A minimalist probabilistic description of root zone soil water

The probabilistic response of depth-integrated soil water to given climatic forcing can be described readily using an existing supply-demand-storage model. An apparently complex interaction of numerous soil, climate, and plant controls can be reduced to a relatively simple expression for the equilibrium probability density function of soil water as a function of only two dimensionless parameters. These are the index of dryness (ratio of mean potential evaporation to mean precipitation) and a dimensionless storage capacity (active root zone soil water capacity divided by mean storm depth). The first parameter is mainly controlled by climate, with surface albedo playing a subsidiary role in determining net radiation. The second is a composite of soil (through moisture retention characteristics), vegetation (through rooting characteristics), and climate (mean storm depth). This minimalist analysis captures many essential features of a more general probabilistic analysis, but with a considerable reduction in complexity and consequent elucidation of the critical controls on soil water variability. In particular, it is shown that (1) the dependence of mean soil water on the index of dryness approaches a step function in the limit of large soil water capacity; (2) soil water variance is usually maximized when the index of dryness equals 1, and the width of the peak varies inversely with dimensionless storage capacity; (3) soil water has a uniform probability density function when the index of dryness is 1 and the dimensionless storage capacity is large; and (4) the soil water probability density function is bimodal if and only if the index of dryness is <1, but this bimodality is pronounced only for artificially small values of the dimensionless storage capacity.