dorsal/arxiv
View SchemaWave duration/persistence statistics, recording interval, and fractal dimension
| Authors | Alastair D. Jenkins |
|---|---|
| Categories | |
| ArXiv ID | physics/0107045 |
| URL | https://arxiv.org/abs/physics/0107045 |
| Journal | International Journal of Offshore and Polar Engineering Vol. 12, No. 2, pp. 109-113, June 2002 (ISSN 1053-5381) |
Abstract
The statistics of sea state duration (persistence) have been found to be dependent upon the recording interval \Delta t. 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, \bar\tau, can have a power-law dependence on \Delta t as \Delta t -> 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", \bar\tau^u, estimated from the formula (\sum\tau_i^2)/(\sum\tau_i), where each interval [t_i,t_i+\tau_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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"abstract": "The statistics of sea state duration (persistence) have been found to be\ndependent upon the recording interval \\Delta t. Such behavior can be explained\nas a consequence of the fact that the graph of a time series of an\nenvironmental parameter such as the significant wave height has an irregular,\n\"fractal\" geometry. The mean duration, \\bar\\tau, can have a power-law\ndependence on \\Delta t as \\Delta t -\u003e 0, with an exponent equal to the fractal\ndimension of the level sets of the time series graph. This recording interval\ndependence means that the mean duration is not a well defined quantity to use\nfor marine operational purposes. A more practical quantity may be the \"useful\nmean duration\", \\bar\\tau^u, estimated from the formula\n(\\sum\\tau_i^2)/(\\sum\\tau_i), where each interval [t_i,t_i+\\tau_i] satisfying\nthe appropriate criterion is weighted by its duration. These results are\nillustrated using wave data from the Frigg gas field in the North Sea.",
"arxiv_id": "physics/0107045",
"authors": [
"Alastair D. Jenkins"
],
"categories": [
"physics.ao-ph",
"physics.data-an"
],
"journal_ref": "International Journal of Offshore and Polar Engineering Vol. 12,\n No. 2, pp. 109-113, June 2002 (ISSN 1053-5381)",
"title": "Wave duration/persistence statistics, recording interval, and fractal dimension",
"url": "https://arxiv.org/abs/physics/0107045"
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