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.
A related notation, Hn, where n is a percentage or a fraction, describes the wave height of the nth percent highest waves. Hn is used to estimate the average maximum wave size (H0.99) and for certain other analysis. To eliminate any confusion with this Hn notation, the notation H1/3 is used by the IMO, the U.S. Code of Federal Regulations, most classification societies, as well as many scientific papers. Hs is a special case of Hn.
Other statistical measures of the wave height are also widely used. The RMS wave height, which is defined as square root of the average of the squares of all wave heights, is approximately equal to Hs divided by 1.4.
For example, according to the Irish Marine Institute:
A New Nonparametric Method to Correct Model Data: Application to Significant Wave Height from the ERA-40 Re-Analysis
Apr 01, 2005; ABSTRACT A new nonparametric method to correct model data is proposed. At any given point in space and time the correction is...