A REM adjoint system and its data assimilation experiments of 4D-Var

The Regional Eta Coordinate Model（REM）has shown an acceptable good forecast ability to the regional heavy rainfall of China in recent years, and developing a FourDimension Data assimilation system(4D-Var) for the REM is an important step to consummate the model as well as to improve its forecast ability. The tangent linear model and adjoint model codes were written according to the “code to code” rule, and the establishment process of the REM adjoint modeling system is introduced in details. The verification of the tangent linear model and adjoint model of the REM model was performed using a lot of observational data, and the correctness of the gradient of the given cost function was also checked. In the verifications of the tangent linear model and cost function, when the magnitude of perturbations reduced, the verification results approached to 1.0, and when the rounding error of computer increased, the verification results departed off 1.0, thus showing that the coding of the tangent linear model is successful and the gradient of cost function is correct calculated. In the verification of the adjoint model, the values at left and right hand side of algebraic formula are the same with 13 digit accuracy. The above results indicate that the REM adjoint modeling system is successfully established. Applying the REM adjoint modeling system, two 4D-Var experiments and extended forecast were performed using the Observational data of two weather cases (00:00 UTC 8 June 1998 to 12:00 UTC 8 June 1998 and 00:00 UTC 1 August 20:00 to 12:00 UTC 1 August 2000). The results show that forecasts of temperature, wind speed and specify humidity using the 4D-Var -assimilated initial data are all improved at both the end of the assimilation window and the end of the forecast time. But forecast results of rainfall are different in the two cases: the location and amount of the accumulated rainfall are closer to the observation in the first case, while in the second case there is no significant improvement. The reason for results in the second case maybe two aspects: the first is that the definition of the cost function is too simple during the primary numerical experiments of 4D-Var, the background term was not considered in the cost function, the errors caused by the numerical model during the 4D-Var were not controlled. And further more the accumulated rainfall was not considered in the cost function too, which affected the 4D-Varassimilated initial data, and especially in the convective weather process, the effect was more obviously; the second aspect is that the observational data used during the 4D-Var was fewer in the assimilation widows, just one at the end of the assimilation windows. This case will be studied in the further research.