# Model Documentation

### | Version 4.0

created with goxygen 0.21.1

# 50_nr_soil_budget

# Nitrogen soil budget (50_nr_soil_budget)

## Description

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.

## Interfaces

Interfaces to other modules

### Input

module inputs (A: exoeff_aug16 | B: off)
| 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 |

### Output

module outputs
| 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 | \(Tg N/yr\)

## Realizations

### (A) exoeff_aug16

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.

### (B) off

This realization sets the demand for inorganic fertilizer and associated costs to zero.

> Limitations There are no known limitations.

## Definitions

### Objects

module-internal objects (A: exoeff_aug16 | B: off)
| 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_pasture (t_all, i) | Balancelfow to account for unrealistically high NUE on pastures | \(10^6 tNr/yr\) | x |
f50_nitrogen_balanceflow (t_all, i) | Balancelfow to account for unrealistically high SNUpEs on croplands | \(10^6 tNr/yr\) | x |
f50_nr_fix_area (kcr) | Nr fixation rates per area | \(tNr/ha\) | x |
f50_nr_fixation_rates_pasture (t_all, i) | Nr fixation rates per pasture area | \(tNr/ha\) | x |
f50_nr_fix_ndfa (t_all, i, kcr) | Nr fixation rates per Nr in plant biomass | \(tNr/tNr\) | 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 |

### Sets

sets in use
| description
--- | ---
attributes | Product attributes characterizing a product (such as weight or energy content)
awms | animal waste management systems
dep_scen50 | Scenario for atmospheric deposition
dm_nr(attributes) | dry matter and nr
i | World regions
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
w | Water supply type

## Authors

Benjamin Bodirsky

## See Also

10_land, 11_costs, 16_demand, 17_production, 18_residues, 30_crop, 50_nr_soil_budget, 51_nitrogen, 55_awms, 59_som

## References