Species-specific growth adjustment - Soil water

The water stress growth reducer $W A T_{t x y s}$ [-] is defined as:

\begin{aligned} W A T_{t x y s} & = {\begin{cases} 0 & if W_{p, t x y} = 0 \\ 1 / (1 + \exp (- β_{W, R S A} \cdot (W_{p, t x y} - x_{0, W, R S A}))) & if 0 < W_{p, t x y} < 1 \\ 1 & if W_{p, t x y} >= 1 \end{cases} \\ x_{0, W, R S A} & = \frac{1}{β_{W, R S A}} \cdot (- δ_{W, R S A} \cdot (T R S A_{t x y s} - (\frac{1}{δ_{W, R S A}} \cdot \log (\frac{1 - α_{W, R S A, 05}}{α_{W, R S A, 05}}) + ϕ_{R S A}))) + 0.5 \\ T R S A_{t x y s} & = \frac{B_{B, t x y s}}{B_{t x y s}} \cdot R S A_{s} \\ W_{p, t x y} & = \frac{W_{t x y} - P W P_{x y}}{W H C_{x y} - P W P_{x y}} \end{aligned}

$ϕ_{R S A}$ reference trait value [m² g⁻¹]
$β_{W, R S A}$ slope of response function [-]
$α_{W, R S A, 05}$ response at $W_{p, t x y} = 0.5$ for species with the reference trait value[-]
$δ_{W, R S A}$ scales the difference in the growth reducer between species [g m⁻²]

Visualization

scaling of the soil water content in the rooting zone by permanent wilting point and water holding capacity

permanent wilting point (PWP)
water holding capacity (WHC)

response at Wₚ = 0.5 for species with the reference trait value (α_WRSA05) (strong to weak growth reduction)
difference between species (δ_WAT_rsa) (no to strong difference)	10
slope of response (β_WAT_rsa)
reference trait value (ϕ_TRSA)

julia

water_reduction!(; container, W, PWP, WHC)

Reduction of growth based on the plant available water and the root surface area per belowground biomass.