Effective Incidence Angles

Two things regarding my previous posts:

1. I used a generic location for the radar location just for debugging.
   
2. I used wave conditions that were fairly small.

Now, in order to get more representative results, I am running a more chllenging wave condition, that of August 11, 2007, at 7 am (Hmo=1.38 m, Tp=7.5 s). I also put Funwave to high strain, since I decreased my grid size to 1 m, rather than 3. The only thing lingering in the air is the actual antenna height, which I don't have because the GPS readings were crazy (it reported 0 m at the antenna base), so I am using a conservative value of 5 m.

Since the antenna is further inland, the grazing angle is even smaller, and that combined with the steeper waves gave a lot of shadowing, which was something expected for nearshore applications.

But the other interesting thing was to compute the actual surface slope, which combined with the local grazing angle (et every grid point), can be used to get the effective incidence or grazing angle. This is relevant, because LGA effects are usually considered to be relevant in the range GA<20 Traditional Bragg theory seems to be best suited to the range 20 < GA < 70. One of the results of our preliminary analysis of field data showed that large waves (steep) yield increased returns, especially under the appropiate water and wind conditions. Wave breaking on the other hand, was rather insensitive to the ambient conditions (although calibrated data is needed to corrboarate this). So, we speculated that the high returns were due to Bragg-like effects. Now the question is wheter the effective angles are compatible with the range were Bragg is known to be the main mechanism.

And it seems that they are.

Here is a snap fo the free surface for this scenario. The upper panel is the free surface, where wave peaks esceeded 1 m. The second panel is the surface slope, with zero value being a horizontal surface (thus crests have zero angle). The third panel is the effective grazing angle, which is the result of the sum of the local grazing angle and the slope. It can be seen that in the front of the waves, local grazing angles can reach 20 deg for these waves, thus no longer being in the LGA regime. Moreover, the choice of z_radar=5 m is a conservative one, since a higher elevation value would shift all the values even more outside the LGA regime.



Hence, it looks reasonable that Bragg mechanisms are responsible for large returns in the front of the waves.  The confirmation of this requires modeling the radar return and compare it with the measurements.

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.

FUNWAVE 2D

I decided to retake my attempts at running Funwave2D, and I am pleased to say they worked!

I've ran succesfully over the Feb 07, Duck bathymetry with low energy conditions in the following computers

• frodo (nearly died): compiler f77
  
• strider (it took about 14 hours to do a test run, 8500 iterations): compiler f77
• Enentarzi (about an hour!!):  I compiled it using pfg77
• My iMac at home (yeah!): It ran pretty fast (no more than two hours) : compiled it with the free compiler gfortran

After that, I created a bunch of matlab scripts that basically take you from the bathymetry and spectrum, add PLB and a flat portion offshore and export these into funwave friendly format. After that, I edited the funwave codes to improve the output, and created another script that reads all the data into Matlab. At the end of the day we get:

• all the info of the funwave2d.data (makes easier to run in batch)
  
• The spatial maps of free surface at 40 instants during the run.
  
• The time series of orbital velocities, eta and vorticity at 20 gages.
• a wave height and wave setup spatial profile.

Samples of these results are here:

Input Spectrum la0702221300.asc


Movie of the surface


Wave height map


Now, let's roll!