Improving Estimation and Prediction of Extremes Using Conditional Bias-Penalized Kalman Filter

The Kalman Filter (KF) and its variants are widely used for real-time updating of model states and prediction in operational hydrology and hydrometeorology. For many applications, the ability of the KF to improve model performance under a broad range of conditions is an important consideration. However, in operational hydrology and hydrometeorology, the accurate prediction of large and extreme events, such as floods and droughts, is particularly important. Because KF is, essentially, a least squares solution, it is subject to conditional biases (CB), which arise from the errors-in-variables, or attenuation, effects when the model dynamics are highly uncertain, the observations have large errors and/or the system is not very predictable. In this presentation, we describe a conditional bias-penalized KF, or CBPKF, which is based on CB-penalized linear estimation. The CBPKF minimizes the weighted sum of error covariance and expectation of Type-II CB squared. We also present the comparative evaluation results between KF and CBPKF, based on a combination of real and synthetic experiments.