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NOAA Definition of Significant Wave Heights


scamlin

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While digging deeper into the NOAA site, I found a couple of good article defining and explaining "significant wave height". They are a bit technical but not much.

A good reason to read it is that this definition is what NOAA uses when it forecasts wave height.

One thing I finally got clear:

Wave height measured by NOAA really is the distance from the trough to the crest of the wave. Why is the significant wave height different from that? Read the articles.

http://www.vos.noaa.gov/MWL/apr_06/waves.shtml

http://www.vos.noaa.gov/MWL/aug_05/nws.shtml

Scott

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The key for me is that for a given NOAA wave height forecast,

10% of waves will be average 25% higher than forecast

1% will average 67% higher

.03% will be twice as high.

So, for example, if the forecast is 5-8 feet (as it was last Sunday in Casco Bay) with a period of 7 seconds, you can expect:

a 13 foot wave every 700 seconds or about once every 20 minutes

a 16 foot wave (peak to trough) every 21,000 seconds, or about once every 6 hours.

Something to keep in mind when punching through surf or playing in rock garden.

Scott

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>So, for example, if the forecast is 5-8 feet (as it was last

>Sunday in Casco Bay) with a period of 7 seconds, you can

>expect:

>

>a 13 foot wave every 700 seconds or about once every 20

>minutes

I would be interested in whether or not the wave spectrum estimates are appropriate for predicting waves in areas within a mile or two of a coast or whether they are designed for and applicable to the open ocean. Leaving aside the issue that big waves are "dragged down" often before they get into shallower water and/or relatively protected water such as Casco Bay.

Ed Lawson

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I assume this is open ocean but the articles don't say. However, the examples involved mariners reporting wave heights while at sea.

The articles do say that the technical definition of "significant height" corresponds closely to estimates of wave height by experienced observers under real world conditions.

Your question did prompt a thought: if these are, in fact, open ocean forecasts and observations, then the wave height when they hit a reef or beach could be even bigger as they feel the bottom and stand up. Yikes!

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>

>Your question did prompt a thought: if these are, in fact,

>open ocean forecasts and observations, then the wave height

>when they hit a reef or beach could be even bigger as they

>feel the bottom and stand up. Yikes!

As Nick Schaede posted recently, waves lose a great deal before they get to shore so you seldom if ever see waves near a shore as high as that reported off shore before they rise and break. For example, hurricanes can generate waves in the 40 to 60 foot range in the open ocean, but the waves seen hitting beaches in the news reports are never even close to that size even when they break on shore.

Based on limited experience, I worry more about those low swells with long periods. Hard to see until they stare you in the face so to speak.

Ed Lawson

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A few general comments - the spectrum of wave heights will vary a lot, depending on a number of factors.

For example, ocean swells that are fully developed, in the open ocean and away from currents will have a much more regular distribution - you won't get the large outlyers in that example. The waves are all sinusoids and more constant.

On the other hand, currents can focus waves and you can get a much higher chance of a large "freak" wave.

Another exception is when you have multiple sources of waves - e.g. a swell coming in, adding to a wind-driven set of waves. This can also generate a higher chance of larger waves.

Finally - the rule of thumb for when waves start to lose their power as the water shallows up is that if the depth is less than about 1.5 times the wavelength, then you're in the "shallow-water" condition and waves start to peak and lose power.

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Hmmmm. Waves lose a great deal....of what? Height? If so, how? Length/period? How? Energy? How?

In other words, does "feeling the bottom" (even when not rearing up or breaking) begin to sap the energy of a wave, thus reducing the height and/or energy when it finally breaks? Or is hitting other near-shore obstructions such as narrow channels, wraping around points, etc.?

Nick, what did you have in mind?

Scott

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Waves typically consist of little parcels of water going in a circular orbit. When water gets shallow, the orbits become more elliptical. The bottom creates drag and, as it gets shallower, the wave velocity decreases. This makes the waves get steeper. At a certain point, the ellipitical orbits are broken and the waves then break.

When the waves get steeper, they tend to break, and this creates chaotic motion, which dissapates (via friction) the energy of the waves.

There are different shore conditions, and these create different drains on the wave energy, based on the amount of drag from the bottom:

1.) A shallow run-up to the beach creates a slow dissapation of the wave energy over some distance.

