Abstract
A practical data assimilation algorithm is presented that explicitly accounts for skewness in the prior distribution. The algorithm operates as a global solve (all observations are considered at once) using a minimization-based approach and Schur–Hadamard (elementwise) localization. The central feature of this technique is the squaring of the innovation and the ensemble perturbations so as to create an extended state space that accounts for the second, third, and fourth moments of the prior distribution. This new technique is illustrated in a simple scalar system as well as in a Boussinesq model configured to simulate nonlinearly evolving shear instabilities (Kelvin–Helmholtz waves). It is shown that an ensemble size of at least 100 members is needed to adequately resolve the third and fourth moments required for the algorithm. For ensembles of this size it is shown that this new technique is superior to a state-of-the-art ensemble Kalman filter in situations with significant skewness; otherwise, the new algorithm reduces to the performance of the ensemble Kalman filter.
