Wave height

Depending on context, wave height may be defined in different ways:

• For a sine wave, the wave height H is twice the amplitude (i.e., the peak-to-peak amplitude):[1]
  $${\displaystyle H=2a.}$$

  
• For a periodic wave, it is simply the difference between the maximum and minimum of the surface elevation z = η(x – c_p t):[1]
  $${\displaystyle H=\max \left\{\eta (x\,-\,c_{p}\,t)\right\}-\min \left\{\eta (x-c_{p}\,t)\right\},}$$

  
  with c_p 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 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 (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]

RMS wave height

Another wave-height statistic in common usage is the root-mean-square (or RMS) wave height H_rms, defined as:[2]

$${\displaystyle H_{\text{rms}}={\sqrt {{\frac {1}{N}}\sum _{m=1}^{N}H_{m}^{2}}},}$$

with H_m again denoting the individual wave heights in a certain time series.

• Sea state
• Wind wave