Preliminary Studies of the Angular Distribution of the Sky Radiation in the Turbid Atmosphere

Abstract

The angular distribution o f the infrared sky radiation whose wavelength is 8000 Å in the turbid atmosphere with the various optical thicknesses corresponding to the variation of turbidity, was calculated on the basis of the primary scattering using an effective “ step-type ” size distribution of the aerosol particles. The calculations were performed for the angular distribution of the above-selected sky radiation in the vertical plane containing the sun and the zenith and for the scattering function. The results obtained are as follows:
The intensity of the sky radiation very near the sun i n the turbid atmosphere is very strong, in which region (whose angular distances from the sun are smaller 5°) the “ larger particles ” mainly contribute to the sky radiation, and in the near region (whose angular distances from the sun are roughly between 5° and 20°) the “ medium particles ”mainly contribute to it, while in the intermediate region (whose angular distances from the sun are roughly between 20° and 50° 90°, the lower limit depending on turbidity) the “ smaller particles ” mainly contribute to it, and in the far region (whose angular distances from the sun are larger than 50°) air molecules mainly contribute to it. The definitions of larger, medium and smaller particles are given below. The region in which air molecules mainly contribute to the sky radiation decrease with the increase of optical thickness corresponding to the increase of turbidity as expected. The scattering functions were also calculated for the various optical thicknesses (turbidities). The results show that as optical thickness (turbidity) becomes larger, the slope of the scattering function becomes steeper. Their agreement with the observed scattering fuctions obtained by ANTHONYis not bad. But in the intermediate region, the departures of calculated scattering functions from the observed one are large. This may principally result from the departure of the size distribution of the aerosol particles in ANTHONY'S results from the a^-3-law of size distribution of the aerosol particles in the mean state of turbid atmosphere.