2.) A very steep run-up to a shore will create dumping waves, which will loose most of the energy right at the point of breaking (e.g. Butler Hole on Monomoy is a good example of this).

3.) A large cliff (e.g Schoodic Head, up in Mt. Desert) will just reflect the wave energy back out to sea, creating a difficult situation with incoming waves colliding with outgoing waves. (i.e. little or now dissapation of energy)

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>2.) A very steep run-up to a shore will create dumping

>waves, which will loose most of the energy right at the

>point of breaking (e.g. Butler Hole on Monomoy is a good

>example of this).

So is Pebble Beach in Rockport, though on a small scale. I was reminded of that as I walked into the water there before launching and noted about a fairly steep, 12-18 inch drop in the bottom perhaps 10-15 feet from shore near high tide. But outside that the bottom is relatively flat. Then I watched a couple of swells come in, and sure enough... as they hit that drop off, they instantly dumped.

>3.) A large cliff (e.g Schoodic Head, up in Mt. Desert)

>will just reflect the wave energy back out to sea, creating

>a difficult situation with incoming waves colliding with

>outgoing waves. (i.e. little or now dissapation of energy)

What you describe as a difficult situation, some people consider an opportunity for some fun! But that's our anthropomorphic view of nature, eh? ;-)))

--David.

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John:

Good description of the basic varieties of energy disapation of a wave.

What I was asking Nick, perhaps not clearly, was what kind of events he had in mind BEFORE the swell hit inshore areas where the typical paddler would observe or confront the wave. My curiousity was about the relative wave height: if a swell in open ocean hit a inshore reef, shallow beach or cliff (as you describe), would the height be that much more than the NOAA forecast because it was cresting, dumping or reflecting? For example, would an eight foot wave in open ocean become 10 or 12 or more feet in height for a kayaker to deal with?

Nick seemed to suggest that it would not be as terrifying as the statistics would suggest because some or most of the energy would have been bled off (via friction as you explain) by near the shore topography. In other words, features of the shore would decrease the energy (and therefore height) BEFORE it hit the shore or reefs near the shore where the kayaker would have to deal with the waves.

In princple that makes sense, but it seems to me that this would be a caprice of the particular shore: in some areas it would happen; in others where there were no offshore obstructions, you'd get the full impact of an 8' swell, enhanced as the swell stood up on reefs, beaches or cliffs.

Scott

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>Hmmmm. Waves lose a great deal....of what? Height? If so,

>how? Length/period? How? Energy? How?

>

For a pure sinusoidal wave, like what you would get from a distant swell, the energy in the wave is proportional to the square of the wave height. In theory, it's independent of period (or wavelength).

If you get into a wave that has a steeper shape - like for waves that are building up under the influence of wind, but are not fully developed, there is still an approximate proportionality to the square of the wave height (amplitude).

In practice, for developing waves, there is only so much energy that can be stored in a given wavelength. As waves develop under the influence of wind, they'll build up until the the "angle" of the peak of the wave hits about 120 degrees, and then the waves break and become unstable. The energy then goes into progressively longer wavelength waves as the seas build. So, the relationship between stability, height and wavelength sets a constraint. Typically, the wavelength has to be about 7x as long as the height for the wave to be stable (not break and form white-caps). That's why the longest period swells indicate the most violent activity out in the ocean. Old mariners could tell about the approach of distant hurricanes from very long period swells arriving.

>In other words, does "feeling the bottom" (even when not

>rearing up or breaking) begin to sap the energy of a wave,

>thus reducing the height and/or energy when it finally

>breaks? Or is hitting other near-shore obstructions such

>as narrow channels, wraping around points, etc.?

>

By "feeling the bottom" - this is when the frictional drag of the orbits of water sap energy as the water moves along the bottom. This distorts the orbits from circles (like in the open ocean) into ellipses. There's some drag that saps a bit of the energy when the depth is about 1.5 times the wavelength. As it gets shallower, the drag becomes so large that the orbits are broken and the wave breaks, and that can take away most of the wave energy. The condition where the waves have elliptical orbits is not so severe, but there is some loss of energy - remember that the wave velocity decreases when this happens and the waves steepen up, so it's not as easy as saying that the amplitude decreases.

Yeah, reflecting waves, clapotis and all that can be fun. I've seen some real geysers develop under the right conditions.

