Probability distributions for offshore wind speeds

In planning offshore wind farms, short-term wind speeds play a central role in estimating various engineering parameters, such as power output, extreme wind load, and fatigue load. Lacking wind speed time series of sufficient length, the probability distribution of wind speed serves as the primary substitute for data when estimating design parameters. It is common practice to model short-term wind speeds with the Weibull distribution. Using 10-min wind speed time series at 178 ocean buoy stations ranging from 1 month to 20 years in duration, we show that the widely-accepted Weibull distribution provides a poor fit to the distribution of wind speeds when compared with more complicated models. We compare distributions in terms of three different metrics: probability plot R2, estimates of average turbine power output, and estimates of extreme wind speed. While the Weibull model generally gives larger R2 than any other 2-parameter distribution, the bimodal Weibull, Kappa, and Wakeby models all show R2 values significantly closer to 1 than the other distributions considered (including the Weibull), with the bimodal Weibull giving the best fits. The Kappa and Wakeby distributions fit the upper tail (higher wind speeds) of a sample better than the bimodal Weibull, but may drastically over-estimate the frequency of lower wind speeds. Because the average turbine power is controlled by high wind speeds, the Kappa and Wakeby estimate average turbine power output very well, with the Kappa giving the least bias and mean square error out of all the distributions. The 2-parameter Lognormal distribution performs best for estimating extreme wind speeds, but still gives estimates with significant error. The fact that different distributions excel under different applications motivates further research on model selection based upon the engineering parameter of interest.