A numerical approach to calculating soil wetness and evapotranspiration over large grid areas

Abstract

Soil wetness is typically highly variable in space over the length scales of general circulation model grid areas (∼100 km), and the stress functions relating the surface evapotranspiration rate to local‐scale (∼1–100 m) soil wetness are very nonlinear. These two factors give rise to significant inaccuracies whenever a single grid area average soil wetness value is inserted into a stress function to calculate the evapotranspiration rate for a large grid area. A numerical method is presented to mitigate this problem. The distribution of soil wetness within a grid area is represented by binning, and a numerical integration of the stress function over this binned distribution provides a spatially integrated wetness stress term for the whole grid area, which permits calculation of grid area fluxes in a single operation. The method is very accurate when 10 or more bins are used. It can deal realistically with spatially variable precipitation, conserves moisture exactly, strongly reduces any oscillations, and allows for precise modification of the soil wetness distribution after every time step.