Choosing an Approximation to the Equation of Radiative Transfer

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  • 1 IBM Scientific Center, Palo Alto, CA 94304
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Abstract

We examine the accuracy of the PL, approximation to the equation of radiative transfer in the presence of scattering/absorbing clouds of various optical thicknesses. We find that very accurate net fluxes can be obtained with the P1, (two-stream) and P3 (four-stream) approximations, although higher orders are sometimes needed. A comparison is made with earlier work which indicated that very high-order approximations are needed to produce this accuracy in the presence of optically thick clouds. We show that the variations found in the earlier work were caused by round-off errors in the computations.

As a guide to the investigator who does not have a method for computing multiple-scattering solutions to the transfer equation, we provide tables giving the number of terms of the spherical harmonies expansion needed to obtain various levels of accuracy for several scattering phase functions. Since the models include clouds of various optical thicknesses, ranging from zero to 106, these tables should be of particular interest to climatologists.

Abstract

We examine the accuracy of the PL, approximation to the equation of radiative transfer in the presence of scattering/absorbing clouds of various optical thicknesses. We find that very accurate net fluxes can be obtained with the P1, (two-stream) and P3 (four-stream) approximations, although higher orders are sometimes needed. A comparison is made with earlier work which indicated that very high-order approximations are needed to produce this accuracy in the presence of optically thick clouds. We show that the variations found in the earlier work were caused by round-off errors in the computations.

As a guide to the investigator who does not have a method for computing multiple-scattering solutions to the transfer equation, we provide tables giving the number of terms of the spherical harmonies expansion needed to obtain various levels of accuracy for several scattering phase functions. Since the models include clouds of various optical thicknesses, ranging from zero to 106, these tables should be of particular interest to climatologists.

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