# Evaluation of a fitted Weibull distribution using the PD method: *R*^{2} (a), RMSE (b), PDE (c), and their relationship to mean wind speed (d)

**Figure 2.** Evaluation of a fitted Weibull distribution using the PD method: *R*^{2} (a), RMSE (b), PDE (c), and their relationship to mean wind speed (d).

**Abstract**

Wind power, a renewable energy source, can play an important role in electrical energy generation. Information regarding wind energy potential is important both for energy related modeling and for decision-making in the policy community. While wind speed datasets with high spatial and temporal resolution are often ultimately used for detailed planning, simpler assumptions are often used in analysis work. An accurate representation of the wind speed frequency distribution is needed in order to properly characterize wind energy potential. Using a power density method, this study estimated global variation in wind parameters as fitted to a Weibull density function using NCEP/climate forecast system reanalysis (CFSR) data over land areas. The Weibull distribution performs well in fitting the time series wind speed data at most locations according to *R*^{2}, root mean square error, and power density error. The wind speed frequency distribution, as represented by the Weibull *k* parameter, exhibits a large amount of spatial variation, a regionally varying amount of seasonal variation, and relatively low decadal variation. We also analyzed the potential error in wind power estimation when a commonly assumed Rayleigh distribution (Weibull *k* = 2) is used. We find that the assumption of the same Weibull parameter across large regions can result in non-negligible errors. While large-scale wind speed data are often presented in the form of mean wind speeds, these results highlight the need to also provide information on the wind speed frequency distribution.