Because wind resources vary from year to year, the
intermonthly and interannual variability (IAV) of wind speed is a key
component of the overall uncertainty in the wind resource assessment
process, thereby creating challenges for wind farm operators and owners. We
present a critical assessment of several common approaches for calculating
variability by applying each of the methods to the same 37-year monthly
wind-speed and energy-production time series to highlight the differences
between these methods. We then assess the accuracy of the variability
calculations by correlating the wind-speed variability estimates to the
variabilities of actual wind farm energy production. We recommend the robust
coefficient of variation (RCoV) for systematically estimating variability,
and we underscore its advantages as well as the importance of using a
statistically robust and resistant method. Using normalized spread metrics,
including RCoV, high variability of monthly mean wind speeds at a location
effectively denotes strong fluctuations of monthly total energy generation,
and vice versa. Meanwhile, the wind-speed IAVs computed with annual-mean
data fail to adequately represent energy-production IAVs of wind farms.
Finally, we find that estimates of energy-generation variability require
The P50, a widely used parameter in the wind-energy industry, is an estimate of the threshold of annual energy production of a wind farm that the facility is expected to exceed 50 % of the time (Clifton et al., 2016). The P50 is usually estimated to apply over the lifetime of a wind farm, typically 20 years. To estimate P50 in the wind resource assessment process, a single percentage value is usually assigned to represent the uncertainty for the desired time period at a wind site (Brower, 2012). The interannual variability (IAV) of wind resources, along with site measurements and wind-power-plant performance, is an important component of the overall uncertainty in power production (Clifton et al., 2016; Klink, 2002; Lackner et al., 2008; Pryor et al., 2006). The IAV is also incorporated in the measure–correlate–predict process (Lackner et al., 2008), which usually considers wind measurements spanning less than 2 years.
Analysts and researchers use numerous metrics to quantify wind-speed
variability, and the most common method is standard deviation (
Because the profitability of wind farms depends on wind variability, past
research has explored the implications of interannual and long-term
variability in wind energy. Pryor et al. (2009) analyze trends of annual wind
speed and IAV, without explicitly quantifying IAV values. Archer and
Jacobson (2013) evaluate the seasonal variability of wind-energy capacity
factor. Lee et al. (2018) assess the spatial discrepancies between wind-speed
variabilities of different temporal scales, from hourly mean to annual-mean
data. Bett et al. (2013) use
To quantify variability, the normalized
Aside from CoV, other metrics representing the spread of data have also been chosen to estimate variability in the literature. For example, the robust coefficient of variation (RCoV) normalizes the median absolute deviation (MAD) with the median. Gunturu and Schlosser (2012) quantify the spatial RCoV of wind-power density in the United States and demonstrate that the regions east of the Rockies, especially the Plains, generally have weaker variability and higher availability of wind resources. The seasonality index, originally used in Walsh and Lawler (1981) for precipitation purposes, is another measure to express variability. The seasonality index is defined as the sum of the absolute deviations of monthly averages from the annual mean, normalized with the annual mean. Chen et al. (2013) use the seasonality index to assess the interannual trend and the variability of wind speed in China, and they relate wind-speed IAVs to climate oscillations.
Alternative variability metrics emphasize the long-term trends via contrasting wind speeds of different periods. The “wind index”, used in Pryor et al. (2006) and Pryor and Barthelmie (2010), is a ratio of wind speeds of a reference period and an analysis period. An entirely different wind index evaluated in Watson et al. (2015) is a ratio of spatially averaged wind speeds during two different periods.
