The module 50_nr_soil_budget balances the nitrogen flows for crop land soils and pasture soils and calculates the resulting demand for inorganic fertilizer and associated costs.
| Description | Unit | A | B | |
|---|---|---|---|---|
| fm_attributes (attributes, kall) |
Conversion factors - where X is ton N P K C DM WM or PJ GE | \(X/tDM\) | x | |
| im_pop_iso (t_all, iso) |
Population | \(10^6/yr\) | x | |
| sm_fix_SSP2 | year until which all parameters are fixed to SSP2 values | \(year\) | x | |
| vm_area (j, kcr, w) |
Agricultural production area | \(10^6 ha\) | x | |
| vm_dem_seed (i, kall) |
Demand for seed | \(10^6 tDM/yr\) | x | |
| vm_land (j, land) |
Land area of the different land types | \(10^6 ha\) | x | |
| vm_manure (i, kli, awms, npk) |
Calculation of manure excreted in confinements | \(10^6 t X\) | x | |
| vm_manure_recycling (i, npk) |
Manure being recycled to croplands | \(10^6 t X\) | x | |
| vm_nr_som_fertilizer (j) |
Uptake of soil organic matter from plants | \(Mt N/yr\) | x | |
| vm_prod_reg (i, kall) |
Regional aggregated production | \(10^6 tDM/yr\) | x | |
| vm_res_biomass_ag (i, kcr, attributes) |
Production of aboveground residues in each region | \(10^6 tDM\) | x | |
| vm_res_biomass_bg (i, kcr, dm_nr) |
Production of belowground residues in each region | \(10^6 tDM\) | x | |
| vm_res_recycling (i, npk) |
Residues recycled to croplands in respective nutrients Nr P K units | \(10^6 tX\) | x |
| Description | Unit | |
|---|---|---|
| vm_nr_eff (i) |
Cropland nutrient uptake efficiency | \(Tg N/yr\) |
| vm_nr_eff_pasture (i) |
Pasture nutrient uptake efficiency | \(Tg N/yr\) |
| vm_nr_inorg_fert_costs (i) |
Cost of inorganic fertilizers | \(10^6 USD_{05MER}/yr\) |
| vm_nr_inorg_fert_reg (i, land_ag) |
Inorganic fertilizer application | \(Tg N/yr\) |
This realization calculates the nitrogen balance for crop land and pasture land using exogenous uptake efficiencies. Several scenarios are available for the efficiency.
For cropland the equation q50_nr_bal_crp balances the withdrawals of nitrogen with the share of all incoming fluxes that can be uptaken by the crop.
\[\begin{multline*} vm\_nr\_eff(i2) \cdot v50\_nr\_inputs(i2) \geq \sum_{kcr}v50\_nr\_withdrawals(i2,kcr) \end{multline*}\]
q50_nr_inputs sums of all nitrogen inputs applied to croplands. Organic nitrogen inputs are largely predefined by other modules. Inorganic fertilizers are a free variable that allow to balance the nutrient inputs with requirements.
\[\begin{multline*} v50\_nr\_inputs(i2) = vm\_res\_recycling(i2,"nr") + \sum_{cell(i2,j2),kcr,w}\left( vm\_area(j2,kcr,w) \cdot f50\_nr\_fix\_area(kcr)\right) + vm\_manure\_recycling(i2,"nr") + \sum_{kli}\left( vm\_manure\left(i2, kli, "stubble\_grazing","nr"\right)\right) + vm\_nr\_inorg\_fert\_reg(i2,"crop") + \sum_{cell(i2,j2)}vm\_nr\_som\_fertilizer(j2) + \sum_{ct}f50\_nitrogen\_balanceflow(ct,i2) + v50\_nr\_deposition(i2,"crop") \end{multline*}\]
withdrawals from cropland consist of nitrogen in the harvested crop plus nitrogen in residues (above and below ground) minus the part of nitrogen which is fixed within the crop, minus nitrogen inflow from seeds.
