Estimation of boundary values and identification of boundary type for numerical models of aquifer flow

Inverse methods which focus on aquifer properties implicitly assume that boundary conditions are known with certainty and can therefore lead to biased results. An inverse procedure is described which allows the simultaneous estimation of not only spatially varying aquifer storage coefficients and transmissivities, but also model parameters which represent both boundary type and boundary values. The weighted least-squares procedure is based on either Bayesian or maximum likelihood arguments and requires both measurements of transient piezometric heads and prior information on all model parameters. Prior estimates and their covariance can be nonconditioned (e.g. a stationary mean and covariance structure) or conditioned on direct measurements (e.g. a kriged transmissivity field with its estimation covariance). Hypothetical examples are presented using an unsteady finite element model. In some cases, with weak prior information on the boundary type, it is possible to distinguish between prescribed head, prescribed flux and mixed boundaries. Simultaneous estimates of aquifer properties and boundary values are always possible, although their accuracy depends on the relative magnitudes of model sensitivities and prior information.