Addendum to “Wind speed trends over the contiguous United States”



[1] An earlier paper (Pryor et al., 2009) reports linear trends for annual percentiles of 10 m wind speeds from across the United States based on ordinary linear regression applied without consideration of temporal autocorrelation. Herein we show significant temporal autocorrelation in annual metrics from approximately half of all surface and upper air wind speed time series and present analyses that indicate at least some fraction of the temporal autocorrelation at the annual time scale may be due to the influence of persistent low-frequency climate modes as manifest in teleconnection indices. Treatment of the temporal autocorrelation slightly reduces the number of stations for which linear trends in10 m wind speeds are deemed significant but does not alter the trend magnitudes relative to those presented by Pryor et al. (2009). Analyses conducted accounting for the autocorrelation indicate 55% of annual 50th percentile 10 m wind speed time series, and 45% of 90th percentile annual 10 m wind speed time series derived from the National Climate Data Center DS3505 data set exhibit significant downward trends over the period 1973–2005. These trends are consistent with previously reported declines in pan evaporation but are not present in 10 m wind speeds from reanalysis products or upper air wind speeds from the radiosonde network.

1. Introduction

[2] An earlier paper [Pryor et al., 2009] reports linear trends in annual 50th and 90th percentile 10 m wind speeds at 0000 and 1200 UTC over approximately 30 years for nearly 1000 measurement time series collected across the continental United States. The data analyzed were drawn from two data sets available from the National Climate Data Center (NCDC): NCDC-6421 [Groisman, 2002] (from which data were selected for 1973–2001) and DS3505 (, DS3505 surface data, global hourly) (from which data were selected for 1973–2005). Data from a given source, station and reporting time were deemed sufficient for analysis if over 300 observations are present in every year of record and more than two thirds of valid observations are available in each climatological season of each year. After computing the yearly summary statistics (i.e., median and 90th percentile wind speed) at a station, Pryor et al. [2009] fitted a regression model on time

equation image

The response yt is the summary statistic (either median or 90th percentile wind speed) at a particular measurement station in year t (t = 1 for year = 1973, until t = n = 33 for year = 2005), and β0, β1 are the regression coefficients with β1 expressing the yearly change (i.e., trend). Assuming independent errors at, Pryor et al. [2009] used ordinary least squares to determine the trend estimate equation image1. Using a bootstrap resampling technique and a confidence level of 90%, they found evidence for a statistically significant reduction in the wind speed percentiles for over half of the stations considered in each of the data sets, sampling times and both percentile values.

[3] Following publication of the aforementioned article it has been suggested that the study may have been biased because it did not address possible temporal autocorrelation in the annual wind speed statistics. This assumption of independence among the errors in model (1) may be incorrect if the regression is carried out on time series data. Positive autocorrelations in the time series lead to a negative bias in the standard error of the usual regression estimate, which implies “spurious” regressions [Box and Newbold, 1971; Granger and Newbold, 1974; Abraham and Ledolter, 2006, chap. 10]. A model that ignores positive autocorrelation is likely to find a significant effect of a regressor variable, despite the fact that no relationship is present. Since annual statistics of wind speeds may exhibit positive autocorrelations, we use the same data time series as Pryor et al. [2009] to address whether either the trend magnitudes and/or trend significance reported in that earlier publication were in error due to temporal autocorrelation in the time series. Specifically, we check whether (1) autocorrelation among the residuals is present, (2) the presence of such autocorrelation led the investigators to conclude too often that the estimated decreases in wind speed are statistically significant, and (3) an analysis that incorporates autocorrelated errors into the model would find different magnitudes for the trend reductions.

[4] We also present analyses focused on (1) determining whether temporal trends evident in the 10 m wind speeds are also evident in direct observations of wind speed at 850 or 700 hPa and how sensitive they are to the specific period of record and (2) providing a first assessment of possible causes of the temporal autocorrelation in annual time series of 50th and 90th percentile wind speeds. For these analyses, twice-daily radiosonde data for 1950–2008 were obtained from the Integrated Global Radiosonde Archive (, and are presented for all stations (23) from which the time series have over 365 data points present in every year of record. The pressure level from which wind speeds were analyzed varies as a function of longitude to account for the higher terrain west of −103°E. Thus data are presented for the 850 hPa level east of −103°E, and the 700 hPa level west of that longitude.

