Offshore Wind Access Windows

What is modelled

The sea state is described by the significant wave height Hs, which in a long record follows a skewed distribution that a Weibull curve fits well. A boat with a limit can go out only in hours when Hs is below it, and a job of several hours needs a whole run of such hours, so the chance of a usable window is lower than the share of calm hours, and it depends on how long sea states last. The record here is a correlated random series whose hourly values keep the Weibull distribution.

Equations

• Weibull distribution function F(h) = 1 − exp[−(h / c)k], median c (ln 2)1/k.
• Hourly series Zt = φ Zt−1 + √(1 − φ2) ε, φ = exp(−1 / persistence), Hs = F−1(Φ(Z)).
• Window chance P(Z1, …, Zn all below z*) with z* = Φ−1(F(limit)).
• Single waves in a sea of height Hs are Rayleigh distributed: P(H > x Hs) = exp(−2 x2).

Checks run in the page

• Simulated operability against the distribution function.
• Simulated window chance against an exact numerical transfer operator.
• Sampled Rayleigh waves against the exceedance formula and the expected largest wave.
• Median and percentile solved numerically against the closed forms.

Honest simplifications

Only the wave height limits the boat: wind, period, direction, visibility and the time to sail out are ignored, there is no seasonal cycle, and a real site has storms that last longer than a simple correlated series suggests.

• Press Better vessel and see how much operability a higher limit buys.
• Press Long repair job and watch the window chance fall.
• Press Fast-changing seas and compare the chance for the same operability.