Estimation of model errors in the Local Ensemble Transform Kalman Filter

The Local Ensemble Transform Kalman Filter (LETKF) (Hunt et al 2005) has been implemented to assimilate simulated observations in the NCEP GFS model, and recently in the NASA fvGCM model (Li et al, 2005). The results are excellent for the perfect model scenario. However, in reality, the forecast model has deficiencies and does not represent the atmospheric behavior exactly. We need to extend the application of LETKF to more realistic weather forecast systems by accounting for systematic model errors.

The main goal in this paper is to investigate techniques for treating model bias in ensemble Kalman Filter data assimilation, building on previous work and to develop a system which is both effective and efficient. Recently, Baek et al (2005) extended the work of Dee and Da Silva (1998) by using a high order bias estimate scheme based on the state augmentation scheme correcting the model errors on each grid point, but also accounting for the cross-correlation of model state variables and bias. They successfully tested this approach with the Lorenz 40-variable model and showed the ability to correct forecast model errors. Miyoshi (2005) tested the high order Dee and Da Silva approach on the SPEEDY primitive equations model (without cross correlation terms) but found it to be unsuccessful. He then tried a low order correction approach based on Danforth et al (2005) in which the model errors are expanded into low order EOFs, with very good results.

In this work we first test the Baek et al high order approach with cross-correlations, to determine whether the failure found by Miyoshi is due to the absence of cross-correlations. However the high order approach of correcting at each grid point is computationally expensive. Therefore we develop a low order approach, and compare both results, under the hypothesis that model errors can be represented by relatively few degrees of freedom and can thus be efficiently corrected. These ideas are first tested in the SPEEDY model, and will be implemented in the operational NASA fvGCM model.