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.

Lags

Though in the images a good agreement can be observed, once we zoom into the details only a few events can be used for the analysis. In particular, I was able to extract only 14 events lasting about 25 seconds each, which correspond to changes in direction associated with the doughnuts we traced with the gator.

I extracted them, and then fitted a second order polynomial to both the video and radar record. The polynomial parameters were applied to a finer resolution temporal grid, from where I extracted the time of the maxima, and computed the difference.

In general, results are very consistent between the runs, as can be seen here:

Run #     Number of Events            Mean(lag) sec              Std Dev (lag) sec
1100                     5                                           -0.29                                    0.41
1200*                   2                                           -0.46                                    0.23
1230                     4                                           -0.25                                    0.15
1400                     3                                           -0.20                                    0.29
Overall                14                                           -0.28                                   0.28

Although 14 events (that is, about 300 seconds, 5 minutes) is hardly statistically robust, the results are in general pretty consistent, showing a small lag, less than a second.

The asterisk denotes a run where the Radar computer clock was reset using the gps. Sadly, only two events where identified in that run. Hence, at this point, we don't know if drift in the windows clock is going to be significant.

Synch

Hi,

The following plots show the paths of the gator as obtained by particle tracking using the video (blue), radar (red) and the garmin GPS we used on the gator.

Radar is quite noisy because the "beach" was very narrow, so it may happen that sometimes the PT algorithm picked a breaking wave or it got confused with the dune. I used the GPS points as predictor-corrector data, in the sense that if a tracked point position was more than 15 m. away from the closest GPS point, it will reset the position of the track to the GPS position for the next iteration. GPS points are thus not included in either the video or radar tracks.

The following plots correspond to the 5 runs where we have all the data. The left panel is time (seconds since midnight) against FRF x coordinate, and the right panel is time against FRF y.

Gaps in the video record typically correspond to areas where data was missing. Most noticeable is that Camera 0 died, but I am expecting to use the full frame to fill this gap. However, it seems that most of the data in that camera will be straight lines, with little structure to quantify the lag.

Gaps in the radar record are areas where a clear identification of the target was not possible.

It must be noted that the video is subject to misregistration, since the pixels were defined at z=0, but the gator traveled at higher elevations. Since we can not correct for this, more important than the actual positions are the relative motions.

Radar 2211031-Video 1186669740- Aug 09, 2007- 14:30 GMT (1030 EST)



Not too much structure in this one. We basically made alongshore transects, and we turned south of the pier. It didn't help that the radar started 1 minute or so later.

Radar 2211100-Video 1186671480- Aug 09, 2007- 15:00 GMT (1100 EST)



One of the best for our purposes. We did doughnuts near the pier, which can be seen as the periodic signal in bot x and y. The idle times near y=900 are affected by misregistration of the video. The second idle time can be used for synch as well as a "start" signal.

Radar 2211200-Video 1186675140- Aug 09, 2007- 16:00 GMT (1200 EST)



Pretty much useless. I can try to fine tune the radar track, but we made doughnuts near the radar antenna, where the dune grass affected significantly.

Radar 2211230-Video 1186677000- Aug 09, 2007- 16:30 GMT (1230 EST)



Another possibly good one. It has the added benefit that the radar gps was not reset, so it can give us a hint of the drift (if any).

Radar 2211400-Video 1186682340- Aug 09, 2007- 18:00 GMT (1400 EST)



Possibly good. Lots of radar noise, but clear y signal with doughnuts.

Now I am going to try to quantify the lag / drift/