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This is not correct. H1/3 and Hs are not the same thing. One is a count of waves and the other is a measure of energy. The fact that they provide similar values is due to the choice of factor that we use to multiply the square root of the zeroeth moment of the spectrum. For a half-ampliude squared spectrum - the most commonly used by engineers - multiplying the square root of the zeroeth moment of the spectrum by 4.0 gives a value similar to H1/3.

I'll return to this and propose an edit when I have more time. Subsea (talk) 18:34, 16 December 2007 (UTC)[reply]

How about this - when tidied up Subsea (talk) 17:32, 17 December 2007 (UTC)[reply]

Significant Wave Height, Hs (sometimes found as Hm0)

The significant wave height is fundamental. It may be estimated in several ways, usually depending on the form of recording. It represents the energy of a given sea state and was originally described as the mean height of the highest one third of the waves in a given record, height being expressed as the vertical distance from crest to trough. It is now usually defined from the energy spectrum as,

Hs=

Where, m0 is the zeroeth moment of a ‘half-amplitude’ squared spectrum

This definition leads to an increasingly preferred symbol for significant wave height of Hm0.

It is usually assumed that the sea state is stationary for a given time and over a given sea area and can be approximated by one representative sample in those intervals. These assumptions are of stationarity in space and time. The sampling duration is usually about 20 minutes when buoys or platform mounted radars are used (actually originally based on 2048 points at ½ second intervals so 17 minutes and 4 seconds). Satellites cover tracks about 7 km diameter wide. The 20 minutes interval and the 7 km are about equivalent for moderate sea states - that is, a 8 second wave will cover about 7 km in 20 minutes. Thus, the common sea state used in engineering is a short sample taken at a point in space and is assumed to be the same over a 7 km diameter and for 3 hours.

Hs related to other H parameters

Before ocean instruments were common the estimates of wave height were made by experienced seamen using their eyes and any objects that provided scale such as masts on their ship. This had the problem of subjectivity and the natural tendency of ships to avoid stormy seas. Weather ships were sent out, however, to heave, roll and pitch their way through long shifts at sea in lonely parts of the oceans – this was not good work! Such estimates are usually given as Hvis. Perhaps surprisingly, experienced seamen were (and are) quite consistent in their estimates of wave height. Linked to these amplitude estimates were estimates of the average period of the waves - quite a difficult thing to do and not nearly so consistent as the wave height estimates.

Sea states were (and are) also subdivided into wind seas where the waves are roughly in line with the wind at the time and swell where the waves are out of line with the wind and have propagated from previous storms or seas. Swell is sometimes called residual sea.

When recordings were first taken this was onto charts and simple counts could be made. First the charts were zero-meaned (the average and trend calculated and drawn through the plot to provide a new axis for measuring) and then the number of times the wave record crossed the mean going up (or sometimes down) was counted and this gave the number of waves and, as a time measure, the zero-crossing period (more of that below).

Within each crossing the maximum height was recorded and that was taken as the zero-crossing wave. It was found that if you sorted the waves by size and took the average of the highest third then you got a parameter H1/3 that was reasonably close to Hvis. People seem to perform a sort of average of the higher waves when they estimate seas.

The next step forward was to record the information digitally and to estimate energy characteristics from the information. One of the simplest characteristics of a signal is the variance – a measure of how much the process is dispersed about or spread out from the mean. The variance is obtained by averaging the squared distance of its possible values from the expected value. Whereas the mean is a way to describe the location of a distribution, the variance is a way to capture its scale or degree of being spread out.

With sea waves the energy is a function of the square of the height or amplitude. Thus we deal with squared spectral ordinates and the zeroeth moment of the spectrum gives us the variance.

If we then take the square root of the variance we have a measure that is similar to the standard deviation of a process. Multiplying this by various factors we can obtain various measures of the spectrum. One of these measures is the significant wave height or Hs.

Serendipity?

Hs, H1/3 & Hvis are reasonably similar. It turns out that the significant wave height or Hs is closely related to H1/3 - so much so that you will find each called the significant wave height - wrongly! The relationship is through m0 which is the variance of the surface and which is heavily dominated by the highest records.

This explanation sounds very plausible. Can you back it up with references? Thunderbird2 (talk) 16:01, 19 December 2007 (UTC)[reply]

The American Meteorological Society defines signicant wave height as
  • significant wave height—Defined traditionally as the mean height of the highest third of the waves, but now usually defined as four times the root-mean-square of the surface elevation (or equivalently as four times the square root of the first moment of the wave spectrum).
Thunderbird2 (talk) 18:12, 20 December 2007 (UTC)[reply]

I'm wrong. I thought the American Met Office were maybe guilty of anachronistic use of the term significant wave height because in my experience (I started working with waves in 1972) H1/3 was used first. Then as Hs and the term significant height took over they were merged in people's minds. But when I checked the sequence I found that one of the earliest uses of the term 'significant' was by Sverdrup and Munk in 1947 (US Navy Hydrographic Office Publication 601)and I believe they did define significant as the average of the highest one-third of wave heights. I'll check Sverdrup & Munk's original text. I'll re-write and although lot comes from my own lecture material, I'll reference using other books and re-submit. Subsea (talk) 18:21, 2 January 2008 (UTC)[reply]

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