EM 1110-2-1100 (Part II)
30 Apr 02
Figure II-1-31. Surface elevation time series of a regular wave and its spectrum
(Briggs et al. 1993)
(g) Before proceeding to the details of how a wave spectrum is derived from a record, it is important
to touch upon some statistical assumptions that are important in analyzing a wave record spectrally. Many
of these assumptions also hold for making a wave-by-wave analysis useful as well. First of all, wave records
are finite in length (typically 17-68 min long) and are made up of samples of surface elevation at a discrete
sampling interval (typically 0.5-2.0 sec). For the wave records to be of general use, the general characteristics
of the record should not be expected to change much if the record was a little shorter or longer, if the
sampling was started some fraction of time earlier or later, or if the records were collected a short distance
away. In addition, it is desirable that there not be any underlying trend in the data.
(h) If the above assumptions are not reasonably valid, it implies that the underlying process is unstable
and may not be characterized by a simple statistical approach. Fortunately, most of the time in ocean and
coastal areas, the underlying processes are not changing too fast and these assumptions reasonably hold. In
principal the statistical goal is to assume that there is some underlying statistical process for which we have
obtained an observation. The observation is processed in such a way that the statistics of the underlying
process are obtained.
Water Wave Mechanics
II-1-79
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