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T. Charlock and B. M. Herman

Abstract

The Elsasser and Culbertson (1960) formulation for calculating radiative fluxes has been widely used by meteorologists. Corrections to the Elsasser and Culbertson scheme have been given by Zdunkowski et al. (1966). Unfortunately, both the Elsasser and Culbertson formulation and the Zdunkowski et al. correction contain a few errors.

Elsasser and Culbertson's analytical expression for the evaluation of downward infrared fluxes on the Elsasser chart is incorrect. This introduces no numerical error in using the chart, however, as a fortuitous second error cancels the first exactly.

Zdunkowski's correction to the Elsasser and Culbertson expression for isothermal slab fluxes is proper; errors are made in the derivation of this corrected form, however. Zdunkowski's expressions for upward and downward fluxes from a realistic atmosphere (as opposed to isothermal slab fluxes) are in error.

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D. O. Staley and B. M. Herman

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D. N. Yarger and B. M. Herman

Abstract

Calculations are presented for the reflected and transmitted intensifies and polarizations for the C wavelength pair used for Umkehr measurements. The present calculations utilize a numerical integration of the transfer equation which includes an orders of scattering as well as absorption. These results are compared with solutions which include only scattering, and solutions which include absorption but only single scattering. The importance of higher order scattering for intensity calculations even at higher absorbing wavelengths is demonstrated, as well as the effects of absorption on the polarization of the emergent radiation.

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R. L. Gall and B. M. Herman

Abstract

The sensitivity of the nocturnal minimum temperature over dry soil under clear calm conditions to changes in the distribution of temperature and humidity aloft is estimated. To make the estimates, the minimum temperature is calculated by means of a simple radiative-conductive model for thermal equilibrium at the surface. Changes due to systematic variations in the temperature and dewpoint depression of three tropospheric layers are computed. The results indicate that relatively small changes in temperature and humidity occurring aloft in the lower layers of the atmosphere produce changes of several degrees in the nocturnal minimum temperature at screen height.

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L. W. Thomason, R. J. Szymber, and B. M. Herman

Abstract

Standard reduction techniques for the Linke turbidity factor are examined and found to yield errors of as much as 10%, resulting from a failure to recognize the importance of the wavelength sensitivities of pyrheliometers and the assumption that the turbidity factor is constant with air mass. A preferred turbidity factor is recommended and is shown to exhibit remarkable linearity with aerosol optical depth.

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B. M. Herman, T. Caudill, D. Flittner, and K. N. Liou

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K. J. Thome, B. M. Herman, and J. A. Reagan

Abstract

A method of determining precipitable water to within 10% from solar radiometer data has been developed. The method uses a modified Langley technique to obtain the water vapor optical depth, and a model developed at the University of Arizona is used to convert this to a precipitable water amount. The method is applied to two-and three-channel radiometric data and is compared to results obtained from empirical methods and to radiosonde data.

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J. D. Spinhirne, J. A. Reagan, and B. M. Herman

Abstract

Vertical profiles of aerosol extinction and backscatter in the troposphere are obtained from multizenith angle lidar measurements. A direct slant path solution was found to be not possible due to horizontal inhomogeneity of the atmosphere. Regression analysis with respect to zenith angle for a layer integration of the angle-dependent lidar equation was thus employed to determine the optical thickness and aerosol extinction-to-backscatter ratio for defined atmospheric layers, and subsequently, cross-section profiles could be evaluated. Measurements were made with an elastic backscatter ruby lidar system with calibration by a standard target procedure. The results from 20 measurement cases are presented. For layer-aerosol optical thicknesses >0.04, useful results were obtained, and corroboration by solar radiometer aerosol optical depth data was found. The mean mixed-layer aerosol extinction-to-backscatter ratio for the measurements was 19.5 sr with a standard deviation of 8.3 sr. With the use of an aerosol size distribution inverted from wavelength-dependent solar aerosol optical depth data, the measured extinction-to-backscatter ratio was compared to Mie theory calculations, and the imaginary index giving best agreement was determined. A maximum upper limit of 0.015 was indicated for the aerosol imaginary index. but the mean result was 0.003 for a real index of 1.52.

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T. Charlock, B. M. Herman, and W. G. Zdunkowski

Abstract

Charlock and Herman (1976, hereafter CH) have criticized the formulation of the radiative flux equation of Zdunkowski et al. (ZBL), 1966. While Zdunkowski (Z) finds their paper very interesting, he does not agree with all of their arguments. Instead of writing a comment on their paper, which would precipitate a reply from CH without satisfactorily resolving the argument, we believe it is best to jointly write some comments. This will eliminate misunderstandings since all three authors are in agreement on the basic physics of the problem, but differ in the point of view of how best to apply the Elsasser scheme. In the following we will try to clarify our positions.

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B. M. Herman, W. Asous, and S. R. Browning

Abstract

A method of fitting polynomials to the intensity distribution as a function of optical depth is described for use with the Gauss-Seidel iterative technique for solving the equation of radiative transfer. This technique enables the τ integration to he performed analytically, thus permitting accurate and rapid solutions for optically thick atmospheres. Results are shown for values of τ up to 50, and various cheeks indicate that the method maintains an accuracy of better than 1%.

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