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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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S. Twomey, B. Herman, and R. Rabinoff

Abstract

An extension of the Chahine relaxation method for inverting the radiative transfer equation is presented. This method is superior to the original method in that it takes into account in a realistic manner the shape of the kernel function, and its extension to nonlinear systems is much more straightforward.

A comparison of the new method with a matrix method due to Twomey (1965), in a problem involving inference of vertical distribution of ozone from spectroscopic measurements in the near ultraviolet, indicates that in this situation this method is stable with errors in the input data up to 4%, whereas the matrix method breaks down at these levels. The problem of non-uniqueness of the solution, which is a property of the system of equations rather than of any particular algorithm for solving them, remains, although it takes on slightly different forms for the two algorithms.

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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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Russ S. Schumacher and Gregory R. Herman

Abstract

We applaud Gourley and Vergara for their thorough investigation of the relationship between precipitation and flash flood reports, as well as their inclusion of information from advanced hydrologic model output. We conducted some additional analysis to identify the reasons for the substantial differences between their findings and ours. The primary reason for the differences was found to be temporal sampling. The high temporal resolution of the MRMS dataset, as well as their use of “rolling” accumulation periods, explains most of the discrepancies. For guidance related to real-time warning decisions for flash flooding, Gourley and Vergara’s analyses provide an important new guide and we recommend the use of their results for this purpose. For other applications, including model postprocessing and for precipitation datasets with lower temporal resolution, our results will continue to prove useful.

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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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L. W. Thomason, B. M. Herman, and J. A. Reagan

Abstract

The effect of vertical inhomogeneities of atmospheric attenuators upon determinations of air mass and upon Langley plot determinations of the extra-atmospheric solar irradiance is examined and found to be significant, especially when accuracies of 0.1% are required, as in our current solar monitoring program. Ozone air mass values are found to differ greatly from those of the homogeneously mixed atmosphere for zenith angles greater than 60°.

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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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