Forest conversion (minimumLandCover) restriction loosened.

GAMS/IntExtOpt.gms

@@ -11,6 +11,7 @@
 
  SET land_cover / cropland, pasture, timberForest, carbonForest, unmanagedForest, otherNatural /;
  SET forest(land_cover) / timberForest, carbonForest, unmanagedForest /;
+ SET non_forest(land_cover) / cropland, pasture, otherNatural /;
  ALIAS (land_cover, land_cover_before);
  ALIAS (land_cover, land_cover_after);
 
@@ -81,7 +82,7 @@ $gdxin
  carbonPrice = carbonPrice * 0.001;
  woodPrice = woodPrice * 0.001;
 
- SCALAR delta use to smooth power function see 7.5 www.gams.com dd docs solversconopt.pdf / 0.00000000001 /;
+ SCALAR delta "use to smooth power function see 7.5 www.gams.com/dd/docs/solversconopt.pdf" / 0.00000000001 /;
 
  demand(cereal_crop) = demand('cereals') * minDemandPerCereal(cereal_crop);
  demand(oilpulse_crop) = demand('oilcropspulses') * minDemandPerOilcrop(oilpulse_crop);
@@ -120,7 +121,7 @@ $gdxin
 *PARAMETER lcTransitionCost(lc_type_previous, lc_type, location) cost of land transitions including carbon cost and conversion cost;
 *lcTransitionCost(lc_type_previous, lc_type, location) = carbonFluxRate(lc_type_previous, lc_type, location) * carbonPrice + agriExpansionCost(location);
 
- SCALAR forestExpansionMaxRate / 0.05 /;
+ SCALAR forestExpansionMaxRate / 0.01 /;
 
  VARIABLES
        cropArea(crop, location)             total area for crops - Mha
@@ -141,10 +142,11 @@ $gdxin
        pastureDecrease(location)
        landCoverArea(land_cover, location)  land cover area in Mha
        landCoverChange(land_cover_before, land_cover_after, location) land cover change
+       prematureDeforestationCost(location)
        woodHarvest(location)              total wood harvested
        carbonFlux(location)               total carbon flux
        totalFeedDM
-*       A                                  artificial variable "https://www.gams.com/blog/2017/07/misbehaving-model-infeasible/"
+*       A                                  "artificial variable https://www.gams.com/blog/2017/07/misbehaving-model-infeasible/"
        total_cost                         total cost of domestic supply including net imports;
 
 
@@ -183,11 +185,12 @@ $gdxin
        PASTURE_TOTAL_CHANGE_CONSTRAINT(location)
        CROPLAND_LAND_COVER_CALC(location) cropland area equals sum of all crop areas
        PASTURE_LAND_COVER_CALC(location)  pasture area (land cover) equals pasture area (land use)
-       MINIMUM_LAND_COVER_CONSTRAINT(land_cover, location) constraint on land cover conversion
+*       MINIMUM_LAND_COVER_CONSTRAINT(land_cover, location) constraint on land cover conversion
        LAND_COVER_CHANGE_CALC(land_cover, location)
        LAND_COVER_CHANGE_CONSTRAINT(land_cover, location) can't convert more land than was previously available
        LAND_COVER_SELF_CHANGE_CONSTRAINT(land_cover, location) calculate no change area (e.g. cropland to cropland)
-       FOREST_EXPANSION_CONSTRAINT(forest, location)
+       FOREST_EXPANSION_CONSTRAINT
+       PREMATURE_DEFORESTATION_COST_CALC(location)
        WOOD_HARVEST_CALC(location)                          calc wood harvested
        CARBON_FLUX_CALC(location)                           calc carbon flux
        COST_EQ                                        total cost objective function;
@@ -259,11 +262,12 @@ $gdxin
  LAND_COVER_SELF_CHANGE_CONSTRAINT(land_cover, location) .. landCoverChange(land_cover, land_cover, location) =E= previousLandCoverArea(land_cover, location) -
                                                             sum(land_cover_after$[not sameAs(land_cover, land_cover_after)], landCoverChange(land_cover, land_cover_after, location));
 
- FOREST_EXPANSION_CONSTRAINT(forest, location) .. landCoverArea(forest, location) - previousLandCoverArea(forest, location) =L= suitableLandArea(location) * forestExpansionMaxRate;
+ FOREST_EXPANSION_CONSTRAINT .. sum((non_forest, forest, location), landCoverChange(non_forest, forest, location)) =L= sum(location, suitableLandArea(location)) * forestExpansionMaxRate;
 
-* minimum of minimumLandCoverArea and previousLandCoverArea corrects for floating point errors
-*  MINIMUM_LAND_COVER_CONSTRAINT(land_cover, location) .. landCoverChange(land_cover, land_cover, location) =G= min(minimumLandCoverArea(land_cover, location), previousLandCoverArea(land_cover, location));
- MINIMUM_LAND_COVER_CONSTRAINT(land_cover, location) .. landCoverChange(land_cover, land_cover, location) =G= minimumLandCoverArea(land_cover, location);
+* MINIMUM_LAND_COVER_CONSTRAINT(land_cover, location) .. landCoverChange(land_cover, land_cover, location) =G= minimumLandCoverArea(land_cover, location);
+
+ PREMATURE_DEFORESTATION_COST_CALC(location) .. prematureDeforestationCost(location) =E= sum(forest, (sum((land_cover_after)$[not sameAs(forest, land_cover_after)], landCoverChange(forest, land_cover_after, location)) -
+                                                         previousLandCoverArea(forest, location) - minimumLandCoverArea(forest, location))) * 1000;
 
  WOOD_HARVEST_CALC(location) .. woodHarvest(location) =E= sum((land_cover_before, land_cover_after), landCoverChange(land_cover_before, land_cover_after, location) * woodYield(land_cover_before, land_cover_after, location));
 
@@ -287,7 +291,8 @@ $gdxin
 
                SUM(location, carbonFlux(location) * carbonPrice) - SUM(location, woodHarvest(location) * woodPrice) +
 
-               SUM(import_crop, importAmount(import_crop) * importPrices(import_crop) - exportAmount(import_crop) * exportPrices(import_crop))
+               SUM(import_crop, importAmount(import_crop) * importPrices(import_crop) - exportAmount(import_crop) * exportPrices(import_crop)) +
+                 SUM(location, prematureDeforestationCost(location))
          );
 
  MODEL LAND_USE /ALL/ ;