The REM Adjoint System and Its 4DVar Data Assimilation Experiments

The Regional Eta-coordinate Model (REM) has performed well in forecasting heavy rainfalls in China in recent years. A four-dimensional variational assimilation system (4DVar) is developed to improve the forecast skill of the REM. The tangent linear model and adjoint model codes are written according to the "code to code" rule, and the establishment of the REM adjoint modeling system is introduced in detail in this paper. The tangent linear and adjoint models of the REM are validated against the observational data, and so is the gradient of the given cost function. It is shown that for the tangent linear model and cost function, when the magnitude of perturbations is reduced, the verification results approach 1.0; when the rounding error of computer is increased, the verification results depart off 1.0. In the validation of the adjoint model, the values on the left- and right-hand sides of the algebraic formula are equal with 13-digit accuracy. These results indicate that the tangent linear model and the adjoint model system of the REM are successfully coded, and the gradient of the cost function is correctly calculated. By using the REM adjoint modeling system, two 4DVar experiments and extended forecasts are performed using observational data for two real cases in June 1998 and August 2000. The results show that forecasts of temperature, wind speed, and specify humidity using the 4DVar-assimilated initial data are all improved at the end of the forecast period. However, the performance of the 4DVar in forcasting rainfall is different in these two cases. The prediction of location and amount of the accumulated rainfall is well improved in the first case, while in the second case the prediction has no significant improvement. The problem may result from the fact that the observational data used in the 4DVar for the second case are inadequate. This case will be studied further in future work.