Identification of non-Gaussian parameters in heterogeneous aquifers by a modified probability conditioning method through hydraulic-head assimilation

Parameter estimation with uncertainty quantification is essential in groundwater modeling to ensure model quality; however, parameter estimation, especially for non-Gaussian distributed parameters in highly heterogeneous aquifers, is still a great challenge. The ensemble smoother with multiple data assimilation (ES-MDA) is one of the most popular and effective ensemble-based data assimilation algorithms. However, it only works for multi-Gaussian fields, since two-point statistics are used to estimate the co-relation between parameters and state variables. The probability conditioning method (PCM) has the capability to integrate nonlinear flow data into facies simulation, but it has an assumption of homogeneity within each facies. Full characterization of facies and estimates of hydraulic conductivity within each facies are equally important. This work firstly modifies the original PCM, introducing a new probability assignment method, to consider within-facies heterogeneities, and then it is further combined with the ES-MDA to estimate non-Gaussian distributed hydraulic parameters in a groundwater model. The proposed method is evaluated using a two-facies case and a three-facies case in groundwater modeling. Both cases demonstrate that the modified PCM is effective for facies delineation, especially to identify high heterogeneities in each facies, as well as non-Gaussian characteristics with good connectivity within certain facies. The results also show that the performances of data reproduction and model prediction are of high accuracy and low uncertainty, which is attributed to the accurate characterization of the non-Gaussian parameters in the heterogeneous aquifers used.