Shadowing

So the idea behind the Funwave bussiness was to simulate the wave field our radar will be seeing. And since Funwave should yield pretty good surface maps and wave geometry, I thought about using it to simulate the characteristcs of shadowing. As far as I know, most shadowing statitics have been developed for deep water, where Pierson-Moskowitz or JONSWAP spectra have been used to generate the surface maps (eg. Nieto-Borge et al, 2004). Since the spectrum evolves quite a bit in the nearshore, this eventually could affect these statisticts.

With a surface map, it is possible to find the relative elevation of the free surface (relative to the radar antenna), hence we can obtain its azimuthal and vertical angles (again, relative to the antenna). Shadowing will occur if two points are in the same line of sight (i.e. same azimuthal angle) and the point closer to the antenna has a smaller grazing angle.

It is possible then to subdivide the domain in azimuthal bins, which physically correspond to a radar ray. We can extract the surface information being illuminated by this ray, and evaluate the occurrence of shadowing. The procedure is somewhat explained in the following figure, where the antenna location is denoted by a red circle, and shadowed points are marked in red.



The process is repeated for all the azimuthal bins, thus we obtain the total shadowed area:



The image is abit noisy. This is a result of performing in cartesian space an analysis that is inherent to a (cylindrical) spherical space. Since the cartesian space yields discrete instances of the azimuth angle, each ray has stair step edges, which are responsible for the linear shadow features in the image. The alternative is to convert the map to cylindrical coordinates, but I didn't do it because it needs two interpolation steps that I don't deem necessary at this point.

Other than that, is working great. Now I should try more energetic conditions.