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

Abstract

The temporal evolution of innovation and residual statistics of the ECMWF 3D- and 4D-Vardata assimilation systems have been studied. First, the observational method is applied on anhourly basis to the innovation sequences in order to partition the perceived forecast errorcovariance into contributions from observation and background errors. The 4D-Var backgroundturns out to be significantly more accurate than the background in the 3D-Var. Theestimated forecast error variance associated with the 4D-Var background trajectory increasesover the assimilation window. There is also a marked broadening of the horizontal errorcovariance length scale over the assimilation window. Second, the standard deviation of theresiduals, i.e., the fit of observations to the analysis is studied on an hourly basis over theassimilation window. This fit should, in theory, reveal the effect of model error in a strongconstraint variational problem. A weakly convex curve is found for this fit implying that theperfect model assumption of 4D-Var may be violated with as short an assimilation window assix hours. For improving the optimality of variational data assimilation systems, a sequence ofretunes are needed, until the specified and diagnosed error covariances agree.