American Wind Energy Association 

Wind Resource and Project 

Energy Assessment Conference

Austin, Texas

Sept. 11–12, 2018

NREL/PO-5000-72215

Effective Quantification of Wind-Speed Variability 

at Different Temporal Scales

Joseph C. Y. Lee,1 M. Jason Fields,1 and Julie K. Lundquist1, 2

1 National Wind Technology Center, National Renewable Energy Laboratory, Golden, Colorado

2 Department of Atmospheric and Ocean Sciences, University of Colorado Boulder, Boulder, Colorado

The Alliance for Sustainable Energy, LLC (Alliance) is the manager and operator of the National Renewable Energy Laboratory (NREL). NREL is a national laboratory of the U.S. Department of

Energy, Office of Energy Efficiency and Renewable Energy. This work was authored by the Alliance and supported by the U.S. Department of Energy under Contract No. DE-AC36-08GO28308.

Funding was provided by the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy, Wind Energy Technologies Office. The views expressed in the article do not necessarily

represent the views of the U.S. Department of Energy or the U.S. government. The U.S. government retains, and the publisher, by accepting the article for publication, acknowledges that the U.S.

government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for U.S. government purposes.

• RCoV, a statistically robust and resistant metric, effectively characterizes and correlates the spreads of the distributions of wind resources and wind-energy productions. Using

RCoV, a wind farm with high wind-speed fluctuations possesses high variations in wind-energy generation and vice versa.

• Skewness and kurtosis drastically change with averaging timescales. Nonzero skewness and kurtosis illustrate that the Gaussian assumption is principally inadequate in most of

the United States for all averaging time frames of wind speeds.

• Because the long-term correlations between the wind-speed and energy-production interannual variabilities are weak and decrease with the length of data, we do not recommend

calculating variabilities with yearly mean data.

Please refer to the following articles for more details:

Lee, J.C.Y., M.J. Fields, and J.K. Lundquist. 2018. (In review). “Assessing Variability of Wind Speed: Comparison and Validation of 27 Methodologies.” Wind Energy Science discussion. https://doi.org/10.5194/wes-2018-49.

Lee, J.C.Y., M.J. Fields, and J.K. Lundquist. 2018. “Determining variabilities of non-Gaussian wind-speed distributions using different metrics and timescales.” The Science of Making Torque from Wind (TORQUE 2018). doi

:10.1088/1742-6596/1037/7/072038.

Key Takeaways

• Quantifying the uncertainty of wind is critical for the wind resource assessment process. Despite the

importance of long-term variability, the wind energy industry lacks a robust and resistant systematic

method to quantify this uncertainty.

• Our goals are to contrast the characteristics of average wind speed at different timescales and to

determine an optimal metric for relating wind-speed variability to energy-production variability.

• We apply the horizontal wind speeds from the National Aeronautics and Space Administration’s ModernEra Retrospective Analysis for Research and Applications, Version 2 reanalysis data set from 1980 to

2016. We also use the net monthly energy production of wind farms in the continental United States

(CONUS) from the Energy Information Administration between 2003 and 2016. We calculate the wind

speeds at 80 meters above the surface using the power law and derived shear components. We compute

the mean wind speeds at six time resolutions: hourly, daily, weekly, monthly, seasonal, and annual. We use

linear regression and prediction interval to remove outliers.

• We use a collection of spread metrics and distribution parameters, described in the blue text on the right.

Motivation and Methodology

Kurtosis =

1

n ∑i=1

n xi

−x� 4

(

1

n ∑i=1

n xi

−x� 2 )2 − 3

Skewness =

1

n ∑i=1

n xi

−x� 3

(

1

n ∑i=1

n xi

−x� 2 )

3

2

Robust coefficient of variation

RCoV = median|xi−median x |

median

Positive skewness 

means the 

distribution tends 

toward low values. 

Positive kurtosis 

means the 

distribution tends to 

cluster near its center. 

Large RCoV 

represents high 

variability. 

Figure 3. The 

skewness of mean 

wind speeds at 

different averaging 

timescales of the 

CONUS over 37 years. 

Figure 4. The kurtosis 

of mean wind speeds 

at different averaging 

timescales of the 

CONUS over 37 years. 

Figure 1. Top: Map of the mean monthly wind speed at 80

meters of 37 years. The CONUS median is 6.45 meters per

second. Middle: Map of RCoV of monthly mean wind speed

normalized using the CONUS RCoV median at 0.100.

Bottom: Map of wind resource and its variability, by

summarizing the two plots above into four categories,

based on the CONUS median wind speed and RCoV.

Figure 2. 

Left: Scatterplots of 

monthly and yearly 

wind-speed and 

energy-production 

RCoVs, based on 37 

years of data of 195 

wind farms. 

Right: Boxplots of 

Pearson’s correlation 

coefficient between 

monthly and yearly 

wind-speed and 

energy-production 

RCoVs for different 

time frames, from 1 

year to 37 years. 

A perfect Gaussian distribution has zero skewness and kurtosis.

With the same means and the same skewness of 0, the kurtosis of

1 and 2 reduce standard deviation by 20% and 26% respectively.