Bivariate Modeling of Wind Speed and Air Density Distribution for Long-Term Wind Energy Estimation

Abstract

In this paper, we investigate the feasibility of bivariate modeling of wind speed and air density based on the data from two observation sites in North Dakota and Colorado. For each site, we first obtain univariate statistical distributions for the two parameters, respectively. Excellent fitting can be achieved for wind speed for both sites using conventional univariate probability distribution functions, but it is found that accurately fitting air density distribution of the North Dakota site can only be obtained using bimodal distributions. Thereafter, we apply the Farlie–Gumbel–Morgenstern approach to construct bivariate joint distributions to describe wind speed and air density simultaneously. Overall, satisfactory goodness-of-fit is achieved with the bivariate modeling approach.

Keywords:

• Air density
• Bivariate distribution
• Farlie–Gumbel–Morgenstern approach
• Univariate distribution
• Wind speed

ACKNOWLEDGMENT

The authors acknowledge the valuable assistance from Ergin Erdem in the process of manuscript preparation.