Evaluation of the Impact of Observations on Analyses in 3D- and 4D-Var Based on Information Content

Abstract The degrees of freedom for signal (DFS) is used in data assimilation applications to measure the self-sensitivity of analysis to different observation types. This paper describes a practical method to estimate the DFS of observations from a posteriori statistics. The method does not require the consistency of the error statistics in the analysis system and it is shown that the observational impact on analyses can be estimated from observation departures with respect to analysis or the forecast. This method is first introduced to investigate the impact of a complete set, or subsets, of observations on the analysis for idealized one-dimensional variational data assimilation (1D-Var) analysis experiments and then applied in the framework of the three dimensional (3D)- and four-dimensional (4D)-Var schemes developed at Environment Canada.