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 may be the “useful mean duration”, τ, estimated from the formula ( ∑ τ i )/( ∑ τi), where each interval [ti, ti + τi] 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.