Herein we present model-based analyses of the IAV in mean wind speeds, WI and estimated AEP using simulations performed with WRF applied at 12 km resolution over the domain shown in Fig. 2a. The domain is extended to the west of the region with the highest numbers of deployed WTs (i.e., the Central Plains) to avoid collocation of the lateral boundaries with a region of strong surface forcing (i.e., the Rocky Mountains). Default settings as specified in the WRF user guide for v3.8 (available at: http://www2.mmm.ucar.edu/wrf/users/docs/user_guide_V3.8/ARWUsersGuideV3.8.pdf, last access: 4 June 2018) are used for the boundary properties (i.e., five cells are added for boundary value nudging, four of which are in the relaxation zone). Further, a buffer zone comprising 19 grid cells along all four edges of the domain are removed from the simulation output (i.e., used as an adjustment zone to the LBC) prior to the analyses conducted herein. Lateral boundary conditions (LBCs) for these simulations are supplied every 6 h from the ERA-Interim reanalysis data (Dee et al., 2011). The NOAA real-time global sea surface temperature (RTG-SST) data set (Gemmill et al., 2007) is used to provide initial SST and Great Lakes conditions and are updated every 24 h. Data from the 30 arcsec Global Multi-resolution Terrain Elevation Data 2010 (GMTED) (Danielson and Gesch, 2011) are used to describe the topography and, for consistency with our use of the Noah land surface scheme, land cover is described using the Noah-modified 21-category IGBP-MODIS land use data set (Friedl et al., 2010).

The time step used for the simulations is 72 s, and there are 41 vertical levels (in sigma hydrostatic pressure coordinate) up to a model top at 50 hPa. A total of 18 of those levels are below 1 km and the lowest 10 levels represent approximate heights (in flat terrain) of 16.7, 50.1, 83.6, 117, 151, 184, 218, 253, 293 and 338 m a.g.l. Wind speeds used herein are derived from the third model layer that represents a height above the ground in flat terrain at mean sea level of approximately 83 m. Variations in the actual height above the local terrain of this layer (Fig. 2b) arise primarily due to topographic variability such as the very high and steep complex terrain of the Rocky Mountains in the west of the simulation domain (where the sigma levels are compressed near the surface). The following physics schemes are employed. Numbering is as in the WRF namelist file.

Longwave radiation: 1. rapid radiative transfer model (RRTM; Mlawer et al., 1997)

Multiple factors impact the IAV of net AEP from operating wind farms, including but not limited to curtailment for system operation and/or WT maintenance (Clifton et al., 2016), WT wake losses (Clifton et al., 2016; Barthelmie et al., 2013) and wind speed variability. Here we focus on this last factor.

Annual mean wind speeds are computed for each grid cell as the arithmetic mean of all 10 min output from the third model layer in each model grid cell. Wind indices (WIs) are computed by applying Eq. (1) to the same WRF output and using a reference time period of 2002–2016. The USGS database of the locations and types of all WTs deployed in the continental USA as of March 2018 indicates that 57 636 WTs were installed in the contiguous USA, of which three-quarters fall within the simulation domain (see Fig. 2a for the locations). The most common WT is a variant of the GE 1.5 SLE that has a hub height (HH) of 80 m, a rotor diameter (D) of 77 m and a rated capacity (RC) of 1.5 MW. Thus, WRF output is post-processed to generate a first-order estimate of AEP in each grid cell by assuming there is a single WT deployed in the center of each WRF grid cell and applying the power curve of a GE 1.5 SLE (Fig. 1) to 10 min wind speeds from the third model level.

Output from three example grid cells (located in Texas (TX), Iowa (IA) and New York state (NY); see Fig. 2a) is used throughout to provide illustrative examples of the simulated wind climate. Time series of 10 min output from the third model layer for each calendar year in these grid cells are fitted to Weibull distributions using maximum likelihood methods (Pryor et al., 2004) wherein the probability of a wind speed of a given magnitude is given by pU|A,k=kAUAk-1exp⁡-UAk, where A is the scale parameter and k is the shape parameter.

