The REM Adjoint Modeling System and its Application to the Study of 4D-VAR and Predictability (in Chinese)
The Regional Eta-coordinate Model (REM) adjoint modeling system is developed by the establishment of the Tangent Linear model and Adjoint model of the REM model in this dissertation. The correctness of the Tangent Linear model and Adjoint model code is verified after the code is written, and it is found that the Tangent Linear model and Adjoint model work well. Then, using the Adjoint model of the REM model, the gradient of the cost function is checked and a twin test is conducted with the ideal observations generated by the REM model. The results indicate that the REM adjoint modeling system is successfully established.
Applying the REM adjoint modeling system, two four-dimensional variational data assimilation (4D-VAR) experiments and extended forecasts are performed using the observational data (0000 UTC 8 June 1998 and 0000 UTC 1 August 2000). The forecast results with 4D-VAR are improved at both the end of the assimilation window and the end of the extended forecast time in the two tests. But the forecast results of the accumulated rainfall with 4D-VAR are different in the two tests: the location and the amount of the accumulated rainfall in the first test is closer to the observation, and there is no significant improvement in the second test. It is concluded that although the forecast result using assimilated initial data shows an improvement at the end of the assimilation window, the results are not necessarily improved during the extended forecast time. The forecast results are sometimes as poor as those without 4D-VAR, especially for rainfall.
Using a scaled equation of specific humidity, an analysis of the effect of the model error on the 4D-VAR of rainfall is performed. From a theoretical analysis and a numerical experiment, the following conclusions are reached: (a) In the case where there is initial data error but the numerical model is correct, if the observational data during the assimilation window are correct, the true initial data will be carried through by the method of 4D-VAR, and the forecast result using the optimal initial data will be close to the observational data during both the assimilation window and the extended forecast time. (b) If there are model errors, these errors will be transferred to the initial data after 4D-VAR, the assimilated initial data will not be the true initial specific humidity, and the improved result in this situation will be a forecast with an incorrect model and incorrect initial data. (c) When the model has errors, especially errors that grow with time, although the forecast result of the accumulated rainfall can approach the observational data during the assimilation window, it will become less advantageous than the forecast without 4D-VAR in the extended time, even becoming worse than it. (d) In order to get an optimal forecast at the latest forecast time, a different background and background error covariance matrix should be used according to different tests during the 4D-VAR.
With the adjoint modeling system and nonlinear optimization method, the predictability is also studied in this dissertation. A theoretical analysis is introduced to identify the predictability of the numerical model and to identify the model error and the initial observational data error using the nonlinear optimization method. A series of ideal tests are performed using the observational data generated by the model of specific humidity, the results showing that the nonlinear optimization method is a useful tool to identify the model error. Then, with the REM adjoint modeling system, three tests are conducted using the observational data (0000 UTC 6 August 2000, 0000 UTC 8 August 2000 and 0000 UTC 24 June 2002). The results suggest that the REM model can give an acceptable forecast with the allowed forecast error in the three synoptic tests. The first test suggests that the REM model can give a satisfactory simulation just using the initial data by interpolation (such as, the Optimal Interpolation) from daily station data. The second and the third tests suggest that the REM model can give a satisfactory simulation by using improved initial data (via the 4D-VAR method).
REM model, Adjoint Modeling System, 4D-VAR, Predictability, Error
Wang Tie 王铁
Wang Tie, 2005: The REM Adjoint Modeling System and its Application to the Study of 4D-VAR and Predictability. PhD Thesis of the Institute of Atmospheric Physics, Chinese Academy of Sciences. (in Chinese)