New realizations diffExp2Lin and diffLin2Lin in 45_carbonprice

CHANGELOG.md

@@ -9,6 +9,7 @@ The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/).
 ### changed
 
 ### added
+- added realizations diffExp2Lin and diffLin2Lin to 45_carbonprice [#1723](https://github.com/remindmodel/remind/pull/1723)
 
 ### fixed
 - included CCS from plastic waste incineration in CCS mass flows so it is

main.gms

@@ -372,12 +372,14 @@ $setglobal emicapregi  none           !! def = none
 *' This module defines the carbon price pm_taxCO2eq, with behaviour across regions governed by similar principles (e.g. global targets, or all following NDC or NPi policies).
 *'
 *' * (none): no tax policy (combined with all emiscens except emiscen = 9)
-*' * (exponential): 5% exponential increase over time of the tax level in 2020 set via cm_co2_tax_2020 (combined with emiscen = 9 and cm_co2_tax_2020>0)
-*' * (expoLinear): 5% exponential increase until c_expoLinear_yearStart, linear increase thereafter
+*' * (exponential): 4.5% exponential increase over time of the tax level in 2020 set via cm_co2_tax_2020 (combined with emiscen = 9 and cm_co2_tax_2020>0)
+*' * (expoLinear): 4.5% exponential increase until c_expoLinear_yearStart, linear increase thereafter
 *' * (exogenous): carbon price is specified using an external input file or using the switch cm_regiExoPrice. Requires cm_emiscen = 9 and cm_iterative_target_adj = 0
 *' * (linear): linear increase over time of the tax level in 2020 set via cm_co2_tax_2020 (combined with emiscen = 9 and cm_co2_tax_2020>0)
 *' * (temperatureNotToExceed): [test and verify before using it!] Find the optimal carbon carbon tax (set cm_emiscen = 1, iterative_target_adj = 9] curved convergence of CO2 prices between regions until cm_CO2priceRegConvEndYr; developed countries have linear path from 0 in 2010 through cm_co2_tax_2020 in 2020;
 *' * (diffCurvPhaseIn2Lin): [REMIND 2.1 default for validation peakBudget runs, in combination with iterative_target_adj = 9] curved convergence of CO2 prices between regions until cm_CO2priceRegConvEndYr; developed countries have linear path from 0 in 2010 through cm_co2_tax_2020 in 2020;
+*' * (diffExp2Lin): quadratic convergence of CO2 prices between regions until cm_CO2priceRegConvEndYr; starting level of differentiation in cm_startyear is given by cm_co2_tax_spread; developed countries have exponential path until peak year (with iterative_target_adj = 9) or until 2100 (with iterative_target_adj = 5);
+*' * (diffLin2Lin): [Variant of diffCurvPhaseIn2Lin, will be further developed before becoming the new default] quadratic convergence of CO2 prices between regions until cm_CO2priceRegConvEndYr; starting level of differentiation in cm_startyear is given by cm_co2_tax_spread; developed countries have linear path until peak year (with iterative_target_adj = 9) or until 2100 (with iterative_target_adj = 5);
 *' * (NDC): implements a carbon price trajectory consistent with the NDC targets (up to 2030) and a trajectory of comparable ambition post 2030 (1.25%/yr price increase and regional convergence of carbon price). Choose version using cm_NDC_version "2023_cond", "2023_uncond", or replace 2023 by 2022, 2021 or 2018 to get all NDC published until end of these years.
 *' * (NPi): National Policies Implemented, extrapolation of historical (until 2020) carbon prices
 $setglobal carbonprice  none           !! def = none
@@ -508,8 +510,8 @@ parameter
 parameter
   cm_co2_tax_growth         "growth rate of carbon tax"
 ;
-  cm_co2_tax_growth = 1.05;            !! def = 1.05  !! regexp = is.numeric
-*'  (any number >= 0): rate of exponential increase over time
+  cm_co2_tax_growth = 1.045;            !! def = 1.045  !! regexp = is.numeric
+*'  (any number >= 0): rate of exponential increase over time, default value chosen to be consistent with interest rate
 parameter
   c_macscen                 "scenario switch on whether or not to use MAC (Marginal Abatement Cost) for certain sectors not related to direct combustion of fossil fuel, e.g. fugitive emissions from old mines, forestry, agriculture and cement"
 ;
@@ -977,10 +979,19 @@ parameter
   c_taxCO2inc_after_peakBudgYr = 0; !! def = 0 . For weak targets (higher than 1100 Peak Budget), this value might need to increased to prevent continually increasing temperatures
 *'
 parameter
-  cm_CO2priceRegConvEndYr      "Year at which regional CO2 taxes converge in module 45 realization diffCurvPhaseIn2Lin"
+  cm_CO2priceRegConvEndYr      "Year at which regional CO2 taxes converge in module 45 for realizations with differentiated carbon prices"
 ;
-  cm_CO2priceRegConvEndYr  = 2050;   !! def = 2050
+  cm_CO2priceRegConvEndYr  = 2050;   !! def = 2050    
 *'
+parameter
+  cm_co2_tax_spread            "spread of carbon prices in 2025 given as a factor"
+;
+  cm_co2_tax_spread        = 10;     !! def = 10  !! regexp = 1|10|20
+*'  Initial spread of carbon prices (in 2025) between the regions with highest respectively lowest GDP per capita (PPP)
+*' * (1) Uniform carbon pricing, i.e. no differentiation
+*' * (10) Spread of carbon prices in 2025 is equal to 10
+*' * (20) Spread of carbon prices in 2025 is equal to 20
+
 parameter
   c_teNoLearngConvEndYr      "Year at which regional costs of non-learning technologies converge"
 ;

