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 (2D) Gaussian rough sea surface are investigated. The emissivity and reflectivity study is 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 involves the fact that their statistical model is based on the first order geometrical-optics method. In this paper, the first order geometrical optics approximation is considered because the higher order approximations can be neglected compared to the first order approximations. Indeed the total reflected electromagnetic field is damped by the multiple reflections on the surface. They introduce the 2D shadowing function, and the observed surface length in the azimuthal direction with respect to the wind direction. Their emissivity and reflectivity model is obtained from recent works. In order to use the 1D (1D) shadowing function, assume that the average slope of the surface is smaller than unity. Assuming an infinite observed surface length as determines only the emissivity with the 2D shadowing function. Applying their emissivity and reflectivity model, the relation determining the apparent ocean surface temperature is given, in the considered wavelength band, according to the following parameters: wind speed, wavelength, polarization, intrinsic surface temperature, atmospheric transmission coefficient as evaluated by the Taylor and Larmor model, receiver location, and the camera field of view