Recent developments in the theory of sea clutter

In an earlier presentation, it was shown from measurements of sea clutter that the illumination of the scattering elements is a combination of direct and surface-reflected fields. Destructive interference between these field components sets in at small depression angles. This interference effect itself is dependent on frequency and wave height. It results in the so-called "critical angle", polarization dependence, and complicated frequency dependence. It also gives rise to "spikiness" at very small depression angles. When the interference effect is separated from the overall phenomenon, the remaining characteristics show a regular and rather simple behavior. Because measurements show that only a small amount of the intercepted power is back-scattered at small depression angles, a rather directive scattering mechanism is indicated. A theory was developed, therefore, based on plane facets as basic scattering elements. It was found that facets having a perimeter of about a half-wavelength back-scatter most effectively at small depression angles, and that the back scattering of a facet increases about as the square of its slope. Thus, facets near the wave crests contribute most strongly to the back scatter. The frequency dependence of the back-scattering parametersigma degthen was shown to be determined by the size distribution of the facets. A relationsigma deg propto lambda^{-n}implies a facet densityN propto A^{-(2+n/2)}, whereArepresents the area of a facet. Experimental results were reported that showedsigma deg propto lambda^{-1}. In this paper additional developments of the theory are reported. Using for the slope distribution of the facets the representation given by Cox and Munk as a result of optical measurements of reflected sunlight, it is found thatsigma degat small depression angles is approximately proportional to wind speed and must ultimately decrease with increasing frequen- y. Assuming the entire surface of the sea is composed of facets, an estimate of the limiting frequency to which the relationsigma deg propto lambda^{-1}can extend is made, and found to be about 2 mm. However, since the Cox and Munk representation of facet slopes omits whitecaps, this estimate likewise omits possible back scattering from whitecaps. It is shown that sufficiently below this limiting frequency,sigma /degis proportional to the fraction surface which is "large". The facet mechanism allows the qualitative variation ofsigma degat large angles to be deduced. At high angles some of the facets are viewed broadside, so that these give a preponderant echo, which will be proportionately stronger the larger the facet. In the main (broadside) back-scattering beam of a large facet, the radar areasigmawill depend onA^{2}/lambda^{2}, but at the same time the average width of the beam will be proportional tolambda/A^{1/2}. Thus, for a distribution of facet slopes, the overlapping of the beams of adjacent slopes will be less the larger the facet. For a two-dimensional slope distribution, the extra gain of a large facet is just counterbalanced by the reduction in the overlapping of adjacent beams due to the narrower beamwidth, so that the total back-scattered power in the main lobe is about equal to the power intercepted by the facet. Since for small facets the total back-scattered power is much less than the power intercepted, it follows that the back-scattered power will be proportional to the fraction of the surface which is "large". Thus, since the fraction of the surface which is "large" determinessigma degboth at small and large depression angles, it follows that the frequency dependence ofsigma^{deg}at high angles is essentially the same as at low angles, as long assigma deg propto lambda^{-n}. However, iflambdais reduced to the point wh