expand emission scaling parameterization to allow representing GWP*

Note that data_load.gms includes dummy code that sets the newly introduced emission_diff_scaling to zero in the absence of the parameter being included in the GDX setup so far.

message_ix/model/MESSAGE/data_load.gms

@@ -52,6 +52,7 @@ rating_bin, reliability_factor, peak_load_factor, flexibility_factor
 renewable_capacity_factor, renewable_potential
 * emission factors, bounds and taxes on emissions (including mapping sets)
 historical_emission, emission_factor, emission_scaling, is_bound_emission, bound_emission, tax_emission,
+* emission_diff_scaling,
 * historical values of new capacity investment, activity and extraction
 historical_new_capacity, historical_activity, historical_extraction
 * parameters for land-use model emulator
@@ -74,7 +75,8 @@ fixed_extraction, fixed_stock, fixed_new_capacity, fixed_capacity, fixed_activit
 storage_initial, storage_self_discharge, time_order
 ;
 
-
+* dummy code to add (empty) emission_diff_scaling parameter
+emission_diff_scaling(type_emission,emission,year_all,year_all) = 0 ;
 *----------------------------------------------------------------------------------------------------------------------*
 * ensure that each node is mapped to itself                                                                            *
 *----------------------------------------------------------------------------------------------------------------------*

message_ix/model/MESSAGE/model_core.gms

@@ -1811,9 +1811,14 @@ EMISSION_EQUIVALENCE(node,emission,type_tec,year)..
 *
 * Equation EMISSION_CONSTRAINT
 * """"""""""""""""""""""""""""
-* This constraint enforces upper bounds on emissions (by emission type). For all bounds that include multiple periods,
-* the parameter :math:`bound\_emission_{n,\widehat{e},\widehat{t},\widehat{y}}` is scaled to represent average annual
-* emissions over all years included in the year-set :math:`\widehat{y}`.
+* This constraint enforces upper bounds on emissions (by emission type), including the possibility to aggregate
+* across different emission species and scale them relateive to each other (e.g., to reflect different emission
+* metrics such as global warming potentials, GWPs). As of release X.Y, the possibility to include scaling metrics
+* that work across multiple periods (e.g., to accommodate implemantation of the GWP* metric that for short-lived
+* emission species applies scaling factors to differences of emissions over time) has been added.
+*
+* For all bounds that include multiple periods, the parameter :math:`bound\_emission_{n,\widehat{e},\widehat{t},\widehat{y}}`
+* is scaled to represent average annual emissions over all years included in the year-set :math:`\widehat{y}`.
 *
 * The formulation includes historical emissions and allows to model constraints ranging over both the model horizon
 * and historical periods.
@@ -1824,6 +1829,9 @@ EMISSION_EQUIVALENCE(node,emission,type_tec,year)..
 *              \begin{array}{l}
 *                  duration\_period_{y'} \cdot emission\_scaling_{\widehat{e},e} \cdot \\
 *                  \Big( EMISS_{n,e,\widehat{t},y'} + \sum_{m} historical\_emission_{n,e,\widehat{t},y'} \Big)
+*                + \sum_{y'' \in (\widehat{y}), y'' \neq y'}
+*                     duration\_period_{y'} \cdot emission\_diff\_scaling_{\widehat{e},e,y', y''} \cdot \\
+*                  \Big( EMISS_{n,e,\widehat{t},y''} + \sum_{m} historical\_emission_{n,e,\widehat{t},y''} \Big)
 *              \end{array}
 *          }
 *        { \sum_{y' \in Y(\widehat{y})} duration\_period_{y'} }
@@ -1835,7 +1843,12 @@ EMISSION_CONSTRAINT(node,type_emission,type_tec,type_year)$is_bound_emission(nod
         duration_period(year_all2) * emission_scaling(type_emission,emission) *
             ( EMISS(node,emission,type_tec,year_all2)$( year(year_all2) )
                 + historical_emission(node,emission,type_tec,year_all2) )
-      )
+      + SUM( (year_all3)$( NOT SAMEAS(year_all2, year_all3) ),
+            duration_period(year_all2) * emission_diff_scaling(type_emission,emission,year_all2,year_all3) *
+                ( EMISS(node,emission,type_tec,year_all3)$( year(year_all3) )
+                    + historical_emission(node,emission,type_tec,year_all3) )
+        )
+    )
     / SUM(year_all2$( cat_year(type_year,year_all2) ), duration_period(year_all2) )
     =L= bound_emission(node,type_emission,type_tec,type_year) ;
 

message_ix/model/MESSAGE/parameter_def.gms

@@ -584,19 +584,26 @@ Parameters
 *      - ``node`` | ``emission`` | ``type_tec`` | ``year``
 *    * - emission_scaling [#em_scaling]_
 *      - ``type_emission`` | ``emission``
+*    * - emission_diff_scaling [#em_diff_scaling]_
+*      - ``type_emission`` | ``emission`` | ``year`` | ``year``
 *    * - bound_emission
 *      - ``node`` | ``type_emission`` | ``type_tec`` | ``type_year``
 *    * - tax_emission
 *      - ``node`` | ``type_emission`` | ``type_tec`` | ``type_year``
 *
-* .. [#em_scaling] The parameter ``emission_scaling`` is the scaling factor to harmonize bounds or taxes across types of
-*    emissions. It allows to efficiently aggregate different emissions/pollutants and set bounds or taxes on various categories.
+* .. [#em_scaling] The parameter ``emission_scaling`` is the scaling factor to aggreagte or scale emissions across types of
+*    emissions. It allows to efficiently aggregate different emissions/pollutants (e.g., to represent Gobal Warming Potentials,
+*    GWPs) and set bounds or taxes on various emission categories.
+* .. [#em_diff_scaling] The parameter ``emission_diff_scaling`` is the scaling factor to aggreagte or scale emissions across types
+*    and different model periods which in combination with the parameter ``emission_scaling`` allows representing metrics such
+*    as GWP*.
 *
 ***
 
 Parameters
     historical_emission(node,emission,type_tec,year_all)    historical emissions by technology type (including land)
-    emission_scaling(type_emission,emission)                scaling factor to harmonize bounds or taxes across types
+    emission_scaling(type_emission,emission)                emission scaling factor to aggreagte or scale emissions across types
+    emission_diff_scaling(type_emission,emission,year_all,year_all)      emission scaling factor to aggreagte or scale emissions across types and different model periods
     bound_emission(node,type_emission,type_tec,type_year)   upper bound on emissions
     tax_emission(node,type_emission,type_tec,type_year)     emission tax
 ;