modules/45_carbonprice/NDC/not_used.txt

@@ -21,3 +21,4 @@ pm_shPPPMER,input,questionnaire
 pm_pop,input,questionnaire
 pm_gdp,input,questionnaire
 cm_CO2priceRegConvEndYr,input,questionnaire
+cm_co2_tax_spread,switch,no carbon price differentiation in this realization

modules/45_carbonprice/NPi/not_used.txt

@@ -29,3 +29,4 @@ cm_NDC_divergentScenario,input,questionnaire
 vm_demFeSector,input,questionnaire
 pm_emifac,input,questionnaire
 cm_startyear,input,added by codeCheck
+cm_co2_tax_spread,input,no carbon price differentiation in this realization

modules/45_carbonprice/diffCurvPhaseIn2Lin/not_used.txt

@@ -23,3 +23,4 @@ pm_consPC,input,questionnaire
 pm_prtp,input,questionnaire
 vm_demFeSector,input,questionnaire
 pm_emifac,input,questionnaire
+cm_co2_tax_spread,input,added by codeCheck

modules/45_carbonprice/diffExp2Lin/datainput.gms

@@ -0,0 +1,81 @@
+*** |  (C) 2006-2023 Potsdam Institute for Climate Impact Research (PIK)
+*** |  authors, and contributors see CITATION.cff file. This file is part
+*** |  of REMIND and licensed under AGPL-3.0-or-later. Under Section 7 of
+*** |  AGPL-3.0, you are granted additional permissions described in the
+*** |  REMIND License Exception, version 1.0 (see LICENSE file).
+*** |  Contact: [email protected]
+*** SOF ./modules/45_carbonprice/diffExp2Lin/datainput.gms
+***---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+*** regional prices are initially differentiated by GDP/capita and converge using quadratic phase-in, 
+*** global price from cm_CO2priceRegConvEndYr (default = 2050)
+*** carbon price of developed regions increases exponentially with rate given by cm_co2_tax_growth until peak year (with iterative_target_adj = 9) or until 2100 (with iterative_target_adj = 5)
+*** linear carbon price curve of developed regions starts at 0 in 2020 
+***---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+
+
+*** convergence to global CO2 price depends on GDP per capita (in 1e3 $ PPP 2005).
+*** benchmark year kept at 2015 since 2020 not suitable. 
+p45_gdppcap2015_PPP(regi) = pm_gdp("2015",regi)/pm_shPPPMER(regi) / pm_pop("2015",regi);
+display p45_gdppcap2015_PPP;
+
+*** Selection of differentiation scheme via cm_co2_tax_spread
+if(cm_co2_tax_spread eq 1,
+p45_phasein_2025ratio(regi) = 1; !! all regions
+);
+
+if(cm_co2_tax_spread eq 10,
+p45_phasein_2025ratio(regi)$(p45_gdppcap2015_PPP(regi) le 3.5) = 0.1; !! SSA
+p45_phasein_2025ratio(regi)$(p45_gdppcap2015_PPP(regi) gt 3.5 and p45_gdppcap2015_PPP(regi) le 5)  = 0.2; !! IND
+p45_phasein_2025ratio(regi)$(p45_gdppcap2015_PPP(regi) gt 5   and p45_gdppcap2015_PPP(regi) le 10) = 0.3; !! OAS
+p45_phasein_2025ratio(regi)$(p45_gdppcap2015_PPP(regi) gt 10  and p45_gdppcap2015_PPP(regi) le 15) = 0.5; !! CHA, REF, LAM
