Given a time-series record of ocean surface elevation, spectral analysis is often used to determine characteristic statistics of the record, such as wave height and mean period. A simple linear analysis shows that the phases of the Fourier components in a time-series have some effect on the value of the resulting characteristic statistics; two records with identical wave components, but different phases, will yield two different sets of bulk statistics (\(H_{m0}\), \(T_p\), etc.). In the linear sense, this variance from different phase realizations is due to “spectral leakage”, or the existence of Fourier components with non-integer number of periods in the record. It is also expected that variance due to nonlinearity should exist in nearshore wave records, as different phase realizations may lead to different low-frequency motions, which may be poorly resolved in a typical time-series record. This phase-driven variance is a type of aleatory uncertainty, and must be quantified statistically. Here, in the context of a high energy wave event in Duck, North Carolina, USA, the behavior of phase uncertainty is examined through numerical simulation. The analysis indicates that nonlinearity does play a role in uncertainty. The primary outcome of this study are empirical relations for the expected value of phase-driven variance, which can be used to understand the baseline precision of spectral statistics derived from time-series records.
