A new adaptive hybrid ensemble Kalman filter and optimal interpolation

Hybridizing the forecast covariance in ensemble Kalman filters with a static background term, often used in variational and optimal interpolation frameworks, has shown a strong potential for improving the prediction accuracy of NWP systems. The hybridization is usually performed through a linear combination between the dynamic and the static covariance. A weighting coefficient(s) is thus needed to determine the weight on each covariance term. In this study, we propose an efficient adaptive algorithm to estimate this weighting coefficient. The algorithm assumes such a coefficient to be random with a prescribed probability density function and uses the data to update its moments following Bayes theorem. Further, we propose an extension of the algorithm to ensemble systems that use a serial two-step update procedure such as DART. The algorithm is evaluated in twin-experiments framework using low-order models (e.g., Lorenz 96), in which different sensitivity experiments (ensemble size, observation network, etc.) are conducted.