Ground-Based Determination of Low Altitude Temperature Profiles by Microwaves

ED R. WESTWATER Environmental Research Laboratories, NOAA, Boulder, Colo., and Department of Physics, University of Colorado, Boulder, Colo.

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Abstract

Vertical temperature profiles of the lower atmosphere are determined from clear air ground-based measurements of microwave thermal emission by oxygen. Angular emission data from two diverse meteorological locations are mathematically inverted by statistical techniques to recover the vertical profiles. Inversion of 52.5 GHz data, gathered at Upolu Point, Hawaii, Hawaii, resulted in an average root-mean-square (rms) difference of 1.27°K between inverted and radiosonde measured profiles from 0 to 10 km. Pressure and humidity profiles are simultaneously estimated from the data; numerical integration of the inverted humidity profiles results in a determination of total vertical water content with a relative accuracy of about 10 percent. Radiometer emission data at 54.0, 54.5, and 55.0 GHz, taken at Salt Lake City, Utah, are inverted with resulting average rms differences of 1.17°K over the height interval from 0 to 6.4 km. A priori temperature variance, corresponding to known surface conditions, is reduced by a factor of 8 to 1. Ground-based thermal inversions are successfully recovered. For both locations, the rms accuracies agree well with predictions based on the theory of statistical estimation.

The statistical inversion equations of Rodgers, and Strand and Westwater are extended for the purpose of inferring profiles from spectrally contaminated radiation measurements. The equations require auto- and cross-covariance matrices of all meteorological variables that contribute to the emission. The general linear estimation equations of Deutsch are applied to a linear approximation to the radiative transfer equation to derive the inversion equations. An analysis of the linearization errors is given.

Abstract

Vertical temperature profiles of the lower atmosphere are determined from clear air ground-based measurements of microwave thermal emission by oxygen. Angular emission data from two diverse meteorological locations are mathematically inverted by statistical techniques to recover the vertical profiles. Inversion of 52.5 GHz data, gathered at Upolu Point, Hawaii, Hawaii, resulted in an average root-mean-square (rms) difference of 1.27°K between inverted and radiosonde measured profiles from 0 to 10 km. Pressure and humidity profiles are simultaneously estimated from the data; numerical integration of the inverted humidity profiles results in a determination of total vertical water content with a relative accuracy of about 10 percent. Radiometer emission data at 54.0, 54.5, and 55.0 GHz, taken at Salt Lake City, Utah, are inverted with resulting average rms differences of 1.17°K over the height interval from 0 to 6.4 km. A priori temperature variance, corresponding to known surface conditions, is reduced by a factor of 8 to 1. Ground-based thermal inversions are successfully recovered. For both locations, the rms accuracies agree well with predictions based on the theory of statistical estimation.

The statistical inversion equations of Rodgers, and Strand and Westwater are extended for the purpose of inferring profiles from spectrally contaminated radiation measurements. The equations require auto- and cross-covariance matrices of all meteorological variables that contribute to the emission. The general linear estimation equations of Deutsch are applied to a linear approximation to the radiative transfer equation to derive the inversion equations. An analysis of the linearization errors is given.

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