.5 / s15_RPCTT1 * ( (s15_RPCTA1 * v15_forcComp(ta10,'TTL') / 3.7 - v15_tempFast(ta10))
+ (s15_RPCTA1 * v15_forcComp(ta10-1,'TTL') / 3.7 - v15_tempFast(ta10-1))
);
q15_clisys2(ta10)$(Ord(ta10) > 1)..
(v15_tempSlow(ta10) - v15_tempSlow(ta10-1)) / s15_deltat_box
=e=
0.5 / s15_RPCTT2 * ( (s15_RPCTA2 * v15_forcComp(ta10,'TTL') / 3.7 - v15_tempSlow(ta10))
+ (s15_RPCTA2 * v15_forcComp(ta10-1,'TTL') / 3.7 - v15_tempSlow(ta10-1))
);
q15_clisys(ta10)..
v15_temp(ta10)
=e=
v15_tempFast(ta10) + v15_tempSlow(ta10);
***---------------------------------------------------------------------------
*' Forcing overshoot for damage function
***---------------------------------------------------------------------------
q15_forc_os(t)..
vm_forcOs(t) =E= v15_forcKyo(t)-s15_gr_forc_kyo+v15_slackForc(t);
*** end of stuff taken from box-model.inc ---------------------------
*-----------------------------------------------------------------------------------------
*** ------------------------link to core--------------------------------------------------
*-----------------------------------------------------------------------------------------
q15_linkEMI(ttot2ta10(ttot, ta10),emis2climate10(enty,FOB10)).. vm_emiAllGlob(ttot,enty) =e= v15_emi(ta10,FOB10);
vm_forcOs(t)
=e=
v15_forcKyo(t) - s15_gr_forc_kyo + v15_slackForc(t);
***-----------------------------------------------------------------------------------------
*' link to core
***-----------------------------------------------------------------------------------------
q15_linkEMI(ttot2ta10(ttot, ta10),emis2climate10(enty,FOB10))..
vm_emiAllGlob(ttot,enty)
=e=
v15_emi(ta10,FOB10);
$IF %cm_so2_out_of_opt% == "on" q15_linkEMI_aer(ttot2ta10(ttot, ta10),emiaer2climate10(emiaer,FOB10)).. p15_so2emi(ttot,emiaer) =e= v15_emi(ta10,FOB10);
*---interpolation for linking (annual resolution of climate modules)
q15_interEMI(ta2ttot10(ta10, ttot),FOBEMI(FOB10)).. v15_emi(ta10,FOB10) =e= (1-p15_interpol(ta10)) * v15_emi(ttot,FOB10) + p15_interpol(ta10) * v15_emi(ttot+1,FOB10);
***-----------------------------------------------------------------------------------------
*' interpolation for linking (annual resolution of climate modules)
***-----------------------------------------------------------------------------------------
q15_interEMI(ta2ttot10(ta10, ttot),FOBEMI(FOB10))..
v15_emi(ta10,FOB10)
=e=
(1-p15_interpol(ta10)) * v15_emi(ttot,FOB10) + p15_interpol(ta10) * v15_emi(ttot+1,FOB10);
*** EOF ./modules/15_climate/box/equations.gms