MAgPIE - An Open Source land-use modeling framework

4.6.0

created with goxygen 1.3.1

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: macceff_aug22)
  Description Unit A
fm_attributes
(attributes, kall)
Conversion factors - where X is ton N P K C DM WM or PJ GE \(X/tDM\) x
im_maccs_mitigation
(t, i, emis_source, pollutants)
Technical mitigation of GHG emissions \(percent\) 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_fallow
(j)
Fallow land \(10^6 ha\) 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

Output

module outputs
  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 \(Tg N/yr\)

Realizations

(A) macceff_aug22

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.

\[\begin{multline*} v50\_nr\_inputs(i2) = vm\_res\_recycling(i2,"nr") + \sum_{cell(i2,j2),kcr,w}\left( vm\_area(j2,kcr,w) \cdot f50\_nr\_fix\_area(kcr)\right) + \sum_{cell(i2,j2)}\left(vm\_fallow(j2) \cdot f50\_nr\_fix\_area("tece")\right) + vm\_manure\_recycling(i2,"nr") + \sum_{kli}\left( vm\_manure\left(i2, kli, "stubble\_grazing","nr"\right)\right) + vm\_nr\_inorg\_fert\_reg(i2,"crop") + \sum_{cell(i2,j2)}vm\_nr\_som\_fertilizer(j2) + \sum_{ct}f50\_nitrogen\_balanceflow(ct,i2) + v50\_nr\_deposition(i2,"crop") \end{multline*}\]

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.

\[\begin{multline*} vm\_nr\_inorg\_fert\_costs(i2) = \sum_{land\_ag}vm\_nr\_inorg\_fert\_reg(i2,land\_ag) \cdot s50\_fertilizer\_costs \end{multline*}\]

We first need to transform the MACC curves from a format where they are a function of inputs (approach 1, IPCC) to a function of losses (approach 2, MAgPIE). Approach 2 is more consistent, as emissions can only come from losses, and in the case of nitrogen use efficiency (NUE=I/H), losses (L=I-H) are zero, but approach 1 would still come up with positive emissions. The two approaches (see module 51_nitrogen) are

  1. E_1 = I_1 * EF * (1 - MACCs_O)

  2. E_2 = I_2 * (1 - NUE_2) / (1 - NUE_ef) * EF

with the further condition:

  1. H = I_i * NUE_i

  2. (1 - NUE_2) = (1 - NUE_b) * (1 - MACCs_T)

E: emissions, I: nutrient inputs, EF: emission factor, NUE: nitrogen use efficiency, H: harvested N NUE_ef: the nitrogen use efficiency for which the EF is made NUE_2: nitrogen use efficiency in our model NUE_b: baseline nitrogen use efficiency before application of MACCs MACCs_O: original MACCs to be applied on fertilizer application MACCs_T: transformed MACCs to be applied on nitrogen surplus

We want to derive Maccs_T under the condition that the measured reduction of emissions (R = E / Eb) in both approaches remains equal. combining 1 + 3 and 2 + 3 (4) R_1 = H / NUE_b * EF * (1 - MACCs_O) / (H / NUE_b * EF) (5) R_2 = (H / NUE2 * (1 - NUE2) / (1 - NUE_ef) * EF) / (H / NUE_b * (1 - NUE_b) / (1 - NUE_ef) * EF) (4+5) MACCs_T = MACCs_O * NUE_b / (1 + MACCs_O * (NUE_b - 1)) If the MACCs are expressed relative to a changing emission factor, this could be accomodated in equation 4. Currently we assume a constant emission factor implicit to the MACCs. The year of NUE_ef should be fixed to the baseyear efficiency, as alternative “baseline” improvements would otherwise not reduce the mitigation potential of the MACCs. If the MACCs relate to a global emission factor NUE_ef should be the global NUE, otherwise the regional NUE. The name of the MACC category “inorg_fert_n2o” actually includes all types of soil N2O emissions. Most of these measures also reduce general Nr surpluses. We therefor apply it here to Nr soil efficiency more generally.

