Maximum-likelihood adjoint-state finite-element estimation of groundwater parameters under steady- and nonsteady-state conditions

A method is presented for estimating the hydraulic parameters of groundwater flow models under steady- and nonsteady-state conditions. The estimation problem is posed in the framework of maximum-likelihood theory by means of a log-likelihood criterion that includes prior estimates of the parameters. To allow for an incomplete knowledge of the covariances of the prior head and parameter errors, these covariances are expressed in terms of a few unknown statistical parameters that may be estimated jointly with the hydraulic parameters. Computational efficiency is achieved by evaluating the gradient of the estimation criterion with an adjoint-state finite-element scheme and using a combination of conjugate-gradient algorithms, coupled with Newton's method for determining the step size to be taken at each iteration. Model structure identification criteria developed in the time-series literature (all of which utilize the maximum-likelihood concept) are shown to be useful for selecting the best way to parametrize a groundwater flow region when a number of alternative schemes of parametrization are given. The paper also demonstrates the potential utility of the proposed estimation method for the optimum design of space-time measurement networks. A case study dealing with three-dimensional flow in a multiaquifer system is briefly discussed.