Simple solution for obtaining a temperature profile from the inferior mirage

Area of Science:

• Atmospheric optics
• Thermodynamics
• Geophysics

Background:

• Inferior mirages occur over horizontal surfaces with heat flux away from the surface, such as warm bodies of water.
• Calculating atmospheric temperature profiles typically requires specialized equipment and complex analysis.

Purpose of the Study:

• To present the first explicit, analytic optical inversion for a refractive-index profile with curvature.
• To enable the calculation of quasi-parabolic height vs. temperature profiles from inferior mirage observations.

Main Methods:

• Utilizes a theodolite, tape measure, and topographic map for data collection.
• Involves four measurements and a pocket calculator for on-site temperature profile determination.
• Applies an analytic optical inversion technique to refractive-index data derived from mirage observations.

Main Results:

• Successfully calculated temperature profiles from inferior mirage observations.
• The method yields a weighted horizontal mean temperature profile over the surface.
• The technique is applicable to inferior mirages with a specific temperature gradient at the observer's eye.

Conclusions:

• The developed optical inversion method provides a practical way to determine atmospheric temperature profiles.
• The findings are validated by thermocouple measurements, confirming the theory's predictions.
• This technique offers a novel approach for in-situ environmental monitoring.