Regularizing the Satellite Temperature-Retrieval Problem through Singular-Value Decomposition of the Radiative Transfer Physics

Abstract

A new method is derived for retrieving atmospheric temperature profiles from satellite-measured spectral radiance that appears, in first tests, to effectively circumvent certain difficulties of other well-known and implemented methods. In particular, the new method provides an elective way to avoid numerical instability without having to force the algorithm toward adherence to a priori statistics not dependent on the radiance measurements. This provides the opportunity to extract more information from satellite sounding instruments, without encountering instabilities owing to overlapping weighting functions. BY implication, this means that retrievals can be obtained without the typically strong external constraints of smoothing or cohesion to historical characteristics of the thermal or moisture structure. The new retrieval method is derived from a singular-value decomposition (SVD) of the radiative transfer physics governing the satellite measurements. The basis is an orthogonal one depending only on the characteristics of the sounding radiometer and not on a priori statistics. The SVD procedure allows one to efficiently structure and extract the information content of satellite observations and to rationally control the numerical, algorithmic instability. This is accomplished by discarding those singular vectors that adversely transform small radiometer errors into large retrieval errors, while retaining those vectors that transform radiance information reliably and unproblematically into thermal information. It is hoped that this new SVD methodology will find useful application for improving the impact of satellite observations on satellite retrievals and thereby improve the impact of retrievals on meteorological problems varying from short-range forecasting to long-range assessment of global change.