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 moist ure is proposed. The novelty of the approach is the use of precipitation me asurements 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 moist ure storage and its rate of change are statistically dependent, but under s tationary conditions the expected value of the change in soil moisture stor age 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 e vapotranspiration, leads to the result that conditionally averaged precipit ation 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 weekl y to monthly) and daily precipitation data are used to estimate the daily t imescale moisture-dependent water loss function for sites in Illinois. The estimated loss function is consistent in magnitude and shape with conventio nal 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., 199 9]. The observed and derived distributions of moisture are in close agreeme nt, lending support for both the methodology and the model. Other uses for the methodology, including the study of scale dependence in water balance s ensitivity to soil moisture, are discussed.