Stochastic identification of recharge, transmissivity, and storativity in aquifer transient flow: A quasi‐steady approach

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Abstract
In this paper, a stochastic method to identify aquifer natural recharge, storativity, and transmissivity under transient conditions is developed. Four main assumptions were adopted: Y, the log transmissivity, is a normal random space function, the aquifer is unbounded, a first‐order approximation of the flow equation is adopted, and the transients are slowly varying. Based on these assumptions, the expected value of Y and of the head H, as well as their covariances and crosscovariances, are expressed by analytical equations which depend on a parameters vector θ. A major part of the first paper is devoted to the development of these expressions, based on the two‐dimensional flow equation. The proposed solution of the inverse problem is a double‐stage procedure. First, θ is identified stochastically, by a maximum likelihood procedure applied to the measurements of Y and H. Then, θ serves to estimate the spatial distributions of Y and H through their conditional mean and variances of estimation. The three main new features of the approach are the possibility to identify the spatial distributions of Y and H through their first two statistical moments based on transient head data and in the presence of pumping‐recharching wells; the identification of the storativity and the stochastic identification of natural recharge. Since the proposed method make use of the analytic solution of the flow equation, it saves the need of laborious numerical schemes. Application of the method to a section of the Israeli Coastal Aquifer illustrates its potential in a real‐life case.