. Compendium of meteorology. Meteorology. SOLAR RADIANT ENERGY 25 lated to wf-NKs, or A's times their geometrical cross section, so that h = Io\exp{-2Trr'NK,), (23) where r is the radius of the drops and A'' is their number. Figure 7 shows K^ as a function of the parameter X = 2Trr/X. Equation (23) holds for nonabsorbing par- ticles and is valid at wave lengths where water ab- sorption is negligibly small; the summation is required over drop radii when the drop sizes are not uniform. For particles where /ix ^ , /v's will differ from the values of Fig. 7; van de Hulst [7G] shows some varia-
. Compendium of meteorology. Meteorology. SOLAR RADIANT ENERGY 25 lated to wf-NKs, or A's times their geometrical cross section, so that h = Io\exp{-2Trr'NK,), (23) where r is the radius of the drops and A'' is their number. Figure 7 shows K^ as a function of the parameter X = 2Trr/X. Equation (23) holds for nonabsorbing par- ticles and is valid at wave lengths where water ab- sorption is negligibly small; the summation is required over drop radii when the drop sizes are not uniform. For particles where /ix ^ , /v's will differ from the values of Fig. 7; van de Hulst [7G] shows some varia- tions. From Fig. 7 it is important to note that for some ratios of particle size to wave length the scattering does not always increase with decreasing wave length. Fig. 7.—Scattering-area coefficient Ks for liquid-water drops in nonabsorbed spectral regions as a function of X and of drop radius r. {After Houghton and Chalker [46].) Multiple Scattering. In the case of pure Rayleigh scat- tering (if it ever can be said to exist in the atmosphere) the scattering is symmetrical about the particle so that, for example, the forward- and backward-scattered energy are equal. But as the particles become larger the scattering increases in the forward direction [34; 55, p. 161]. Calculations of the effect of such particles, es- pecially for multiple scattering, become rather complex; however they have been undertaken by several authors [76]. The energy which is scattered from the original solar beam will in general be scattered more than once on its way down to the earth's surface or else out to space. From an empirical viewpoint, regarding the contribu- tion of the cloudless sky radiation to the total radiation on a horizontal surface, Kimball [52] states that of the radiation scattered from the direct solar beam, half will be scattered down and half up. In a pure Rayleigh atmosphere this would be the case. But for the actual conditions of the atmosphere, it serves only
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