Estimating the moisture dependence of root zone water toss using conditionally averaged precipitation

A new method for estimating the dependence of soil water loss on soil moisture is proposed. The novelty of the approach is the use of precipitation measurements P, conditionally averaged according to soil moisture storage S, as a surrogate for moisture-dependent outflow (evapotranspiration (ET) plus runoff R and drainage D. The basis of the method is as follows: Soil moisture storage and its rate of change are statistically dependent, but under stationary conditions the expected value of the change in soil moisture storage over an interval DeltaS, conditioned on the storage during the interval (S) over bar, is zero. This stationarity property, which results from the tendency of wetter soils to dry faster via enhanced drainage, runoff, and evapotranspiration, leads to the result that conditionally averaged precipitation can be used to estimate moisture-dependent water loss, i.e.: E[P\(S) over bar] = E[ET\(S) over bar] + E[R\(S) over bar] + E[D\(S) over bar]. As an example application, sparsely sampled soil moisture (approximately weekly to monthly) and daily precipitation data are used to estimate the daily timescale moisture-dependent water loss function for sites in Illinois. The estimated loss function is consistent in magnitude and shape with conventional models of evapotranspiration efficiency and percolation. The estimated loss function is then used to test a physically based stochastic model for the probability distribution of soil moisture [Rodriguez-Iturbe et al., 1999]. The observed and derived distributions of moisture are in close agreement, lending support for both the methodology and the model. Other uses for the methodology, including the study of scale dependence in water balance sensitivity to soil moisture, are discussed.