Environmental contour: Useful definitions

A contour implements a method to define multivariate extremes based on a joint probabilistic model of variables like significant wave height, wind speed or spectral peak period. Contour curves or surfaces for more than two environmental parameters give combination of environmental parameters which approximately describe the various actions corresponding to the given exceedance probability 1.

Exceedance probability

Probability that an environmental contour is exceeded (exceedance probability). The exceedance probability \(\alpha\) corresponds to a certain recurrence or return period, Tr, which describes the average time period between two consecutive environmental states that exceed the contour. In the following formula, the return period Tr is given in years, while Ts, the state duration of independent events is given in hours.

\(\alpha= \frac{T_s}{T_r * 365.25 * 24}\)

Note that exceedance can be defined in various ways for environmental contours (Mackay and Haselsteiner, 2021) 2 .

State duration Ts

Time period for which an environmental state is measured, usually expressed in hours.

Return period Tr

Describes the average time period between two consecutive environmental states that exceed a contour. In the univariate case the contour is a threshold.

Different types of environmental contours

The figure below visualizes different types of environmental contours 2.

1

NORSOK standard N-003, Edition 2, September 2007, Actions and action effects.

2(1,2)

Mackay, E., & Haselsteiner, A. F. (2021): Marginal and total exceedance probabilities of environmental contours. Marine Structures, 75. https://doi.org/10.1016/j.marstruc.2020.102863