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P Loss Pathways

Phosphorus reaches watercourses from agricultural fields through three distinct physical mechanisms. The model tracks each pathway separately and assigns different measures to different pathways based on where and how they intercept P.

The three pathways

1. Erosion (erosion_field(i))

Physical process: Surface runoff detaches and transports P-enriched soil particles into ditches and streams. Dominant on sloping fields with erodible soils, especially on bare soil in late autumn/winter.

Parameter: erosion_field(i) = total annual P loss via erosion from field i (kg P/yr)

Measures that reduce erosion: | Measure | Reduction factor | |---|---| | PPC | 0.90 × erosion_field | | BZ10 | 0.62 × erosion_field [if BZ10Pot > 0.2] | | BZ20 | 0.75 × erosion_field [if BZ20Pot > 0.2] | | OT | 0.50 × erosion_field | | PWET | 15 × PotV (flat rate, not proportional to erosion_field) | | FO | erosion_field × (PotV/IniPotV) | | LRh | (1−lav) × erosion_field | | LRl | 0 (explicitly set to zero) | | NPB10 | erosion_field × 0.05 | | NPB20 | erosion_field × 0.20 |

2. Macropore flow (macropore_field(i))

Physical process: Preferential flow through biopores, cracks, and earthworm channels carries dissolved P rapidly to drains. Dominant on heavy clay soils with high P saturation. This pathway bypasses the soil matrix and can be a major P loss route in spring/autumn.

Parameter: macropore_field(i) = total annual P loss via macropores from field i (kg P/yr)

Measures that reduce macropore P: | Measure | Reduction factor | |---|---| | NPB10 | macropore_field × 0.05 | | NPB20 | macropore_field × 0.20 | | FO | macropore_field × 0.35 × (PotV/IniPotV) | | LRh | (1−lav) × macropore_field × 0.35 |

3. Matrix flow (matrix_ha(i))

Physical process: Slow, diffuse movement of dissolved P through the soil matrix to drains. Usually a background loss pathway, less episodic than macropore. Expressed as kg P/ha/yr rather than kg P/yr because it depends on the treated area.

Parameter: matrix_ha(i) = P loss per hectare via matrix flow (kg P/ha/yr)

Measures that reduce matrix P: | Measure | Formula | |---|---| | NPB10 | PotV × matrix_ha × 0.05 | | NPB20 | PotV × matrix_ha × 0.20 |

Note: matrix_ha is a per-ha rate, so it must be multiplied by PotV(i,j) to get total kg P reduction.

Total P effect

P_Effects_Total(i,j) = P_Effects_erosion(i,j) + P_Effects_macropore(i,j) + P_Effects_matrix(i,j)

This is computed for all field measures and then used in the P reduction equations. Fields where MarkAccess(2018) is an excluded crop code have all P effects set to zero (same crop exclusion as for N).

Mini-wetland P effects

MW treats drainage water at the catchment outlet, intercepting P from all three pathways. The model uses a single combined effect: 

P_Effects_MW_Matrix(ret) = 0.45 × avg(matrix_ha over fields with macropore loss)
P_Effects_MW_macropore(ret) = 0.45 × avg(macropore_field/ha over fields with macropore loss)
(Note: the 0.45 factor was 0.43 prior to Nov 2024 update.)

Only fields with macropore loss > 0 are included in the ret-level average (per Hans Estrup, Nov 2024).

Which fields have high P loss?

The model selects P measures cost-effectively — they will tend to be chosen on fields where: - erosion_field(i) is high (sloping, erodible) - macropore_field(i) is high (heavy clay, high P saturation) - matrix_ha(i) is high

The commented-out code x.UP(i,j) = 0; x.UP(i,j)$(...) = 1 scenarios that were explored filtered fields to just the high P loss ones (using 75th and 90th percentile thresholds for erosion, matrix, and macropore).

Data sources

Parameter File
erosion_field(i) erosion_field.inc
macropore_field(i) macropore_field.inc
matrix_ha(i) matrix_ha.inc
P_loss_stretch P_loss_stretch.inc (for stream stretches)
Total_P_loss(up_lakecatch) Total_P_loss.inc

Model structure: - P Reduction equations

Erosion-pathway measures: - PPC — permanent plant cover; 90% erosion reduction - OT — overwintering stubble; 50% erosion reduction - BZ10 — 10 m buffer zone; 62% erosion reduction (P threshold applies) - BZ20 — 20 m buffer zone; 75% erosion reduction - PWET — P wetland; flat 15 kg P/ha/yr via sedimentation - FO — afforestation; proportional erosion reduction - LRh — high-land retirement; non-low-lying fraction erosion

Macropore-pathway measures: - NPB10 — 10 ha nature/peatland buffer; 5% macropore reduction - NPB20 — 20 ha nature/peatland buffer; 20% macropore reduction - FO — also reduces macropore P (35%) - LRh — also reduces macropore P (35%)

Matrix-pathway measures: - NPB10, NPB20 — 5% / 20% matrix reduction

Stream and catchment-level P: - MW — mini-wetlands intercept matrix + macropore P at catchment outlet - IBZ — in-stream buffer zone; field-level stream bank measure - Stream measures — ochre traps, sand traps, re-meandering, raising, trees