The results are used to demonstrate the year-to-year variability in the probability distribution parameters. These time series from each calendar year are also used with the power curve from the GE 1.5 MW WT to generate empirical estimates of the contribution of wind speed bins to the overall estimated power production in each year. Output from these grid cells over the entire period from 1 January 2002 to 31 December 2016 is also used to illustrate the temporal scales of variability in the entire sample using fast Fourier transform (FFT) applied to compute the variance across a range of frequencies and to present power spectra in the range f≈1×10-3 to 50 day-1. Lastly, time series from these grid cells are also used to consider the question “how long is long enough?” In other words, what duration of time series is sufficient to characterize the overall annual mean wind speed and AEP with a certain level of confidence? Time series of the annual mean wind speed and AEP from the three grid cells highlighted in Fig. 2a (TX, IA and NY) are subject to a bootstrap analysis (Wilks, 2011) in which the annual mean wind speed and AEP estimates are resampled (with replacement) to generate a synthetic resampled data set of 1000 samples. These are used to compute an estimate of 95 % confidence intervals on the long-term mean wind speed AEP and identify the calendar years that differ most profoundly from the bootstrapped mean values in those three locations (Table 2).

Although it is common practice to describe the IAV of annual wind speeds using a standard deviation around the mean, the assumption that the samples of annual mean wind speed conform to a Gaussian distribution is not always evaluated. The distributions of the 15 values of annual mean wind speed, WI and AEP from each grid cell considered herein are not normally distributed, rendering the mean and standard deviation poor descriptors of both the central tendency and the dispersion around the central tendency. Indeed, the samples of 15 annual mean wind speed and AEP estimates fail the Anderson–Darling test for normalcy (Wilks, 2011) in 97.7 % and 96.3 % of grid cells (for a 95 % confidence level). Thus, herein we describe the central tendency using the median value (P50) and use the interquartile range (IQR; i.e., 25th to 75th percentile range) to describe the dispersion. We also derive estimates of the 90 % intervals around the median annual mean wind speed and AEP (i.e., the range within which 9 out of 10 years are expected to fall), but emphasize that these are based on a very small sample size (of 15) and thus are subject to relatively large uncertainty. They are presented solely to permit comparison with 90 % intervals around the mean computed using 1.645σ (for normally distributed variables; Wilks, 2011) applied to past literature that has stated variability in terms of the standard deviation around the mean (Table 1).

P50(AEP) and P90(AEP) are computed for individual calendar years and for rolling consecutive 12-month periods. In the former, 10 min output wind speeds from all grid cells for each of the 15 full calendar years (i.e., 2002, 2003 etc.) are subject to the WT power curve and used to compute AEP for each calendar year. In the latter, 10 min output wind speeds from all grid cells for rolling 12-month periods (i.e., March 2001 to February 2002, April 2001 to March 2002) are subject to the WT power curve and used to compute AEP for all consecutive 12-month periods. Output from the rolling 12-month periods is used to identify the 12-month period with the highest and lowest AEP, and those values are evaluated spatially to examine the degree to which that time index and hence the timing of periods with the highest and lowest AEP are spatially coherent. The results are considered in the context of monthly indices of the phase of three important internal climate modes that have previously been shown to influence the intra-annual and interannual variability of wind speeds over the USA (Schoof and Pryor, 2014; Pryor and Ledolter, 2010): the Pacific North American (PNA) (Leathers et al., 1991), North Atlantic Oscillation (NAO) (Hurrell et al., 2003) and Niño Oceanic Index (ONI), which is a 3-month running mean of sea surface temperature anomalies in the Niño 3.4 region (Ren and Jin, 2011).

The mean gross capacity factor (CF) for each grid cell is computed as the amount of electrical power produced in each calendar year by applying the power curve for the GE 1.5 MW machine to output from each 10 min period and comparing the result to the maximum possible as determined by the rated capacity (1.5 MW) multiplied by the number of hours in a year.

