Incremental Ensemble Data Assimilation Updates with Local Regression for Nongaussian Prior Distributions

There is a long history of using incremental modifications to data assimilation algorithms for atmospheric applications. Perhaps the most common is the incremental analysis update in which data assimilation increments are gradually added to the forecast model state over an interval of model time.

The algorithm described here extends traditional ensemble Kalman filter algorithms to be able to exploit nongaussian prior ensemble distributions by incrementally regressing observation space increments on to state variables. Unlike the incremental analysis update, the increments to state variables in this new algorithm are all added in at the analysis time. The algorithm also incorporates local linear regression. The regression coefficient (analogous to the Kalman gain) for each ensemble member is computed using a subset of the prior ensemble members. Combining local regression with an incremental update allows ensemble filters to compute significantly improved posteriors for a wide range of nongaussian prior distributions with little degradation to solutions for Gaussian cases. It is also trivial to implement the algorithm in a sequential ensemble Kalman filter code.

Examples are shown for specific classes of nongaussian priors and for low-order dynamical systems. Results are also presented for nonlinear forward operators in observing system simulation experiments with an atmospheric general circulation model. A discussion of the relative cost and capability of the new algorithm compared to other nongaussian algorithms like the localized particle filter is presented.