1. Introduction
Wind speed is, therefore, one of the metrics used to quantify the wind available for wind energy generation (the “wind resource”) at a location. Wind resource data are usually collected for at least a year before the resource is quantified as part of a wind resource assessment and combined with a turbine power curve to estimate energy production (Brower 2012). During the resource assessment, an estimate is made of the interannual variability of the hub-height wind resource at the site (Rohatgi and Nelson 1994). This interannual variability is caused by global and regional climate variability as well as by local changes in vegetation and surface cover (Klink 2002; Pryor et al. 2006).
Global or regional climate variability is quantified by using a set of meteorological parameters such as air temperature, sea surface temperature, or surface pressure. Some indices are linked to well-known climatological phenomena, such as El Niño/La Niña–Southern Oscillation (ENSO) or the Arctic Oscillation (AO). In some cases, the phenomena quantified by these indices are correlated with variations in wind activity. For example, previous work has suggested that winds in southern Alberta and Saskatchewan, Canada, vary with ENSO (St. George and Wolfe 2009) and that extreme winds around the United Kingdom vary with the North Atlantic Oscillation index (Pirazzoli et al. 2010). Analysis by Klink (2007) showed that the AO and Niño-3.4 climate indices explained a significant proportion of variations in wind resource at 80 m above ground level in Minnesota. Comparatively low wind energy production during the winter of 2009/10 at a site in Texas has been linked to El Niño events seen in the multivariate ENSO climate index (MEI) and Southern Oscillation index (Oliver 2010). Because climate indices also can be forecast over time scales from days to years, historical observations of wind can be compared with climate-index records, and the results can be used to understand how wind resources might vary in the future. In one application of this approach, long-term predictions of climate indices that are based on climate models have been used to assess the impact of climate variability on wind power production in Europe (Pryor et al. 2006).
In this investigation, we examine the role of the AO, Pacific–North American pattern (PNA), and ENSO in altering wind resources at the National Wind Technology Center (NWTC), in Colorado, using a new approach to synthesize long-term wind observations. The AO has been shown to influence wind resources in Minnesota (Klink 2007), and changes in the PNA have been linked to the location of the jet stream (Notaro et al. 2006). ENSO variation has been linked to changes in wind speed over North America (Wolter 1987; Klink 2007; St. George and Wolfe 2009; Oliver 2010) and also has been linked to changes in seasonal precipitation over Colorado (Hereford and Webb 1992) and the Rocky Mountains in Utah, Colorado, and Wyoming (Hidalgo and Dracup 2003). ENSO variability has been quantified with several indices; recent work by Wolter and Timlin (2011) has shown the utility of the MEI. Because the MEI is a bimonthly index and so is on a different time base than the other indices, it is not used here. Analysis by Klink (2007) showed that the dominant forcing on the mean monthly wind speed at 70 m above ground in Minnesota was the maximum local pressure gradient at the 500-hPa level ΔZ500.
In flat, uniform, and homogenous terrain, variation in the hub-height wind speed is more important than changes in wind direction for production of energy by wind turbines; this is because the wind speed and profile do not depend on direction. In complex terrain, local changes in wind direction may lead to changes in the velocity profile; in mountainous regions, on the other hand, changes in mesoscale pressure fields or ground cover may result in radically different flows than would otherwise occur (Turnipseed et al. 2004; Whiteman 2000). Changes in velocity profile can induce changes in turbulence profile, which will affect turbine productivity (Wharton and Lundquist 2010, 2012a,b). Because of these factors, it is essential to understand how both wind direction and wind speed might be influenced by climate variability when considering locations in even mildly complex terrain.
To assess climate variability at a wind site, several years of high-frequency data are required. The analyst must reduce those data to a relatively small number that can be used to diagnose long-term trends. One approach calculates relatively long (monthly or seasonal) averages and then calculates the anomaly [i.e., the variation from the mean, as in Klink (2007)] and groups data according to wind direction or month of the year. Grouping into directional bins (e.g., 5°, 10°, or 45° sectors) would be arbitrary, however, and if bin sizes are similar to the instrument uncertainty then there is a risk of incorrectly binning data. Furthermore, the advantages of having time-resolved data are lost in this averaging process.
