This is the third post in a series about reading surf forecasts. Here are the first and second articles.
Swell Height[1] is a deceptively difficult thing to measure. The first thing to realize is that this isn’t an objective number — it doesn’t correspond one-to-one with any specific thing in reality. Instead, it’s a number that should be close to the height of an average wave in some swell. I know how squishy and odd that sounds but stick with me because the metric is worth it in the end.
So how to get it? You might think, “I’ll get a boat, drive out a ways, drop anchor, sit there for a bit and keep track of the highest and lowest points the ocean surface touched on the anchor line.”
Nope. That’ll get you the crest of the tallest wave minus the trough of the lowest wave. Odds are good that there was no single wave that was close to as tall as this measurement. Not quite what we want for swell height.
“Well ok. I’ll sit out there for an hour and write down the heights of all the crests and troughs of all the waves that pass. I’ll then calculate each individual wave height and take the average.”
Closer —you’ve now got a good set of crest-and-trough data through time. The problem here is that you’ll have recorded quite a few very small waves. Including these in the average will result in a very small swell height — one that doesn’t capture the intention of the metric.
“Alrighty, I’ll throw out the smallest two-thirds of the waves and then take the average of the rest.”[2]
That’s an odd suggestion but yes — it turns out this tends to give us a number that corresponds well to the close-to-the-height-of-an-average-wave-in-some-swell idea we set out to capture. Unfortunately there’s one more nasty wiggle that you’ve forgotten about — there will most likely be multiple swells in the water.
“Uhhhh. How can I tell which swell the wave I’m measuring is part of? They are all jumbled together.”
They sure are. How should we unmelt this gnarly bar of wax that dripped into our car vents and cup holders?
Math is how. We use the Fourier Transform[3]. We could spend all day on this puppy but we’re going to say only that it allows us to convert our crest-and-trough data into this[4] —
Here’s a plot of a single row of the above data—
This plot shows the period (on top) vs. the energy density. You can see that in this case we have a high energy spike at a 15 second period and a bunch of energy in the (less interesting for surfers) 8–2 second band.
In addition to period vs. energy we can use the above plot to get height — we would integrate under the whole curve to get the height for all swells combined or under a part of the line to get the height for a specific period swell[5].
Note that picking a part of the plot that represents “the 15 second period swell” is not well defined — it could be a very narrow band just around 15 seconds, but it also could include the somewhat gentle slopes that go from 18 seconds to 12 seconds. How this is chosen varies among surf forecasts[6].
Fun Sidenote: We can also use the fourier transform to get period vs. swell direction which allows us to generate really cool plots like this —
Finding swell height can be an arduous process and the end result is a pretty squishy metric. Consider that swell height is almost meaningless by itself in the sense that no one really cares what the average height of the tallest 1/3 of waves in a given area are — what we really care about is how tall are the waves compared to yesterday/last week/this morning and what is the range of swell heights that make the best waves at our favorite breaks.
This last point is one I will continue to stress throughout this series of articles — if you want to put yourself in the best position to catch good waves then you must keep track of which conditions work best for each of your local breaks. Too many surfers see 5–6 feet on the forecast and run to the closest beach all hot in the biscuit. This is a mistake — be more thorough in your study of conditions and you’ll score better surf.
In our next post, we’ll talk about how to best use buoy readings to make better decisions about where and when to surf.
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[1] You might also see the term significant wave height (SWH) in forecasts — SWH usually encompasses all swells passing through some area of the ocean whereas I’m taking swell height to mean the SWH of a single swell passing through some area.
[2] This is almost exactly what the NOAA buoys do. The only difference is that they use accelerometers to measure the heights of the individual waves instead of an anchor line. You might remember from Calc I that if you have an initial position and an initial velocity then you can use acceleration measurements over time to get back to position over time.
[3] The Fourier Transform does a ton of heavy lifting in physics and engineering. The reason it is so useful is that 1). waves are everywhere in nature (ocean, sound, light, radio, bluetooth, wifi, and on and on (those last few are all just different frequencies of electromagnetic waves)) and 2). it allows us gain information about the individual waves that make up a jumbled-up mess of waves. Here’s a really good explanation of how it works.
[4] This is the raw spectral data from the LJPC1 NOAA buoy on 10:41 8/20/2019 UTC. To see the current data go here.
[5] Note that this isn’t the same as counting all the waves and taking the average of the top 1/3. In practice though (and only in deep water) it ends up being just about the same with the added benefit of being able to separate out the heights for swells with different periods.
[6] NOAA does a very simple split of the frequency range into two halves — one is the “swell waves” section and the other is the “wind waves” section. You can see the frequency at which they separate in each row of the spectral data. It’s under the header “Sep_Freq”. See the “Spectral Wave Data” section here.