Phosphorus in the humus fraction is partitioned between the active and stable organic pools using the ratio of humus active organic N to stable organic N. The amount of phosphorus in the active and stable organic pools is calculated:

$orgP_{act,ly}=orgP_{hum,ly}*\frac{orgN_{act,ly}}{orgN_{act,ly}+orgN_{sta,ly}}$ 3:2.2.3

$orgP_{sta,ly}=orgP_{hum,ly}*\frac{orgN_{sta,ly}}{orgN_{act,ly}+orgN_{sta,ly}}$ 3:2.2.4

where $orgP_{act,ly}$ is the amount of phosphorus in the active organic pool (kg P/ha), $orgP_{sta,ly}$ is the amount of phosphorus in the stable organic pool (kg P/ha), $orgP_{hum,ly}$ is the concentration of humic organic phosphorus in the layer (kg P/ha), $orgN_{act,ly}$ is the amount of nitrogen in the active organic pool (kg N/ha), and $orgN_{sta,ly}$ is the amount of nitrogen in the stable organic pool (kg N/ha).

Mineralization from the humus active organic P pool is calculated:

$P_{mina,ly}=1.4*\beta_{min}*(\gamma_{tmp,ly}*\gamma_{sw,ly})^{1/2}*orgP_{act,ly}$ 3:2.2.5

where $P_{mina,ly}$ is the phosphorus mineralized from the humus active organic $P$ pool (kg P/ha), $\beta_{min}$ is the rate coefficient for mineralization of the humus active organic nutrients, $\gamma_{tmp,ly}$ is the nutrient cycling temperature factor for layer $ly$, $\gamma_{sw,ly}$ is the nutrient cycling water factor for layer $ly$, and $orgP_{act,ly}$ is the amount of phosphorus in the active organic pool (kg P/ha).

Phosphorus mineralized from the humus active organic pool is added to the solution P pool in the layer.

Decomposition and mineralization of the fresh organic phosphorus pool is allowed only in the first soil layer. Decomposition and mineralization are controlled by a decay rate constant that is updated daily. The decay rate constant is calculated as a function of the C:N ratio and C:P ratio of the residue, temperature and soil water content.

The C:N ratio of the residue is calculated:

$\varepsilon_{C:N}=\frac{0.58*rsd_{ly}}{orgN_{frsh,ly}+NO3_{ly}}$ 3:2.2.6

where $\varepsilon_{C:N}$ is the C:N ratio of the residue in the soil layer, $rsd_{ly}$ is the residue in layer $ly$ (kg/ha), 0.58 is the fraction of residue that is carbon, $orgN_{frsh,ly}$ is the nitrogen in the fresh organic pool in layer $ly$ (kg N/ha), and $NO3_{ly}$ is the amount of nitrate in layer $ly$ (kg N/ha).

The C:P ratio of the residue is calculated:

$\varepsilon_{C:P}=\frac{0.58*rsd_{ly}}{orgP_{frsh,ly}+P_{solution,ly}}$ 3:2.2.7

where $\varepsilon_{C:P}$ is the C:P ratio of the residue in the soil layer, $rsd_{ly}$ is the residue in layer $ly$ (kg/ha), 0.58 is the fraction of residue that is carbon, $orgP_{frsh,ly}$ is the phosphorus in the fresh organic pool in layer $ly$ (kg P/ha), and $P_{solution,ly}$ is the amount of phosphorus in solution in layer $ly$ (kg P/ha).

The decay rate constant defines the fraction of residue that is decomposed. The decay rate constant is calculated:

$\delta_{ntr,ly}=\beta_{rsd}*\gamma_{ntr,ly}*(\gamma_{tmp,ly}*\gamma_{sw,ly})^{1/2}$ 3:2.2.8

where $\delta_{ntr,ly}$ is the residue decay rate constant, $\beta_{rsd}$ is the rate coefficient for mineralization of the residue fresh organic nutrients, $\gamma_{ntr,ly}$ is the nutrient cycling residue composition factor for layer $ly$, $\gamma_{tmp,ly}$ is the nutrient cycling temperature factor for layer $ly$, and $\gamma_{sw,ly}$ is the nutrient cycling water factor for layer $ly$.

