Sampling‐Rate Errors in Statistics of Wave Heights and Periods

The usual analysis of zero up‐crossing properties in a wave record requires digitization of the record at a finite sampling rate. This process and the resulting errors are examined utilizing simple models, theoretical arguments, and simulations derived from frequency spectra of variable bandwidth. It appears that large wave heights can be determined within an error of −0.5% relative to their actual values if $\Delta /\overline{T}<1/20$, where $\Delta$ represents the sampling time interval, and $\overline{T}$ the spectral mean period. When $\Delta /\overline{T}\ge 1/20$, the observed heights can be corrected for the sampling‐rate errors by way of a simple multiplicative factor dependent on $\Delta /\overline{T}$. Wave‐period statistics are relatively more sensitive to finite sampling rates due to attendant aliasing. Thus, to obtain nearly error‐free results, it is generally necessary to sample a wave record at a rate much larger than twice the Nyquist frequency. Various consequences of not complying with this criterion are explored to some extent. In specific, simulations suggest that for wave records characterized by spectra that decay as ${\omega }^{-5}\left({\omega }^{-4}\right)$ toward high frequencies, some key statistics such the mean period and variance can be determined with errors of less than ±1% if $\Delta /\overline{T}<1/30(<1/50)$.