The impact of observational and model errors on four-dimensional variational data assimilation

The impact of observational and model errors on four-dimensional variational (4DVAR) data assimilation is analyzed for a general dynamical system. Numerical experiments with both the barotropic vorticity equation and the shallow water system are conducted. It is shown from the analysis 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 systematic or biased, the 4DVAR assimilation method tends to either converge to the erroneous observations or introduce the model error into the data 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 field). Forecasts using the assimilated initial condition with an imperfect model indicate that the forecasts may or may not be improved, depending upon the nature of the model and observational errors, and the length of the assimilation and forecast periods.