A data assimilation approach for groundwater parameter estimation under Bayesian maximum entropy framework

Spatial heterogeneity in groundwater system introduces significant challenges in groundwater modeling and parameter calibration. In order to mitigate the modeling uncertainty, data assiilation methods have been applied in the parameter estimation by assessing the uncertainties from both groundwater model and observations. In practice, the observations from groundwater system can be limited, and furthermore, boundary conditions and hydrogeological parameters, such as hydraulic conductivity, can be uncertain and biased. In order to handle the uncertain observations, this study applied the Bayesian maximum entropy (BME) for a data assimilation approach that integrates groundwater model, MODFLOW, and a variety of observations with uncertainties. In BME, no distributional assumption is imposed in the uncertain observations. We conducted numerical simulation with datasets of hard data of heads and hydrogeological parameters, uncertain head data on boundary, and uncertain hydrogeological parameters, i.e., hydraulic conductivity and storage coefficient. Three numerical scenarios with differerent combinations of datasets were conducted. Results show that the proposed data assimilation approach can gradually improve the modeling performance in the sense of lower mean squared errors over time. Moreover, the inclusion of uncertain observations can further improve the efficiency and accuracy in parameter estimation and hydraulic head prediction.