In this investigation, we apply automated cluster analysis to objectively classify 14 years of turbine hub-height wind data, collected at the NWTC in Colorado, into groups and compare the occurrence of winds in those clusters with climate indices. The effect of climate variability on the wind resource in Colorado is important because 1299 MW of wind energy capacity has been installed in the state, contributing 6.6% of Colorado’s power (American Wind Energy Association 2011). Although cluster analysis is an established data-mining technique that has been applied to synoptic winds (Burlando 2009) and to group wind energy production facilities (Vallee et al. 2011), to our knowledge this effort represents the first time that cluster analysis has been applied to understand climate variability and how that might affect wind turbine operations. We have applied the clustering method to understand climate impacts on wind resources, but the method also could be applied to the analysis of gridded model output data over several years, or in choosing flow cases to simulate using high-resolution models, allowing intensive analysis to be focused on the most important wind conditions.
2. Winds at the National Wind Technology Center
a. Meteorological tower data
Wind speed and direction data have been collected at the NWTC near Boulder, Colorado, on an 80-m lattice tower since September of 1996. The “M2” tower is located at 39°54′38.34″N and 105°14′5.28″W (datum WGS84), with its base at an elevation of 1855 m (6085 ft) above mean sea level. Wind speeds are measured by using annually calibrated cup anemometers (Met One Instruments, Inc., SS-201) with an accuracy of the greater of 2% of reading or 0.5 m s−1. Wind vanes (Met One SD-201) measure wind direction with an accuracy of 3.6° at 2, 5, 10, 20, 50, and 80 m above ground. The cup anemometers and vanes are mounted on booms oriented toward the prevailing wind direction of 292°. All boom lengths are 3.5 times the tower face width to reduce the tower influence on measured wind speeds and directions. Air temperatures are measured with platinum resistance thermometers (Met One T200A) at 2, 50, and 80 m, and dewpoint is measured at 2 m (Therm-X 9400ASTD).
Data were collected from late 1996 to 2001 at 0.5 Hz and stored as 10-min averages. From August of 2001 to 2011, data were collected at 1 Hz and then stored as 1-min averages. Data obtained during 2001 are neglected because that year’s dataset was affected by the change of data-processing routines. The datasets have been processed into unified datasets of 10-min-average wind speed and direction for the period 1997–2010 (without 2001) at each measurement height. Wind speed and direction are further processed to give the meteorological zonal (west–east; u) and meridional (south–north; υ) winds at each measurement height. The time series of the monthly average winds at 80 m on the tower (Fig. 1) shows strong seasonal changes. Occasional strong monthly anomalies (relative to the long-term-average wind speed for that month) are present in, for example, 1999, 2004, and 2010.
Time series of wind speed and climate indices. (a) Mean monthly wind speed at 80 m at the NWTC; (b) ΔZ500, (c) AO, (d) PNA, and (e) Niño-3.4. Climate-index data plotted in (c)–(e) were obtained from the NWS Climate Prediction Center. NWTC wind speed data are not available for 2001.
Citation: Journal of Applied Meteorology and Climatology 51, 8; 10.1175/JAMC-D-11-0227.1
Winds at the NWTC are frequently below the threshold for wind turbine operation, called the cut-in speed. Figure 2 shows the relative frequency of winds at 80 m above ground, measured by the M2 tower. Winds are below 3.5 m s−1, which is a representative speed for the cut-in of utility-scale turbines (Hu and Cheng 2007) in 46% of observations at that height. Those data were removed from the plot for clarity. The proportion of calm winds increases closer to the ground.
Frequency of winds at 80 m binned by wind speed and direction. Data are limited to wind speeds above 3.5 m s−1 and are grouped into 5° and 1 m s−1 bins. Contours show the relative frequency in each bin on a linear scale.
Citation: Journal of Applied Meteorology and Climatology 51, 8; 10.1175/JAMC-D-11-0227.1
Winds that are above the cut-in speed and thus important for turbine operation tend to be concentrated into flows from the north (≈350°), west-northwest (≈290°), and south-southeast (≈170°) (Fig. 2). Each group has different wind speed frequency distributions, however, and any selection of groups from visual clues would be subjective.
