Garden with Insight v1.0 Help: Plant Growth - Phosphorus

Crop use of P is estimated with the supply and demand approach described in the N model. The daily demand is computed with equation 276 written in the form [Equation 291] where UPD is the P demand for the plant in kg/ha, UP is the actual P uptake in kg/ha, and c(PB) is the optimal P concentration for the plant.

Equation 291

UPD = c(PB) * B - (sum with k from 1 to i-1 of) UP(k)
Code:
same
Variables:
UPD = PlantPhosphorusDemand_kgPha
c(PB) = plantOptimalPConc_kgPkg
B = totalPlantBiomass_tPha
UP(k) = plantPUptake_kgPha
sum of UP(k) = lifeTotalPlantPUptake_kgPha (summed daily)

As in the case of N, the optimal plant P concentration is computed with equation 277 written in the form [Equation 292] where bp(1), bp(2), and bp(3) are parameters calculated from crop-specific optimum P concentration at the seedling stage, halfway through the season and at maturity.

Equation 292

c(PB) = bp(1) + bp(2) * exp(-bp(3) * HUI)
Code:
c(PB) = (bp(1) - bp(3)) * (1.0 - HUI / (HUI + exp(bp(1) - bp(2) * HUI))) + bp(3)
Variables:
c(PB) = PlantoptimalPConc_kgPkg
bp(1) = plantOptimalPConcParams[0
bp(2) = plantOptimalPConcParams[1
bp(3) = plantOptimalPConcParams[2
HUI = heatUnitIndex

Soil supply of P is estimated using the equation [Equation 293] where UPS is the amount of P supplied by the soil in kg/ha, LF(u) is the labile P factor for uptake, RW is the root weight in layer l in kg/ha, and RWT is the total root weight on day i in kg/ha. The constant 1.5 allows 2/3 of the roots to meet the P demand of the plant if labile P is not limiting. This approach is consistent with studies suggesting that roots of P-deficient plants (or plants whose root systems have been pruned) can absorb P faster than the roots of normal plants (Andrews and Norman, 1970. DeJager, 1979. Jungk and Barber, 1974).

Equation 293

UPS = 1.5 * UPD * (sum with l from 1 to M of) LF(u) * RW / RWT
Code:
LF(u) is for layer of interest only, not summed
if UPS > labile p in layer, UPS = 0.9 * labile p in layer
GWI change: this was P uptake, but since we added a nutrient competition component
where the soil patch partitions N and P to its plants, what the plant calculates
as uptake is actually now a request made to the soil patch.
Variables:
UPS = PSupplyForLayer_kgPha
UPD = pDemand_kgPha
LF(u) = labilePUptakeFactor_frn
RW = rootWeight_tPha (layer)
RWT = totalRootWeight_tPha

The labile P factor for uptake ranges from 0.0 to 1.0 according to the equation [Equation 294] where c(LP) is the labile P concentration in soil layer l in g/t. Equation 294 allows optimum uptake rates when c(LP) is above 20 g/t. This is consistent with critical labile P concentrations for a range of crops and soils (Sharpley et al., 1990). Sharpley et al. (1984, 1985) described methods of estimating c(LP) from soil test P and other soil characteristics.

Equation 294

LF = 0.1 + 0.9 * c(LP) / (c(LP) + exp(8.01 - 0.360 * c(LP)))
Code:
same except if c(LP) > 30, LF = 1.0
Variables:
LF(u) = LabilePUptakeFactorForLayer_frn
c(LP) = labilePConc_gPt