The retrieval of vertical profiles of temperature and water vapor from atmospheric radiances is an ill-posed, nonlinear inversion problem. A linear retrieval estimator must be cast in a form which both minimizes the effects of unmodeled nonlinear processes, and provides retrieval constraints that are pertinent to the sounded atmospheres.

Here, the ill-posed aspect of the problem is resolved by defining a set of meteorologically reasonable retrieval estimator constraints through typical shape function (TSF) classification of a large sample of radiosonde observations. The companion problem of discriminating the TSF constraints to be applied to a particular retrieval estimator, given a set of observed radiances, is investigated. Since the particular linear model chosen to represent the radiance measurements will also have some impact on the retrieval estimator, the effects of errors arising from both simple and simultaneous linearization models for the radiative transfer equation are examined. A TSF constrained, simultaneous, maximum a posteriori retrieval estimator is formulated. Also, a classified, single field-of-view, cloud detection and clear radiance estimator is developed for overcast soundings.

The fundamental properties of the new retrieval estimator are examined and specified via synthetic TOVS radiance data experiments. The retrieval algorithm is also applied to two successive NOAA-7 passes over the New Zealand region, and the retrievals compared with those from a regression retrieval scheme, and operational NWP analysis fields.

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