For each 1 m s−1 (zonal) by 1 m s−1 (meridional) bin of winds at the NWTC, the most frequently occurring stability class within that bin is shown in Fig. 3. Stable conditions occur most frequently at low wind speeds, as would be expected, and unstable conditions dominate the easterly-flow cases. In general, the stronger the winds are, the more that conditions tend to be neutral.
Most commonly occurring 2–80-m-layer stability category associated with winds at 80 m grouped into 1 m s−1 meridional and zonal wind speed bins.
Citation: Journal of Applied Meteorology and Climatology 51, 8; 10.1175/JAMC-D-11-0227.1
b. Large-scale wind forcing at the NWTC
Large-scale wind forcing at the NWTC is quantified by the monthly mean values of ΔZ500 and the AO, PNA, and Niño-3.4. The monthly time series of the AO, PNA, and Niño-3.4 indices were obtained from the National Weather Service (NWS) Climate Prediction Center. Data sources are listed in the acknowledgments. The pressure gradient ΔZ500 was calculated for the NWTC from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis data as the maximum difference in the height of the 500-hPa level along a line from 20° to 60°N at 105°W, following the example of Klink (2007) for Minnesota.
Climate-index data for the period 1997–2010 are shown in Fig. 1 alongside the mean wind speed and anomaly at 80 m above ground at the NWTC. The climate indices have markedly different low-frequency components, with the Niño-3.4 exhibiting the slowest changes over periods of more than a year and ΔZ500 showing a regular annual cycle.
A linear regression between the mean monthly wind speed at 80 m (calculated as the mean of all wind speed data recorded during the month) and ΔZ500 showed that 40% of the variation in monthly wind speed could be explained by changes in the local pressure gradient alone (Fig. 4 and Table 2). Only 6% of the change of the residual is explained by changes in the AO, PNA, and Niño-3.4. The largest contribution to the change in residuals comes from changes to the Niño-3.4 index. The monthly mean wind speed is underpredicted by ΔZ500 during three distinct periods: early 1998, 2006, and 2009. The Niño-3.4 index is strongly positive in the two latter periods, indicating El Niño conditions, and 1998 is a period of strong La Niña.
Results of a regression analysis between 80-m wind speeds and ΔZ500: (a) data and least squares best-fit line, (b) histogram of residuals, and (c) time series of residuals.
Citation: Journal of Applied Meteorology and Climatology 51, 8; 10.1175/JAMC-D-11-0227.1
Least squares regression analysis coefficient b and model r2 for mean monthly wind speed regressed against ΔZ500 using linear regression (first row) and residuals from that calculation compared against climate indices using multivariate linear regression (last three rows); the value of r2 is given for the entire multivariate regression.
Results of the regression analysis between the mean monthly wind speed and climate indices (Table 2) are similar to those reported by Klink (2007), who observed that the local pressure gradient, which is influenced by climate oscillations, gave the largest correlation to mean monthly wind speed. After the pressure gradient influence (quantified by ΔZ500) is removed from the mean wind speed at 80 m above ground, we also found that the residuals weakly correlate with the sea surface temperature anomaly captured in the Niño-3.4 index.
3. Cluster analysis
Cluster analysis can identify groups in the wind components and assign representative values of wind speed and wind direction to these groups. A wide variety of different methods have been proposed to identify clusters in n-dimensional data; a detailed description of the different methods is beyond the scope of this article, but overviews may be found in Kaufman and Rousseeuw (2005) and Jain et al. (2000).
