Inversion of superior mirage data to compute temperature profiles

Abstract

Information derived from the superior mirage is used to compute the average vertical temperature profile in the atmosphere between the observer and a known object. The image is described by a plot of ray-elevation angle at the eye against elevation at which that ray intersects the object. The computational algorithm, based on the tracing of rays that have at most one vertex, iteratively adjusts the temperature profile until the observed image characteristics are reproduced. An example based on an observation made on the Beaufort Sea illustrates the process.

Microwave propagation over the Earth: image inversion

“…[15][16][17][18][19][20][21][22] used the concept of Modified Index of Refraction N (originally due to Schelling et al in 1933 [7]) to take into account the Earth-curvature effect, reducing the problem again to rectangular coordinates but with an extended range of applicability. Since that time a number of approaches to the solution of the forward problem have been taken; see [4,[8][9][10][11][12][13][14][15][16][17][18]. Of particular note is the extension by Kropla and Lehn [19] of the parabolic-ray-curvature approach of Lehn [4], applicable to spherical layers containing constant refractive-index gradients.…”

“…A great advantage of the approximate ray-path description (8) is that exact solutions are available for simple index profiles of practical importance, and the result for quadratic index profiles is especially significant. Explicitly, if the profile (after scaling) is given by…”

Optical Refraction Measurements Across Chesapeake Bay

“…If the surface layer has a constant lapse rate, optical rays passing through the layer follow a constant trajectory with a constant curvature (Lehn, 1983): 2r"…”

“…curvature -'-Light #2 min. curvature (6) where K f is the fitted curvature, A is the temperature gradient, and the parameters for the tower fit are 0.85, -0.28, 0.54, 0.55, and 0.0063. A similar curve was fit to the buoy #5 data where the fit parameters are 1.35, -1.13, 0.28, 1.28, and 7.05; however, the buoy data differs significantly from the tower data.…”

“…In theory (Ref. [3][4][5][6], it is possible to reconstruct the temperature profile from the amount of bending. To this end, a preliminary study was conceived and conducted to measure the bending of light rays in order to recover the temperature profiles above a water surface.…”