THE IMPACT OF OBSERVATIONAL AND MODEL ERRORS ON 4-DIMENSIONAL VARIATIONAL DATA ASSIMILATION

The impact of observational and model errors on four-dimensional varia tional (4DVAR) data assimilation is analyzed for a general dynamical s ystem. Numerical experiments with both the barotropic vorticity equati on and the shallow water system are conducted. It is shown from the an alysis and the numerical experiments that when there are random errors in observations or in model parameterizations, the 4DVAR assimilation method can suppress these errors; however when the errors are systema tic or biased, the 4DVAR assimilation method tends to either converge to the erroneous observations or introduce the model error into the da ta analysis, or both. For a multiple-timescale fluid dynamical system, such as the shallow water equations with fluid depth corresponding to the external mode, the skewness in the system can amplify the errors, especially in the fast variable (e.g., the geopotential or height fie ld). Forecasts using the assimilated initial condition with an imperfe ct model indicate that the forecasts may or may not be improved, depen ding upon the nature of the model and observational errors, and the le ngth of the assimilation and forecast periods.