Although plant phosphorus demand is considerably less than nitrogen demand, phosphorus is required for many essential functions. The most important of these is its role in energy storage and transfer. Energy obtained from photosynthesis and metabolism of carbohydrates is stored in phosphorus compounds for later use in growth and reproductive processes.

The three major forms of phosphorus in mineral soils are organic phosphorus associated with humus, insoluble forms of mineral phosphorus, and plant-available phosphorus in soil solution. Phosphorus may be added to the soil by fertilizer, manure or residue application. Phosphorus is removed from the soil by plant uptake and erosion. Figure 3:2-1 shows the major components of the phosphorus cycle.

Unlike nitrogen which is highly mobile, phosphorus solubility is limited in most environments. Phosphorus combines with other ions to form a number of insoluble compounds that precipitate out of solution. These characteristics contribute to a build-up of phosphorus near the soil surface that is readily available for transport in surface runoff. Sharpley and Syers (1979) observed that surface runoff is the primary mechanism by which phosphorus is exported from most catchments.

SWAT+ monitors six different pools of phosphorus in the soil (Figure 3:2-2). Three pools are inorganic forms of phosphorus while the other three pools are organic forms of phosphorus. Fresh organic P is associated with crop residue and microbial biomass while the active and stable organic P pools are associated with the soil humus. The organic phosphorus associated with humus is partitioned into two pools to account for the variation in availability of humic substances to mineralization. Soil inorganic P is divided into solution, active, and stable pools. The solution pool is in rapid equilibrium (several days or weeks) with the active pool. The active pool is in slow equilibrium with the stable pool.

Users may define the amount of soluble P and organic phosphorus contained in humic substances for all soil layers at the beginning of the simulation. If the user does not specify initial phosphorus concentrations, SWAT+ will initialize levels of phosphorus in the different pools.

The concentration of solution phosphorus in all layers is initially set to 5 mg/kg soil. This concentration is representative of unmanaged land under native vegetation. A concentration of 25 mg/kg soil in the plow layer is considered representative of cropland (Cope et al., 1981).

The concentration of phosphorus in the active mineral pool is initialized to (Jones et al., 1984):

$minP_{act,ly}=P_{solution,ly}*\frac{1-pai}{pai}$ 3:2.1.1

where $minP_{act,ly}$ is the amount of phosphorus in the active mineral pool (mg/kg), $P_{solution,ly}$ is the amount of phosphorus in solution (mg/kg), and $pai$ is the phosphorus availability index.

The concentration of phosphorus in the stable mineral pool is initialized to (Jones et al., 1984):

$minP_{sta,ly}=4*minP_{act,ly}$ 3:2.1.2

where $minP_{sta,ly}$ is the amount of phosphorus in the stable mineral pool (mg/kg), and $minP_{act,ly}$ is the amount of phosphorus in the active mineral pool (mg/kg).

Organic phosphorus levels are assigned assuming that the N:P ratio for humic materials is 8:1. The concentration of humic organic phosphorus in a soil layer is calculated:

$orgP_{hum,ly}=0.125*orgN_{hum,ly}$ 3:2.1.3

where $orgP_{hum,ly}$ is the concentration of humic organic phosphorus in the layer (mg/kg) and $orgN_{hum,ly}$ is the concentration of humic organic nitrogen in the layer (mg/kg).

Phosphorus in the fresh organic pool is set to zero in all layers except the top 10mm of soil. In the top 10 mm, the fresh organic phosphorus pool is set to 0.03% of the initial amount of residue on the soil surface.

$orgP_{frsh,surf}=0.0003*rsd_{surf}$ 3:2.1.4

where $orgP_{frsh,surf}$ is the phosphorus in the fresh organic pool in the top 10mm (kg P/ha), and $rsd_{surf}$ is material in the residue pool for the top 10mm of soil (kg/ha).

