Number of Waves in a Record (Length over the Zero-Crossing Period)

How many waves went past in a record? Oceanographers count them one way: each time the sea surface rises through its mean level is one wave. If the mean time between those upward crossings is the zero-crossing period $T_z$, a record of length $t$ holds about $N = \frac{t}{T_z}$ of them. This is close to a definition, and the answer is an expected count, which is why it need not come out as a whole number.

The count matters because the largest wave in a record grows with how many waves there are: the tallest of $N$ waves is $H_s$ times the square root of half the natural log of $N$. A buoy reports the period of a half-hour record, and this page turns that period into the number of waves in the half hour.

Use the zero-crossing period, which buoys call the zero-upcrossing or mean period, and not the peak period. The peak period is where the swell sits, and in a mixed sea it is much longer than the zero-crossing period, so using it would count far too few waves. A reading from the Rincon buoy on 23 Oct 2026 had a 12.5 s peak period and a 6.8 s zero-crossing period.

The worked example is half an hour, 1 800 s, at a zero-crossing period of 6 s: 300 waves. A three-hour record, 10 800 s, at 9 s holds 1 200, and SMHI's Brofjorden station, with a mean period of 4.32 s, gives 416.67 in 1 800 s. The basis is Rice's 1944 result for the expected number of zero crossings of a Gaussian signal, from the second and zeroth moments of its spectrum. A simulated Gaussian sea with a period of 7.227 s should cross upward 249.07 times in 1 800 s, and three draws counted 249, 252 and 255.