Alternative approaches to develop environmental contours from metocean data

It is necessary to evaluate site-specific extreme environmental conditions in the design of wave energy converters (WECs) as well as other offshore structures. As WECs are generally resonance-driven devices, critical metocean parameters associated with a target return period of interest (e.g., 50 years) must generally be established using combinations, say, of significant wave height and spectral peak period, as opposed to identifying single-valued wave height levels alone. We present several methods for developing so-called “environmental contours” for any target return period. The environmental contour (EC) method has been widely acknowledged as an efficient way to derive design loads for offshore oil and gas platforms and for land-based as well as offshore wind turbines. The use of this method for WECs is also being considered. A challenge associated with its use relates to the need to accurately characterize the uncertainties in metocean variables that define the “environment”. The joint occurrence frequency of values of two or more random variables needs to be defined formally. There are many ways this can be done—the most thorough and complete of these is to define a multivariate joint probability distribution of the random variables. However, challenges arise when data from the site where the WEC device is to be deployed are limited, making it difficult to estimate the joint probability distribution. A more easily estimated set of inputs consists of marginal distribution functions for each random variable and pairwise correlation coefficients. Pearson correlation coefficients convey information that rely on up to the second moment of each variable and on the expected value of the product of the paired variables. Kendall’s rank correlation coefficients, on the other hand, convey information on similarity in the “rank” of two variables and are useful especially in dealing with extreme values. The EC method is easily used with Rosenblatt transformations when joint distributions are available. In cases where Pearson’s correlation coefficients have been estimated along with marginal distributions, a Nataf transformation can be used, and if Kendall’s rank coefficients have been estimated and are available, a copula-based transformation can be used. We demonstrate the derivation of 50-year sea state parameters using the EC method with all three approaches where we consider data from the National Data Buoy Center Station 46022 (which can be considered the site for potential WEC deployment). A comparison of the derived environmental contours using the three approaches is presented. The focus of this study is on investigating differences between the derived environmental contours and, thus, on associated sea states arising from the different dependence structure assumptions for the metocean random variables. Both parametric and non-parametric approaches are used to define the probability distributions.