Monday, December 17, 2012

Judging swell height while at sea

While I was on a recent paddle down the coast several folks were wondering as to the height of the swell. The prediction for the day was 4-5ft at 10 seconds, or there about. Of course everyone attempts to estimate swell and wind wave size while they're out there. Usually, not always but usually, people are wildly off in their estimates.

When I was doing a BCU 3* assessment a couple years ago we were at the further edge of conditions that we could have been assessed in and the coaches asked everyone how big the waves we had just been in were. 2 to 3 foot was the common response. It was actually like 1 to 1.5 feet. On the trip down the coast some folks were throwing out numbers like 8 feet, as big as a house, and stuff like that. There was talk about the swell being influenced by the bottom and so jacking up a bit.

Anyway, despite the fact that there are approximately 1.83 million web pages that talk about wave dynamics, I figured I'd take a few minutes and come at the subject from the perspective of a sea paddler. Fair warning, there is some math ahead.

There's a book called Waves and Beaches by Willard Bascom. Even though it's quite old (mine is from 1964) there is a huge amount of profoundly useful information in it. One subject it discusses is when a wave is influenced by the bottom. Waves that are influenced by the bottom are called shallow water waves. Shallow water waves are defined those that moving through water that has a depth of:

\begin{equation}.5 L\end{equation}

where L is the wavelength of the wave. The wavelength of the wave can be approximated by

\begin{equation}\frac{g}{2\pi}T^2 = 5.12\times T^2\end{equation}

where T is the period of the wave. Note please this formula is for a perfect sine wave. There are far more accurate formulas that take into account the height of the wave and so forth. But I think for this discussion the approximation is sufficiently accurate.
I didn't actually measure it while I was out there, but the prediction was for a period of 10 seconds. If we plug that in to the equation above we get

\begin{equation}5.12\times10^2=5.12\times100=512\end{equation}

From the definition of a shallow wave water above we get

\begin{equation}.5\times512=256\end{equation}

So if we were in less than 256 feet of water then the wave would be influenced by the bottom and, in fact, we were in far less than 256 feet of water. Absent this fact then we would have a deep water wave which could not have real cause, generally, to deviate far from the predicted values. Which get's us to the real heart of the matter.

We now have to calculate what I'll call the jack up factor. The jack up factor is basically the factor one can apply to the predicted swell height so as to arrive at the swell height at a specific location. There are actually 2 components to the jack up factor. The first is the HS component.

The HS component ranges from 0 to 2 with a nominal value of 1. The value for the HS factor is proportional to the degree of surprise one felt when the swell jacked up. Typically, though not always, the value of HS is directly proportional to the volume of the exclamation "holy shit" that frequently accompanies someone turning around and seeing an unexpectedly large wave behind them. Note that it is not the wording of the exclamation (e.g. "oh boy", "oh no", "lookit that" are all acceptable) but the volume that is significant here. One thing that can influence the value of HS is the audience to which the swell height estimate is being presented. For example an audience of well experienced paddlers that one wishes to impress might cause one to reasonably reduce the value of HS substantially.

The next component of the jack up factor is the BS component. The BS component ranges has a range from 1-5 with a nominal value of 5. The specific value of the BS component is influenced by many things. The naïveté of the audience of the estimate has a large influence on the value as can, for male estimators, the maximum attractiveness of the set of females present in the audience of the estimate. It is also the case that the BS component value is inversely proportional to the estimators self esteem.

Given all of this we can see then that given the prediction of 4-5 feet at 10 seconds in the depth of water we were in fact in (47 feet or so) there is basis for a reasonable estimate of swell height outside of the rather boring prediction of expert agencies and their frequently mis-calibrated buoys. Specifically we can say that the swell ranged from

\begin{equation}[4\times HS\times BS, 5\times HS\times BS]
=
[4\times 0 \times 1, 5\times 2 \times 5]
=
[0, 50]
\end{equation}

That is, the swell was from 0 to 50 feet that day at a specific place along the route taken.

