. ao - p h ] 1 8 Ju l 2 00 1 Wave duration / persistence statistics , recording interval , and fractal dimension ∗

The statistics of sea state duration (persistence) have been found to be dependent upon the recording interval ∆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 τ can have a power-law dependence on ∆t as ∆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 would be the “useful mean duration” τ =E[( ∑