A Method for Combining Radiances and Wind Shear to Define the Temperature Structure of the Atmosphere

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  • 1 NOAA/NESDIS Systems Design and Applications Branch, Madison, Wisconsin
  • | 2 Cooperative Institute for Meteorological Satellite Studies, University of Wisconsin, Madison, Wisconsin
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Abstract

The retrieval of temperature from satellite-observed radiances has traditionally been addressed as a one-dimensional or columnar problem which uses a guess profile of temperature. In this study, the traditional approach is augmented by incorporating observed wind shear as a general thermal wind constraint in the inversion of radiances to make a three-dimensional temperature analysis.

The problem is cast as a classical variational problem that minimizes a weighted sum of squares subject to constraint. The constraints are the general thermal wind equation and a set of regression equations expressing the radiances in terms of the temperature profile. The solution is found by the method of conjugate gradients.

Experiments using observed winds with both simulated and observed radiances for the GOES VISSR Atmospheric Sounder (VAS) are described. In both cases, a first guess from a numerical forecast is used. Simulated radiances are used to establish the optimal relative weighting of the wind versus radiance observations and to determine the limits of accuracy on the retrieved temperature under idealized conditions. These relative weights are used in the real data experiments. Experiments are included where weights are varied horizontally and vertically to simulate uneven distribution or confidence in the data. Results indicate that (i) the inclusion of wind shear with simulated radiances reduces the cumulative error variance in the temperature estimate and reduces guess dependence; (ii) horizontal and vertical variations in parameter weighting is viable and well-behaved; and (iii) the algorithm's rate of convergence makes it suitable for small computer applications.

Experiments with observed radiances are not as successful. The measured radiances do not improve the forecast. The principal deficiency appears to be that the regression model for expressing the radiances is inadequate to account for the influence of water vapor which affect the VAS measurements or the nonlinearity of radiance with respect to temperature. Extensions to the model as well as application to microwave measurements, which do not suffer these deficiencies, are discussed.

Abstract

The retrieval of temperature from satellite-observed radiances has traditionally been addressed as a one-dimensional or columnar problem which uses a guess profile of temperature. In this study, the traditional approach is augmented by incorporating observed wind shear as a general thermal wind constraint in the inversion of radiances to make a three-dimensional temperature analysis.

The problem is cast as a classical variational problem that minimizes a weighted sum of squares subject to constraint. The constraints are the general thermal wind equation and a set of regression equations expressing the radiances in terms of the temperature profile. The solution is found by the method of conjugate gradients.

Experiments using observed winds with both simulated and observed radiances for the GOES VISSR Atmospheric Sounder (VAS) are described. In both cases, a first guess from a numerical forecast is used. Simulated radiances are used to establish the optimal relative weighting of the wind versus radiance observations and to determine the limits of accuracy on the retrieved temperature under idealized conditions. These relative weights are used in the real data experiments. Experiments are included where weights are varied horizontally and vertically to simulate uneven distribution or confidence in the data. Results indicate that (i) the inclusion of wind shear with simulated radiances reduces the cumulative error variance in the temperature estimate and reduces guess dependence; (ii) horizontal and vertical variations in parameter weighting is viable and well-behaved; and (iii) the algorithm's rate of convergence makes it suitable for small computer applications.

Experiments with observed radiances are not as successful. The measured radiances do not improve the forecast. The principal deficiency appears to be that the regression model for expressing the radiances is inadequate to account for the influence of water vapor which affect the VAS measurements or the nonlinearity of radiance with respect to temperature. Extensions to the model as well as application to microwave measurements, which do not suffer these deficiencies, are discussed.

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