[5] While there is considerable interannual variability in wind climates [Klink, 2002; Petersen et al., 1998], as described herein, there is also substantial temporal autocorrelation. Near-surface wind climates at many midlatitude locations are strongly linked to extratropical cyclone activity and hence are a function of cyclone frequency, intensity or tracking, which in turn are linked to persistent large-scale climatic patterns or regimes as manifest in teleconnection indices [Enloe et al., 2004; Klink, 2007; Schoof and Pryor, 2006]. Thus herein we analyze annual 90th percentile wind speeds in the context of three dominant key teleconnection indices: El Niño–Southern Oscillation (ENSO), North Atlantic Oscillation (NAO) and the Pacific North American (PNA) index.

2. Methods

[6] Instead of the regression model in (1), we base our analyses on the regression model with first-order autoregressive errors,

equation image

where ϕ is the autoregressive parameter and B is the backshift operator commonly used in the time series literature [Box et al., 2008; Abraham and Ledolter, 2005]. The autoregressive model represents a flexible model formulation that ranges from independent errors when ϕ = 0 to nonstationary random walk errors when ϕ = 1. We use the “arima” and “lm” commands in the statistical software package R to estimate the models in equations (1) and (2), and apply them to the original time series of 10 m wind speeds used by Pryor et al. [2009] and upper-level wind speeds from the national radiosonde network.

[7] To provide a first assessment of the degree to which teleconnection indices may dictate the temporal autocorrelation (and inherent variability) in annual wind speed anomalies at different regions of the United States, twice-daily radiosonde derived wind speeds (1950–2008) are used to compute annual 90th percentile wind speed (p90) anomalies which are conditionally sampled on the phase of three key teleconnection indices: El Niño–Southern Oscillation (ENSO) (metric used: SOI computed as the normalized pressure difference from Tahiti and Darwin), North Atlantic Oscillation (NAO) and the Pacific North American (PNA) index (indices from: The regionally averaged p90 anomalies are conditionally sampled for years in the highest and lowest quartile of each teleconnection index, and the results are compared using a t test applied with the assumption of uneven variance.

3. Results

[8] Detailed summaries of our fitting results for the 10 m wind speeds are shown in Tables 1 and 2. In summary, we find the following.

Table 1. Number and Proportion of Time Series That Exhibit Significant Positive Temporal Autocorrelation With Lag = 1 and Significance Level of 0.05a
Data Source_Time of ObservationNumber of Stations50th Percentile90th Percentile
Sig. AR (Number)Sig. AR (%)Sig. AR (Number)Sig. AR (%)
  • a

    The two measurement times are 0000 and 1200 UTC, abbreviated to 00 and 12 here. The presence of significant autocorrelation at lag = 1 is assessed using a test with significance level 0.05 of ϕ = 0 against the alternative ϕ > 0. The two data sets (NCDC 6421 and NCDC DS3505) are described in more detail by Pryor et al. [2009]. Sig. AR, significant positive temporal autocorrelation.

NCDC 6421_0032916148.913340.4
NCDC 6421_1229114349.111639.9
NCDC DS3505_0018810555.97942.0
NCDC DS3505_121689456.06538.7
Overall  503/976 = 51.5 393/976 = 40.3
Table 2. Number of Significant Trends in the Original Analysis and in the Analysis Including Autoregressive Errors for the Annual 50th and 90th Percentile Wind Speedsa
Data Set_Observation TimeMetric Total SampleCoidentified: NegativeCoidentified: PositiveAdditional Negative (Original/AR)Additional Positive (Original/AR)Median Trend Original (%/yr)Median Trend AR (%/yr)Median Trend Original (m s−1/yr)Median Trend AR (m s−1/yr)
  • a

    Original analysis is from Pryor et al. [2009], labeled Original. Analyses including autoregressive errors are labeled AR. The results are shown as the number of time series coidentified in both analyses as exhibiting significant negative or positive trends (Coidentified: Negative and Coidentified: Positive columns), and as the additional numbers that were identified as having significant trends of the specified sign in only one of the analyses (Additional Negative (Original/AR) and Additional Positive (Original/AR) columns). Also shown is the median annual trend magnitude expressed as percentage (%) of the predicted 1972 value and in m s−1/yr from the original analysis (Original) and that conducted including the autoregressive term (AR).

