Ensemble Kalman Inversion for upstream parameter estimation and indirect streamflow correction: A simulation study

Data assimilation (DA) techniques such as the Ensemble Kalman filter (EnKF) and its extensions allow for realtime corrections of state-space models and model parameters based on an assumption of Gaussian error. The hydrological DA literature primarily documents applications of the EnKF to solve sequential state estimation problems. Recent advances in the DA literature demonstrate the potential of applying EnKF-based methods as efficient, derivative-free algorithms to solve various general Bayesian inverse problems, such as parameter estimation, while simultaneously providing Uncertainty Quantification (UQ). In this paper, the authors employ the Ensemble Kalman Inversion (EKI) algorithm to infer the distribution of a set of routing parameters. Through this correction, we improve streamflow at locations upstream of the gauged site in a virtual catchment setting. The algorithm enables learning spatially distributed routing parameters with observations available only at the outlet. The study reveals that this method sufficiently improves model performance throughout the basin. The performance of this method is demonstrated in a virtual catchment for three different model/data configurations. Favorable results, even with model misspecification, indicate that this method holds promise for operational application and more general hydrologic parameter estimation problems.