A Direct Method of Parameter Estimation for Steady State Flow in Heterogeneous Aquifers with Unknown Boundary Conditions

We propose a novel direct method for estimating steady state hydrogeological model parameters and model state variables in an aquifer where boundary conditions are unknown. The method is adapted from a recently developed potential theory technique for solving general inverse/reconstruction problems. Unlike many inverse techniques used for groundwater model calibration, the new method is not based on fitting and optimizing an objective function, which usually requires forward simulation and iterative parameter updates. Instead, it directly incorporates noisy observed data (hydraulic heads and flow rates) at the measurement points in a single step, without solving a boundary value problem. The new method is computationally efficient and is robust to the presence of observation errors. It has been tested on two-dimensional groundwater flow problems with regular and irregular geometries, different heterogeneity patterns, variances of heterogeneity, and error magnitudes. In all cases, parameters (hydraulic conductivities) converge to the correct or expected values and are thus unique, based on which heads and flow fields are constructed directly via a set of analytical expressions. Accurate boundary conditions are then inferred from these fields. The accuracy of the direct method also improves with increasing amount of observed data, lower measurement errors, and grid refinement. Under natural flow (i.e., no pumping), the direct method yields an equivalent conductivity of the aquifer, suggesting that the method can be used as an inexpensive characterization tool with which both aquifer parameters and aquifer boundary conditions can be inferred