Environmental contours for circular‐linear variables based on the direct sampling method

Environmental contours are often used in the design of engineering structures to identify extreme environmental conditions that may give rise to extreme loads and responses. The perhaps most common application of environmental contours is for wave climate variables such as significant wave height and wave period. However, for the design of wind energy installations, the joint distribution of wind speed and wind direction may be equally important. In this case, joint modelling of linear (wind speed) and circular (wind direction) variables are needed, and methods for establishing environmental contours for circular‐linear variables will be required. In this paper, different ways of establishing environmental contours for circular‐linear variables will be presented and applied to a joint distribution model for wind speed and wind direction. In particular, the direct sampling approach to environmental contours will be modified to the case where one of the variables is cyclic. In addition, contours based on exceedance planes in polar coordinates will be established, and circular‐linear contours will also be calculated based on the inverse FORM (I‐FORM) approach.