Correcting Unintended Perturbation Biases in Hydrologic Data Assimilation

Abstract

Hydrologic data assimilation has become an important tool for improving hydrologic model predictions by using observations from ground, aircraft, and satellite sensors. Among existing data assimilation methods, the ensemble Kalman filter (EnKF) provides a robust framework for optimally updating nonlinear model predictions using observations. In the EnKF, background prediction uncertainty is obtained using a Monte Carlo approach where state variables, parameters, and forcing data for the model are synthetically perturbed to explicitly simulate the error-prone representation of hydrologic processes in the model. However, it is shown here that, owing to the nonlinear nature of these processes, an ensemble of model forecasts perturbed by mean-zero Gaussian noise can produce biased background predictions. This ensemble perturbation bias in soil moisture states can lead to significant mass balance errors and degrade the performance of the EnKF analysis in deeper soil layers. Here, a simple method of bias correction is introduced in which such perturbation bias is corrected using an unperturbed model simulation run in parallel with the EnKF analysis. The proposed bias-correction scheme effectively removes biases in soil moisture and reduces soil water mass balance errors. The performance of the EnKF is improved in deeper layers when the filter is applied with the bias-correction scheme. The interplay of nonlinear hydrologic processes is discussed in the context of perturbation biases, and implications of the bias correction for real-data assimilation cases are presented.