Effect of plant-uptake representation on the water-optimal root depth

The depth of roots depends on a variety of conditions, including soil properties, plant type, nutrient availability, and climate. A focus on water enables the determination of a water-optimal root depth by equating the marginal carbon cost of deeper roots with the benefit of those roots to continued transpiration and carbon assimilation. Calculation of the transpiration benefit requires the mathematical representation of plant uptake as a function of root depth and soil moisture. This work compares the effect of two bounding representations of plant uptake on the water-optimal root depth and the response of that depth to changes in precipitation. Soil-moisture dynamics are driven by precipitation events that arrive as a Poisson process and are characterized by a mean frequency and depth. Infiltration and drainage are instantaneous, filling the root zone up to a maximum field capacity. Plant uptake is represented in one case as a step function of soil moisture; transpiration proceeds at a potential rate until the wilting-point saturation is reached when uptake drops to zero. Until that critical threshold, soil moisture has no effect on transpiration. In the second case, transpiration decreases linearly from its potential at field capacity to zero at the wilting point; soil moisture exerts a continuous and gradual influence on plant uptake throughout the drying cycle. With both the linear and step-function representations, the water-optimal root depth is more sensitive to changes in precipitation depth than frequency under dry conditions and more sensitive to precipitation frequency when the climate is wet. Under wet conditions, optimal root depths predicted with the step function show a greater sensitivity to climate than do those based on the linear model. Under dry conditions, the reverse is true; the water-optimal root depth is slightly more sensitive to changes in precipitation when the linear model is employed than when the step function is used. For all climate conditions, the water-optimal root depth is deeper and average transpiration is lower when plant uptake is represented as a linear function of soil moisture.