Despite the importance of long-term variability, the wind-energy industry lacks a systematic method to quantify this uncertainty. As various metrics to assess variability exist, a comprehensive comparison of measures is necessary. Therefore, the goal of this study is to evaluate various methods of estimating intermonthly and IAV in a reliable way using a long-term, consistent database. Specifically, our objective is to determine an optimal metric or metrics for relating wind-speed variability to energy-production variability. We describe the wind-speed and energy-generation data, the methodology, and the chosen variability metrics in Sect. 2. We evaluate different variability measures via two case studies in Sect. 3. We also contrast the results computed from monthly mean and annual-mean data, and we illustrate the spatial distribution of wind-speed variability in Sect. 3. We then recommend the best practice in using the ideal method in Sect. 4. We focus on the applicability of imposing such metrics to quantify the variabilities of wind speeds and wind-energy production.
In this study, we use a 37-year time series of monthly mean wind speed and
monthly total wind-energy production in the contiguous United States (CONUS).
For wind speed, we use hourly horizontal wind components in the National
Atmospheric and Space Administration's Modern-Era Retrospective Analysis for
Research and Applications, Version 2 (MERRA-2), reanalysis data set (Gelaro et
al., 2017; GMAO, 2015) from 1980 to 2016. We use these components to derive
the monthly mean wind speed at 80 m above the surface, which represents hub
height in this study, via the power law (Eq. 1) and the hypsometric equation
(Eq. 2):
The horizontal resolution of the MERRA-2 is 0.5
For energy-production data, we use the net monthly energy production of wind
farms in megawatt hours (MWh) from the US Energy Information Administration
(EIA) between 2003 and 2016. Each of the wind farms has a unique EIA
identification number. After we leave out about 300 wind sites with
incomplete or substantially zero production data, a total of 607 wind farms
in the CONUS are selected for this analysis. For simplicity, the CONUS in
this analysis is defined as the area bounded by 127
We focus on the direct relationship between wind speed and energy production
to investigate approaches for calculating long-term variability. Therefore,
we must minimize the influence from other determinants of energy production,
such as curtailment and maintenance. First, we eliminate data with zero
values for monthly energy production, which is typical in the first months of
a new wind farm. Next, we linearly regress the monthly total energy
production on the monthly mean MERRA-2 80 m wind speed at the closest grid
point to each wind farm from 2003 to 2016. In other words, each wind site is
assigned its own regression equation. We then remove any production data
below the 90 % prediction interval to exclude underproduction for reasons
other than low wind speeds, and omit the data above the 99 % prediction
interval, or potentially erroneous overproduction. Prediction intervals are
calculated via the
After regressing the outlier-free energy data on wind speed, we then filter
the wind farms based on the coefficient of determination (
We then further apply a second filter using the Pearson's correlation
coefficient (
The nonfiltered,
Wind farm locations in the CONUS: nonfiltered 607 sites in dark red,
Recognizing that the horizontal resolution of the MERRA-2 data could be
perceived as undermining the linear regressions, we explore any possible role
of the distance between the closest MERRA-2 grid point and the actual wind
farm, but we find no statistical relationship. In particular, horizontal and
vertical discrepancies between the model and the observations do not affect
the resultant
Additionally, we analyze the uncertainty of the linear-regression method. We
first test the influence of the error term in the regression, to account for
the uncertainty associated with the input data. After a wind farm passes the
We test other factors that could undermine these regressions. We considered
the hub-height air density extrapolated from MERRA-2 as another regressor in
the regressions, but air density is a statistically insignificant predictor
and thus is not discussed in the rest of this study. When we replace
the prediction interval with the confidence interval, the sample sizes increase from
349 and 195 sites to 555 and 209 wind farms. However, at least 7 years of
energy data are derived from the regression for 99 % of the samples,
because confidence intervals are smaller than prediction intervals by
definition. We also considered removing the long-term means and the impacts
of annual cycles, yet the sample sizes decrease to 121 and 69 locations, and
the regression fills at least some of the energy data for more than 99 %
of the sites. Finally, to ensure these results were not specific to the
MERRA-2 data set, we perform the same analysis on the ERA-Interim reanalysis
data set (Dee et al., 2011). The results of the key variability parameters
such as
Our analysis, although comprehensive, is constrained by the quality of our data. On the one hand, reanalysis data sets have errors and biases in wind-speed predictions from complexities in elevation and surface roughness (Rose and Apt, 2016). Reanalysis data sets also demonstrate long-term trends of surface wind speeds (Torralba et al., 2017). The MERRA-2 data set can also depict different meteorological environments than those at the wind farm locations, especially in complex terrain. The MERRA-2 data of coarse temporal and spatial resolutions may also represent a lower intermonthly or IAV than the wind sites actually experience. Thus, regressing actual energy production on reanalysis wind speed adds uncertainty to our analysis. On the other hand, constrained by the monthly total energy-production data from the EIA, our analysis ignores the signals finer than monthly cycles. The quality of the EIA data also varies across wind sites; therefore the filtering process via linear regression is necessary.
