Quantitative comparison of environmental contour approaches

Environmental contours are a pragmatic and widespread method to estimate the long-term extreme response of marine structures. Over the years, a range of approaches have been proposed. A benchmarking study was recently conducted to compare the various methods using a common set of data. The current work extends this benchmark study by providing a quantitative assessment of the contours submitted to the exercise. The estimates of long-term responses from the contours were compared against a response-based analysis (RBA) for a wide range of responses. While some contour methods agreed well with estimates from the RBA (relative errors less than 10%), most methods were found to give large errors relative to the RBA. For the 1-year responses most methods showed a large positive bias, whilst both positive and negative biases were found for the 20-year responses. The reasons for the differences between the contours and RBA were explored. It was shown that the fitted statistical models accounted for a large portion of the error in some approaches, with both positive and negative biases of the order of 50% for some contributions, depending on the response type. Whilst for other methods, the statistical model gave accurate predictions for most responses, no models were able to capture all response behaviours for all locations. Secondly, most contour methods do not account for serial correlation in the data. It is shown that this introduces a significant positive bias into long-term response estimates, especially for lower return periods. The level of error introduced by the type of contour method is dependent on the assumption made about the shape of the failure region in the contour definition. For the predominantly unimodal response types considered, contours which approximate the failure region as having a linear boundary (IFORM and direct sampling contours), introduce relatively little error for most responses. However, for some responses, the direct sampling contours were found to introduce errors in the range 20%–40%, depending on the variable space in which they are constructed. The ISORM and highest density contours were found to have a significant over-conservatism bias, which would be expected for the response types considered.