Estimation of the hydraulic parameters of the Rio-Maior aquifer in Portugal by using stochastic inverse modeling

This paper describes a preliminary study of a section of the Rio-Maior aquifer in Portugal. The aim of the study is to identify the transmissivity and head regional distributions and the natural recharge as a function of time. A small number of transmissivity measurements on one hand and a relative abundance of head measurements (taken over a long period of time) on the other led to the casting of the identification problem in the framework of stochastic inverse modeling. The basic assumptions of the approach, which was developed earlier, are that the log-transmissivity Y is a normal and stationary random space function, the aquifer is unbounded, and a first-order approximation of the flow equation is adopted. The expected value of the piezometric head H as well as the Y unconditional autocovariance function are supposed to have analytical expressions which depend on a parameter vector θ. The proposed solution of the inverse problem consists of identifying θ based on the model and the measurements of Y and H by use of a maximum likelihood procedure and subsequently computing the statistical moments of Y and H conditioned on the same data. A general description is given of the theoretical approach, as well as a detailed description of its application to the Rio-Maior aquifer, starting from screening of the data and identification of outliers among measurements, through unconditional identification of θ and the recharge, and finally drawing of the regional maps of the conditional Y and H with their error of estimation. Evaluation of the transmissivity distribution obtained by this method showed an improvement when compared with transmissivity distribution obtained without using the head measurements.