To evaluate the variabilities of both the wind speeds and the predicted
energy generation from the filtered wind farms, we investigate a total of 27
combinations and variations of existing methods describing the spread of
data. We categorize different variability metrics according to statistical
robustness (insensitivity to assumptions about the data; for example,
Gaussian distribution) and statistical resistance (insensitivity to outliers)
(Wilks, 2011). Of the 27 variability methods tested, we select four
representative measures to perform a comparison and discuss in detail,
according to their robustness, resistance, and the nature of normalization by
an average metric:
RCoV, defined as the MAD divided by the median (Gunturu and Schlosser, 2012;
Watson, 2014), is a spread metric divided by an average metric and is both
statistically robust and resistant. Range (maximum minus minimum) divided by trimean (weighted average among
quartiles) is a spread metric normalized by an average metric, and the
numerator is not resistant. CoV (Baker et al., 1990; Bodini et al., 2016; Hdidouan and Staffell, 2017;
Krakauer and Cohan, 2017; Rose and Apt, 2015; Wan, 2004), defined as the
Among the four measures, only RCoV is completely statistically robust and
resistant, and the first three methods are all normalized spread metrics. We
further describe all the tested variability methods comprehensively in
Table B1 in Appendix B. Each of these metrics is easy to implement via basic Python
packages such as NumPy and SciPy with no more than a few lines of code. In
addition, based on the exponential scaling relationship between power and
wind speed developed by Bandi and Apt (2016), we also analyze the results
from the exponential CoV and the exponential RCoV in this paper (Table B1).
In addition to calculating variabilities with the spread measures, we evaluate other diagnostics that describe distribution characteristics. These diagnostics include averaging metrics, such as the arithmetic mean (not resistant) and median (the 50th percentile, which is resistant); symmetry metrics, such as skewness (involving the third moment, not robust or resistant) and the Yule–Kendall Index (YKI, robust and resistant); a tailedness metric, namely kurtosis (involving the fourth moment, not robust or resistant); the Weibull scale and shape parameters (not robust); and the autocorrelation with a 1-year lag to dissect the interannual cycles. We summarize the diagnostics evaluated in this analysis in Table B2. Along with the regression results, results from the four representative variability metrics and other distribution diagnostics demonstrate differences between the two selected sites (Table 2).
Herein, we quantify the variabilities of the 37-year extended time series of
wind speed and energy production via different methods, using a range of time
frames: 1 year, 2 years, and up to 37 years for each wind farm. A metric is
considered useful when the resultant wind-speed variability correlates well
with the resultant energy-production variability across wind farms, even when
random errors are implemented and the thresholds
Details of the three correlation metrics applied, adapted from
Wilks (2011). All three metrics yield values between
To assess the applicable time frames of various variability metrics, we
evaluate the asymptote period of correlations for each method. In most
cases, the correlation coefficients approach the 37-year value after a
certain analysis time frame. Using RCoV as an example, the Pearson's
To relate the IAVs between wind speed and energy production, we also perform the same analysis for annual-mean data. Strictly speaking, calculating the variabilities using monthly mean data yields intermonthly variabilities, because the results account for monthly, seasonal, and annual signals. To isolate the signals from interannual variations, we also examine the metrics and their correlations between the annual means of hub-height wind speeds and energy production, after linear regressing and filtering via monthly data. However, the samples from each site are then limited to 37 data points of annual wind speed and energy production. Besides, selecting de-trended data from long-term means to calculate variabilities and their correlations leads to trivial results because of the small sample sizes and hence is omitted in this study.