While SWAT+ allows nutrient levels to be input as concentrations, it performs all calculations on a mass basis. To convert a concentration to a mass, the concentration is multiplied by the bulk density and depth of the layer and divided by 100:

$\frac{conc_P*\rho_b*depth_{ly}}{100}=\frac{kgP}{ha}$ 3:2.1.5

where $conc_P$ is the concentration of phosphorus in a layer (mg/kg or ppm), $\rho_b$ is the bulk density of the layer (Mg/m$^3$), and $depth_{ly}$ is the depth of the layer (mm).

Table 3:2-1: SWAT+ input variables that pertain to nitrogen pools.

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:

3:2.2.3

3:2.2.4

where is the amount of phosphorus in the active organic pool (kg P/ha), is the amount of phosphorus in the stable organic pool (kg P/ha), is the concentration of humic organic phosphorus in the layer (kg P/ha), is the amount of nitrogen in the active organic pool (kg N/ha), and is the amount of nitrogen in the stable organic pool (kg N/ha).

Mineralization from the humus active organic P pool is calculated:

3:2.2.5

where is the phosphorus mineralized from the humus active organic pool (kg P/ha), is the rate coefficient for mineralization of the humus active organic nutrients, is the nutrient cycling temperature factor for layer , is the nutrient cycling water factor for layer , and 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 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:

3:2.2.1

where is the nutrient cycling temperature factor for layer , and is the temperature of layer (°C). The nutrient cycling temperature factor is never allowed to fall below 0.1.

The nutrient cycling water factor is calculated:

3:2.2.2

where is the nutrient cycling water factor for layer , is the water content of layer on a given day (mm HO), and is the water content of layer at field capacity (mm HO). ). The nutrient cycling water factor is never allowed to fall below 0.05.

Many studies have shown that after an application of soluble P fertilizer, solution P concentration decreases rapidly with time due to reaction with the soil. This initial “fast” reaction is followed by a much slower decrease in solution P that may continue for several years (Barrow and Shaw, 1975; Munns and Fox, 1976; Rajan and Fox, 1972; Sharpley, 1982). In order to account for the initial rapid decrease in solution P, SWAT+ assumes a rapid equilibrium exists between solution P and an “active” mineral pool. The subsequent slow reaction is simulated by the slow equilibrium assumed to exist between the “active” and “stable” mineral pools. The algorithms governing movement of inorganic phosphorus between these three pools are taken from Jones et al. (1984).

Equilibration between the solution and active mineral pool is governed by the phosphorus availability index. This index specifies the fraction of fertilizer P which is in solution after an incubation period, i.e. after the rapid reaction period.

A number of methods have been developed to measure the phosphorus availability index. Jones et al. (1984) recommends a method outlined by Sharpley et al. (1984) in which various amounts of phosphorus are added in solution to the soil as K$_2$HPO$_4$. The soil is wetted to field capacity and then dried slowly at 25°C. When dry, the soil is rewetted with deionized water. The soil is exposed to several wetting and drying cycles over a 6-month incubation period. At the end of the incubation period, solution phosphorus is determined by extraction with anion exchange resin.

The $P$ availability index is then calculated:

$pai=\frac{P_{solution,f}-P_{solution,i}}{fert_{min,P}}$ 3:2.3.1

where $pai$ is the phosphorus availability index, $P_{solution,f}$ is the amount of phosphorus in solution after fertilization and incubation, $P_{solution,i}$ is the amount of phosphorus in solution before fertilization, and $fert_{min,P}$ is the amount of soluble $P$ fertilizer added to the sample.