The nutrient cycling residue composition factor is calculated:

$\gamma_{ntr,ly}=min[exp[0.693*\frac{\varepsilon_{C:N}-25}{25}],exp[-0.693*\frac{(\varepsilon_{C:P}-200}{200}],1.0]$3:2.2.9

where $\gamma_{ntr,ly}$ is the nutrient cycling residue composition factor for layer $ly$, $\varepsilon_{C:N}$ is the C:N ratio on the residue in the soil layer, and $\varepsilon_{C:P}$ is the C:P ratio on the residue in the soil layer.

Mineralization from the residue fresh organic P pool is then calculated:

$P_{minf,ly}=0.8*\delta_{ntr,ly}*orgP_{frsh,ly}$ 3:2.2.10

where $P_{minf,ly}$ is the phosphorus mineralized from the fresh organic $P$ pool (kg P/ha), $\delta_{ntr,ly}$ is the residue decay rate constant, and $orgP_{frsh,ly}$ is the phosphorus in the fresh organic pool in layer $ly$ (kg P/ha). Phosphorus mineralized from the fresh organic pool is added to the solution $P$ pool in the layer.

Decomposition from the residue fresh organic P pool is calculated:

$P_{dec,ly}=0.2*\delta_{ntr,ly}*orgP_{frsh,ly}$ 3:2.2.11

where $P_{dec,ly}$ is the phosphorus decomposed from the fresh organic $P$ pool (kg P/ha), $\delta_{ntr,ly}$ is the residue decay rate constant, and $orgP_{frsh,ly}$ is the phosphorus in the fresh organic pool in layer $ly$ (kg P/ha). Phosphorus decomposed from the fresh organic pool is added to the humus organic pool in the layer.

Table 3:2-2: SWAT+ input variables that pertain to mineralization.

Decomposition is the breakdown of fresh organic residue into simpler organic components. Mineralization is the microbial conversion of organic, plant-unavailable phosphorus to inorganic, plant-available phosphorus. Immobilization is the microbial conversion of plant-available inorganic soil phosphorus to plant-unavailable organic phosphorus.

The phosphorus mineralization algorithms in SWAT+ are net mineralization algorithms which incorporate immobilization into the equations. The phosphorus mineralization algorithms developed by Jones et al. (1984) are similar in structure to the nitrogen mineralization algorithms. Two sources are considered for mineralization: the fresh organic P pool associated with crop residue and microbial biomass and the active organic P pool associated with soil humus. Mineralization and decomposition are allowed to occur only if the temperature of the soil layer is above 0°C.

Mineralization and decomposition are dependent on water availability and temperature. Two factors are used in the mineralization and decomposition equations to account for the impact of temperature and water on these processes.

The nutrient cycling temperature factor is calculated:

$\gamma_{tmp,ly}=0.9*\frac{T_{soil,ly}}{T_{soil,ly}+exp[9.93-0.312*T_{soil,ly}]}+0.1$ 3:2.2.1

where $\gamma_{tmp,ly}$ is the nutrient cycling temperature factor for layer $ly$, and $T_{soil,ly}$ is the temperature of layer $ly$ (°C). The nutrient cycling temperature factor is never allowed to fall below 0.1.

The nutrient cycling water factor is calculated:

$\gamma_{sw,ly}=\frac{SW_{ly}}{FC_{ly}}$ 3:2.2.2

where $\gamma_{sw,ly}$ is the nutrient cycling water factor for layer $ly$, $SW_{ly}$ is the water content of layer $ly$ on a given day (mm H$_2$O), and $FC_{ly}$ is the water content of layer $ly$ at field capacity (mm H$_2$O). ). The nutrient cycling water factor is never allowed to fall below 0.05.