Extreme N-year current profiles for Loop Current and Eddies (LCE) are required for the strength and fatigue assessment of the risers and wellhead/casing systems. The profiles for different return periods (i.e., N = 1, 10, 100, etc.) are derived from an extreme value analysis (EVA) of the available data.
The traditional derivation of N-year profiles is based on the parametric EVA. These methods consist of fitting a parametric joint probability distribution to two or three mode amplitudes from an Empirical Orthogonal Function (EOF) analysis. The parametric method is intended for and most used when statistical extrapolation is required, i.e., the duration of available data is shorter than the desired return period. The parametric methods often require the user to make a few subjective choices relating to the distribution fitting.
In the present paper, a new non-parametric method is introduced to derive N-year current profiles from a multivariate EVA of the three EOF mode amplitudes. The method is completely objective and no subjective decisions are required. The method is applied to 1,000 years of hindcast current data that is simulated from GEM42 model for a site in the Gulf of Mexico. The current data consists of mode shapes and amplitudes of the first three empirical orthogonal functions. Profiles for return period up to 100 years are computed so the statistical extrapolation is not required.
In the non-parametric method, a peaks-over-threshold (POT) technique is first used to extract extremes of a controlling variable such as the surface current velocity or total energy of the current profile. The mode amplitudes at the time steps of those extremes are then extracted; the mode superposition relationship among the mode amplitudes is thus maintained. The set of mode amplitudes for a return period of N years is obtained from the empirical cumulative distribution function of the controlling variable, i.e., only the order statistics are utilized. The uncertainty associated with using only the order statistics is minimized by using the bootstrap technique. It is shown that N-year values thus derived are largely independent of threshold choice, which is also an advantage of this method. N-year current profiles derived from the non-parametric method are found to be similar as those derived from a parametric method; however, non-parametric estimates have the advantage of being objective.
Agarwal, P., Forristall, G., “Non-Parametric Method for Estimating Extreme N-Year Profiles for Loop Current and Eddies,” Proceedings of the Offshore Technology Conference 2017 (OTC- 27520-MS), Houston, TX, May 1– 4, 2017.