The movement of phosphorus between the solution and active mineral pools is governed by the equilibration equations:

$P_{sol|act,ly}=0.1(P_{solution,ly}-minP_{act,ly}*(\frac{pai}{1-pai}))$

if $P_{solution,ly}>minP_{act,ly}*(\frac{pai}{1-pai})$ 3:2.3.2

$P_{sol|act,ly}=0.6*(P_{solution,ly}-minP_{act,ly}*(\frac{pai}{1-pai}))$

if $P_{solution,ly}<minP_{act,ly}*(\frac{pai}{1-pai})$ 3:2.3.3

where $P_{sol|act,ly}$ is the amount of phosphorus transferred between the soluble and active mineral pool (kg P/ha), $P_{solution,ly}$ is the amount of phosphorus in solution (kg P/ha), $minP_{act,ly}$ is the amount of phosphorus in the active mineral pool (kg P/ha), and $pai$ is the phosphorus availability index. When $P_{sol|act,ly}$ is positive, phosphorus is being transferred from solution to the active mineral pool. When $P_{sol|act,ly}$ is negative, phosphorus is being transferred from the active mineral pool to solution. Note that the rate of flow from the active mineral pool to solution is 1/10th the rate of flow from solution to the active mineral pool.

SWAT+ simulates slow phosphorus sorption by assuming the active mineral phosphorus pool is in slow equilibrium with the stable mineral phosphorus pool. At equilibrium, the stable mineral pool is 4 times the size of the active mineral pool.

When not in equilibrium, the movement of phosphorus between the active and stable mineral pools is governed by the equations:

$P_{act|sta,ly}=\beta_{eqP}*(4*minP_{act,ly}-minP_{sta,ly})$

if $minP_{sta,ly}<4*minP_{act,ly}$ 3:2.3.4

$P_{act|sta,ly}=0.1*\beta_{eqP}*(4*minP_{act,ly}-minP_{sta,ly})$

if $minP_{sta,ly}>4*minP_{act,ly}$ 3:2.3.5

where $P_{act|sta,ly}$ is the amount of phosphorus transferred between the active and stable mineral pools (kg P/ha), $\beta_{eqP}$ is the slow equilibration rate constant (0.0006 d$^{-1}$), $minP_{act,ly}$ is the amount of phosphorus in the active mineral pool (kg P/ha), and $minP_{sta,ly}$ is the amount of phosphorus in the stable mineral pool (kg P/ha). When $P_{act|sta,ly}$ is positive, phosphorus is being transferred from the active mineral pool to the stable mineral pool. When $P_{act|sta,ly}$ is negative, phosphorus is being transferred from the stable mineral pool to the active mineral pool. Note that the rate of flow from the stable mineral pool to the active mineral pool is 1/10th the rate of flow from the active mineral pool to the stable mineral pool.

Table 3:2-3: SWAT+ input variables that pertain to inorganic P sorption processes.

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.

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. The concentration gradient is created when plant roots remove soluble phosphorus from soil solution, depleting solution P in the root zone.

Due to the low mobility of phosphorus, SWAT+ allows soluble P to leach only from the top 10 mm of soil into the first soil layer. The amount of solution P moving from the top 10 mm into the first soil layer is:

3:2.4.1

where is the amount of phosphorus moving from the top 10 mm into the first soil layer (kg P/ha), is the amount of phosphorus in solution in the top 10 mm (kg P/ha), is the amount of water percolating to the first soil layer from the top 10 mm on a given day (mm HO), is the bulk density of the top 10 mm (Mg/m) (assumed to be equivalent to bulk density of first soil layer), is the depth of the “surface” layer (10 mm), and is the phosphorus percolation coefficient (m/Mg). The phosphorus percolation coefficient is the ratio of the phosphorus concentration in the surface 10 mm of soil to the concentration of phosphorus in percolate.

Table 3:2-4: SWAT+ input variables that pertain to phosphorus leaching.

Groundwater flow entering the main channel from the shallow aquifer can contain soluble phosphorus. With SWAT+ the soluble phosphorus pool in the shallow aquifer is not directly modeled. However, a concentration of soluble phosphorus in the shallow aquifer and groundwater flow can be specified to account for loadings of phosphorus with groundwater. This concentration remains constant throughout the simulation period.

Table 3:2-5: SWAT+ input variables that pertain to phosphorus in groundwater.