“Useful Mean Duration”: An Alternative to the “Mean Duration” Statistic for Wave Height and Other Metocean Parameters

The probability distribution of the duration of events where the wave height or other metocean parameter X(t) is under or over a specified level X = u is of great importance for the planning of offshore engineering operations. The mean duration, estimated by adding up the durations of the events and dividing by the number of such events, is an often-used measure, but it depends on the recording interval (the time interval between successive measurements). We show that the dependence of the estimated mean dura-tion on the recording interval Δt is related to the behavior of the mean absolute discrete derivative E[|X(t + Δt) − X(t)|/Δt] as a function of Δt, and also to the fractal dimension of the level set of points where X(t) crosses X = u. An alternative useful mean duration is proposed, which weights each event by its own duration. Analysis of offshore wave data confirms the stability of this parameter to changes in recording interval.