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.
Definitions
Depending on context, wave height may be defined in different ways:
For a
periodic wave, it is simply the difference between the
maximum and
minimum of the surface elevation z = η(x – cpt):[1]
with cp the
phase speed (or propagation speed) of the wave. The sine wave is a specific case of a periodic wave.
In random waves at sea, when the surface elevations are measured with a
wave buoy, the individual wave height Hm of each individual wave—with an
integer label m, running from 1 to N, to denote its position in a sequence of N waves—is the difference in elevation between a wave crest and trough in that wave. For this to be possible, it is necessary to first split the measured
time series of the surface elevation into individual waves. Commonly, an individual wave is denoted as the
time interval between two successive downward-crossings through the
average surface elevation (upward crossings might also be used). Then the individual wave height of each wave is again the difference between maximum and minimum elevation in the time interval of the wave under consideration.[2]
In
physical oceanography, the
significant wave height (SWH, HTSGW[3] 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.[4] 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.