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N Reduction — Equations and Routing

The N reduction chain

N reductions flow from individual fields through retention in the landscape to coastal targets:

Field N effect (kg N/ha/yr × ha)
    × (1 − retention fraction)
    → N arriving at coast from that field
    → summed over all fields in ID15 → rr(ret)   [kg N/yr]
    + MW N reduction → MW_Red_ret(ret)            [kg N/yr]
    → summed over all ret in k → kr(k)            [tons N/yr]
    + WWT reduction → WWTkr(k)                    [tons N/yr]
    + overflow treatment → OF_N_red(k)             [tons N/yr]
    = Total_reduction_k(k) ≥ var_N × N_Targets(k)

Core equation: N reduction in ID15 (Nredwater)

Nredwater(ret)..  rr(ret) =e=
    sum(i$Reti(ret,i),  sum(j$NR(j),  PotV(i,j) * NEffM(i,j) * x(i,j)))             [No retention]
  + sum(i$Reti(ret,i),  PotV(i,"BZ10") * NEffM(i,"BZ10") * x(i,"BZ10") * (1-SurfRet(i)/100))
  + sum(i$Reti(ret,i),  PotV(i,"BZ20") * NEffM(i,"BZ20") * x(i,"BZ20") * (1-SurfRet(i)/100))  [Surface retention]
  + sum(i$Reti(ret,i),  sum(j$TR(j),  PotV(i,j) * NEffM(i,j) * x(i,j) * (1-TotRet(i)/100)))   [Total retention]
  + sum(i$Reti(ret,i),  sum(j$comb2(j), NEffM(i,j) * x(i,j)));                                 [Combined BZ measures: pre-calculated]

Note on comb2: For combined measures that include a buffer zone component (NPB10_BZ10, NPB10_BZ20, NPB20_BZ10, NPB20_BZ20), the N effect (NEffM(i,j)) is pre-calculated as a total kg/yr value (not per ha) that already incorporates the BZ potential and retention fraction. Hence no further multiplication by PotV or retention factor.

Retention types

See Retention concepts for full explanation. Summary:

Set Measures Retention applied Factor
TR(j) — Total retention CCS, CCW, EC, IC, SA, FO, EW, LRh, N20, N10 Full landscape retention (1 − TotRet(i)/100)
SR(j) — Surface retention BZ10, BZ20 Surface-flow retention only (1 − SurfRet(i)/100)
NR(j) — No retention WL, LRl No additional retention 1 (no factor)

Why WL and LRl use no retention: These convert wet/low-lying fields entirely out of agricultural production. The N reduction happens at the field itself, and no further routing through the landscape drainage system is assumed.

Mini-wetland N reduction (MW_red_ret_eq)

MW_Red_ret(ret) =e=
    (sum(mw1$mw1ret(ret,mw1), mw1eff * mw1x(mw1))
   + sum(mw2$mw2ret(ret,mw2), mw2eff * mw2x(mw2))
   + sum(mw3$mw3ret(ret,mw3), mw3eff * mw3x(mw3)))
   × (1 − SurfRet_ID15(ret)/100)

MW N effects (kg N/yr per wetland): | Size | Catchment area | N effect (mwXeff) | |---|---|---| | MW1 | 20 ha | 94.4 kg N/yr | | MW2 | 50 ha | 236 kg N/yr | | MW3 | 100 ha | 472 kg N/yr |

The surface retention of the ID15 (SurfRet_ID15) is applied to MW — added Dec 2024 at Hans Estrup's request.

MW potential cap: Total MW area in a ret cannot exceed the natural potential (MW_precalc2, derived from MiniPot files) or the VP2-implemented MW area (VP2_adapt), whichever is larger. This prevents over-counting relative to prior plans.

Coastal catchment aggregation (KystReductionN)

KystReductionN(k)..  kr(k) =e= sum(ret$kret(k,ret), rr(ret) + MW_Red_ret(ret)) / 1000;

Division by 1000 converts kg N/yr → tons N/yr to match target units.

WWT and overflow contributions

WWTReductionN(k)..   WWTkr(k) =e= sum(p$kp(k,p), sum(j, (1-WWTRetention(p)/100) * WWTNeff(p,j) * WWTx(p,j))) / 1000;

OF_N_red_eq(k)..     OF_N_red(k) =e= sum(pp$kpp(k,pp), OFNeff(pp) * OFx(pp)) / 1000;

WWT N reduction is also subject to retention at the plant location (WWTRetention(p)).

Target constraint (KysttargetN)

KysttargetN(k)..  Total_reduction_k(k) + exceed(k) =g= var_N × N_Targets(k);
  • Total_reduction_k(k) = kr(k) + WWTkr(k) + OF_N_red(k)
  • exceed(k) is a positive variable with penalty Penalty1 = 9.999×10¹² DKK per ton N in the objective. It will only be non-zero if the target genuinely cannot be met.
  • var_N = 0 deactivates all N targets (the constraint becomes non-binding).
  • N targets loaded from N_targets_DEC2024.inc (104 records; 81 active catchments; total 13,800 tons N/yr).

N effectiveness parameters (NEffM)

Key values by measure (kg N/ha/yr):

Measure Soil Livestock NEffM
CCS Sandy (<5) High (≥0.8) 45
CCS Sandy (<5) Low (<0.8) 32
CCS Clay (≥5) High (≥0.8) 24
CCS Clay (≥5) Low (<0.8) 12
CCW Same as CCS — Same as CCS
EC Sandy (<5) any 51
EC Clay (≥5) any 34
WL any any 90 (changed 2026-01-20; was 190/120 by soil)
IC any any 14
EW any any 17
LRl any any 40
N20 any any 0.2 × 0.18 × Nhan(i) (field-specific)
N10 any any 0.1 × 0.18 × Nhan(i) (field-specific)
FO any any leaching(i) − 8 (field-specific)
BZ10 any any leaching(i) − 12 (field-specific)
BZ20 any any leaching(i) − 12 (same as BZ10)
LRh any any see differentiation_effects.inc
SA any any see differentiation_effects.inc

Note on LRh and SA: Both are spatially differentiated per coastal catchment via differentiation_effects.inc (108 catchments, updated 2026-04-05). LRh corrections = 6–18 (NEffM = prodeff(i) − 6 to − 18); SA corrections = 6–27 (NEffM = prodeff(i) − 6 to − 27). See LRh.md and SA.md for per-catchment tables.

Open questions

  1. ✅ LRh and SA N effects: confirmed from differentiation_effects.inc. See individual measure pages.
  2. The WL N effect change (90 kg/ha flat) — is this final for VP3 or still under discussion?
  3. ✅ SurfRet_ID15: confirmed from direct file read (2026-04-05) — it is a separate dataset at sub-catchment (ret) level, ~3,305 entries, Sep 2023 vintage. Not the same as averaging field-level SurfRet(i) values.

Concepts: - Retention types — TR / SR / NR explained with measure lists - Spatial Hierarchy — ID15 / coastal catchment / WWT routing

NR measures (no retention): - WL, LRl

SR measures (surface retention): - BZ10, BZ20

TR measures (total retention): - CCS, CCW — catch crops - EC — energy crops - IC, EW — interrow cover / early sowing - SA, LRh — spatially differentiated (108 catchments) - FO — afforestation - N10, N20 — N norm reductions

Infrastructure: - MW — mini-wetlands (SurfRet_ID15 applied) - WWT — wastewater treatment N reduction