Improving flood forecasting using conditional bias-penalized ensemble Kalman filter

Abstract

We present a novel ensemble extension of the conditional bias-penalized Kalman filter, referred to herein as the conditional bias-penalized ensemble Kalman filter (CBEnKF), and apply it to flood forecasting. The CBEnKF differs from most data assimilation (DA) techniques in that it minimizes a weighted sum of the error variance and the expected value of the Type-II conditional bias squared for improved estimation and prediction of extremes. To assess the ability of the CBEnKF to improve flood prediction, we carried out real-world DA experiments in which the CBEnKF and the EnKF were applied under identical conditions for assimilation of hourly streamflow observations into the lumped Sacramento soil moisture accounting and unit hydrograph models. Ten headwater basins in Texas, whose drainage areas and times-to-peak range from 137 to 1037 km2 and from 3 to 21 hrs, respectively, were used in the twin experiments. All events in a 10-yr period with peak flow exceeding 100 m3/s were used. Verification of the ensemble mean predictions indicates that the CBEnKF improves the multi-basin mean of the mean square error skill score over the EnKF by about 0.15 over lead times of up to the time-to-peak of the basin. Verification of the ensemble predictions indicates that the CBEnKF improves the mean continuous ranked probability skill score by about 0.2 on average over the EnKF for all ranges of flow within the significant events, and by about 0.3 for flows exceeding the 95th percentile in those events. That the gain in skill is larger for larger flows makes the CBEnKF very appealing despite the significantly higher computational cost.