Spatial met-ocean data analysis for the North Sea using copulas: application in lumping of offshore wind turbine fatigue load cases

Knowledge about stochastic environmental loads and the response of the substructure are essential in fatigue damage calculations for offshore wind turbines. Site-specific and high-quality met-ocean data that contains joint measurements of wind and waves however, are not always available. An approach based on copulas was used to generate lumped joint met-ocean data in a location where only marginals (i.e., individual, univariate probability distributions) are known. Empirical copulas were calculated for different stations in the North Sea for pairs of wind speed and wave height variables. These copulas are then combined with marginals from another station to generate lumped data. The generated data is compared with the known lumped joint data, and the difference of two methods is measured. The lumped values are used to estimate fatigue damage based on simple formulas. The results show that the joint behaviour of wind speed and wave height follows a similar pattern around the North Sea. In addition, the mean difference of generated lumped wind speeds based on this technique from lumped wind speeds based on real measurements is less than 5%. The mean difference of the fatigue damage caused by the generated lumped wind speeds relative to lumped wind speeds based on real measurements is less than 5% at two locations, and less than 15% in another location. This suggests that the approach is promising for estimating joint met-ocean data at new locations in the North Sea where only marginals are available, which is of major interest for wind farm planning and design