Abstract
Starting from Mecke's analysis of the absorption and scattering by water droplets, a system of equations is derived from which may be computed the fractions of the sun and sky radiation incident on a fog or cloud which will be reflected, absorbed and transmitted. These fractions are found to vary with the size of the droplets, the thickness of the fog or cloud, and the density, or amount of liquid water per cubic metre. The zenith distance of the sun also has a slight effect, but this is very small by comparison with the effects of the other variable factors.
Drops of radius 2 Γ 10^β3^ cm. are taken as typical of fog, and drops of radius 5 Γ 10^β4^ as typical of cloud. Table I gives, for fog and cloud, for three values of the density, 0.1 gm./m.^3^ (diffuse), 1.0 gm./m.^3^ (moderate) and 5 gm./m.^3^ (dense), and for thickness of cloud or fog of 20 m., 80 m. and 200 m., and also, for 1,000 m,. and 4,000 m. for cloud, the theoretically computed values of the fractions of incident radiation which are scattered, absorbed and transmitted.
A fog is found to reflect less, absorb more, and transmit more, than cloud of the same density and thickness (vertical extent). A diffuse fog of density 0.1 gm/m.^3^ transmits 98.5 per cent if its thickness is only 20 m., and 86.6 per cent if its thickness is 200 m. In order to reflect 80 per cent of the incident radiation, a cloud of density 1.0 gm./m.^3^ must have a thickness of at least 150 m., while a cloud of density 5.0 gm./m.^3^ must have a thickness of at least about 50m.
The absorption is greatest in the upper layers of the cloud or fog, and so tends to increase the lapse rte within the liquid bearing layer, but this tendency is masked by the interchange by longβwave radiation, which cools the upper part of the cloud while warming the lower layers.
No observational data are available in a suitable form for comparison with the results displayed in Table I.