A 3D DIRECT METHOD OF AQUIFER INVERSION WITH UNKNOWN BOUNDARY CONDITIONS

In this work, the 2D direct method of Irsa & Zhang (2012) is extended to three-dimensions (3D) for estimating steady-state hydrogeological model parameters and model state variables for an aquifer with unknown boundary conditions. Unlike many inverse techniques used in groundwater model calibration, the new method directly incorporates noisy observed data (hydraulic heads, fluxes, and flow rates) at measurement points in a single step, without solving a boundary value problem. The unknown boundary conditions can be inferred from the results of the inversion, which can also be used to determine aquifer geometry via streamline analysis. The direct method is tested here on 3D synthetic problems with linear and strongly nonlinear flow fields for which hydraulic head and flow rate data are used as observations. These data, computed with MODFLOW, are assumed “error free” upon which random measurement errors are imposed. For increasing amount of randomly sampled head (from one to 100 measurements), a set of 100 inversion experiments are conducted for each dataset (only a single observed flow rate is used). For the set of boundary conditions driving linear flow, we find that as little as 3 head observations can provide accurate results in terms of the estimated aquifer conductivity, boundary conditions, and streamlines. For the set of boundary conditions driving nonlinear flow, however, more than 30 observed heads are needed for accurate results in this case. Using composite scale statistics did not yield accurate observation sensitivity metrics, thus we propose a new procedure to indicate whether a given set of observation data lead to a unique solution or whether more data are needed. In this study, we further test and compare quadratic and cubic approximations for the reconstructed hydraulic head functions. For the same observation data and grid resolution, we find that the cubic approximation leads to 2~ 9% improvement in the estimated conductivity. In the future, the 3D method will be tested with noisy observation data with increasing measurement errors. To account for estimation uncertainty, aquifer heterogeneity will also be incorporated within a geostatistical indicator simulation framework.