+p45_phasein_2025ratio(regi)$(p45_gdppcap2015_PPP(regi) gt 15  and p45_gdppcap2015_PPP(regi) le 20) = 0.7; !! MEA, NEU
+p45_phasein_2025ratio(regi)$(p45_gdppcap2015_PPP(regi) gt 20) = 1; !! EUR, JPN, USA, CAZ
+);
+
+if(cm_co2_tax_spread eq 20,
+p45_phasein_2025ratio(regi)$(p45_gdppcap2015_PPP(regi) le 3.5) = 0.05; !! SSA
+p45_phasein_2025ratio(regi)$(p45_gdppcap2015_PPP(regi) gt 3.5 and p45_gdppcap2015_PPP(regi) le 5)  = 0.1; !! IND
+p45_phasein_2025ratio(regi)$(p45_gdppcap2015_PPP(regi) gt 5   and p45_gdppcap2015_PPP(regi) le 10) = 0.2; !! OAS
+p45_phasein_2025ratio(regi)$(p45_gdppcap2015_PPP(regi) gt 10  and p45_gdppcap2015_PPP(regi) le 15) = 0.4; !! CHA, REF, LAM
+p45_phasein_2025ratio(regi)$(p45_gdppcap2015_PPP(regi) gt 15  and p45_gdppcap2015_PPP(regi) le 20) = 0.6; !! MEA, NEU
+p45_phasein_2025ratio(regi)$(p45_gdppcap2015_PPP(regi) gt 20) = 1; !! EUR, JPN, USA, CAZ
+);
+display p45_phasein_2025ratio;
+
+
+*GL: tax path in 10^12$/GtC = 1000 $/tC
+*** according to Asian Modeling Excercise tax case setup, 30$/t CO2eq in 2020 = 0.110 k$/tC
+
+*** for the current implementation, use the following trajectory for rich countries:
+*** price increases exponentially from cm_co2_tax_2020 in 2020
+if(cm_co2_tax_2020 lt 0,
+abort "please choose a valid cm_co2_tax_2020"
+elseif cm_co2_tax_2020 ge 0,
+*** convert tax value from $/t CO2eq to T$/GtC
+p45_CO2priceTrajDeveloped("2020") = cm_co2_tax_2020 * sm_DptCO2_2_TDpGtC;
+);
+
+p45_CO2priceTrajDeveloped(t)$(t.val gt 2005) = p45_CO2priceTrajDeveloped("2020") * cm_co2_tax_growth**(t.val-2020);
+p45_CO2priceTrajDeveloped(t)$(t.val gt 2110) = p45_CO2priceTrajDeveloped("2110"); !! to prevent huge taxes after 2110 and the resulting convergence problems, set taxes after 2110 equal to 2110 value
+
+*** Then create regional phase-in:
+*** Set regional CO2 price factor equal to p45_phasein_2025ratio until 2025:
+p45_regCO2priceFactor(t,regi)$(t.val le 2025) = p45_phasein_2025ratio(regi);
+*** Then define quadratic phase-in until cm_CO2priceRegConvEndYr:
+loop(t$((t.val gt 2025) and (t.val le cm_CO2priceRegConvEndYr)),
+  p45_regCO2priceFactor(t,regi) = 
+   min(1,
+       max(0, 
+	        p45_phasein_2025ratio(regi) + (1 - p45_phasein_2025ratio(regi)) * Power( (t.val - 2025) / (cm_CO2priceRegConvEndYr - 2025), 2) 
+       )				 
+   );
+);
+p45_regCO2priceFactor(t,regi)$(t.val ge cm_CO2priceRegConvEndYr) = 1;
+
+
+*** transition to global price - starting point depends on GDP/cap
+pm_taxCO2eq(t,regi) = p45_regCO2priceFactor(t,regi) * p45_CO2priceTrajDeveloped(t);
+
+
+display p45_regCO2priceFactor, p45_CO2priceTrajDeveloped, pm_taxCO2eq;
+*** EOF ./modules/45_carbonprice/diffExp2Lin/datainput.gms

