A particle-filter based adaptive inflation scheme for the ensemble Kalman filter

An adaptive covariance inflation scheme is proposed for the ensemble Kalman filter (EnKF) to mitigate the loss of ensemble variance. Adaptive inflation methods are mostly based on a Bayesian approach, which considers the inflation factor as a random variable with a given prior probability distribution and then combines it with the inflation likelihood through Bayes' rule to obtain its posterior distribution. In this work, we introduce a numerical implementation of this generic Bayesian approach that uses a particle filter (PF) to compute a Monte Carlo approximation of the inflation posterior distribution. To alleviate the sample attrition issue, the proposed PF employs an artificial dynamical model for the inflation factor based on the well-known smoothing-kernel West and Liu model. The positivity constraint on the inflation factor is further imposed through an inverse-Gamma transition density, with parameters that suggest analytical expressions. The resulting PF-EnKF scheme is straightforward to implement, and can use different numbers of particles in its EnKF and PF components. Numerical experiments are conducted with the Lorenz-96 model to demonstrate the effectiveness of the proposed method under various experimental scenarios.