Hooray?

In an attempt to find if I had some bugs on my codes, I went back to the basics and tried to reproduce the figures found in Tsang (2001), Vol I, Chapter 8, regarding the scattering from a half space of spherical particles using the radiative transfer method. I was able to get all the figures (codes are working!), and that enocuraged me to go ahead and try to model something closer to our scenario.

So I got two complex permitivities for water (fresh and salty, respectively) from the literature (Ray, 1972 and Plant, 1997), set up a range of ka values and solve the same set of equations at 10 GHz.

The results seems to be pretty interesting. The resonance region typical of Mie scatterers seems to be well recovered (e.g. Sharkov, 2007) and I take this as a confirmation that using Mie is better than Rayleigh and indeed is the regime appropiate for the particle sizes used. Aditionally, the sizes seem to be reasonable for water droplets. But perhaps more important is that it seems that the backscattered power is at least of the order of the values we have seen in the MR-SENSO data (O(-10) dB). Now that's encouraging!

I need to address if we are talking about the same variable though (backscattering coefficient versus NRCS), but I'll do that on monday. The other thing is that it seems that the result is insensitive to the volume fraction of scatterers. I think is due to the normalization of the scattering based on the extinction coefficient, which is also linearly proportional to the number of particles (remember, this is independent scattering), and the two could cancel out.

In the meantime, this simple plot has made me very, very happy.

Attempt to Calibrate MR

Now that we have the georeferencing sorted out, we can start plauyin a bit with the data to make some comparisons. There was a bit of trouble due to the radars being non concentrical. Therefore, only the line of sight at 46 degrees was imaged as a single ray by the two radars. In order to overcome this, I calculated the x-y locations of all the points imaged by RiverRad, and converted them to polar coordinates relative to the Marine Radar and extract them from the Marine Radar file. This introduces a certain error due to the different acquisition time of the points, but it is in general small (I am working on the numbers).

Once that is being done, I tried to convert the intensity signal from the Marine Radar to normalized cross sections, in a similar way to Gommenginger et al (2000). The transformation is of the form

sigma_0 (dB) =-C1*I+ 10 log(R^3) + C2

where C2 accounts for the radar characteristics (gain, pattern, beam width, wavelength, etc) and the R^3 accounts for range fall off and the target area. In the following I am using values I determined by visual inspection only (C1=0.2, C2=20 dB)

Once this is done, it is possible to compare the normalized cross sections at several look angles, for example:









where it can be seen for instance that:

• River Rad is more sensitive offshore. This was expected since we reduced the offset of the acquisition in the Marine Radar to avoid saturation of breaking events. We knew that the trade off of that decision would be that we would see less of the waves offshore.
• The pier has a larger effect on the MR data, where is casts a shadow zone from which only strong events are visible.
• Breaking events tend to be brighter in the Marine Radar than in RR. in fact, it seems that the RiverRad is saturating at about -dB (something we noticed in Duck already). However, the difference in values could be attributed to a poor choice of constants C1 and C2. Probably C1 has a larger influence on this.

  All times are epoch times of each sample, relative to a common reference time, so the data is synchronized. Distances are Ground Range relative to the MR.

Another way to compare the time series is to play a movie of the range evolution of the waves, as shown here (movie is 2.6 Mb)




The upper panel is the grayscale intensity from MR, and the lower panel shows the signal from RR (red) and the Marine Rad (cyan and blue). The blue line shows only the points were MR is larger than 10. Notice that there it seems to be a phase drift between the signals, which is simply due to the fact that I am comparing samples that are not exactly synchronous. Doing so would require to interpolate one signal into the other's time domain.

This interpolation was done to compare how good is the fit between the measured (RR) and the dB-converted, time-interpolated MR signal, considering the data collected during a full swath of the River Rad (about 90deg scan). The colorcode represents different RR runs (1818 to 1824). I am working on trying to quantify the agreement, to validate the conversion from Intensity to dB, or in other words, the calibration of the marine radar. This analysis includes some undesired effects such as

• the presence of the pier, that  is large values of MR whereas in RR are low because they were removed as non moving signals. This would explain data concentrated near the upper left corner 
  

• Areas where MR falls too low (near the sensitivity level) whilst RR has relatively large values. (lower right corner)
  

It seems, however, that I am going to take a look at my phase functions for a while.


Aditionally

Back to posting: Radar Overlays

I've been playing with the code I have from Bill, and also with the few data sets we brought back from Duck. I've been able to automate (well, sort of) an algorithm to identify which runs are synchronous. To do that I have converted the GPS times from RiverRad and the Marine radar to epoch times, to make them compatible with the ARGUS. Book keeping should be easier this way. That also enables me to figure out when the radar changed directions. By doing this I was able toidentify the slow scan used to estimate the zero azimuth of RiverRad, by targeting the pier. And obviously I went ahead and tried to find the angle.