After we demonstrate that RCoV is the most systematic approach in linking wind-speed and energy-generation variabilities in Sect. 3.2, we further examine the details of using RCoV, specifically determining the minimum length of wind-speed data necessary to quantify variability effectively. We use 37 years of wind speed in every MERRA-2 grid cell in the CONUS (a total of 5049 grid points), and we calculate the RCoVs with 1 to 37 years of data for each grid cell. Because the RCoVs calculated using data between 1980 and 2016 are only samples of the true long-term wind-speed variability and hence the results involve uncertainty, we select a confidence interval approach.
Site details, monthly means, and annual means of various metrics at the two selected sites based on 37 years of monthly and annual wind speeds, and 37 years of predicted and actual energy production; and the CONUS medians of wind-speed metrics using 37 years of monthly and annual-mean data.
We assume that the distribution of RCoV is Gaussian with infinite years of
wind speed. Hence, we use a chi-square (
In summary, for each grid point, we first determine an uncertainty bound
based on the 37-year wind-speed RCoV of the location: we assign a 37-year
We select two sites from two different geographical regions with considerable
wind-energy deployment, the southern Plains and the Pacific Northwest in the
United States, to contrast the results of various variability metrics. Based
on the site-specific regressions, we extend the monthly energy-production
time series to 37 years (Fig. 3a and b) for the two sites. Both sites pass
the
None of the monthly and annual wind-speed distributions of the sites are
perfectly Gaussian. According to the kurtosis, skewness, and YKI values of
the monthly mean wind speeds (Table 2), the monthly wind-speed distribution
at the OR site skews towards lower wind speeds with more and stronger
extremes (Fig. 3c). The skewed distribution at the OR site leads to
71.2 % of the monthly wind speeds located within
Scatterplots of 37-year wind-speed variability and energy
variability via four metrics:
The four selected variability methods yield similar resultant monthly variabilities that are close to the respective CONUS medians based on the 37-year monthly data. For variabilities of monthly wind speeds, the differences between the two sites are slight because the comparison among the results of the four metrics is inconclusive (Table 2): the monthly variabilities are not far from the national medians (Table 2). However, results from the normalized spread metrics (RCoVs, range divided by trimean, and CoV) using the 37-year and the observed energy production illustrate that the OR site generates more variable wind power than the TX site (Table 2). The magnitudes of the variabilities between the 37-year and the actual monthly energy production are also comparable, and the discrepancies between them are larger at the TX site than the OR site. Nonetheless, the predicted and the observed monthly energy production of the two sites demonstrate similar variability characteristics overall.
Moreover, when we apply the four selected methods to the annual-mean data,
the metrics describe IAV exactly. For both variables, wind speed and energy
generation, nearly all metrics illustrate that the OR site has stronger IAV
than the TX site, except for using
Additionally, the magnitudes of energy variabilities and IAVs are also nearly or more than twice as large as those of wind speed (Table 2). The reason is the nature of the power curve: wind-power generation is a function of wind speed cubed at wind speeds below rated. Therefore, small wind-speed variations propagate into large energy-production fluctuations that are discernible in monthly and yearly data.
