Assimilation of satellite sounder radiances in NWP: the importance of background error specification

Optimal estimation theory, on which most retrieval and data assimilation methods are based, assumes that the error covariances of the observations and of the a priori (background) information are known, and that they are used (at least approximately) in the retrieval/analysis procedure. In data assimilation for numerical weather prediction (NWP), background errors may be known reasonably well in the sense of global statistics. However, this can disguise substantial spatial and temporal variability. Moreover, it is possible for the overall error variance to be correct whilst the partitioning of errors between different spatial scales, e.g. between different vertical eigen-modes, is significantly incorrect. The specification of the magnitude and vertical structure of the background error covariance is crucial to the appropriate interpretation of radiance information from satellite sounders within a NWP data assimilation system. Uncertainties in the specification of error covariances are inevitable, but an improved understanding of the acceptable range of mis-specification is likely to lead to improved impact of these data in NWP. This problem is likely to be more important for advanced infra-red sounders, as we attempt to extract information on smaller vertical scales, whilst retaining the information that the NWP model often contains on sharp vertical structures.

We investigate the sensitivity of analysis error to the mis-specification of background error. We first present the general theory and then apply it to the scalar case. We identify a “danger zone”, i.e. a level of mis-specification of background error that will degrade the analysis, and quantify it as a function of the ratio of observation error to background error. We then extend this to the vertical eigen-modes of a forecast error covariance matrix and present preliminary results for the application of this approach to the assimilation of radiances from the Infra-red Atmospheric Sounding Interferometer (IASI) within the 4D-Var data assimilation system at the Met Office. We consider the implications of these results for the robustness of currently used error covariances.