modules/45_carbonprice/diffExp2Lin/declarations.gms

@@ -0,0 +1,23 @@
+*** |  (C) 2006-2023 Potsdam Institute for Climate Impact Research (PIK)
+*** |  authors, and contributors see CITATION.cff file. This file is part
+*** |  of REMIND and licensed under AGPL-3.0-or-later. Under Section 7 of
+*** |  AGPL-3.0, you are granted additional permissions described in the
+*** |  REMIND License Exception, version 1.0 (see LICENSE file).
+*** |  Contact: [email protected]
+*** SOF ./modules/45_carbonprice/diffExp2Lin/datainput.gms
+***---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+*** regional prices are initially differentiated by GDP/capita and converge using quadratic phase-in, 
+*** global price from cm_CO2priceRegConvEndYr (default = 2050)
+*** carbon price of developed regions increases exponentially with rate given by cm_co2_tax_growth until peak year (with iterative_target_adj = 9) or until 2100 (with iterative_target_adj = 5)
+*** linear carbon price curve of developed regions starts at 0 in 2020 
+***---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+parameters
+p45_gdppcap2015_PPP(all_regi)               "2015 GDP per capita (k $ PPP 2005)"
+p45_phasein_2025ratio(all_regi)             "ratio of CO2 price to that of developed region in 2025"
+
+p45_regCO2priceFactor(ttot,all_regi)                    "regional multiplicative factor to the CO2 price of the developed countries"
+p45_CO2priceTrajDeveloped(ttot)                         "CO2 price trajectory for developed/rich countries"
+;
+
+
+*** EOF ./modules/45_carbonprice/diffExp2Lin/declarations.gms

