The effect of Earth's atmosphere on contrast reduction·for a nonuniform surface albedo and ‘two‐halves’ field

A model for contrast reduction by atmospheric haze is developed for the ‘two‐halves’ field of the earth's surface (two halves of field of a different surface albedo such as in the case of a seashore) and other geometries of the earth's surface albedo. The model is based on a simplified solution of the equation of radiative transfer in two dimensions, resulting in a method for calculation of the upward zenith intensity in the atmosphere, as a function of the distance from the border between the two half planes, for an unabsorbing atmosphere. The adjacency effect between two infinitesimal areas of different albedos is calculated. The resultant simplified solution is used to develop expressions for the line‐spread function of the atmosphere and the modulation transfer function. This modulation transfer function is a general form to express the atmospheric effect on the transmission of radiation from the earth's surface to the detection instrument looking downward at zenith. It contains the effect of atmospheric scattering by attenuation of the signal from earth's surface and by an effective transfer of radiation from bright surfaces to adjacent dark surfaces. The line‐spread function is used to calculate the point‐spread function, which can be used to calculate the intensity above any surface with given spatial dependence of the reflectivity. In the present paper an example is given in applying this point‐spread function for the calculation of intensity above the center of a square of different reflectivity than its surrounding. The results of the intensity above the two‐halves field and above the center of the square, as was detected by a satellite of a 30‐m square pixel, are compared with numerical results calculated by the Monte Carlo method. The modulation transfer function is also compared with Monte Carlo results. A good agreement is shown, This model is applicable for remote sensing of the earth's surface albedo, in the presence of seashores or other borders between areas of different albedos. A correlation between the vertical aerosol distribution and the range of the adjacency effects is shown. This correlation can be used to estimate the vertical scale height of the aerosol layer from satellite images.