A Three-Parameter Inferior Mirage Model for Optical Sensing of Surface Layer Temperature Profiles

Abstract

Inferior mirages provide a sensitive and fairly accurate probe for determining vertical temperature distributions in the atmospheric surface layer. Optical measurements on the image can be used to calculate the parameters in a temperature profile model, in this case a function with three adjustable parameters. The function contains an exponential term (two parameters) and an additive linear term (one parameter). The optical observations, for which a known target is required, consist of the elevation angles of the apparent peak, caustic, and horizon. Analytic expressions that must be simultaneously satisfied are derived for all three conditions. The parameter values are extracted numerically by minimizing a positive definite function of the three conditions. The model is tested on a set of images for which nearly simultaneous photographs, theodolite readings, and temperature profiles were available. For each image the three calculated elevations matched the measured values very closely. The complete images also match well in most of the cases. The results, a distinct improvement over previous two-parameter models, also provide a more accurate reconstruction than is obtained from the thermodynamic model for unstable stratification.