**Jeff Anderson**

Data Assimilation Research Section

IMAGe, NCAR

### Data Assimilation Using Small Ensemble Filters

Atmospheric data assimilation merges observations with a numerical model to produce initial conditions for predictions. Ensemble assimilation methods use Monte Carlo techniques to compute the impact of observations on a prior model estimate of the atmospheric state.

Ensemble filters with sample sizes as small as 20 are routinely applied to geophysical models with millions of state vector elements. Sampling error leads to state estimates with too little variance and erroneous correlations between observations and state. Hierarchical Bayesian algorithms that automatically detect and correct for sampling errors as well as some errors in the prediction model are presented. An algorithm to correct variance uses a deterministic filter in concert with an ensemble filter. An algorithm to correct correlations uses an ensemble of ensemble filters. Results will be shown for a numerical weather prediction application.