\[\begin{multline*} v50\_nr\_withdrawals(i2,kcr) = \left(1-\sum_{ct}f50\_nr\_fix\_ndfa(ct,i2,kcr)\right) \cdot \left(vm\_prod\_reg(i2,kcr) \cdot fm\_attributes("nr",kcr) + vm\_res\_biomass\_ag(i2,kcr,"nr") + vm\_res\_biomass\_bg(i2,kcr,"nr")\right) - vm\_dem\_seed(i2,kcr) \cdot fm\_attributes("nr",kcr) \end{multline*}\]
The nitrogen surplus is defined as inputs minus withdrawals
\[\begin{multline*} v50\_nr\_surplus\_cropland(i2) = v50\_nr\_inputs(i2) - \sum_{kcr} v50\_nr\_withdrawals(i2,kcr) \end{multline*}\]
For pasture land the equation q50_nr_bal_pasture balances nitrogen withdrawals from pasture production with the nitrogen inputs, using a nitrogen use efficiency as scenario parameter (or potentially an endogenous solution).
\[\begin{multline*} vm\_nr\_eff\_pasture(i2) \cdot v50\_nr\_inputs\_pasture(i2) \geq v50\_nr\_withdrawals\_pasture(i2) \end{multline*}\]
The nitrogen surplus of pastures is the difference between inputs and withdrawals:
\[\begin{multline*} v50\_nr\_surplus\_pasture(i2) = v50\_nr\_inputs\_pasture(i2) - v50\_nr\_withdrawals\_pasture(i2) \end{multline*}\]
Inputs include manure excreted during grazing, inorganic fertilizers, atmospheric deposition and biological fixation In contrast to crop land where the nitrogen fixation rates are crop specific and production-dependent (applied to ton dry matter of crops produces) for pastures the fixation rates are given per area. Again, this equation defines the amount of inorganic fertilizer required (vm_nr_inorg_fert_reg), since all other influxes are given by other modules.
\[\begin{multline*} v50\_nr\_inputs\_pasture(i2) = \sum_{kli}\left(vm\_manure\left(i2, kli, "grazing", "nr"\right)\right) + vm\_nr\_inorg\_fert\_reg(i2,"past") + \sum_{cell(i2,j2)} vm\_land(j2,"past") \cdot \sum_{ct}f50\_nr\_fixation\_rates\_pasture(ct,i2) + v50\_nr\_deposition(i2,"past") \end{multline*}\]
Withdrawals include gras harvest by grazing animals and mowing
\[\begin{multline*} v50\_nr\_withdrawals\_pasture(i2) = vm\_prod\_reg(i2,"pasture") \cdot fm\_attributes("nr","pasture") \end{multline*}\]
For both crop land and pasture land, this equation gives the amount of nitrogen deposited from the atmosphere.
\[\begin{multline*} v50\_nr\_deposition(i2,land) = \sum_{ct,cell(i2,j2)}\left(i50\_atmospheric\_deposition\_rates(ct,j2,land) \cdot vm\_land(j2,land)\right) \end{multline*}\]
Having calculated the amount of nitrogen fertilizer required (see above) now the resulting cost are derived. They are part of the objective function.
\[\begin{multline*} vm\_nr\_inorg\_fert\_costs(i2) = \sum_{land\_ag}vm\_nr\_inorg\_fert\_reg(i2,land\_ag) \cdot s50\_fertilizer\_costs \end{multline*}\]
Limitations There are no known limitations.
This realization sets the demand for inorganic fertilizer and associated costs to zero.
Limitations There are no known limitations.
