Determination of the variance of rough water surface slopes by the distortion of Snell’s circle boundary

We studied the opportunities of diagnostic of the wind roughness by distortions of Snell’s circle boundary images, i.e., images of the sky observed from underwater through a rough water surface. Models of random realization and statistically average image of Snell’s circle which takes into account various condition of illumination (overcast sky, clear sky and isotropic distribution of sky radiance) have been developed. Formulas for definition of slope variance of the sea surface by distortion of Snell’s circle boundary for one-dimensional roughness have been received. Dependence of accuracy of definition of slope variance on time of image averaging, depth of receiver diving, wind speed, range of waves forming the roughness, have been analyzed by the method of computer modeling. It has been shown on the basis of numerical calculation and experimental data that waves with length from millimeters to meters can be shown in the image of Snell’s circle depending from depth of receiver diving, receiver resolution and water turbidity.