Matching the wind-speed and energy variabilities over 37 years at each
Box plots of Pearson's
By increasing the years included in the variability calculations using
monthly data, the resultant correlations of most metrics vary less, the
correlations gradually converge to their 37-year values, and their asymptote
periods vary. The 37-year Pearson's
The three correlation coefficients (Pearson's
Correlations and the associated asymptote periods of wind-speed
variability and energy variability using various spread methods and
distribution diagnostics with different correlation metrics, based on the
monthly data of the 195
In addition to the spread metrics, other distribution diagnostics also yield
strong correlations between the 37-year monthly wind speed and energy
production. For example, kurtosis and skewness result in
Additionally, we also perform the same correlation and asymptote analyses on
the data from changing the
Further, normalized and simple spread metrics yield different relative
wind-speed variabilities between wind sites. On the one hand, the correlations
coefficients between 37-year monthly mean wind-speed RCoV and CoV, two spread
metrics that are normalized by average metrics, are nearly unity (Fig. 6a).
The comparison between two simple spread metrics, MAD and
Similar to Fig. 4, but for scatterplots to compare 37-year
wind-speed variability metrics:
Meanwhile, using annual-mean data to compute IAVs can lead to misleading
interpretations. Scatterplots of the 37-year wind-speed and energy IAVs
similar to Fig. 4 are illustrated in Fig. A1, via the same 195
As in Fig. 5, but for annual-mean data.
Box plots of wind-speed RCoV using monthly MERRA-2 data for different
time frames from 1 year to 37 years at
Now that we have established that RCoV is a powerful and accurate way to
relate wind-speed and energy-generation variations, we assess the required
amount of data to calculate the RCoV of wind speed. We compute the
site-specific RCoVs using different spans of monthly mean wind speeds,
including the OR and the TX sites (Fig. 8). The variations of RCoVs decrease
as more years are included in the calculations, and for each location we use
the 37-year wind-speed RCoV as the long-term benchmark. For example, the
37-year wind-speed RCoV of 0.082 at the OR site means that the median among
the absolute deviations from the median is 8.2 % of the median monthly
mean wind speed (Fig. 8a and Table 2). We determine the 37-year
To quantify the intermonthly variability of wind speed at a wind farm, RCoV
requires 10 years of monthly wind-speed records with a 90 % confidence. In
general, the
Moreover, raising the confidence level extends the minimum length of
wind-speed data to compute RCoV. At the 95 % confidence level, the median
convergence year is 20 years, and 2.5 % of grid points in the CONUS
require more than 37 years of monthly mean data to calculate RCoV (Fig. 9b
and Table B5). Additionally, using yearly mean wind speeds instead of monthly
data to calculate RCoV requires much longer time to reach convergence. At
a 95 % confidence, 33 years of annual-mean data is the average required
length, and half of the CONUS grid points have convergence years of more than
37 years (Fig. 9b and Table B5). We also perform the same analysis on CoV and
Spatial distributions of wind-speed RCoVs across the CONUS identify locations with reliable wind resources. Based on the site-specific convergence years at a 90 % confidence level (Fig. 10a), we calculate the RCoVs with monthly mean wind speeds of the particular time spans at each grid point and normalize with the CONUS median (Fig. 10b). Regions requiring long wind-speed records are irregularly scattered across the continent, such as the Northeast, the Dakotas, and Texas. The mountainous states generally illustrate high RCoVs, including the Appalachians and the Rockies. Given the strong correlations between the wind-speed RCoV and energy-production RCoV, Fig. 10b offers a realistic estimation of the general spatial pattern of the variability in wind-energy production as well. Note that, qualitatively, Fig. 10b is similar to the maps of wind-speed variability in Fig. 13a of Gunturu and Schlosser (2012) and in Fig. 3 in Hamlington et al. (2015), which also illustrate the variability of wind resources in the CONUS. In addition, using a 10-year fixed length of wind-speed data for all CONUS grid points to compute RCoV results in a nearly identical spatial distribution to the pattern in Fig. 10b.