NCDC 6421_00p50 N = 329166937/114/0−0.44−0.45−0.019−0.020
NCDC 6421_12p50 N = 291169927/13/1−0.58−0.59−0.019−0.021
NCDC DS350_00p50 N = 188911622/14/0−0.25−0.25−0.010−0.010
NCDC DS350_12p50 N = 16890621/17/0−0.28−0.27−0.013−0.012
NCDC 6421_00p90 N = 3291951033/23/1−0.39−0.38−0.030−0.030
NCDC 6421_12p90 N = 291191820/14/0−0.47−0.48−0.031−0.032
NCDC DS350_00p90 N = 18884910/07/0−0.16−0.16−0.012−0.012
NCDC DS350_12p90 N = 1687559/13/0−0.18−0.17−0.013−0.014

[9] 1. Approximately half of the (observationally derived) data time series analyzed by Pryor et al. [2009] exhibit temporal autocorrelation based on a test of ϕ = 0 against the alternative ϕ > 0 (Table 1). At a significance level (α) of 0.05, between 39 and 56% of the time series of annual median and 90th percentile wind speed from the two data sets and two data observing times exhibit significant positive autocorrelation. Similarly, nearly half of upper-level wind speed time series from the radiosonde network also exhibit positive autocorrelation at α = 0.05.

[10] 2. While Pryor et al. [2009] overreport the significance of the temporal trends, the difference in the numbers of stations with significant negative trends between the regression model in (1) and the regression model with autoregressive errors in (2) is small (Table 2). Summed over both data sets, the difference amounts to 10.6% for the regressions of annual median (calculated from [(37 − 1) + (27 − 1) + (22 − 1) + (21 − 1)]/976), and 7.0% for regressions of annual 90th percentile wind speed. In the analysis conducted including an autoregressive term, 55% of all time series exhibit declines in the 50th and 90th percentile annual wind speeds for both the 0000 and 1200 UTC observation times (Table 2).

[11] 3. We find that the conclusions presented by Pryor et al. [2009] regarding the magnitude of annual trend reductions and annual percent trend reductions are not affected by the autocorrelation. The median value of annual trends in wind speeds, expressed either in m s−1 or as percentage of the predicted 1972 value [100(equation image)], are essentially the same in the regression analysis applied with and without inclusion of the autoregressive term (Table 2).

[12] As in the results published by Pryor et al. [2009], the linear trend magnitudes are generally larger in data drawn from the NCDC 6421 data set (on average by a factor of 2) and a larger fraction of the time series from this data set exhibit statistically significant declines at the 90% confidence level (Table 2). These differences appear to be linked to data treatment post collection including application of corrections for measurement height and station moves (see Pryor et al. [2009] for details). As in the earlier publication, while declines computed accounting for the temporal autocorrelation are manifest at stations distributed across the United States, they are not spatially uniform. To assist in visualizing this spatial variability, in Figure 1 we present regional summaries of the trend magnitudes derived using the NCDC DS3505 data set for both percentile levels and observation times. The regions used in Figure 1 broadly represent the six regions used in the national assessment, and although it should be noted that no spatial weighting has been applied to account for variations in the geographic distribution of stations, this summary emphasizes that trends in the 50th percentile wind speeds are typically larger in all regions than the 90th percentile wind speed and that there is little variation in trend magnitude with observation time. Furthermore this summary indicates that when the trends are averaged over all stations within each region, trends in the 50th percentile wind speeds range from −0.31%/yr in the northeast to −0.09%/yr in the west. The regionally averaged trend in the 90th percentile wind speed ranges from −0.25%/yr in the Midwest to +0.01%/yr in the west. Thus, contrary to the other regions, the median trend in the annual 90th percentile wind speed averaged across all stations in the West is slightly positive. Similar regional variability is also reflected in analyses of data from across Australia. While approximately 88% of the continental surface experienced reductions in wind speeds over the period 1975–2006, there were also distinct areas where near-surface wind speeds exhibited increases over this period [McVicar et al., 2008].

Figure 1.

Regional synthesis of temporal trends in the annual median (p50) and 90th percentile (p90) wind speeds from the NCDC DS3505 data set for the 0000 and 1200 UTC observation times (shown as (00) and (12) in the box plots). The box plots are the synthesis of trends computed for all stations within the six regions: Pacific Northwest, west, Central Plains, Midwest, Northeast, and Southeast (the numbers in the title of each frame indicate the number of stations in each region). The horizontal bar in the center of the box plots shows the median value of the annual trend (in %/yr) and the upper and lower bars on the box show the 25th and 75th percentile values, while the vertical bars extend from the minimum to the maximum values.

