Soluble Phosphorus Movement

The primary mechanism of phosphorus movement in the soil is by diffusion. Diffusion is the migration of ions over small distances (1-2 mm) in the soil solution in response to a concentration gradient. Due to the low mobility of solution phosphorus, surface runoff will only partially interact with the solution P stored in the top 10 mm of soil. The amount of solution P transported in surface runoff is:

$P_{surf}=\frac{P_{solution,surf}*Q_{surf}}{\rho_b*depth_{surf}*k_{d,surf}}$ 4:2.3.1

where $P_{surf}$ is the amount of soluble phosphorus lost in surface runoff (kg P/ha), $P_{solution,surf}$ is the amount of phosphorus in solution in the top 10 mm (kg P/ha), $Q_{surf}$ is the amount of surface runoff on a given day (mm H$_2$O), $\rho_b$ is the bulk density of the top 10 mm (Mg/m$^3$) (assumed to be equivalent to bulk density of first soil layer), $depth_{surf}$ is the depth of the “surface” layer (10 mm), and $k_{d,surf}$ is the phosphorus soil partitioning coefficient (m$^3$/Mg). The phosphorus soil partitioning coefficient is the ratio of the soluble phosphorus concentration in the surface 10 mm of soil to the concentration of soluble phosphorus in surface runoff.

Table 4:2-3: SWAT+ input variables that pertain to soluble P runoff.

Variable Name	Definition	Input File
SOL_BD	$\rho_b$: Bulk density(Mg/m$^3$)	.sol
PHOSKD	$k_{d,surf}$: Phosphorus soil partitioning coefficient (m$^3$/Mg)	.bsn