Eta-Adjoint Based 4DVAR

Dusanka Zupanski and Milija Zupanski

This advanced assimilation method uses the adjoint of the Eta Model in the process of deriving initial conditions which produce the smallest forecast error. A complete 4D-VAR system has been constructed based on the Eta model adjoint with advanced pre-conditioning and minimization techniques such that a convergent solution is attainable in only a few iterations. Recently, efforts have found that with no loss of accuracy some aspects of the 4DVAR can be performed at lower resolution and the treatment of the error covariance can be approximated. Because of the expense of the 4DVAR method, this efficiency is absolutely paramount. An updated version of NCEP's 4DVAR system is now available and includes the updated physical processes and corresponding adjoint model (excluding radiation & cloud).

During 1998, testing of the new system was curtailed due to funding cuts and lack of computer resources. The plan to perform a three-way comparison with OI based EDAS and the 3DVAR based EDAS had to be canceled. Fortunately, a two week parallel test of the mixed resolution 4DVAR system was conducted in late January 1999.

Major characteristics of the new 4DVAR system are: (1) minimization space is defined in coarse resolution, (2) only NONLINEAR models used in forecast, (3) only COARSE resolution adjoint model used, (4) 1-hour observational window, (5) observational operator is same as in the regional 3DVAR system, (6) forecast model used as a weak constraint (model error), (7) lateral boundary conditions are adjusted, and (8) background and model error covariances are anisotropic and non-homogeneous. The defined coarse resolution was 160km/38lyrs and the fine resolution was 80km/38lyrs. Only 10 minimization iterations were performed: 7 in coarse, followed by 3 iterations using fine resolution eta model.

The results indicate an improvement over 3DVAR for longer forecast periods (36-48 h) while the short-term forecasts (0-24 h) were worse than 3DVAR forecasts, measured by observational RMS errors. A probable improvement would be by performing a few more minimization iterations (10 were not sufficient for convergence). An improvement over these 4DVAR results was noted when, after completing the 4DVAR assimilation, an additional 3DVAR was performed at t=0. Then, short-term forecast errors were greatly improved, still leaving the long-term forecasts virtually unchanged (and better than 3DVAR alone). Future experiments will make use of other available continuous observational data sources collected by during these real-time experiments for subsequent running / testing in retrospective mode.