Theoretical study on two-dimensional Gaussian rough sea surface emission and reflection in the infrared frequencies with shadowing effect

The emission and reflection properties of a two-dimensional (2-D) Gaussian rough sea surface are investigated. The emissivity and reflectivity study i s of importance for accurate measurement of the temperature distribution of a wind-roughened water surface by infrared thermal imaging. The radius of curvature of the capillary waves being much larger than the wavelength invo lves the fact that our statistical model is based on the first order geomet rical-optics method. In this paper, the first order geometrical optics appr oximation is considered because the higher order approximations can be negl ected compared to the first order approximations. Indeed the total reflecte d electromagnetic field is damped by the multiple reflections on the surfac e. We introduce the 2-D shadowing function, and the observed surface length in the azimuthal direction with respect to the wind direction. Our emissiv ity and reflectivity model is obtained from recent works [1]-[3], In order to use the 1-D (1-D) shadowing function [1], [2], assume that the average s lope of the surface is smaller than unity. Assuming an infinite observed su rface length as [1]-[3] determines only the emissivity with the 2-D shadowi ng function. Applying our emissivity and reflectivity model, the relation d etermining the apparent ocean surface temperature is given, in the consider ed wavelength band, according to the following parameters: wind speed, wave length, polarization, intrinsic surface temperature, atmospheric transmissi on coefficient as evaluated by the Taylor and Larmor model [4], receiver lo cation, and the camera field of view,