| Description | Unit | A | B | |
|---|---|---|---|---|
| f50_atmospheric_deposition_rates (t_all, j, land, dep_scen50) |
Nr deposition rates per area | \(tNr/ha\) | x | |
| f50_nitrogen_balanceflow (t_all, i) |
Balancelfow to account for unrealistically high SNUpEs on croplands | \(10^6 tNr/yr\) | x | |
| f50_nitrogen_balanceflow_pasture (t_all, i) |
Balancelfow to account for unrealistically high NUE on pastures | \(10^6 tNr/yr\) | x | |
| f50_nr_fix_area (kcr) |
Nr fixation rates per area | \(tNr/ha\) | x | |
| f50_nr_fix_ndfa (t_all, i, kcr) |
Nr fixation rates per Nr in plant biomass | \(tNr/tNr\) | x | |
| f50_nr_fixation_rates_pasture (t_all, i) |
Nr fixation rates per pasture area | \(tNr/ha\) | x | |
| f50_nue_pasture (t_all, i, scen_neff50) |
selected scenario values for soil nitrogen uptake efficiency | \(1\) | x | |
| f50_snupe (t_all, i, scen_neff50) |
selected scenario values for soil nitrogen uptake efficiency | \(1\) | x | |
| i50_atmospheric_deposition_rates (t, j, land) |
Atmospheric deposition rate | \(t N/ha\) | x | |
| p50_country_dummy_cropneff (iso) |
Dummy parameter indicating whether country is affected by crop neff scenario | \(1\) | x | |
| p50_country_dummy_pastneff (iso) |
Dummy parameter indicating whether country is affected by pasture neff scenario | \(1\) | x | |
| p50_cropneff_region_shr (t, i) |
Weighted share of region with regards to crop neff scenario of countries | \(1\) | x | |
| p50_pastneff_region_shr (t, i) |
Weighted share of region with regards to pasture neff scenario of countries | \(1\) | x | |
| q50_nr_bal_crp (i) |
Cropland nutrient inputs have to equal withdrawals and losses | \(Tg N/yr\) | x | |
| q50_nr_bal_pasture (i) |
Nitrogen balance pasture lands | \(Tg N/yr\) | x | |
| q50_nr_cost_fert (i) |
Fertilizer costs | \(10^6 USD_{05MER}/yr\) | x | |
| q50_nr_deposition (i, land) |
Atmospheric deposition | \(Tg N/yr\) | x | |
| q50_nr_inputs (i) |
Calculating nr withdrawals | \(Tg N/yr\) | x | |
| q50_nr_inputs_pasture (i) |
Nitrogen inputs to pastures | \(Tg N/yr\) | x | |
| q50_nr_surplus (i) |
Calculating nr surplus | \(Tg N/yr\) | x | |
| q50_nr_surplus_pasture (i) |
Nitrogen surplus on pastures | \(Tg N/yr\) | x | |
| q50_nr_withdrawals (i, kcr) |
Calculating nr withdrawals | \(Tg N/yr\) | x | |
| q50_nr_withdrawals_pasture (i) |
Nitrogen withdrawals from pastures | \(Tg N/yr\) | x | |
| s50_fertilizer_costs | Costs of fertilizer | \(USD_{05MER}/tN\) | x | |
| v50_nr_deposition (i, land) |
Atmospheric deposition | \(Tg N/yr\) | x | |
| v50_nr_inputs (i) |
Total inputs to croplands | \(Tg N/yr\) | x | |
| v50_nr_inputs_pasture (i) |
Total inputs to croplands | \(Tg N/yr\) | x | |
| v50_nr_surplus_cropland (i) |
Total Nr surplus on cropland soils | \(Tg N/yr\) | x | |
| v50_nr_surplus_pasture (i) |
Total Nr surplus on pasture soils | \(Tg N/yr\) | x | |
| v50_nr_withdrawals (i, kcr) |
Withdrawals of Nr from cropland soils | \(Tg N/yr\) | x | |
| v50_nr_withdrawals_pasture (i) |
Withdrawals of Nr from pasture soils | \(Tg N/yr\) | x |
| description | |
|---|---|
| attributes | Product attributes characterizing a product (such as weight or energy content) |
| awms | animal waste management systems |
| cell(i, j) | number of LPJ cells per region i |
| cropneff_countries(iso) | countries to be affected by chosen crop neff scenario |
| ct(t) | Current time period |
| dep_scen50 | Scenario for atmospheric deposition |
| deposition_source51 | Source of atmospheric deposition |
| dm_nr(attributes) | dry matter and nr |
| i | all economic regions |
| i_to_iso(i, iso) | mapping regions to iso countries |
| i2(i) | World regions (dynamic set) |
| iso | list of iso countries |
| j | number of LPJ cells |
| j2(j) | Spatial Clusters (dynamic set) |
| kall | All products in the sectoral version |
| kcr(kve) | Cropping activities |
| kli(kap) | Livestock products |
| land | Land pools |
| land_ag(land) | Agricultural land pools |
| npk(nutrients) | Plant nutrients |
| pastneff_countries(iso) | countries to be affected by chosen pasture neff scenario |
| scen_neff50 | Scenario for uptake efficiency |
| t_all(t_ext) | 5-year time periods |
| t(t_all) | Simulated time periods |
| type | GAMS variable attribute used for the output |
| w | Water supply type |
Benjamin Bodirsky
09_drivers, 10_land, 11_costs, 16_demand, 17_production, 18_residues, 30_crop, 50_nr_soil_budget, 51_nitrogen, 55_awms, 59_som