Inversion Of Non-Gaussian Hydrogeological Parameters By Modified Probability Conditioning Method

Parameter estimation with uncertainty quantification is essential in groundwater modeling to ensure model quality,but parameter estimation,especially for nonGaussian 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 non-linear flow data into facies simulation,but it has an assumption of homogeneity within each facies.Full characterization of facies and hydraulic conductivity within each facies are equally important.In this work,we firstly modify 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 groundwater model.The proposed method is evaluated using a two-facies case and a three-facies case in groundwater modeling for the first time,to the best of our knowledge.Both cases demonstrate that the modified PCM is effective for facies delineation,especially to identify high heterogeneities in each facies as well as nonGaussian characteristics with good connectivity within certain facies.Results also show that the performance of data reproduction and model prediction is of high accuracy and low uncertainty,which is attributed to the accurate characterization of the non-Gaussian parameters in heterogeneous aquifers.Additionally,the impact of ensemble size and assimilation steps on parameter estimation is also discussed in this work.It shows that larger ensemble size and more assimilation steps could increase the accuracy of parameter estimation,while it would introduce more error and lead into heavier computational burden as well.