Organic and mineral P attached to soil particles may be transported by surface runoff to the main channel. This form of phosphorus is associated with the sediment loading from the HRU and changes in sediment loading will be reflected in the loading of these forms of phosphorus. The amount of phosphorus transported with sediment to the stream is calculated with a loading function developed by McElroy et al. (1976) and modified by Williams and Hann (1978).

$sedP_{surf}=0.001*conc_{sedP}*\frac{sed}{area_{hru}}*\varepsilon_{P:sed}$ 4:2.4.1

where $sedP_{surf}$ is the amount of phosphorus transported with sediment to the main channel in surface runoff (kg P/ha), $conc_{sedP}$ is the concentration of phosphorus attached to sediment in the top 10 mm (g P/ metric ton soil), $sed$ is the sediment yield on a given day (metric tons), $area_{hru}$ is the HRU area (ha), and $\varepsilon_{P:sed}$ is the phosphorus enrichment ratio.

The concentration of phosphorus attached to sediment in the soil surface layer, $conc_{sedP}$, is calculated:

4:2.4.2

where is the amount of phosphorus in the active mineral pool in the top 10 mm (kg P/ha), is the amount of phosphorus in the stable mineral pool in the top 10 mm (kg P/ha), is the amount of phosphorus in humic organic pool in the top 10 mm (kg P/ha), is the amount of phosphorus in the fresh organic pool in the top 10 mm (kg P/ha), is the bulk density of the first soil layer (Mg/m), and is the depth of the soil surface layer (10 mm).

The enrichment ratio is defined as the ratio of the concentration of phosphorus transported with the sediment to the concentration of phosphorus in the soil surface layer. SWAT+ will calculate an enrichment ratio for each storm event, or allow the user to define a particular enrichment ratio for phosphorus attached to sediment that is used for all storms during the simulation. To calculate the enrichment ratio, SWAT+ uses a relationship described by Menzel (1980) in which the enrichment ratio is logarithmically related to sediment concentration. The equation used to calculate the phosphorus enrichment ratio, $\varepsilon_{P:sed}$, for each storm event is:

$\varepsilon_{P:sed}=0.78*(conc_{sed,surq})^{-0.2468}$ 4:2.4.3

where $conc_{sed,surq}$ is the concentration of sediment in surface runoff (Mg $sed$/m$^3$ H$_2$O). The concentration of sediment in surface runoff is calculated:

$conc_{sed,surq}=\frac{sed}{10*area_{hru}*Q_{surf}}$ 4:2.4.4

where is the sediment yield on a given day (metric tons), is the HRU area (ha), and is the amount of surface runoff on a given day (mm HO).

Table 4:2-4: SWAT+ input variables that pertain to loading of P attached to sediment.