Choosing an approximation of radiative transfer

The accuracy of the P sub(L) approximation to the equation of radiative transfer in the presence of scattering/absorbing clouds of various optical thicknesses is examined. Very accurate net fluxes can be obtained with the P sub(1) (two-stream) and P sub(3) (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. It is shown 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, tables are provided which give the number of terms of the spherical harmonics 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 10 super(6) , these tables should be of particular interest to climatologists.