Inversion of cloudy satellite sounding radiances by nonlinear optimal estimation. I: Theory and simulation for TOVS

Abstract A new approach is proposed for inverting satellite sounding data for use in numerical weather prediction (NWP). It may be considered in two ways: either as a retrieval scheme which uses a forecast profile as a background or ‘first guess’ and the covariance of forecast error as a constraint in order to produce retrieved profiles compatible with the subsequent NWP analysis; or as a module within a NWP analysis scheme to perform the vertical analysis of satellite radiances at the observation points (i.e. to project the information in the radiances on to the NWP analysis levels in the vertical). The new scheme performs an inversion of the radiances to retrieve simultaneously the temperature and humidity profiles, the surface temperature and microwave emissivity, and the cloud‐top pressure and amount. It employs an iterative method which finds the maximum probability solution to a nonlinear retrieval/analysis problem. It operates on ‘raw’, potentially cloud‐affected radiances and thus bypasses the separate pre‐processing and cloud‐clearing stages necessary in many retrieval schemes. The technique is a fully ‘physical’ method, involving calculations for each profile of corresponding radiances (and of derivatives of radiance with respect to profile parameters). It is also a ‘statistical’ method, since it uses the covariance of forecast error as a constraint. The paper develops the theory of the new approach and examines its convergence properties and inherent quality control characteristics. The application of the scheme to data from the TIROS Operational Vertical Sounder (TOVS) is then discussed. The theoretical error characteristics of the scheme are investigated, and the results of retrievals from simulated TOVS radiances are presented. The theoretical advantages of retrieving cloud parameters simultaneously with other variables are demonstrated, in terms of both the temperature retrieval accuracies in cloudy conditions and the skill with which the cloud parameters themselves may be obtained.