ANALYSIS OF THE INVERSE PROBLEM FOR UNSTEADY UNSATURATED FLOW

Abstract

Important factors which need consideration for reliable estimation of unsaturated soil parameters through inverse procedure are (i) identifiability, (ii) errors in the data and (iii) proper choice of objective function. The effect of data error and proper choice of objective function have been discussed in this study in the context of unsaturated ground water flow. Values of calibrated parameters embedded in unsaturated flow equations are ascertained using observation data that often contain measurement errors. These measurement errors induce errors in the estimated soil parameters obtained using inverse procedures. For reliable estimation of the parameters, investigations are needed to establish the influence of data errors and choice of objective functions on the parameter estimates. A statistical analysis is carried out to study the effect of data errors and the bias induced by three different objective functions on the parameter estimates. The inverse problem is solved using the Levenberg Marquardt algorithm while the forward problem is solved by a mass conservative finite difference numerical scheme. The investigation showed that the identified parameters could be affected by such factors as data error and objective functions. However, through a better understanding of the behavior of the induced errors the mean of the identified parameters was found to lie with in a prescribed confidence interval that contains the true value, even in the presence of high noise levels.