Swell estimation, as I think has been made clear, is not easy. One cannot rely on data from buoys that were located, in many cases, miles away from where one actually experienced the swells to be estimated. Rather it is the application of scientific formulas, as above, that provides the basis for understanding and, far more importantly, the describing of the conditions one paddles in.

I hope this brief treatment of such a complex subject proves useful for both those who estimate swell height and for those who must consider the accuracy of swell height descriptions one may be subject to at the bar following a paddle.

Tuesday, December 11, 2012

Our harsh winter environs

Living in central California has some pretty serious drawbacks. It's incredibly crowded for one. Housing is ridiculously expensive. Road rage is something you at least come to understand if not fight against. One thing that helps make up for some of that is the weather. This past weekend I joined a few fellow club members and braved the elements in an attempt to paddle from Moss Landing down to the beach behind Monterey Bay Kayaks which is aptly located in Monterey.

This paddle is something of a right of passage I guess. The coast along the entire route is pretty much sandy beach backed by dunes so, scenically speaking, it's pretty monotonous. On a direct route it's about a 14 mile paddle, and the point of the thing is to do the thing in a single go. No stopping. Not that you always could. The beach is steep for much of that part of the coast and therefore can be pretty dumpy. So depending on conditions and skills stopping may not be feasible anyway.

I'm not sure it would be possible to even invent better conditions than we had. A hazy day gave us enough sun to keep us smiling and not enough to roast us. Winds were all of 5kts and we had a 5-6 foot WNW swell at about 8 seconds or so. It was...well, it was glorious. One of those I-need-to-do-this-everyday days.

One of the participants arrived about an hour late apparently due to a change of plans and a communication breakdown. As she was getting ready on shore a couple of folks jumped on the water to wait.



You can probably see why they might want to get going as soon as possible, but I decided to wait. We were going to have enough time in the boats today.

Right around the corner from were we put in there's a dock that pretty routinely gets taken over by gobs of California sea lions. If you look closely you can see that there are so many sea lions hauled out on the dock that it's rather sinking.


Some years ago, and I forget when, these guys became a real nuisance in Monterey. Sinking boats, chasing people, stuff like that. Today though it was just a bunch of that noisy sea lion back and forth that sounds something like a holiday dinner when the entire family shows up.

We headed out into Monterey Bay proper and spectacular conditions.



Almost immediately after leaving the entrance to Elkhorn Slough we ran into a bunch of birds clearly excited about something that was almost certainly food. Pictures of a loose group of birds don't really do the groupiness of them justice I think, but there were a whole bunch.


Sadly I'm confident in only identifying a few kind of sea birds, but there were lots of different species represented in this bunch.

After we'd paddled for sometime we ran across another sea bird I can identify, at least in the general sense.


We were a couple of miles or so offshore and, all by himself (or herself, I can't tell) was this guy. I don't know what he was doing although if someone told me he was just enjoying a fine day on the coast I'd totally understand that.

These guys were hanging out just a little further on.


Generally there weren't any other creatures about, at least not that we could see so it was nice to happen upon these guys. It gave the place that sense of life that really makes time on the water quite out of the ordinary, at least for me.

Here's a view of our destination from about the halfway point.


Here's the shore.


And, dead center, here's where we started from.


That's more or less how the rest of the paddle was. Things in front of us got bigger, things behind us got smaller, and things to the left of us went boom with the dumping surf. After about 4 hours and a few minutes some folks get pretty motivated to get off the water. Here's two of our group who rabbited ahead and landed a little while before the rest of us.


And here, finally, is a picture of where we started from a viewed from where we ended at.


Close to the direct center of the far (far, far) shore is were the day started. We ended, as you can see, on a nice beach under a mostly blue sky. We made about 16 miles in 4 hours and 30 minutes. It was a long time to be sitting in the boat and I was, truth be told, pretty happy to get out and stretch my legs.

I don't know if days like this make up entirely for the crowds and cost and noise of California. It helps though. It helps quite a bit.