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.