Light refraction by mean temperature gradients in the near-earth atmosphere

Abstract

Visible light ray paths in the atmospheric surface layer are numerically computed by division of 500- to 5000-m ranges into small intervals so that the ray path height and thus refractive index gradient is nearly constant for each step. Meteorological conditions are varied by using different combinations of sensible heat fluxes, surface stresses, and surface roughnesses. Although the effect of water vapor gradients can be substantial, their effect is not included here. The results are confined to heights of less than 5 m because of the restrictive values chosen for the ratio of the eddy diffusivity of heat to that of momentum. Mirages hide lower portions of images and the minimum height seen varies approximately inversely proportionally to the observer height. Image distortion and laser beam displacement or angle of arrival can be used to determine the mean refractive index gradient, which determines the temperature gradient in the absence of large moisture gradients along the propagation path. A simple, non-iterative formula relating laser beam displacement or angle of arrival to the average temperature gradient can be used only if the beam height varies less than 10% throughout the path.