if(s50_maccs_global_ef = 1,
  i50_maccs_mitigation_transf(t,i) =
    im_maccs_mitigation(t,i,"inorg_fert","n2o_n_direct")*s50_maccs_implicit_nue_glo / (1 + im_maccs_mitigation(t,i,"inorg_fert","n2o_n_direct") * (s50_maccs_implicit_nue_glo - 1));
  i50_maccs_mitigation_pasture_transf(t,i) =
    im_maccs_mitigation(t,i,"inorg_fert","n2o_n_direct")*s50_maccs_implicit_nue_glo / (1 + im_maccs_mitigation(t,i,"inorg_fert","n2o_n_direct") * (s50_maccs_implicit_nue_glo - 1));
else
  i50_maccs_mitigation_transf(t,i) =
    im_maccs_mitigation(t,i,"inorg_fert","n2o_n_direct")*i50_nr_eff_bau("y2010",i) / (1 + im_maccs_mitigation(t,i,"inorg_fert","n2o_n_direct") * (i50_nr_eff_bau("y2010",i) - 1));
  i50_maccs_mitigation_pasture_transf(t,i) =
    im_maccs_mitigation(t,i,"inorg_fert","n2o_n_direct")*i50_nr_eff_pasture_bau("y2010",i) / (1 + im_maccs_mitigation(t,i,"inorg_fert","n2o_n_direct") * (i50_nr_eff_pasture_bau("y2010",i) - 1));
);

After transformation of the MACCs, we can calculate NUE_2 (vm_nr_eff) as the result of a baseline NUE improvement and an MACC-driven further increase of NUE. The nitrogen use efficiency is the inverse of the nitrogen loss share. The loss share is estimated as a baseline loss share that describes the baseline technological improvement of NUE, and a reduction of this loss share by technical mitigation. We assume that the MACCs reduce the remaining losses proportional, so that emissions cannot become negative, and the baseline improvement reduces the mitigation potential of the MACCs.

 vm_nr_eff.fx(i) = 1 - (1-i50_nr_eff_bau(t,i)) * (1 - i50_maccs_mitigation_transf(t,i));
 vm_nr_eff_pasture.fx(i)= 1 - (1-i50_nr_eff_pasture_bau(t,i)) * (1 - i50_maccs_mitigation_pasture_transf(t,i));

Limitations There are no known limitations.

Definitions

Objects

module-internal objects (A: macceff_aug22)
  Description Unit A
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_base_pasture
(t_all, i, scen_neff_pasture50)
selected scenario values for soil nitrogen uptake efficiency \(1\) x
f50_snupe_base
(t_all, i, scen_neff_cropland50)
selected scenario values for soil nitrogen uptake efficiency \(1\) x
i50_atmospheric_deposition_rates
(t, j, land)
Atmospheric deposition rate \(t N/ha\) x
i50_maccs_mitigation_pasture_transf
(t, i)
Transformed marginal abatement cost curves to be consistent with pasture NUE implementaton \(1\) x
i50_maccs_mitigation_transf
(t, i)
Transformed marginal abatement cost curves to be consistent with cropland SNuPE implementaton \(1\) x
i50_nr_eff_bau
(t_all, i)
Business as usual soil nitrogen uptake efficiency before MACCs mitigation \(1\) x
i50_nr_eff_pasture_bau
(t_all, i)
Business as usual pasture nitrogen use efficiency before MACCs mitigation \(1\) 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
s50_maccs_global_ef Do maccs assume global emission factor \(binary\) x
s50_maccs_implicit_nue_glo Global nitrogen use efficiency implicit to MACCs 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

Sets

sets in use
  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
emis_source Emission sources
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
pollutants(pollutants_all) subset of pollutants_all that can be taxed
scen_neff_cropland50 Scenario for SNUpE on croplands
scen_neff_pasture50 Scenario for NUE on pastures
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

Authors

Benjamin Bodirsky

See Also

09_drivers, 10_land, 11_costs, 16_demand, 17_production, 18_residues, 30_crop, 50_nr_soil_budget, 51_nitrogen, 55_awms, 57_maccs, 59_som

References