Piecewise Soil Moisture Stress
This page documents the piecewise (linear/threshold with curvature) soil moisture stress function used in ClimaLand's vegetation module. The stress factor $\beta \in [0,1]$ scales leaf photosynthesis (and thus stomatal conductance) as soil moisture declines, following a simple, interpretable formulation. See Egea et al. [27], the ClimaLand code is here.
Summary
- Purpose: convert soil wetness to a stress multiplier that reduces assimilation and stomatal conductance.
- Inputs: volumetric soil water content $\theta$ (or relative water content), model thresholds.
- Outputs: scalar stress factor $\beta$ applied within the photosynthesis/stomatal sub-models.
Model formulation
Let $\theta$ be the volumetric water content at some depth. Define two thresholds:
First, $\theta_{low}$ — wilting (or residual) water content: below this, stress is total ($\beta = 0$).
Second, $\theta_{high}$ — Field capacity (or porosity) water content: above this, no stress ($\beta = 1$).
With $\theta_{low} < \theta_{high}$, the stress factor is
\[\beta(\theta) = \begin{cases} 0, & \theta \leq \theta_{low}, \\ \left( \dfrac{\theta - \theta_{low}}{\theta_{high} - \theta_{low}} \right)^c, & \theta_{low} < \theta < \theta_{high}, \\ 1, & \theta \geq \theta_{high}. \\ \end{cases}\]
Variables & units
| Quantity | Symbol | Units | Notes |
|---|---|---|---|
| Volumetric water content | $\theta$ | m³ m⁻³ | root-zone or layer-weighted |
| Low water content threshold | $\theta_{low}$ | m³ m⁻³ | wilting point or residual |
| High water content threshold | $\theta_{high}$ | m³ m⁻³ | field capacity or porosity |
| Stress multiplier | $\beta$ | – | 0 (full stress) … 1 (no stress) |
| Curvature parameter | $c$ | – | controls concavity of the stress response |
Parameters
| Parameter | Description | Example range |
|---|---|---|
| $\theta_{low}$ | lower threshold (wilting or residual) | 0.05–0.15 |
| $\theta_{high}$ | upper threshold (field capacity or porosity) | 0.55–0.75 |
| $c$ | curvature parameter shaping the transition | 1–5 |
Numerical details & coupling
Soil moisture, $\theta$, is either prescribed as a single value in the root zone (for standalone canopy models, with a prescribed soil component), or else we compute $\beta$ as a factor of depth using $\theta$ as a function of depth, as specified by the prognostic soil model. In the latter case, we then average $\beta(z)$ over the column using the root distribution function (also a function of$z$), as a weighting factor.
Scalar stress, $\beta$, multiplies leaf assimilation, $A_{n}$, which in turn reduces $g_{s}$ that scales with $A_{n}$.