Model-Data

OK, so I realized a few things while continuing to work with the data.

1. Many of the sensors were buried and I wasn't excluding them all at first or taking the exponential decay in the seabed into account. So now I am using ALL instruments and I am accounting for the exponential pressure decay in the seabed.

2. While we give SWAN a frequency range of 0.05 - 0.25 in the input spectra and input file, it uses a high frequency "tail" tacked onto the spectra and uses the entire spectrum for calculating integral wave parameters (i.e. Hs). So it is OK to compute wave height from the pressure sensors using 0.05 < style="font-weight: bold;">Leadbetter Beach:
Using Thornton & Guza 1986, I computed the cross-shore wave height profile with gamma 0.42 and offshore conditions that correspond to Feb. 4th. I also ran SWAN with gamma = 0.6 (because of Hs instead of Hrms). Heres the results:

While the profiles aren't the same, the breaking locations are certainly similar.

Model-Data Comparison - Comparing gamma
I ran October 10th, 17th, and 31st with two different values of gamma (default (0.73) and 0.60 (0.42 for Hrms)). I tried to categorize the results to see if we do better based on:

1. deep or swallow water
2. large or small Ho
3. near canyon or north of the canyon
4. offshore incident angle





NOTE: For October 31, if I use only instruments in h < 2m the r-squared values increases to 0.956 (not as much of an improvement for the other days)!!! You can see why if you look at the transects for that day:





I won't post all of the days on here but the scatter plots do show an improvement in model accuracy with a decrease in gamma.

Thoughts:
For three full days with such varying conditions, I think these look relatively good. One thing I've considered is using the 'universal curve' proposed by Apotsos 2007 which gives gamma as a function of the offshore wave height. This would hopefully improve the predictions on 10/17 (low wave day) because currently model breaks too far onshore compared to the data. It wouldn't affect runtime of the simulations we would just write a new input file for each run based on Ho. All depends on if we want to try and show the skill associated with an uncalibrated (I use that term loosely) model versus having better comparisons.

Interpolation

I interpolated the nearshore bathymetry at the Northern end of the NCEX domain for each of the October bathy files. The downfall of this means that I can not use the stationary runs that we performed earlier (which would have sped things up because I would have only had to run the mid-hour simulations) but its better than getting everything run and wishing sometime down that road that I had model information at that northern instrument array.

I'm running SWAN and circulation model for on full day to make sure thing run ok and that tides are correct, etc. Then I can feel comfortable starting the month long run.

Bathymetry Issues

I wanted to make sure the circulation domain would cover the region encompassing all of the instruments (especially the large cross-shore array at the northern end of the site). Circulation model doesn't like part of the domain that is conveniently located around that array though. Maybe the surveys were tough in that area because of all the instruments? Or bad merging of data, who knows. I'd have to go through and smooth that part of the bathy in all the surveys if we want that region. The problem is highlighted in the figs below. I need a little space from the wall of the circ domain to that array which I can't get with that weird feature.

Life's about compromises...

Well I still wanted a smaller domain from the perspective of runtime but there was too much percent error in forcing for cases with southern swell (whether is was the dominant peak or not). So I chose to chop the domain at the Northern end only, leaving the southern end (Point La Jolla) in tact. The runtime is still good (35; 44 minutes corresponding to 3 or 4 iterations respectively) compared to the full domain (50; 67 minutes).

Here's the plots, note the change in the color axis for the percent difference (max is 5% instead of 20%).


October 10, 2003 1900 GMT
Hs = 1.5m, NW swell at 12 degrees, T = 10 sec



October 17, 2003 1800 GMT
Hs = 0.75m, SW swell at 70 degrees, T = 15 sec



October 31, 2003 1500 GMT
Hs = 1.3m, NW swell at 23 degrees, T = 6 sec

Stationary vs. Non-stationary

Trying to confirm the correct mode for which I should be running SWAN for the NCEX cases. While the non-stationary method is good when considering changes in wave/wind climate it all depends on the size of the domain you are considering and how often you have forcing updates.

Analytically, the only difference is that for the non-stationary cases the time variations in action balance (dN/dt) are computed while the stationary case the action balance equation is the same except it does not include that term. Thus integration occurs in x,y,f,theta (4 dimensions instead of 5).


