Ocean waves are random processes, and accurate wave measurements therefore require sampling over a period of time that statistically represents the sea state. The objective is to measure the wave event for a sufficient duration so that the random process can be properly characterized.
Sampling theory suggests, as a rule of thumb, that the measurement duration should be long enough to capture at least 100 wave cycles. When measuring ocean waves, the longest expected wave period must therefore be considered. Capturing 100 cycles of this longest wave defines the minimum required burst duration.
To use the Nortek waves post-processing software, the instrument must be configured in burst mode. The number of samples should typically be set to 1024, 2048, or another value consistent with the chosen sampling rate to ensure that more than 15 minutes of data are collected. If the number of samples is set to a value not supported by the processing sequence, the software will use the next lowest supported value. For example, if the number of samples is set to 2400, only the first 2048 samples will be used to calculate wave parameters.
Sampling Rate
The sampling rate applies to both pressure and velocity measurements and defines the highest frequency that can be resolved. To resolve a signal without ambiguity, the sampling rate must be at least twice the highest frequency of interest. The highest resolvable frequency is equal to half the sampling rate, known as the Nyquist frequency.
The selection of sampling rate therefore requires estimates of the relevant time scales and wave processes of interest.
For example, waves sampled at 1 Hz can resolve frequencies up to 0.5 Hz, while waves sampled at 2 Hz can resolve frequencies up to 1 Hz. It should be noted that other factors, such as deployment depth, may impose stronger limitations on the resolvable wave frequency range.
If the sampling rate is too low relative to the time variation of the wave motion, under-sampling occurs and aliasing results. In such cases, higher-frequency wave energy is incorrectly represented as lower-frequency motion, and the wave field cannot be properly resolved.
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Aliasing In an oceanographic context, aliasing occurs when waves are sampled too coarsely in time or space, causing higher-frequency wave components to be misrepresented as lower-frequency waves. As a result, energy from unresolved waves appears at incorrect frequencies, producing wave components that do not accurately reflect the true sea state. As discussed in the Wave types and characteristics, the sea surface can be described as a superposition of simple sinusoidal functions. In Figure 1, individual sine functions are shown with an arbitrary amplitude of 0.25 (units are not relevant for this illustration) and are vertically offset for clarity so that they can be viewed separately. The yellow points represent the discrete locations where the sea surface elevation is sampled. If the wavelength of a wave component is too short relative to the spacing between measurement points, the sampling scheme cannot resolve it correctly. Instead, the sampled points may align in a way that suggests a longer wavelength (lower frequency) wave. This misrepresentation is aliasing. |
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