The 1612 of the 281×281 (i.e., 78 961) total grid cells (with adjustment zone removed) that contain operating WTs as of March 2018 are the primary focus of the analyses presented herein (and are referred to as WT grids). Results are also compared to output from the other grid cells (without WTs, referred to herein as “no”) to determine whether areas that currently have WTs deployed in them exhibit higher or lower interannual variability than typifies the study domain.

There are a number of “bottlenecks” to improved estimation of IAV in mean wind speeds at WT relevant heights and in AEP from WTs. These include the lack of publicly accessible high-accuracy data at WT relevant heights and high temporal resolution for the evaluation of numerical simulations such as those presented herein (Kusiak, 2016). The National Weather Service (NWS) operates over 900 stations where wind speeds are measured at a height of 10 m a.g.l., but these data are not at or close to WT hub heights and the actual vertical profile of wind speed is strongly dependent on stability, making vertical extrapolation highly uncertain (Badger et al., 2016; Barthelmie et al., 1993; Motta et al., 2005). Additionally, wind speeds as measured by 2-D sonic anemometers at NWS stations are recorded at a resolution of 1 knot (0.514 ms-1) rounded up to the nearest knot when they are archived. The resulting sample is thus systematically biased and pseudo-categorical. Further, in terms of model validation, local topography and obstacles greatly impact near-surface observations of wind speeds, which makes comparison with grid cell mean values as derived from a numerical model challenging. For these and other reasons, herein we contextualize the results of our numerical simulations using observationally derived estimates of the IAV of annual net power production from operating wind farms. Power production data for nearly 1000 operating wind farms as obtained from the US Energy Information Administration (EIA) (downloaded from https://www.eia.gov/electricity/data/eia923/, last access: 4 June 2018) are used to estimate monthly capacity factors for each calendar month; January 2001 to December 2016. Sites with ≥9 years of data with ≥9 months of data availability in each year are used to compute the median annual mean net CF and the normalized IAV therein as represented by the interquartile range of annual net CF divided by the median net CF (IQR(CF) / P50(CF)). A total of 68 sites meet this data completeness criterion. It is important to note that the application of these selection criteria is necessary to ensure that the resulting IQRs in CF estimates are robust, but it biases the resulting sample in two important ways: the overwhelming majority of these wind farms are located in the Central Plains (Fig. 3b) and they tend to represent older-generation wind farms in which WTs may no longer be under warranty and may experience declining performance (Olauson et al., 2017), potentially leading to inflation of the IAV(CF).

Median annual mean wind speeds from the third model level exhibit the expected spatial variability with the highest wind speeds over the Central Plains and in a swath across the upper Midwest into the northeastern states (Fig. 3a). This is consistent with the placement of WTs in the domain (Fig. 2a) and previous resource assessments (Pryor and Barthelmie, 2011; U.S. Department of Energy, 2015; Clifton et al., 2018). Annual gross capacity factors (CFs) for grid cells with WTs currently deployed in them (WT grid) as derived from the approximations used herein are also consistent with direct observations. The median gross CF computed herein is 40.4 % (Fig. 3d), which is higher than the net CF derived from the 68 operating wind farms (shown in Fig. 3c) of 36 % and slightly lower than the value of 42.5 % for WT installations commissioned in 2016 (Wiser and Bolinger, 2017). The median gross CF computed herein for WT grids is higher than the observed net CF from the 68 operating wind farms because the net CF also incorporates reductions in power production due to WT maintenance activities, wind turbine wake effects and curtailment for grid management. Observed levels of curtailment over much of the study domain considered herein were ≤4 % during 2007–2012 (Bird et al., 2014). Wind power plant efficiency reductions due to wind turbine wakes are known to be smaller in onshore wind farms than those offshore due to the irregular layouts, higher ambient turbulence intensity and the typically smaller wind turbine densities. Typical wind-turbine-induced wakes losses for onshore wind farms are often estimated to be ≤5 % (Staid et al., 2018), while those offshore are frequently in excess of 10 % (Barthelmie et al., 2013). Onshore availability typically exceeds 98 % (Carroll et al., 2017), but tends to decrease with WT age (Olauson et al., 2017). Thus gross CF derived from the WRF simulations that assume 100 % WT availability (i.e., no downtime for maintenance or curtailment of production) and no wake losses is inevitably higher than the observed values derived from wind farms that have been in operation for more than 10 years. The estimated median CFs derived herein are lower than observed values for new WT deployments in 2016 because the newer WTs that are currently being installed have higher WT hub heights and larger rotors and RCs than the GE 1.5 MW WT applied herein.

