An evaluation study of the DRP-4-DVar approach with the Lorenz-96 model

The study evaluates the performance of the dimension-reduced projection four-dimensional variational data assimilation (DRP-4-DVar) with the Lorenz-96 model. Idealized experiments over a period of 200 days have been conducted. The results show that the DRP-4-DVar works well. It generates an analysis equivalent to that of the Ensemble Kalman Filter (EnKF) if the synchronous observations are assimilated at the analysis time, while it produces more accurate analysis than the EnKF does when assimilating observations in an 18-h assimilation window. The experiments also reveal that the impact of the tangent linear assumption for the Lorenz-96 model in the DRP-4-DVar over a 24-h or shorter assimilation window is negligible. Furthermore, with a background error covariance matrix (B-matrix) that has a non-singular projection onto the ensemble space or is explicitly flow-dependent, the DRP-4-DVar performs even better than with a B-matrix that has a singular projection or is not explicitly flow-dependent.