Comparing an Ensemble Kalman Filter to a 4DVAR Data Assimilation System in Chaotic Dynamics

ABSTRACT: In this paper, the Ensemble Kalman Filter is compared with a 4DVAR Data Assimilation System in chaotic dynamics. The Lorenz model is chosen for its simplicity in structure and the dynamic similarities with primitive equations models, such as modern numerical weather forecasting. It was examined if the Ensemble Kalman Filter and 4DVAR are effective to track the Control for 10, 20 and 40% of error at the Initial Conditions. With 10% of noise, the trajectories of both are almost perfect. With 20% of noise, the differences between the simulated trajectories and the observations as well as "true trajectories" are rather small for the Ensemble Kalman Filter but almost perfect for 4DVAR. However, the differences are increasingly significant at the later part of the integration period for the Ensemble Kalman Filter, due the chaotic behavior system. However, for the case with 40% error at the Initial Condition, neither the Ensemble Kalman Filter or 4DVAR could track the Control with only 3 observations ingested. To evaluate a more realistic assimilation application, it was created an experiment in which the Ensemble Kalman Filter ingested single observation at the 180th time step in the X, Y, and Z Lorenz variables and only in the X variable. The results show a perfect fit of 4DVAR and the Control during a complete integrations period, but the Ensemble Kalman Filter has a disagreement after the 80th time step. On the other hand, it was shown a considerable disagreement between the Ensemble Kalman Filter trajectories and the Control as well as a total fail of 4DVAR. Better results were obtained for the case in which observation covers all the components of the model vector.