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Combined N+P Measures

Combined measures encode a single farm decision that simultaneously produces N and P effects, with cost savings or synergies relative to implementing the measures separately.

comb(j) — P-only combined measures

These have no N effect. They combine a P-only measure (PPC or OT) with an NPB measure.

Code Components P Effect Cost
PPC_NPB10 PPC + NPB10 0.9 × NPB10 P effects (erosion + macropore + matrix) PPC cost + 0.9 × NPB10 cost
PPC_NPB20 PPC + NPB20 0.9 × NPB20 P effects PPC cost + 0.9 × NPB20 cost
NPB10_OT NPB10 + OT NPB10 P effects (erosion + macropore + matrix) NPB10 + OT
NPB20_OT NPB20 + OT NPB20 P effects NPB20 + OT

PPC synergy: When combined with NPB, PPC reduces erosion (0.9 × full erosion_field) while NPB provides macropore and matrix pathways. The 0.9 factor for PPC_NPB reflects that when NPB already covers 10–20% of the field, the PPC erosion effect is slightly discounted.

Cost formula for comb(j): 

CostM(i,"PPC_NPB10") = (80 + 0.1×prodcost) + 0.9×50
CostM(i,"PPC_NPB20") = (80 + 0.1×prodcost) + 0.9×100
CostM(i,"NPB10_OT")  = 50 + 200
CostM(i,"NPB20_OT")  = 100 + 200

In total cost equations, comb(j) costs are multiplied by PotV(i,j).

comb2(j) — N+P combined measures

These have both N and P effects. They combine an NPB measure with a BZ (buffer zone) measure.

Code N Component P Component Cost formula
NPB10_BZ10 BZ10 N effect × BZ10pot × (1−SurfRet) NPB10 P effects 50×(NPB10 area − BZ10 area) + prodcost×BZ10 area
NPB10_BZ20 BZ20 N effect × BZ20pot × (1−SurfRet) NPB10 P effects 50×(NPB10 area − BZ20 area) + prodcost×BZ20 area
NPB20_BZ10 BZ10 N effect × (1−SurfRet) NPB20 P effects 100×(NPB20 area − BZ10 area) + prodcost×BZ10 area
NPB20_BZ20 BZ20 N effect × (1−SurfRet) NPB20 P effects 100×(NPB20 area − BZ20 area) + prodcost×BZ20 area

N effect for comb2 (pre-calculated): 

NEffM(i,"NPB10_BZ10") = NEffM(i,"BZ10") × PotV(i,"BZ10") × (1 − SurfRet(i)/100)   [total kg N/yr]
This is already a total reduction in kg N/yr (not per ha), so in Nredwater it enters without further multiplication by PotV or retention.

Cost formula for comb2: 

CostM(i,"NPB10_BZ10") = 50 × (PotV(i,"NPB10") − PotV(i,"BZ10")) + prodcost(i) × PotV(i,"BZ10")
This reflects: NPB covers the whole field at 50 DKK/ha, except the BZ portion which must also forgo production (prodcost). The BZ strips are more expensive because of opportunity cost.

In total cost equations, comb2(j) costs are NOT multiplied by PotV (because CostM already incorporates the area calculation).

Why combined measures?

Implementing PPC and NPB separately would require two binary decisions per field, creating integer combinations that the solver can't efficiently handle. By pre-encoding the combination as a single measure, the model avoids this combinatorial complexity while still capturing the joint N+P effects and any cost synergies.

Open questions

  1. The 0.9 discount for PPC effects in PPC_NPB — is this a calibrated synergy factor or a modeling convenience?
  2. For comb2, the N effect pre-calculation already applies SurfRet — is this the correct retention for a BZ-containing combination?