Output for each calendar year from the three grid cells (in Texas (TX), Iowa (IA) and New York (NY); see Fig. 2a for locations) conforms to two-parameter Weibull distributions as indicated by narrow 95 % confidence intervals around the distribution parameters and also illustrate relatively high consistency across the calendar years (Fig. 4a). The fraction of power production from each wind speed bin (also plotted in Fig. 4a) highlights the fact that the variability of the tail of the wind speed distribution dominates IAV in power production rather than values below the annual mean. Indeed, wind speeds in excess of the annual mean contribute an average of 69 %, 66 % and 57 % of the estimated annual total power production in these grid cells from TX, IA and NY. This emphasizes important potential disconnects between the variability of the annual mean wind speed and AEP. The bootstrapped estimate of the annual mean wind speed (and 95 % confidence intervals based thereon) in the illustrative grid cells from TX, IA and NY state fall at a place on the power curve that is relatively close to the wind speed at which the GE 1.5 MW WT generates rated power (i.e., the power output ceases to increase with increasing wind speeds). This implies that small changes in annual mean wind speeds may not greatly impact the cumulative power output.

Analyses of time series of 10 min output from these three grid cells in the frequency domain indicate that in all of these grid cells the variance is dominated by the meso-α to synoptic timescale (f≈0.2–0.5 day-1, thus periods of 2–5 days) (Fig. 4b). There is also a clear diurnal peak, particularly in IA and NY, while in TX this local maximum is displaced to periods slightly shorter than 1 day. Power spectra derived from output from all three grid cells also exhibit maxima in the frequency range 2 to 5×10-3 day-1 (i.e., on annual timescales). This timescale exhibits the greatest magnitude of variance in the grid cell from New York state and is of lowest magnitude in Iowa. Variability across all these timescales contributes to the variations in power output from WTs, the resulting AEP, and thus both P50(AEP) and P90(AEP). Although the power spectra of wind speeds exhibit a height dependence in the planetary boundary layer and due to the parameterizations used mesoscale model simulations are deficit in high-frequency variability (Larsén et al., 2012, 2016), Fig. 4b further reemphasizes the motivation for this research. As shown, the variance at virtually all frequencies considered herein is highest in output from the NY grid cell. This inevitably leads to the question of whether the use of a constant factor to represent IAV (as in work that has used σ=6 %) on annual mean wind speeds and/or AEP is appropriate everywhere.

The normalized IQR of annual mean wind speeds (IQR(WS) / P50(WS)) is <4 % in nearly 60 % of WT grid cells, <5 % in 83 % of WT grid cells and <6 % in 96 % of WT grid cells (Fig. 3b and c; see summary in Table 1). Recall that a large IQR(X) / P50(X) indicates a site or area with high IAV in parameter X. Thus, this analysis indicates that in 5 out of 10 years the annual mean wind speed will fall within ±4 % of the long-term average in 90 % of the simulation grid cells that contain operating wind turbines. The estimated 90 % confidence interval around the median annual mean wind speed (i.e., 5th to 95th percentile span in values divided by the median, P50) is <8 % in half of all WT grid cells and <11 % in 90 % of WT grid cells. Thus, this implies that in 9 out of 10 years the annual mean wind speed is expected to fall within ±5.5 % of the long-term average in 90 % of the simulation grid cells that contain currently operating wind turbines. Comparative estimates of the range of expected annual mean wind speeds derived assuming a Gaussian distribution and σ of 6 % are considerably larger. They yield 90 % confidence intervals around of mean that span 19 % (i.e., in 9 out of 10 years the annual mean wind speed is expected to fall within ±10 % of the long-term average). Several grid cells in the Southern Great Plains indicate higher IQR(WS) / P50(WS) than the median value of 3.8 %. However, the lowest 50 % of IQR(WS) / P50(WS) of annual mean wind speeds in WT cells is lower than in grid cells without WTs. This indicates that, on average, the locations at which WTs are currently operating are characterized by lower IAV in wind speeds than typifies the eastern half of North America.

