  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.

Atmospheric and Oceanic Physics;Data Analysis, Statistics and Probability