Temporal evolution of innovation and residual statistics in the ECMWF variational data assimilation systems

The temporal evolution of innovation and residual statistics of the ECMWF 3 D- and 4D-Var data assimilation systems have been studied. First, the obser vational method is applied on an hourly basis to the innovation sequences i n order to partition the perceived forecast error covariance into contribut ions from observation and background errors. The 4D-Var background turns ou t to he significantly more accurate than the background in the 3D-Var. The estimated forecast error variance associated with the 4D-Var background tra jectory increases over the assimilation window. There is also a marked broa dening of the horizontal error covariance length scale over the assimilatio n window. Second, the standard deviation of the residuals, i.e., the fit of observations to the analysis is studied on an hourly basis over the assimi lation window. This lit should, in theory, reveal the effect of model error in a strong constraint variational problem. A weakly convex curve is found for this fit implying that the perfect model assumption of 4D-Var may be v iolated with as short an assimilation window as six hours. For improving th e optimality of variational data assimilation systems, a sequence of retune s are needed, until the specified and diagnosed error covariances agree.