Garden with Insight v1.0 Help: Phosphorus - Mineral P Cycling

The mineral P model was developed by Jones et al. (1984). Mineral P is transferred among three pools: labile, active mineral, and stable mineral. Fertilizer P is labile (available for plant use) at application but may be quickly transferred to the active mineral pool. Flow between the labile and active mineral pools is governed by the equilibrium equation [Equation 211] where MPR is the mineral P flow rate for layer l in kg/ha, MP(a) is the amount in the active mineral P pool in kg/ha, and PSP is the P sorption coefficient defined as the fraction of fertilizer P remaining in the labile pool after the initial rapid phase of P sorption is complete. The daily amount of P computed with equation 211 flows to the active mineral P pool and is, therefore, added to that pool and subtracted from the labile pool. Obviously, the flow reverses when labile P is less than MP(a) * PSP / (1-PSP). Since reverse flow is much slower, equation 211 is multiplied by 0.1 when the resulting MPR is negative.

Equation 211

MPR = AP - MP(a) * (PSP / (1.0 - PSP))
if MPR < 0, MPR *= 0.1
Code:
same except PSP / (1.0 - PSP) is bounded at 0.8
Variables:
MPR = PFlowFromLabileToActiveMineral_kgPha
AP = labileP_kgPha
MP(a) = mineralPActive_kgPha
PSP = pSorptionCoeff_frn

The P sorption coefficient is a function of chemical and physical soil properties as described by the following equations (Jones et al., 1984). In calcareous soils, [Equation 212]. In noncalcareous, slightly weathered soils, [Equation 213]. In noncalcareous, moderately weathered soils, [Equation 214]. In noncalcareous, highly weathered soils, [Equation 215] where PSP is the P sorption coefficient for soil layer l, CAC is the CaCO3 concentration in g/t, and BSA is the base saturation by the ammonium acetate (NH4OAc) method in percent. PSP is constrained within the limits of 0.05 <= PSP <= 0.75.

Equation 212, 213, 214, 215

in calcareous soils,
PSP = 0.58 - 0.0061 * CAC
in noncalcareous, slightly weathered soils,
PSP = 0.02 + 0.0104 * AP
in noncalcareous, moderately weathered soils,
PSP = 0.0054 * BSA + 0.116 * PH - 0.73
in noncalcareous, highly weathered soils,
PSP = 0.46 - 0.0916 * ln(CLA)
PSP is constrained within the limits of 0.05 <= PSP <= 0.75
Code:
in calcareous soils,
if CAC > 0 PSP = 0.58 - 0.0061 * CAC
if CAC <= 0 PSP = 0.5
otherwise the same
Variables:
PSP = PSorptionCoeffForLayer_frn
CAC = calciumCarbonateConcForLayer_gPt
AP = labileP_kgPha
BSA = baseSaturation_pct
PH = soilpH
CLA = clayContent_pct

At equilibrium the stable P pool is assumed to be four times as large as the active mineral P pool. Flow between the P pools is governed by the equation [Equation 216] where ASPR is the flow rate between the active and stable mineral P pools in kg/ha for soil layer l, omega is the flow coefficient in /day, and MP(s) is the amount of stable mineral P in kg/ha. The daily amount of P computed with equation 216 flows into the stable pool and is subtracted from the active pool. Obviously, the flow reverses when MP(s) > 4MP(a). Since reverse flow is much slower, equation 216 is multiplied by 0.1 when the resulting ASPR is negative.

Equation 216

ASPR = omega * (4 * MP(a) - MP(s))
if ASPR < 0.0, ASPR *= 0.1
Code:
same
Variables:
ASPR = MineralPFlowFromActiveToStableForLayer_kgPha
omega = mineralPFlowCoeff_Pday
MP(a) = mineralPActive_kgPha
MP(s) = mineralPStable_kgPha

The flow coefficient, omega, is a function of PSP as expressed by the equations (Jones et al., 1984) [Equation 217] for noncalcareous soils, and [Equation 218] for calcareous soils.

Equation 217

in noncalcareous soils,
omega = exp(-1.77 * PSP - 7.05)
in calcareous soils,
omega = 0.0076
Code:
same
Variables:
omega = MineralPFlowCoeffForLayer_Pday
PSP = pSorptionCoeff_frn