So here is an overlay of synchronous data from both sensor, with the pier almost perfectly aligned. I found that a rotation pf 37.5 degrees was the best for RiverRad. I used the GCP coordinates put both radars in FRF space. Data from RiverRad uses horizontal range, our data currently uses only slant range. I think agreement is pretty good, but I am curious about the curvature shown by RiverRad.



Now I am going to try to see if I can overlap timestacks for the same (or at least similar) circular sectors.

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!

FBW 2

Update
I recalculated the results of my previous post, but instead of using a fixed value for the depth (SWL), I used as input for the threshold an instantaneous depth, where the modulation was given by the low frequency signal from the gage record. This signal had a low amplitude (O(5 cm)), and the resuls did not differ that much from the ones posted previoulsy. This can be seen in the first plot of today, where the time evolving signal is shown as a dashed line, and the constant threshold as a dotted line.

New Bussiness

After looking carefully to the events that showed a wave height larger than the threshold at offshore gage in Run 25, I noticed that many of them turned into active breakers within 5 m of the gage. This behavior can be seen in the following figure (Run 26 instead)



Note that there is a good visual correlation between the wave heights exceeding the threshold and waves breaking within 5 m down the tank. The exception are the 3 large waves near t=175 s, which didn't break at all.

That seemed to suggest that the breaking criterion was working well to determine the onset of breaking. Hence, I pursued the idea used by David Huntley, in the sense that if I know the offshore wave condition, the bathymetry and the location of the breaking point, the classical depth limited model should allow us to compute the breaker height. All that is needed then is a suitable formulation of gamma.

Hence, I found the location of the onset of breaking for each of the waves I identified using the FBW code. That gave me a specific point in space and time, which could be correlated with the (fixed) bathymetry at that location, and with gamma (from Nairn, 1990), I could get the wave height.

It turned out that since this gamma value is fixed for a given wave condition,
this procedure yields that the wave height profile is a scaled version of the bathymetric profile, as shown in the following figure:



where a poor agreement is observed. According to Ruessink et al, (2003), this should not be surprising because gamma was found to be a function of kh, rather than h alone.

FBW

Hi,

Let's see if the wording of this post is more uplifting than the previous one.

Rayleigh vs PDFs

First thing is the comparison between the measured wave heights (using a zero upcrossing and a high pass filter with frequecny cutoff 0.02 Hz)
In general, the offshore wave gages show a very good agreement with the theoretical PDF, but as we proegress shoreward the agreement deteriorates. In some cases, it seems that the distribution departs from the Rayleigh significatively (close to the shore). Anyhow, here is the plot (rows are runs (REU irregular) and colums are cross-shore locations):




Breaking wave heights

Next thing is the comparison of the breaker wave height. What I did is to use a zero upcrossing to get all the wave heights in the wave gage record, and then used the results of the FBW algorithm (the one that identified the breaking events) to retrieve the wave heights of those events that were breaking at the wave gage.
Note that this is slightly different than the breaker wave height in the traditional sense, since the latter is related with the maximum unbroken wave height at a given location (or the onset of breaking). Since the algorithm also detects persistent breakers (waves that broke earlier spacewise, but continue to break at this location), these could yield broken wave heights smaller than the threshold. However, the opposite should not be true (in the classical sense), since a wave larger than the threshold must break.

The comparsion is shown in the following figure. The left panel is the video stack overlain with the identified breakers (works as a visual check) and the wave gage time series. The right panels are the time series of individual wave heights (broken and unbroken, blue dots), the broken ones (red circles) and the threshold wave height based on Nairn 1990:

Hb=h(0.39+0.56 tanh (33 So))

where So was determined using the offshore wave gage Hrms, shoaled to deep water and the peak period.
It can be seen that at x=60.04 m, all the wave heights are below the thershold, but we still have broken waves, suggesting that they were old breakers. However, more interesting is the case of x=52.73 m, where there are waves whose height exceeds the threshold, yet they are not breaking. This would suggest an overestimation of the fraction of breaking waves, consistent with our previous results.

Here are the plots




The follwing is zoomed in version, where it can be seen the identification of the broken waves in the time series (purple line over a yellow line). The x-axis of the plots are synchronized, hence the wave heights shown on the right correspond to the wave heights of the waves shown on the left. It can be seen that the algorithm is missing a broken wave, but is adding a false one. I need to fine tune this, but overall is working well.