In this investigation, we applied the k-means clustering approach to the zonal and meridional wind speed at each level. The k-means algorithm is useful to identify discrete, nonoverlapping groups of data and is a commonly available algorithm that has been used to identify clusters in meteorological observations (e.g., Kaufmann and Whiteman 1999). The k-means algorithm splits N data points into k clusters and assumes that data belong to the cluster with the nearest mean value and that the centroid of the group defines the mean (Lloyd 1982; Jain 2010). Clustering is an iterative process that initially generates k random centroids and then optimizes the centroid location to reduce the total variance between the data and the centroids. We repeated the clustering 100 times using random initial centroids to generate an optimum set of centroids that is independent of the initial centroid location. This requires significant computation resources (Wilkin and Huang 2007) but can be applied using commercially available tools. In this study, the clustering was carried out on a standard desktop computer using the “kmeans” function from the “Statistics Toolbox” in Matlab R2010b.
a. Quantifying the solution accuracy
The k-means algorithm requires the user to choose the number of clusters k to use and categorizes data into the selected number of groups. After grouping the data using many different values of k, the user then must select the “best” number of categories to use, on the basis of any preferred criteria. To find a solution that maximizes the information retained (i.e., minimizes variance) but is not overly complex, we quantify the fit of each cluster model using the Bayesian information criterion (BIC). This metric is frequently used to assess the “goodness of fit” of the clustering model to the data (Jain et al. 2000).
We use k means to group the NWTC meridional and zonal wind speeds into a number of clusters. For each number of clusters, we calculate the BIC. The BIC for a range of different numbers of clusters calculated using k means for the data at each height on the tower is shown in Fig. 5, where an inflection point appears at every height at k = 4. This trend indicates that beyond this inflection point the reduction in error is offset by the increase in model complexity (Zhao et al. 2008a,b).
Variation of normalized BIC values with number of clusters when M2 meridional and zonal winds are grouped into k clusters at each height. Data are plotted as [BIC(k) − BIC(k = 1)]/[BIC(k = 20) − BIC(k = 1)].
Citation: Journal of Applied Meteorology and Climatology 51, 8; 10.1175/JAMC-D-11-0227.1
b. Optimum clusters at the NWTC
To objectively identify the optimum solution, we used an automated inflection-point detection routine based on the “angle-based BIC method” (ABIC method) of Zhao et al. (2008a). This routine uses the first and second derivative of the BIC, with increasing k, to identify the point at which an increase in k does not meaningfully add to the solution quality. This approach has been shown to perform well with complex, two-dimensional datasets used in machine-learning applications (Zhao et al. 2008a). At each height, the ABIC algorithm detected an inflection point in the BIC at k = 4, indicating that the optimal solution is 4 clusters (Fig. 5). Although each height was considered separately, cluster centers were found at similar wind speeds and directions at each height. These are listed together with the frequency of winds in each cluster at each height in Table 3. The cluster centers identified using k means agree qualitatively with the frequency peaks seen in the data.
Wind clusters at each height z above ground. Data shown include the mean wind speed and direction for each cluster, f(k) (the relative frequency of that cluster in all data with wind speeds over 3.5 m s−1), and f(obs) (the frequency with which each cluster appears in the data at that height). Calm includes winds below 3.5 m s−1.
The four wind clusters that are seen at all heights are a weak northerly flow (denoted “N” in tables and in Figs. 6 and 7); a weak southerly flow (denoted “S”); a weak westerly [denoted “W(L)”], and a strong westerly [denoted “W(H)”].
Optimal wind clusters at 80 m at the NWTC near Boulder. Labels correspond to those in Table 3 and Fig. 7.
Citation: Journal of Applied Meteorology and Climatology 51, 8; 10.1175/JAMC-D-11-0227.1
Box plot of monthly frequency of different wind clusters at 80 m above ground on the NWTC M2 tower. Panel labels give the wind speed and direction of the cluster centroids (see Table 3). The median for each month is marked with a horizontal line inside the box. Boxes extend to the 25th and 75th percentiles; whiskers extend to ±2.7σ or 99.3% of a normal distribution. Outliers are marked with crosses.
Citation: Journal of Applied Meteorology and Climatology 51, 8; 10.1175/JAMC-D-11-0227.1
Each hourly averaged wind speed and direction observation has been categorized into one of the clusters listed in Table 3. This allows us to create a time series of the occurrence of each cluster. From this time series, we can calculate the annual cycle for each cluster. Figure 7 is a box plot of the number of hours that each cluster occurs for each month of the year. Strong westerly winds are common in the winter months; a shift to north–south winds starts in the spring and is sustained through the summer. The same four clusters emerge at each height above ground, suggesting consistent forcing at all levels.
c. Wind phenomena at the NWTC
The data clustering reveals four main wind phenomena at the NWTC (Fig. 6, Table 3). Westerly winds occur more frequently than the others, and the northerly and southerly winds dominate in the spring and summer months (Fig. 7).
