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 3D‐ and 4D‐Var data assimilation systems have been studied. First, the observational method is applied on an hourly basis to the innovation sequences in order to partition the perceived forecast error covariance into contributions from observation and background errors. The 4D‐Var background turns out to be ignificantly more accurate than the background in the 3D‐Var. The estimated forecast error variance associated with the 4D‐Var background trajectory increases over the assimilation window. There is also a marked broadening of the horizontal error covariance length scale over the assimilation 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 assimilation window. This fit 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 violated with as short an assimilation window as six hours. For improving the optimality of variational data assimilation systems, a sequence of retunes are needed, until the specified and diagnosed error covariances agree.