Functional relationship to describe temporal statistics of soil moisture averaged over different depths

Detailed simulation studies, highly resolved in space and time, show that a physical relationship exists among instantaneous soil-moisture values integrated over different soil depths. This dynamic relationship evolves in time as a function of the hydrologic inputs and soil and vegetation characteristics. When depth-averaged soil moisture is sampled at a low temporal frequency, the structure of the relationship breaks down and becomes undetectable. Statistical measures can overcome the limitation of sampling frequency, and predictions of mean and variance for soil moisture can be defined over any soil averaging depth d. For a water-limited ecosystem, a detailed simulation model is used to compute the mean and variance of soil moisture for different averaging depths over a number of growing seasons. We present a framework that predicts the mean of soil moisture as a function of averaging depth given soil moisture over a shallow d and the average daily rainfall reaching the soil.