Further, an ideal location for wind farms should exhibit ample wind speeds with low variability. We combine the spatial variations of the normalized RCoV and the long-term wind resource (Fig. 10b and c), and we differentiate regions according to the CONUS median RCoV and wind speed (Fig. 10d). Favorable candidates for wind farm developments have above-average wind speeds and below-average variabilities, such as the Plains, parts of the upper Midwest, spots in the Columbia River region, and pockets nears the coasts of the Carolinas; poor places for wind power with weak winds and strong variabilities include the Appalachians and most of the Northeast.
The convergence years in some CONUS grid points are beyond 37 years when we
increase the confidence level from 90 % to 95 % (Fig. 9b and
Table B5), and those grid points do not demonstrate any geographical pattern
as in Fig. 10a. Additionally, when using RCoV to represent IAV, the spatial
patterns of required data lengths and the resultant normalized RCoVs for
annual data are notably different from the monthly mean results, and
geographical features seem to be irrelevant (Fig. A3). Furthermore, the
categorical features of CoV resemble those of RCoV for onshore wind resources
in the CONUS, whereas using
When using statistically robust and resistant variability metrics, higher
correlations between variabilities of wind speed and energy production
emerge. Statistically robust methods do not assume or require any underlying
wind-speed distributions, and statistically resistant methods are insensitive
to wind-speed extremes. Of all methods, three robust and resistant metrics,
RCoV, MAD divided by trimean, and IQR divided by median, result in the
largest three
Overall, of all the methods we considered, RCoV consistently yields the
strongest correlations between wind-speed and energy variabilities and
exhibits reasonable asymptote periods (Tables 3 and B1), even after
accounting for random standard errors and modifying the
Annual-mean data are inadequate to relate wind-speed and energy-production
IAVs or to represent wind-speed IAVs. We cannot determine the minimum years
of data to relate annual wind-speed and energy IAVs because their
correlations decline with the length of data (Fig. 7). Moreover, the coarse
time resolution of annual averages smooths out the fluctuations of smaller
timescales. Yearly mean wind speeds also possess different distribution
characteristics, such as skewness and kurtosis, compared to those of finer
temporal resolutions (Lee et al., 2018). The nonzero kurtosis and skewness in
Table 2 and in Lee et al. (2018) illustrate that most of the distributions of
annual-mean wind speeds in the CONUS are non-Gaussian. Hence, using nonrobust
metrics, such as
Additionally, extended years of wind-speed data are also necessary to compute
RCoV and represent IAV (Fig. A3a), and the resultant IAVs (Fig. A3b) differ
from the variabilities calculated via monthly wind speeds (Fig. 10b). For
instance, the low IAVs in the Appalachians (Fig. A3b) calculated with yearly
mean wind speeds contradict the pattern of high monthly mean wind-speed RCoVs
in mountainous areas (Fig. 10b) as well as the findings in past research
(Gunturu and Schlosser, 2012; Hamlington et al., 2015). Furthermore, some of
the grid points require more than 37 years of yearly mean data to calculate
wind-speed RCoV with statistical confidence (Fig. 9 and Table B5). Although
RCoV does not yield the strongest 37-year
Regions with ample wind resources and low variability favor wind-energy developments, coinciding with the locations of many existing wind farms in the CONUS (Fig. 10d). Wind farms in the Plains and parts of the upper Midwest benefit from the above-average wind speeds and the below-average wind-speed RCoVs. Other regions, such as parts of the Columbia River region and the Carolinas, also experience strong, consistent winds. The Northeast and the Appalachians are relatively unfavorable for producing a stable, onshore wind-energy supply, whereas the area east of Cape Cod in Massachusetts and the sections along the West Coast exhibit a promising offshore wind resource. Wind farm developers should account for wind resource as well as its long-term variability in repowering existing turbines and building new wind farms.
