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 | |
| 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 (j) |
Release of soil organic matter | \(Tg N/yr\) | 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_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 withdrawls (see below) with the share of all incoming fluxes that can be uptaken by the crop land. Since all other inflows except vm_nr_inorg_fert_reg are given (by other modules) this equation defines the amount of inorganic fertilizer required.
\[\begin{multline*} v50\_nr\_eff(i2) \cdot \left( vm\_res\_recycling(i2,"nr") + \sum_{cell(i2,j2),kcr,w}\left( vm\_area(j2,kcr,w) \cdot f50\_nr\_fix\_area(kcr)\right) + vm\_manure\_recycling(i2,"nr") + \sum_{kli}\left( vm\_manure\left(i2, kli, "stubble\_grazing","nr"\right)\right) + vm\_nr\_inorg\_fert\_reg(i2,"crop") + \sum_{cell(i2,j2)}vm\_nr\_som(j2) + \sum_{ct}f50\_nitrogen\_balanceflow(ct,i2) + v50\_nr\_deposition(i2,"crop")\right) \geq \sum_{kcr}v50\_nr\_withdrawals(i2,kcr) \end{multline*}\]
Withdrawls from crop land consist of nitrogen that can not be fixed by crop production or by residues (above and below ground), less the nitrogen inflow from seeds.
\[\begin{multline*} v50\_nr\_withdrawals(i2,kcr) = \left(1-\sum_{ct}f50\_nr\_fix\_ndfa(ct,i2,kcr)\right) \cdot \left(vm\_prod\_reg(i2,kcr) \cdot fm\_attributes("nr",kcr) + vm\_res\_biomass\_ag(i2,kcr,"nr") + vm\_res\_biomass\_bg(i2,kcr,"nr")\right) - vm\_dem\_seed(i2,kcr) \cdot fm\_attributes("nr",kcr) \end{multline*}\]
For pasture land the equation q50_nr_bal_pasture balances nitrogen discharge from pasture production with the share of all inflows that can be uptaken by pasture land such as manure, plant fixation, and atmospheric deposition. In contrast to crop land where the nitrogen fixation rates are crop specific (applied to ton dry matter of crops produces) for paste 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).
\[\begin{multline*} v50\_nr\_eff\_pasture(i2) \cdot \left(\sum_{kli}\left(vm\_manure\left(i2, kli, "grazing", "nr"\right)\right) + vm\_nr\_inorg\_fert\_reg(i2,"past") + \sum_{cell(i2,j2)} vm\_land(j2,"past") \cdot \sum_{ct}f50\_nr\_fixation\_rates\_pasture(ct,i2) + v50\_nr\_deposition(i2,"past")\right) \geq vm\_prod\_reg(i2,"pasture") \cdot fm\_attributes("nr","pasture") \end{multline*}\]
For both crop land and pasture land, this equation gives the amount of nitrogen deposited from the atmosphere.
\[\begin{multline*} v50\_nr\_deposition(i2,land) = \sum_{cell(i2,j2)}\left(ic50\_atmospheric\_deposition\_rates(i2,land) \cdot vm\_land(j2,land)\right) \end{multline*}\]
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, i, 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 | |
| ic50_atmospheric_deposition_rates (i, land) |
atmospheric deposition rate | \(t N/ha\) | 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_withdrawals (i, kcr) |
calculating nr withdrawals | \(Tg N/yr\) | x | |
| s50_fertilizer_costs | Costs of fertilizer | \(USD_{05MER}/tN\) | x | |
| v50_nr_deposition (i, land) |
atmospheric deposition | \(Tg N/yr\) | x | |
| v50_nr_eff (i) |
cropland nutrient uptake efficiency | \(Tg N/yr\) | x | |
| v50_nr_eff_pasture (i) |
pasture nutrient uptake efficiency | \(Tg N/yr\) | x | |
| v50_nr_withdrawals (i, kcr) |
withdrawals of Nr from 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) | Mapping between regions i and clusters j |
| 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 | World regions |
| i2(i) | World regions (dynamic set) |
| j | Spatial clusters |
| 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 |
| scen_neff50 | Scenario for uptake efficiency |
| t_all | 5-year time periods |
| t(t_all) | Simulated time periods |
| type | GAMS variable attribute used for the output |
| w | Water supply type |
Benjamin Bodirsky
10_land, 11_costs, 16_demand, 17_production, 18_residues, 30_crop, 50_nr_soil_budget, 51_nitrogen, 55_awms, 59_som