A linear dynamical prediction model is combined with a linear analysis scheme to give a formula for the expected squared forecast error, as a function of space and time, given a knowledge of observational error covariance and spectrum of the true field. The formula is applied with a two-layer geostrophic model to estimate the maximum impact of tropospheric temperatures derived from satellite radiances over oceanic areas on the accuracy of 500 mb forecasts over North America. The results show a positive impact if the observations are analyzed by an unrealistically efficient optimum interpolation method, but they show a negative impact at all but the smallest satellite error values if the observations are analyzed by a method that ignores observational errors. Eight conclusions are reached concerning routine numerical forecasts and the First GARP Global Experiment.

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