Observations of Colorado Front Range winds in the 1990s showed that some westerly winds at the NWTC are caused by drainage flows through Eldorado Canyon (Banta et al. 1993). This canyon is about 5 km to the west-northwest of the NWTC on an approximate bearing of 292°. During the observations described by Banta et al. (1993), winds were light locally except for those coming from the canyon, which reached 6–8 m s−1 at some hundreds of meters above ground. Sustained westerly or northwest surface winds frequently began in the evenings as the surface cooled and the atmosphere stratified. In the mornings, as the ground warmed, the surface westerly flow was reduced.
Of the two westerly flow structures that have been identified, the weak westerly flow continues to occur during the summer, but at a much-reduced rate. This flow is likely due to a katabatic flow down the slope of the Front Range. The stronger westerly flow occurs more frequently in the winter than in the summer, suggesting that this flow is driven by the jet stream, which moves south over Colorado during the winter but is typically farther north in the summer.
d. Correlations between cluster frequency and climate indices
To correlate the clusters to the climate oscillations, a time series for each cluster was calculated. For each month and each cluster, we calculated the total number of hours of winds that were within that cluster during that month, in the period from January 1996 to December 2011. Each hour could only belong to one cluster. This frequency-data time series of the cluster frequency at each height z, denoted f(z, i), is of the same time resolution as the monthly climate indices. Results of a linear regression between ΔZ500 and the cluster frequencies are given in Table 4.
Results of correlations between cluster monthly frequency and ΔZ500. Data include the least squares regression coefficient b, the p value, and r2. Significance at the 95% level or greater is in boldface type.
To compare the contribution of the local pressure gradient and the climate indices to the changes in frequency of the different clusters, both ΔZ500 and the frequency were converted to standardized departures 
Results of linear multivariate regression between standardized departure of cluster monthly frequency and standardized departure of ΔZ500, AO, PNA, and Niño-3.4. Data include the least squares regression coefficient b, the p value for each variable, and the model r2. Significance at the 95% level or greater is in boldface type.
The climate indices are calculated as standardized departures relative to the mean and standard deviation from 1981 to 2000, and the wind cluster frequency is calculated for the 1996–2010 period. In this respect, data in Table 5 show the change of winds during the period of interest, as compared with variations in the forcing about their long-term means. Because the base periods used for the climate indices do not change, we do not consider this to be an important factor in the analysis.
Comparison of the standardized departure of the frequency of winds in each cluster with the standardized departure of ΔZ500 and the AO, PNA, and Niño-3.4 indices (Table 5) shows that the westerly winds are more highly correlated with the pressure gradient and climate indices (r2 > 0.32) than are the southerly and northerly winds identified by the clustering (r2 < 0.28). A comparison with Table 4 shows that in each case inclusion of the climate indices in the regression increases the percentage of the variance explained. Because the regression in Table 5 was a regression between standardized departures of the frequency of winds in each cluster and standardized departure of the predictors, we can compare the contribution of ΔZ500 and each of the climate indices, indicated by the regression coefficient b.
The strongest contribution to the variation of the frequency of winds in each cluster is ΔZ500, which can be considered to be an aggregation of all climate and weather variability. A statistically significant negative correlation between strong westerly winds and the Niño-3.4 anomaly also emerges. A second strong negative correlation arises between variations in the PNA and winds in the southerly flow sector. The next strongest correlation is a negative correlation between the PNA variation and weak westerly winds, although this is only statistically significant if the criteria for p are relaxed to p ≤ 0.1. By comparison, changes in the winds in the northern sector are only weakly correlated with changes in any of the climate indices that we have included in this analysis. Correlation between the AO and wind frequency does not appear to be statistically significant (p > 0.05), and the contribution to change, quantified by b, is generally small. Although the correlations are not statistically significant, it is worth noting that changes in both the AO and PNA are negatively correlated with the frequency of weaker westerly winds and with larger contribution than changes in the Niño-3.4 index.
