In physical oceanography, the significant wave height (SWH, HTSGW or Hs)
is defined traditionally as the mean wave height (trough to crest) of the highest third of the waves (H1/3). It is usually defined as four times the standard deviation of the surface elevation – or equivalently as four times the square root of the zeroth-order moment (area) of the wave spectrum. The symbol Hm0 is usually used for that latter definition. The significant wave height (Hs) may thus refer to Hm0 or H1/3; the difference in magnitude between the two definitions is only a few percent.
SWH is used to characterize sea state, including winds and swell.
The original definition resulted from work by the oceanographer Walter Munk during World War II. The significant wave height was intended to mathematically express the height estimated by a "trained observer". It is commonly used as a measure of the height of ocean waves.
Significant wave height H1/3, or Hs or Hsig, as determined in the time domain, directly from the time series of the surface elevation, is defined as the average height of that one-third of the N measured waves having the greatest heights: where Hm represents the individual wave heights, sorted into descending order of height as m increases from 1 to N. Only the highest one-third is used, since this corresponds best with visual observations of experienced mariners, whose vision apparently focuses on the higher waves.
Significant wave height Hm0, defined in the frequency domain, is used both for measured and forecasted wave variance spectra. Most easily, it is defined in terms of the variance m0 or standard deviation ση of the surface elevation: where m0, the zeroth-moment of the variance spectrum, is obtained by integration of the variance spectrum. In case of a measurement, the standard deviation ση is the easiest and most accurate statistic to be used.
Another wave-height statistic in common usage is the root-mean-square (or RMS) wave height Hrms, defined as: with Hm again denoting the individual wave heights in a certain time series.
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In fluid dynamics, the wave height of a surface wave is the difference between the elevations of a crest and a neighboring trough. Wave height is a term used by mariners, as well as in coastal, ocean and naval engineering. At sea, the term significant wave height is used as a means to introduce a well-defined and standardized statistic to denote the characteristic height of the random waves in a sea state, including wind sea and swell. It is defined in such a way that it more or less corresponds to what a mariner observes when estimating visually the average wave height.
vignette|Mer calme à mer ridée (Øresund) : pas ou peu d'ondulation, phénomène de miroir (on parle aussi de mer d'huile) vignette|Mer belle (Sables d'Olonne) : ondulation sans moutonnements vignette|Mer peu agitée à mer agitée (Collioure), des moutonnements se forment, leur nombre augmente avec l'intensité du vent. vignette|Mer grosse et mer forte (port de Penhors) suivant l'intensité des vagues (hauteur) : mer blanchie par l'écume. L'état de la mer est la description de la surface de la mer soumise à l'influence du vent (qui génère le système de vagues) et de la houle.
Une vague () est une déformation de la surface d'une masse d'eau le plus souvent sous l'effet du vent. À l'interface des deux fluides principaux de la Terre, le vent crée des vagues sur les océans, mers et lacs. Ces mouvements irréguliers se dispersent à la surface de l'eau et sont collectivement appelés état de la mer. D'autres phénomènes, moins fréquents, sont aussi la source de vagues. Ainsi, les séismes majeurs, éruptions volcaniques ou chutes de météorites créent également des vagues appelées tsunamis ou raz-de-marée.
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