Conditioning Multi-Gaussian Groundwater Flow Parameters to Transient Hydraulic Head and Flowrate Data With Iterative Ensemble Smoothers: A Synthetic Case Study

Over the last decade, data assimilation methods based on the ensemble Kalman filter (EnKF) have been particularly explored in various geoscience fields to solve inverse problems. Although this type of ensemble methods can handle high-dimensional systems, they assume that the errors coming from whether the observations or the numerical model are multivariate Gaussian. To handle existing non-linearities between the observations and the variables to estimate, iterative methods have been proposed. In this paper, we investigate the feasibility of using the ensemble smoother and two iterative variants for the calibration of a synthetic 2D groundwater model inspired by a real nuclear storage problem in France. Using the same set of sparse and transient flow data, we compare the results of each method when employing them to condition an ensemble of multi-Gaussian groundwater flow parameter fields. In particular, we explore the benefit of transforming the state observations to improve the parameter identification performed by one of the two iterative algorithms tested. Despite the favorable case of a multi-Gaussian parameter distribution addressed, we show the importance of defining an ensemble size of at least 200 to obtain sufficiently accurate parameter and uncertainty estimates for the groundwater flow inverse problem considered.