Simple solution for obtaining a temperature profile from the inferior mirage

Abstract

The first-known, explicit, analytic optical inversion for a refractive-index profile with curvature is given. It enables a quasi-parabolic profile of height vs temperature to be calculated from observations of the inferior mirage of natural objects. Given sufficient fetch, an inferior mirage will occur anytime the heat flux is away from a horizontal surface such as a large body of warm water. All that is needed to obtain the data for a temperature profile over such a surface is a theodolite, a tape measure, and a topographic map. A total of four measurements and a pocket calculator are sufficient to determine the temperature profile on the spot. The resulting profile represents a weighted horizontal mean over the surface. Not all inferior mirages are amenable to the technique, but only those where the temperature gradient at the eye is no less than half the mean gradient, a situation that seems to require some minimum wind. The predictions of the theory are verified with measurements from thermocouples.