Garden with Insight v1.0 Help: Plant Growth - Water Use

The potential water use, E(p), is estimated as described in the evapotranspiration section. The potential water use from the soil surface to any root depth is estimated with the function

U(p) = E(p) / (1.0 - exp(-lambda) * (1.0 - exp(-lambda * (Z/RZ))) (Equation 270)

where U(p) is the total water use rate in mm/day to depth Z in m on day i, RZ is the root zone depth in m, and lambda is a water use distribution parameter.

The amount used in a particular layer can be calculated by taking the difference between U(p) values at the layer boundaries:

U(pl) = E(p) / (1.0 - exp(-lambda) * (1.0 - exp(-lambda * (Z(l)/RZ))
... - (1.0 - exp(-lambda) * (1.0 - exp(-lambda * (Z(l-1)/RZ)) (Equation 271)

where U(pl) is the potential water use rate for layer l in mm/day.

Equation 271 applies to a soil that provides poor conditions for root development when lambda is set to a high value like 10. The high lambda value gives high water use near the surface and very low use in the lower half of the root zone. Since there is no provision for water deficiency compensation in any layer, considerable water stress may be incorrectly indicated if equation 271 is used. To overcome this problem, equation 271 was modified to allow plants to compensate for water deficiency in a layer by using more water from other layers. Total compensation can be accomplished by taking the difference between U(pl) at the bottom of a layer and the sum of water use above a layer:

U(pl) = E(p) / (1.0 - exp(-lambda) * (1.0 - exp(-lambda * (Z(l)/RZ))
... - the sum from 1 to l-1 of U(k) (Equation 272)

where U(k) is the actual water use rate in mm/day for all layers above layer l. Thus, any deficit can be overcome if a layer that is encountered has adequate water storage.

Neither equation 271 (no compensation) nor equation 272 (total compensation) is satisfactory to simulate a wide range of soil conditions. A combination of the two equations, however, provides a very general water use function [Equation 273] where UC varies over a range (0.0-1.0) and is the water deficit compensation factor. In soils with a good rooting environment, UC = 1.0 gives total compensation. The other extreme, poor conditions, allow no compensation (UC = 0.0). The procedure for estimating UC is described in the Growth Constraints section of this section.

Equation 273

u(p) = E(p) * (1 - exp(-lambda * (Z(l) / RZ)) - (1 - UC) * (1 - exp(-lambda * (Z(l-1) / RZ)))
/ (1 - exp(-lambda))
- UC * (sum with k from 1 to l-1 of) u(k)
Code:
multiplying E(p) / (1 - exp(-lambda)) over the difference, you get
u(p) = E(p) * (1 - exp(-lambda * Z(l) / RZ) / (1 - exp(-lambda)
- (1 - UC) * E(p) * (1 - exp(-lambda * Z(l-1) / RZ)) / (1 - exp(-lambda)
- UC * (sum with k from 1 to l-1 of) u(k)

so if WUT = E(p) * (1 - exp(-lambda * Z(l) / RZ)) / (1 - exp(-lambda))
and WUT(l-1) = E(p) * (1 - exp(-lambda * Z(l-1) / RZ)) / (1 - exp(-lambda))
then the equation reduces to
u(p) = WUT - (1 - UC) * WUT(l-1)
- UC * (sum with k from 1 to l-1 of) u(k)
so it is exactly the same.
GWI change: this was water use, but since we added a water competition component
where the soil patch partitions water to its plants, what the plant calculates
as water use is actually now a request made to the soil patch.
Variables:
WUT = WaterDemandTermForLayer_mm
E(p) = potPlantEvap_mm
lambda = plantWaterUseDistribParam
Z(l) = maxOfDepthThisLayerOrRootDepth_m
RZ = soilProfileDepth_m

The potential water use in each layer calculated with equation 273 is reduced when the soil water storage is less than 25% of plant-available soil water (Jones and Kiniry, 1986) by using the equation [Equation 274] and [Equation 275] where SW is the soil water content in layer l on day i in mm and FC and WP are the soil water contents at field capacity and wilting point for layer l.

Equation 274, 275

if SW < (FC - WP) / 4 + WP
u(l) = u(p(l)) * exp(5.0 * (4.0 * (SW - WP) / (FC - WP) - 1.0))
else
u(l) = u(p(l))
Code:
this code treats the part in the exp as a variable which is later
multiplied by u(p) (in PlantWaterDemandForLayer_mm)
calling this variable WUC,
WUC = 4.0 * (SW - WP) / (FC - WP)
note there is no exp, no 5.0 and no - 1.0
Variables:
WUC = WaterDemandConstraintForLayer_mm
SW = waterContent_mm
WP = lowerWaterLimit_mm
FC = fieldCapacity_mm

The final estimates of water use for each layer are obtained by multiplying the u(l) values in equations 274 and 275 by RGF (the root growth constraint factor) [Equation 312].

Equation 312

u*(l) = u(l) * RGF
Code:
same (incorporating the part of equation 274 where the water use constraint
is multiplied by the unconstrained water use u(p))
Variables:
u*(l) = PlantWaterDemandForLayer_mm
u(l) = unconstrainedWaterDemand_mm
RGF = rootGrowthConstraint_frn