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Wave duration/persistence statistics, recording interval, and fractal dimension

Alastair D. Jenkins
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Abstract

The statistics of sea state duration (persistence) have been found to be dependent upon the recording interval Δt. Such behavior can be explained as a consequence of the fact that the graph of a time series of an environmental parameter such as the significant wave height has an irregular, "fractal" geometry. The mean duration, \barτ, can have a power-law dependence on Δt as Δt -> 0, with an exponent equal to the fractal dimension of the level sets of the time series graph. This recording interval dependence means that the mean duration is not a well defined quantity to use for marine operational purposes. A more practical quantity may be the "useful mean duration", \barτ^u, estimated from the formula (\sumτ_i^2)/(\sumτ_i), where each interval [t_i,t_i+τ_i] satisfying the appropriate criterion is weighted by its duration. These results are illustrated using wave data from the Frigg gas field in the North Sea.

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Alastair D. Jenkins. 2003-07-04. Wave duration/persistence statistics, recording interval, and fractal dimension. https://arxiv.org/abs/physics/0107045

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