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My curiousity was about the relative wave height: if

>a swell in open ocean hit a inshore reef, shallow beach or

>cliff (as you describe), would the height be that much more

>than the NOAA forecast because it was cresting, dumping or

>reflecting? For example, would an eight foot wave in open

>ocean become 10 or 12 or more feet in height for a kayaker

>to deal with?

Well, one situation would be where an 8 ft. swell goes from deep water to a shallow patch. If it doesn't break, the wave velocity decreases, and the waves "heap-up". After hearing about the Plum Island incident, I calculated the wave height based on the bathymetric information of that shoal off of Plum Island. A crude estimate is that the waves probably hit 12+ feet as they first hit that shoal. The outgoing current would've further magnified the effect. Currents going against a wave direction can cause the waves to heap up even further.

Once they start to break, that's where the significant energy loss occurs - before they break, there's not so much loss of energy, but some.

>

>Nick seemed to suggest that it would not be as terrifying as

>the statistics would suggest because some or most of the

>energy would have been bled off (via friction as you

>explain) by near the shore topography. In other words,

>features of the shore would decrease the energy (and

>therefore height) BEFORE it hit the shore or reefs near the

>shore where the kayaker would have to deal with the waves.

>

It totally depends on the underwater topography, how developed the waves are, and currents. In some cases, you'll get larger outlyers than that prediction, in some cases, other times, you won't get the large outlyers.

A guy I work with has done extensive work on freak waves and has developed a mathematical framework that describes freak-wave data very well. The normal oceanographic models fail to predict the biggest outlyers - in part because these models neglect the effect of currents. Once he put in the effect of currents, he was able to get a better approximation to the unexpectedly high incidence of freak-waves. Currents tend to focus wave energy.

I keep thinking about the conditions at Plum Island that Sunday. There was a significant swell coming from the east, a wind from the NNE producing wind-driven waves - both coming from deep water and hitting a shoal, and an outgoing current that would magnify the wave heights. All of those would've added up to something a lot more significant than what a distant buoy would indicate. On the other hand, if you'd been at the shore-end of the shoal, a lot of the wave energy would've been bled off by the breaking.

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I have statistical comments on the first of the two articles, as the author seems to misrepresent the significant values.

"height of the highest 10%" (H p0.1) should read "MINIMUM height...".

Similarly "height of the highest 1%" (H p0.01) should read "MINIMUM height" as both stats indicate the LOWEST sizes of these wave height groups.

As well, theoretical max wave height (Hmax) is stated as approx equal to 2 Hs. The Raleigh (one-tailed distribution mentioned in the second article) distribution rightly indicates that Hmax is infinity...I guess a true roguw wave.

Further, if significant wave height (Hs) is computed as 1/0.64=1.56 Hm, H p0.1 as 1.27 Hs, and H p0.01 as 1.67 Hs, then isn't it just easier for us to use a 2/3 Hs value for a safe "average", and maybe a 1.5 Hs value for approx 95% of the waves?

Example would be that if Hs were 8 feet, the average would a bit under 6 feet, with MOST (approx 95%) being under 12 feet. I guess that 2x Hs stat for max wave is a PRACTICAL limit, suggesting a rogue

16 footer.

Having now read the second article, I see that Rayleigh actually predicts even lower values (5/8, 0.625) for Hmean, etc., given its

more skewed nature than gaussian, but the 2/3, 1.5, and 2x factors seem easier and safer for my Level 2.5 abilities!

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For those with (free) online NYTimes subscriptions...

http://tinyurl.com/nybvn

The storm was nothing special. Its waves rocked the Norwegian Dawn just enough so that bartenders on the cruise ship turned to the usual palliative — free drinks.

Then, off the coast of Georgia, early on Saturday, April 16, 2005, a giant, seven-story wave appeared out of nowhere. It crashed into the bow, sent deck chairs flying, smashed windows, raced as high as the 10th deck, flooded 62 cabins, injured 4 passengers and sowed widespread fear and panic.

“The ship was like a cork in a bathtub”

...

http://graphics8.nytimes.com/images/2006/0...1wave.1.395.jpg

...Drawing on recent tallies and making tentative extrapolations, Dr. Rosenthal estimated that at any given moment 10 of the giants are churning through the world’s oceans....

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