Examining dynamic interactions among experimental factors influencing hydrologic data assimilation with the ensemble Kalman filter

The ensemble Kalman filter (EnKF) is recognized as a powerful data assimilation technique that generates an ensemble of model variables through stochastic perturbations of forcing data and observations. However, relatively little guidance exists with regard to the proper specification of the magnitude of the perturbation and the ensemble size, posing a significant challenge in optimally implementing the EnKF. This paper presents a robust data assimilation system (RDAS), in which a multi-factorial design of the EnKF experiments is first proposed for hydrologic ensemble predictions. A multi-way analysis of variance is then used to examine potential interactions among factors affecting the EnKF experiments, achieving optimality of the RDAS with maximized performance of hydrologic predictions. The RDAS is applied to the Xiangxi River watershed which is the most representative watershed in China's Three Gorges Reservoir region to demonstrate its validity and applicability. Results reveal that the pairwise interaction between perturbed precipitation and streamflow observations has the most significant impact on the performance of the EnKF system, and their interactions vary dynamically across different settings of the ensemble size and the evapotranspiration perturbation. In addition, the interactions among experimental factors vary greatly in magnitude and direction depending on different statistical metrics for model evaluation including the Nash–Sutcliffe efficiency and the Box–Cox transformed root-mean-square error. It is thus necessary to test various evaluation metrics in order to enhance the robustness of hydrologic prediction systems.