Significant Wave Height Calculator

Significant wave height, written Hs or H one-third, is the mean height of the highest one third of waves in a record, defined that way because it matches what a trained observer reports by eye. For a narrow-banded random sea the wave heights follow a Rayleigh distribution, from which Hs equals about four times the standard deviation of the surface elevation, the highest one in ten waves reaches roughly 1.27 Hs, and the largest wave in a 1000-wave record averages about 1.86 Hs. Wind-driven growth depends on three inputs: wind speed U, fetch F, and duration. The SMB formula Hs = 0.283 (U squared / g) tanh[0.0125 (gF / U squared) to the 0.42] captures fetch-limited growth, and the hyperbolic tangent saturates at the fully developed limit where the sea can absorb no more energy from that wind. Because both fetch-limited and duration-limited growth are possible, the smaller of the two predictions governs. Hs varies with roughly the square of wind speed, so doubling wind speed near-quadruples wave height. Douglas sea state 4 corresponds to Hs of 1.25 to 2.5 m, state 6 to 4 to 6 m, and state 9 exceeds 14 m; the largest reliably measured Hs, 19.0 m, was recorded by a buoy in the North Atlantic in February 2013. The SMB method assumes deep water, steady uniform wind, and no swell from other sources, and it degrades where depth is under about half the wavelength, since breaking limits Hs to roughly 0.5 to 0.6 times water depth.

The concept and the notation come from Harald Sverdrup and Walter Munk at Scripps Institution of Oceanography, who developed wave forecasting under wartime urgency. Amphibious landings in North Africa in 1942 and the planning for Normandy required surf predictions, and their classified 1943 report, published openly in 1947 as Wind, Sea and Swell: Theory of Relations for Forecasting, introduced significant wave height along with the first systematic wind-fetch-duration forecasting curves. Their method was extended by Charles Bretschneider through the 1950s using additional field data, producing the combined SMB curves still named for all three. The statistical foundation followed. Michael Longuet-Higgins established in 1952 that the heights of a narrow-band random sea are Rayleigh distributed, which converted Hs from an observational convention into a well-defined statistical parameter and supplied the factor of four relating it to surface variance. Willard Pierson and Lionel Moskowitz published their fully developed spectrum in 1964, and the JONSWAP experiment in the North Sea from 1968 to 1969, led by Klaus Hasselmann, produced the fetch-limited spectral form that underlies modern models. Empirical curves were progressively replaced by spectral wave models solving the energy balance equation, with the third-generation WAM model appearing in the late 1980s and WAVEWATCH III, developed at NOAA by Hendrik Tolman, now running operational global forecasts. Satellite altimeters have measured Hs directly since Seasat in 1978.