Stochastic Simulation Of Groundwater Flow. Estimation Of Hydrogeological Parameters Of Regional Porous Aquifers By Inverse Modelling
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M. M. Pacheco Figueiredo, L. Ribeiro & J. M. P. Ferreira Lemos
When modelling an environmental system, as a regional porous aquifer, we have to deal with the heterogeneity of the natural medium. System parameters that represent hydrogeological properties, such as hydraulic conductivity and drainage porosity, can no longer be seen as deterministic as before. If these parameters, or their transforms, are represented by random functions, the differential equation which rules the groundwater flow turns to be stochastic and its state variable, the piezometric head, also becomes a random function, even if initial and boundary conditions are considered deterministic. In order to perform the direct stochastic simulation, the estimated fields of the hydrogeological parameters have to be previously known as well as their covariances of estimation. In this paper, we intend to describe the main steps of a methodology developed with the aim of estimating simultaneously – in a stochastic framework – the hydrogeological parameters and the effective diffuse recharge of the aquifer and, also, present its application to a synthetic unconfined aquifer. This inverse stochastic methodology, which admits the deterministic knowledge of the initial and boundary conditions, is based on a numerical algorithm of inverse modelling complemented by a cokriging technique. The numerical integration of the several differential equations involved in this methodology is done with the help of the Finite Element Method. The deduction of the correspondent matricial expressions is supported by weighted residuals and Bubnov-Galerkin formulations.