Weighted ensemble filters for assimilation of discrete structures

Ensemble filter methods for data assimilation have been widely tested in global numerical weather prediction applications where they are competitive with variational methods. Ensemble methods that have been applied successfully assume that the state distributions are roughly gaussian. While this appears to be a good approximation for global models with the present-day observing system, it may not be appropriate for assimilation of high impact convective weather on smaller space and time scales. The assimilation and prediction of the genesis of convective cells is an example of a problem that may be highly non-gaussian with present-day modeling and observational capabilities.

Traditional ensemble filters perform poorly when confronted with prior estimates and observations of 'discrete structures'. If a single convective cell forms in a region, model ensemble priors may produce their own cells, but the position and intensity of these may be incorrect. Ensemble filters making a gaussian assumption produce posterior estimates in which the prior and observed cells are 'smeared' together. The resulting ensemble is not an accurate depiction of anything that could happen in the real atmosphere. Particle filters are a standard technique that could address this problem, but the number of particles required for reasonable performance scales hyper-exponentially with model degrees of freedom.

A method that combines features of traditional ensemble filters and particle filters is presented. The prior ensemble distribution is converted to an approximate continuous density. This density is convolved with the observational error density and the result is a weighted ensemble posterior estimate. A final step converts the weighted ensemble estimate back into a uniformly weighted ensemble like those used in traditional filters. The method enjoys the ease of implementation and computational cost of traditional filters but gives a vastly improved representation of discrete features like convective cells. Comparisons of assimilations with the new method and traditional ensemble filters are be presented in idealized assimilations of convective cell genesis.