How are significant wave height, dominant period, and wave steepness calculated?

Significant wave height, Hs, is approximately equal to the average of the highest one-third of the waves. Hs is calculated using:

where m₀ is the variance of the wave displacement time series acquired during the wave acquisition period. However, since wave displacement time series are not returned from NDBC's wave measurement systems, variance is calculated using the nondirectional wave spectrum according to the following relationship:

where the summation of spectral density, S(f), is over all frequency bands, f, of the nondirectional wave spectrum and df is the bandwidth of each band. NDBC wave analysis systems typically sum over the range from 0.03 to 0.40 Hz with frequency bandwidths of 0.01 Hz. Some newer systems sum up to 0.485 Hz with bandwidths that vary from 0.005 Hz at low frequencies to 0.02 Hz at high frequencies.

Dominant, or peak, wave period, Tp, is the period corresponding to the frequency band with the maximum value of spectral density in the nondirectional wave spectrum. It is the reciprocal of the peak frequency, fp:

Dominant period is representative of the higher waves encountered during the wave sampling period. Greater detail on the processing of NDBC wave data can be found in the 1996 technical document, Nondirectional and Directional Wave Data Analysis Procedures (a pdf file).

NDBC also provides estimates of the height and period of wind-seas and swell on each station page. Values for these quantities are calculated by applying the above process to the respective wind-sea and swell portions of the wave spectrum.

The algorithm used to estimate wave steepness is taken from work done by William Buckley, discussed in a paper that appeared in the Journal of Naval Engineers, September, 1988, titled " Extreme and Climatic Wave Spectra for Use in the Structural Design of Ships". The algorithm involves the relationship between significant wave height (Hs) and dominant wave period, or more precisely, its inverse, peak wave frequency (fp).

The algorithm follows:

      val = exp(-3.3 * ln(fp))
      if Hs > (1/250  * val)
         steepness = 'very steep';
      elseif Hs > (1/500  * val)
         steepness = 'steep';
      elseif Hs > (1/1000 * val)
         steepness = 'average';
      else 
         if Hswell >= Hwindwv
            steepness = 'swell';
         else
            steepness = 'average';