A Hybrid Nudging-EnKF Approach to Data Assimilation

A hybrid nudging-ensemble Kalman Filter (EnKF) approach with potential use for numerical weather prediction (NWP) is explored using the non-linear Lorenz three-variable model system. The nudging method uses the full set of model equations and allows corrections to be made gradually while allowing them to influence other variables and future time periods through the model equations' interactions rather than through approximate dynamic relationships and constraints. The EnKF takes advantage of ensemble forecasts which are becoming more widely available, to get flow-dependent background error covariances which can be used to spread the corrections and more efficiently seek the optimum state between the model background and the observations. Thus this hybrid approach allows the EnKF to provide flow-dependent, time-varying error covariances to further correct the model fields and to compute the nudging coefficients rather than using ad-hoc nudging coefficients derived from experience and experimentation.

From another perspective, the hybrid nudging-EnKF approach determines a more accurate direction of the drag from observations to the background than the traditional nudging data assimilation scheme. A group of average hybrid nudging-EnKF coefficients are obtained by analyzing the Lorenz system during a historical period by way of the hybrid nudging-EnKF approach. These average hybrid nudging-EnKF coefficients are found to work successfully in other periods. Therefore, archived hybrid nudging-EnKF coefficients may provide useful statistical information for defining the nudging coefficients for future applications since the EnKF can be quite expensive in real-time NWP applications. This work serves as a test bed for concurrent experimentation in the shallow water model equations and future work in WRF. Proof of concept for this hybrid data assimilation approach is investigated first using these simpler, reduced dimension models.