e. Regional similarities
The results from this study may be site specific in that the wind climate at the NWTC is dominated by westerly winds coming from the Rocky Mountains, and so the same clusters and their relationship to climate indices would not necessarily be expected at other sites farther away from the mountains or where terrain is different. Some trends evident at the NWTC agree with those of other sites in midwestern North America, however. At the NWTC, El Niño conditions correlate with reduced frequency of flow from the west, as in the southern Canadian Prairies [reported by St. George and Wolfe (2009)]. This reduction in winds may be related to a change in the north–south temperature gradient and the subsequent shift of the winter jet stream to the south during El Niño periods (positive Niño-3.4 anomaly) and away from these areas, or to the north, during La Niña (negative anomaly).
Analysis of data from 70 m above ground in Minnesota by Klink (2007) suggested that during a strong El Niño event in 1997/98 winds in Minnesota showed an anomaly of around −1 m s−1. North–south pressure gradients strongly influenced the Minnesota winds from 1995 to 2003. When ENSO forcing was weak, anomalies in wind speeds correlated with anomalies in the AO. In contrast, at the NWTC, the AO does not appear to be a significant driver of overall wind activity. Together, these data suggest that wind speeds at turbine hub heights are negatively impacted during El Niño events in a region from Texas to the southern Canadian Prairies, although it is not clear whether this affects the whole region or just these particular sites.
4. Conclusions
To delineate the impacts of climate oscillations on wind resources, it is necessary to reduce large wind speed and wind direction datasets. We have used k-means data clustering to identify four types of frequent flow phenomena that occurred at the National Wind Technology Center near Boulder, Colorado, from 1997 to 2010. These phenomena include two flows from the west (high speed and weak), a flow from the south that increases in frequency during the spring and summer months, and a northerly flow that dominates in the summer. The different flow phenomena occur at all heights on the mast and exhibit distinct seasonal and interannual variations.
Comparison of time series of the frequency of winds in each cluster with the local pressure gradient ΔZ500 and the AO, PNA, and Niño-3.4 climate indices shows that the pressure gradient is the dominant term in a regression of the frequency of all of those clusters but that stronger westerly winds are also negatively influenced by El Niño conditions. By comparison, northerly winds are only weakly correlated with the north–south pressure gradient and climate indices, suggesting that these are more locally driven than driven by regional or mesoscale forcing. These observations, made in Colorado, agree qualitatively with observations from Alberta and Saskatchewan (St. George and Wolfe 2009), Minnesota (Klink 2007), and Texas (Oliver 2010), suggesting that El Niño conditions may be important for wind resources across the North American wind corridor.
This method of identifying the most important wind phenomena at a particular location could be extended by including more variables, such as a vertical temperature difference or a Richardson number, so as to include atmospheric stability. Even without the extra data, this technique could aid in estimating the wind resource at a potential wind farm location or for siting wind turbines—for example, by using it to choose objectively the number of inflow cases to simulate using computational fluid dynamics tools (Abiven et al. 2011; Bechmann et al. 2011; Churchfield et al. 2012) or mesoscale modeling. The results of the comparison with climate indices may be useful in understanding variations in wind energy production over short time scales (represented by the PNA and AO) and over longer time periods, as represented by variations in the north–south pressure gradient and Niño-3.4 climate index.
Acknowledgments
The M2 tower data were downloaded from online on 21 September 2011 (http://www.nrel.gov/midc/nwtc_m2/). PNA data were downloaded from online on 21 September 2011 (http://www.cpc.ncep.noaa.gov/products/precip/CWlink/pna/norm.pna.monthly.b5001.current.ascii). The AO data were also downloaded on 21 September 2011 (http://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/monthly.ao.index.b50.current.ascii). NCEP–NCAR reanalysis-derived data were provided by the NOAA/OAR/ESRL PSD in Boulder from their website (http://www.esrl.noaa.gov/psd/). Niño-3.4 data were downloaded on 21 September 2011 (
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