I've found papers (Booij et al. 1999, Zijlema & van der Westhuysen 2005, Rodgers et al. 2007) that look at stationarity. The first two indicate that for small scale (coastal scale rather than ocean basin scale), stationary (hence assuming that changes in wave conditions occur instantaneously) is accurate. Rodgers et al show significant RMS errors can occur when using stationary simulations for regional scales, mainly because it predicts that waves arrive at a certain location faster than if non-stationary conditions are assumed.

In our case, we have a small scale (~ 11km x 11km) and we do not consider wind forcing, only boundary forcing. Our forcing changes every half hour and this is longer than the residence time of waves in our domain (i.e. using shallow water wave speed (sqrt(gh)) for a 10 sec wave in 10-m water depth, the waves take 26 min to propagate through the domain - conservative since the waves will be traveling much faster than this up until the 10m contour).

Forcing Differences b/w Model Domains

Ok I've been putting off uploading these as I searched for mistakes I make while computing the percent difference. Unfortunately I didn't find any mistakes. From the looks of the differences I'm no longer sure the smaller domain is sufficient.


Hs = 1.5m, NW swell at 12 degrees, T = 10 sec






Hs = 0.75m, SW swell at 70 degrees, T = 15 sec




Hs = 1.3m, NW swell at 23 degrees, T = 6 sec

Wave height differences in circulation domain

Some updated plots that focus on the circulation domain. Max wave height differences in the circulation domain (not including one or two errant shoreline differences) are listed in the title of the difference plot for each day.

Ranges from 2-6cm based on the wave conditions but in all cases the spatial patterns remain the same. In my opinion its good enough to say that the smaller domain can be used for the simulations.


Hs = 1.5m, NW swell at 12 degrees, T = 10 sec















Hs = 0.75m, SW swell at 70 degrees, T = 15 sec















Hs = 1.3m, NW swell at 23 degrees, T = 6 sec

Speeding up the process

In anticipation of needing to re-run the SWAN cases for October 2003 I'm trying to figure out the best way to speed up the processing time. The easiest solution is to reduce our domain size, but what does that do to the wave field in the nearshore, around where the circulation model will be run. Here's 3 cases:

October 10, 2003 1900 GMT
Hs = 1.5m, NW swell at 12 degrees, T = 10 sec


October 17, 2003 1800 GMT
Hs = 0.75m, SW swell at 70 degrees, T = 15 sec


October 31, 2003 1500 GMT
Hs = 1.3m, NW swell at 23 degrees, T = 6 sec


Certainly waves from the SW are most affected by the southern portion of the domain that I eliminated. It's also likely that it is affected because those waves are rather long (15sec). Looking at the transects though I'm not sure it is something that make a large enough difference to worry about. The wave height patterns are in fact the same, just slightly (<10cm) different magnitudes.

BEST of all, these simulations finish is 29-37 minutes depending on the number of iterations required instead of 50-67 minutes for the runs using the larger domain.

Tides matter ...

I thought the data files were instantaneous water & sensor depth (h & z) but they are relative to MSL so I needed to account for the tide. Comparison is certainly a bit better during the storm conditions but still not perfect.


As for the transect, its much better than it was. BUT there are hours that are better and hours that are worse. More intriguing is that if I use the SWAN prediction for 1900 GMT, its worse, but if I used the prediction from 1930 GMT, it is rather good (shown above). It's not a huge surprise because if you look at the time series plot on the left you see that the model compares better to the blue curve at 1930, (where there is no blue circle) than at 1900. So if the data average is over the 51.2 minute record its hard to determine which to use. Maybe I should average the two model predictions like I average the data. Thinking out loud ...

Ok, heres that plot, it's worse than above but better than the comparison using 1900 (probably a no-brainer since the "averaging" a good and a bad will give a mediocre...).

Why the wave height decay...

Still looking into the model-data differences in wave height. This plot shows the offshore wave height from the measured spectrum (green), the measured wave height at 15m water depth from the pressure sensor (computed by averaging over the first 30 minutes of the data record) (blue) and the modeled wave height at the instrument location (red). The pressure sensor has 1hr time increment and the offshore and modeled wave height have a 30 min time increment.

I was curious to see if there was any time shift in when the wave energy increased offshore and when it was measured in the surf zone but that doesn't seem to be the case. I also wanted to see if the three curves gave the same "shape" or general trend in wave energy, and they do. Both the model and data show a decrease in the wave height from that measured offshore that really can't be depth-induced breaking dissipation since it is in 15m water depth. Comparisons between hour 4 and hour 11 look pretty good.