Furthermore, mathematically, a normalized spread metric, namely a spread
statistic divided by an average metric, is more useful than solely a spread
metric in assessing variability, and a normalized spread metric should always
be presented with the corresponding averaging metric. For example, RCoV and
CoV between wind speed and energy yield larger
Distribution diagnostics, other than the variability metrics, are also
effective in identifying the characteristics of wind-energy production. We
examine distribution parameters resulting in strong wind-speed–energy
correlations, including kurtosis and YKI (Tables 3 and B2), which assess the
degree of deviations from a Gaussian distribution. For example, we confirm
that the monthly and annual wind-speed distributions for our case studies in
OR and TX are not perfectly Gaussian because of their nonzero kurtosis and
skewness values (Table 2), as well as their portions of data within
Wind-speed variability is a crucial component in assessing the
overall uncertainty of P50, which is the estimated average energy production
of a wind farm. This study highlights the importance of using rigorous methods to estimate
intermonthly and interannual variability. To search for suitable ways to
quantify this uncertainty under different conditions, we investigate 27
combinations of spread metrics over 607 wind farms in the United States, with
closer examination of two geographically distinct sites. We evaluate the
methods for robustness to non-Gaussian distributions and resistance to
extreme values, in contrast to the common practice of using only standard
deviation (
We recommend using the robust coefficient of variation (RCoV) to quantify
variabilities of wind resource and energy production. RCoV, defined as the
median of absolute deviation from the median wind speed divided by the median
of the wind speed, is a robust and resistant spread metric, in contrast to
RCoV characterizes the spreads of the distributions of wind resources and wind-energy production. The relatively low monthly mean wind-speed RCoVs in the central United States indicate stable long-term wind resources, and the RCoV overall spatial distribution in the CONUS agrees with the findings from past research. Other distribution diagnostics, such as kurtosis and skewness, also result in strong correlations between monthly mean wind speed and energy generation, and thus they adequately represent energy-production characteristics.
Because the long-term correlations between the wind-speed and
energy-production interannual variabilities (IAVs) are weak (a Pearson's
Now that we have highlighted the preferred structure of using RCoV, we can assess finer-scale variations using high-resolution wind-speed and energy-production data. With data of different temporal scales, the autocorrelation of wind resources and its relationship with long-term energy-production variations can also be quantified. The influence of climatic cycles on energy production can be explored. Furthermore, applying the concept of RCoV to reduce the uncertainty of P50 and assist financial decisions can be beneficial to the industry.
The MERRA-2 data and the EIA data used in this study are
publicly available at
As in Fig. 4, but the metrics are calculated using annual-mean wind speed and energy production.
As in Fig. 6, but the metrics are calculated using yearly mean wind speed.
As in Fig. 10a and b, but the data plotted are annual-mean wind
speeds:
As in Fig. 10d, but the spread metrics are
Description of the 26 spread metrics tested, adapted from
Wilks (2011), and the 37-year
Description of the distribution diagnostics tested, adapted from
Wilks (2011) and the 37-year
As in Table 3, but with the calculated metrics, the associated
correlations, and asymptote periods using different
As in Table 3,
but with the calculated metrics, the associated correlations, and asymptote
periods using annual-mean wind speed and energy production using the 195
Convergence years based on the
All authors formulated the research idea and designed the methodology together. JCYL performed the analysis; MJF and JKL provided critical feedback. JCYL prepared the manuscript with contributions from the two co-authors.
Julie K. Lundquist is an Associate Editor of Wind Energy Science. Joseph C. Y. Lee and M. Jason Fields have no conflict of interest.
This work was authored by the National Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, LLC, for the U.S. Department of Energy (DOE), under contract no. DE-AC36-08GO28308. Funding was provided by the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy's Wind Energy Technologies Office. The views expressed in the article do not necessarily represent the views of the DOE or 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.
The authors would like to thank our collaborators, Vineel Yettella and Mark Handschy of the Cooperative Institute for Research in Environmental Sciences (CIRES) at the University of Colorado Boulder; our colleagues at NREL, especially Paul Veers; and Cory Jog at EDF Renewable Energy. Edited by: Christian Masson Reviewed by: two anonymous referees