MAgPIE - An Open Source land-use modeling framework

4.6.0

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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

Input

Output

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:

3. H = I_i * NUE_i

4. (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

Sets

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