Aquifer Heterogeneity Estimation and Uncertainty Analysis Using a Multi-Parameterization Method

Understanding of subsurface heterogeneity, e.g., hydraulic conductivity, is inherently difficult in that natural heterogeneity and processes are extremely complex and the available data are limited. Although the parameter structure error in groundwater modeling has been assessed with one parameterization method (zonation or interpolation), with limited information many parameterization methods may interpret the same data satisfactorily. To cope with the non-uniqueness problem of parameterization, we develop a Bayesian multi-parameterization (BMP) method to integrate multiple parameterization methods in a Bayesian geostatistical framework. Moreover, a generalized parameterization (GP) method is adopted to estimate the highly complex spatial distribution of parameter heterogeneity. In this study, we combine BMP and GP as a multi-GP method to better represent the heterogeneity and reduce the model prediction uncertainty. The BMP with GP approach avoids overconfidence in one type of a single parameterization method. The proposed methodology is conducted in a numerical example where the spatially distributed hydraulic conductivity is estimated. The optimal weighting coefficients embedded in GP are identified through the maximum likelihood estimation (MLE) where the misfits between the observed and calculated groundwater heads are minimized. The conditional means and conditional variances of the estimated hydraulic conductivity distribution are obtained to assess the estimation uncertainty.