[13] As described in more detail below, time series of near-surface measurements of wind speed are subject to inhomogeneities that may be manifest as temporal trends but have no origin in climate system nonstationarity. Where the inhomogeneities derive from changes in land cover (and hence roughness, or changed surface energy balance) around the station [Ozdogan et al., 2006], the station fetch, or the instrumentation, these inhomogeneities may lead to inconsistencies between tendencies computed from surface stations and those derived from reanalysis data sets or upper air observations. To examine this further in the context of wind speeds over the contiguous United States, wind speed data from the twice daily radiosonde releases (1950–2008) were subject to trend analyses as for the 10 m wind speeds. The results indicate that consistent with the reanalysis data sets presented by Pryor et al. [2009], radiosonde derived 50th and 90th percentile wind speeds at 850 hPa (east of −103°E, i.e., approximately the Rocky Mountains) and 700 hPa (west of −103°E) generally do not exhibit significant temporal trends for over the 1950–2008 period and that in the 1973–2005 time frame, 50th percentile upper-level wind speeds generally increased (Figure 2). Twelve of 23 stations exhibit significant positive trends in 50th percentile annual wind speeds (1973–2005) when the regression model is applied with autoregressive errors in (2) (Figure 2). This is consistent with analyses of 10 m winds from the NCEP reanalysis data set [Kalnay et al., 1996] for 1973–2005 which also implies increases in 50th percentile wind speeds over much of the contiguous United States. However, unlike the 10 m wind speeds from the NCEP reanalysis data set presented by Pryor et al. [2009], the radiosonde wind speeds at 850 or 700 hPa do not imply positive tendencies in the 90th percentile wind speeds.

Figure 2.

Temporal trends in annual 50th and 90th percentile radiosonde wind speeds for (a, b) 1950–2008 and (c, d) 1973–2005. The data were derived from the 700 hPa level at sites west of −103°E and at 850 hPa east of that longitude. As in the analysis of the 10 m wind speeds, the regression analysis is undertaken accounting for first-order temporal autocorrelation. Stations with significant trends at the 90% confidence level are shown by solid blue circles (for declines) and solid red circles (for increases), with the diameter of the circle representing the square root of the annual percentage change. Stations with insignificant trends are indicated by pluses.

[14] The climate system exhibits temporal autocorrelation on multiple time scales. Nearly half of the annual time series of 10 m and upper-level wind speeds exhibit significant autocorrelation for lag = 1. As shown in Table 1, the temporal autocorrelation is generally larger in the time series of 50th percentile wind speeds. At least a partial explanation for this is as follows: Let us denote the true deviation of the annual wind speed in year t from its long-term average by μt and consider a first-order autoregressive model for its time progression, μt = ϕμt−1 + ɛt, with innovations ɛt (with variance σɛ2) expressing the amount of yearly change. The median (or the 90th percentile) of the daily measurements is used as an estimate of μt. The measured annual statistic yt = μt + nt incorporates an independent measurement error nt (with variance σn2). Extremes and 90th percentiles are more variable than medians; hence the variance σn2 of a 90th percentile is larger than the variance of a median. Using these “noisy” measurements to estimate the autoregressive parameter, the least squares estimate converges to

equation image

Large uncertainty in the measurements (large σn2) diminishes the estimate of the autoregressive parameter ϕ. This explains why we see fewer significant autoregressive estimates for 90th percentiles and why the median estimate of ϕ for 90th percentiles (average median is 0.25 when averaged over the four data sets of 10 m wind speeds) is smaller than the median estimate of ϕ for medians (average median = 0.32).

[15] Results of conditional sampling of annual wind speed anomalies on the phase and magnitude of three teleconnection indices implies they may indeed be a significant source of the temporal autocorrelation. Consistent with prior research, in all regions at least one teleconnection index exhibits explanatory power of the upper air p90 anomalies (Figure 3). The regional dependencies on the teleconnection indices are physically intuitive; in the three northern regions the PNA exerts greatest influence: with a more zonal pattern (negative PNA) being associated with highest wind anomalies, for the west and southeast the SOI exhibits the greatest influence, while in the northeast the NAO is the dominant teleconnection in terms of explanation of 90th percentile wind speeds.

Figure 3.

