Wave height

Several definitions for different situations

• For a sine wave, the wave height H is twice the amplitude:
• For a periodic wave, it is simply the difference between the maximum and minimum of the surface elevation z = η:
• In random waves at sea, when the surface elevations are measured with a wave buoy, the individual wave height H_m 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. 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.
• Significant wave height H_1/3, or H_s or H_sig, as determined 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:
• Significant wave height H_m0, 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 σ_η of the surface elevation:
• Another wave-height statistic in common usage is the root-mean-square wave height H_rms, defined as: