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

The statistics of sea state duration (persistence) are dependent upon the recording interval At, since the graph of a time series of an environmental parameter such as the significant wave height has an irregular, "fractal" geometry. The mean duration T can have a power-law dependence on Deltat as Deltat --> 0, with an exponent equal to the fractal dimension of the level sets of the time series graph. A more practical quantity for operational purposes is the "useful mean duration" (tau) over bar (u) = (Sigma tau(i)(2))/(Sigma tau(i)), where each interval satisfying the appropriate criterion is weighted by its duration tau(i). The above results are illustrated using wave data from the Frigg gas field in the North Sea.