Box plots showing the dependence of regionally averaged annual 90th percentile wind speed anomaly (deviation from the mean p90 computed for 1950–2008) on the phase of three teleconnection indices. The horizontal bar in the center of the box plots shows the median value of the p90 anomaly and the upper and lower bars on the box show the 25th and 75th percentile values, while the vertical bars extend from the minimum to the maximum values. The text above the abscissa indicates the index under consideration and whether the mean values of p90 anomaly differed for the phase of that teleconnection index (Low versus High) according to the t test along with the confidence level (CL) at which the mean p90 anomaly differed. The numbers reported in the frame titles denotes the number of radiosonde stations from which data are used in each region. The radiosonde release locations are shown by the large black squares in the central map.

4. Discussion

[16] Data analyses presented herein demonstrate that treatment of temporal autocorrelation slightly reduces the number of stations for which the linear trends in 10 m wind speed percentiles are deemed significant (at the 90% confidence level) but does not alter the trend magnitudes relative to those presented by Pryor et al. [2009]. The finding from this addendum suggests that the magnitudes of the wind speed trends reported in other studies using ordinary linear regression [e.g., Brázdil et al., 2009; Jiang et al., 2010; McVicar et al., 2008; Roderick et al., 2007] may also be relatively insensitive to (untreated) temporal autocorrelation.

[17] These analyses reaffirm the presence of negative trends in observed near-surface (10 m) wind speeds over the periods 1973–2001 and 1973–2005, which is consistent with analyses which indicate recent declines in pan evaporation over the continental United States [Fu et al., 2009; Hobbins et al., 2004; Lawrimore and Peterson, 2000]. However, it is important to reiterate some of the caveats articulated in the article by Pryor et al. [2009], particularly in light of misreporting of that research in other subsequent publications:

[18] 1. While the two observational data sets both exhibit a dominance of trends toward declining values of the 50th and 90th percentile and annual mean wind speeds over the period 1973–2001 or 1973–2005, even in the observational time series presented herein, in all regions at least some of the station time series exhibit positive trends (Figure 1). Additionally, opposite trends (i.e., increases with time) are seen in output from the North American Regional Reanalysis (for 1979–2006), global reanalysis data sets (NCEP/NCAR (1973–2005) and ERA-40 (1973–2001)) and a Regional Climate Model applied within the NCEP-DoE reanalysis for 1979–2004 [Pryor et al. 2009], and in time series of upper-level wind speeds for the 1973–2005 period (Figure 2). These discrepancies, coupled with high interannual variability and multiple periodicities in wind speeds [Pryor and Barthelmie, 2010], imply that it would be premature to assert any long-term tendency in wind speeds or wind energy density over the continental United States.

[19] 2. There is no evidence to suggest that temporal trends manifest over the study period (1973–2001 or 1973–2005) will continue into the future. The short duration of the time series precludes analysis of nonlinear trends; thus development of high-resolution, high-fidelity records with extended temporal coverage should be a matter of high priority.

[20] 3. Despite careful treatment of the observational data sets included in the prior analysis by Pryor et al. [2009] and herein, it is critical to recall that observed wind speed time series are subject to numerous sources of discontinuities including, but not limited to, unreported station moves, anemometer height changes, degradation of anemometer performance due to incorrect or poor maintenance, instrument malfunction, changes in land use around the instrument leading to increased surface roughness or sheltering. Such influences may be manifest as temporal trends that have no origin in climate system nonstationarity and may be the cause of the discrepancies between trends computed using radiosonde wind speeds (see Figure 2) and reanalysis products and those calculated for the 10 m wind speeds (Figure 1). Additionally, the coarse data resolution of the wind speed records (1 knot, or 0.51 m s−1), incomplete data series and high temporal variability confounds trend identification.

[21] The data analysis presented herein demonstrates that treatment of data temporal autocorrelation slightly reduces the number of stations for which the linear trends in wind speed are deemed significant (at the 90% confidence level) but does not alter the trend magnitudes relative to those presented by Pryor et al. [2009]. Our analysis corroborates the conclusions in Pryor et al. [2009] and shows that their findings are robust toward misspecifications in the autocorrelations of the errors.


[22] S.C.P. acknowledges financial support from the National Science Foundation (grants 0618364 and 0828655). Some of the analyses presented were conducted using the R data processing and analysis language, which is freely available at Comments of three anonymous reviewers are appreciated.