Adaptive conditional bias-penalized Kalman filter with minimization of degrees of freedom for noise for superior state estimation and prediction of extremes

摘要

We describe adaptive conditional bias (CB)-penalized ensemble Kalman filter (AEnKF) to improve estimation and prediction of extremes. Environmental variables are generally observed with significant uncertainties. Geo -scientific data assimilation (DA) is hence often subject to CB which adversely impacts estimation of extremes. A generalization of EnKF, AEnKF accounts for CB by dynamically reflecting the flow-dependent information content in the model prediction relative to that in the observation via a scaler weight. The implicit dependence of the weight on the posterior state renders the AEnKF solution nonlinear for superior performance over the tails of the predictand as well as in the (unconditional) mean sense. AEnKF prescribes the weight in real time by minimizing the degrees of freedom for noise. Real-time optimization of the weight also means that AEnKF ob-viates or reduces the need for calibration of uncertainty parameters which is often subjective and expensive. Comparative evaluation for flood prediction shows that AEnKF outperforms EnKF by a very significant margin but is about two to three times more expensive computationally. Because AEnKF uses the EnKF solution, it can be easily implemented in any EnKF code with the addition of the weight optimization module. Given superior performance and relative ease of implementation, AEnKF should be favored over KF in a wide range of geo-scientific DA, particularly when performance over tails is important.