modules/45_carbonprice/diffExp2Lin/not_used.txt

@@ -0,0 +1,25 @@
+# |  (C) 2006-2023 Potsdam Institute for Climate Impact Research (PIK)
+# |  authors, and contributors see CITATION.cff file. This file is part
+# |  of REMIND and licensed under AGPL-3.0-or-later. Under Section 7 of
+# |  AGPL-3.0, you are granted additional permissions described in the
+# |  REMIND License Exception, version 1.0 (see LICENSE file).
+# |  Contact: [email protected]
+name,type,reason
+cm_emiscen, switch, ???
+sm_c_2_co2,switch, ???
+pm_ttot_val,parameter,???
+cm_startyear,switch,???
+cm_iterative_target_adj,switch,???
+cm_expoLinear_yearStart,switch,???
+vm_co2eq,variable,???
+vm_emiFgas,input,questionnaire
+pm_globalMeanTemperature,input,questionnaire
+pm_temperatureImpulseResponseCO2,input,questionnaire
+pm_consPC,input,questionnaire
+pm_GDPGross,input,questionnaire
+pm_prtp,input,questionnaire
+cm_carbonprice_temperatureLimit,input,questionnaire
+pm_ttot_2_tall,input,questionnaire
+cm_NDC_divergentScenario,input,questionnaire
+vm_demFeSector,input,questionnaire
+pm_emifac,input,questionnaire

modules/45_carbonprice/diffExp2Lin/postsolve.gms

@@ -0,0 +1,25 @@
+*** |  (C) 2006-2023 Potsdam Institute for Climate Impact Research (PIK)
+*** |  authors, and contributors see CITATION.cff file. This file is part
+*** |  of REMIND and licensed under AGPL-3.0-or-later. Under Section 7 of
+*** |  AGPL-3.0, you are granted additional permissions described in the
+*** |  REMIND License Exception, version 1.0 (see LICENSE file).
+*** |  Contact: [email protected]
+*** SOF ./modules/45_carbonprice/diffExp2Lin/postsolve.gms
+***---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+*** regional prices are initially differentiated by GDP/capita and converge using quadratic phase-in, 
+*** global price from cm_CO2priceRegConvEndYr (default = 2050)
+*** carbon price of developed regions increases exponentially with rate given by cm_co2_tax_growth until peak year (with iterative_target_adj = 9) or until 2100 (with iterative_target_adj = 5)
+*** linear carbon price curve of developed regions starts at 0 in 2020 
+***---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+
+*** re-create the regional differentation, use path from developed countries as the basis.
+*** This doesn't need to be a loop, but it will be correct for any cycle of the loop, so also for the last cycle.
+loop(regi$(p45_gdppcap2015_PPP(regi) gt 20),
+  p45_CO2priceTrajDeveloped(t) = pm_taxCO2eq(t,regi);
+);
+
+*** quadratic transition to global price - starting point depends on GDP/cap
+pm_taxCO2eq(t,regi) = p45_regCO2priceFactor(t,regi) * p45_CO2priceTrajDeveloped(t);
+
+display pm_taxCO2eq;
+*** EOF ./modules/45_carbonprice/diffExp2Lin/postsolve.gms

modules/45_carbonprice/diffExp2Lin/realization.gms

@@ -0,0 +1,16 @@
+*** |  (C) 2006-2023 Potsdam Institute for Climate Impact Research (PIK)
+*** |  authors, and contributors see CITATION.cff file. This file is part
+*** |  of REMIND and licensed under AGPL-3.0-or-later. Under Section 7 of
+*** |  AGPL-3.0, you are granted additional permissions described in the
+*** |  REMIND License Exception, version 1.0 (see LICENSE file).
+*** |  Contact: [email protected]
+*** SOF ./modules/45_carbonprice/diffExp2Lin/realization.gms
+
+*#' @description: This realization implements exponentially increasing carbon price - either until 2100 or until peak year (constant or linear thereafter). Optional carbon price differentiation and quadratic phase-in can be activated via switch cm_co2_tax_spread.
+
+*####################### R SECTION START (PHASES) ##############################
+$Ifi "%phase%" == "declarations" $include "./modules/45_carbonprice/diffExp2Lin/declarations.gms"
+$Ifi "%phase%" == "datainput" $include "./modules/45_carbonprice/diffExp2Lin/datainput.gms"
+$Ifi "%phase%" == "postsolve" $include "./modules/45_carbonprice/diffExp2Lin/postsolve.gms"
+*######################## R SECTION END (PHASES) ###############################
+*** EOF ./modules/45_carbonprice/diffExp2Lin/realization.gms