The spatial mean P90(AEP) from WT grid cells is 5157 MWhyr-1, while P50(AEP) is 5323 MWhyr-1 (Figs. 5c, d and 6). Comparable figures from grid cells that do not contain the locations of currently operating WTs (i.e., no WT grid) are 4893 and 5078 MWhyr-1, indicating that WTs are deployed in locations that have atypically high wind speeds and projected AEP.

WIs (computed using Eq. 1) naturally exhibit larger normalized IQR than annual mean wind speeds (cf. Figs. 5a and 3b). Normalized IQR of WI (IQR(WI) / P50(WI)) is <11 % in 60 % of WT grid cells, <14 % in 83 % of WT grid cells and <15 % in 95 % of WT grid cells (Fig. 5b; see summary in Table 1). However, a similar inflation of IAV is not anticipated for AEP because of the nature of wind turbine power curves (see example in Fig. 1). This expectation is realized within the estimated AEP values. The spatial median value of normalized IQR of AEP (i.e., IQR(AEP) / P50(AEP)) is 3.4 %, and thus half of all years are estimated to fall within ±3.4 % of the median (P50) AEP for half of all WT grid cells. The 90 % confidence interval tentatively derived as the 5th to 95th percentile of annual median AEP in each grid cell indicates that WT grid cells range from 5.0 % to 13.5 % with a median of 7.9 %. Thus, in half of all simulation grid cells that cover areas where WTs are currently operating, in 9 out of 10 years AEP is expected to fall within ±4 % of the long-term average (Table 1). Comparative estimates of the range of expected AEP derived assuming a Gaussian distribution and σ of 6 % are considerably larger and yield 90 % confidence intervals around the mean that span 19 % (i.e., in 9 out of 10 years the AEP is expected to fall within ±10 % of the long-term average). Thus, it would appear that assuming a standard deviation (σ) of 6 % for the climate-induced interannual variability in AEP is conservative and potentially could be reduced. Under the assumption that the WTs deployed are GE 1.5 SLE and that they are harvesting wind speeds at a height equal to the third model layer, the normalized difference between P90(AEP) and P50(AEP) in WT grid cells is <3.1 % in 50 % of grid cells and is below 4.6 % in 90 % of WT grid cells (Figs. 5c and d and 6c). Indeed, only 1 % of WT grid cells exhibit values in excess of 6.4 %.

The mean normalized IQR of gross AEP as derived using output from the WRF simulations and the GE 1.5 MW power curve for grid cells containing the 68 operating wind farms considered herein is 3.5 % (Fig. 6d). The normalized IQR of net CF derived from power production data at these wind farms ranges from 3 % to 18 % and has a median value of 9 % (Fig. 6e). Thus, the power production data from these operating wind farms indicate that in half of them the production during half of all years lies within <±9 % of the long-term average (see summary in Table 1). Our simulations imply that the climate-induced variability at these locations is likely to mean that AEP in half of all years should lie within ±2 % of the long-term average, with the remaining variability being derived from other factors such as performance deductions due to WT aging, curtailment and maintenance. These estimates are tentative because the power production data sets are of short duration and contain missing data, and the model simulations are also only 15 years in duration and make a number of assumptions (including the use of a single WT power curve). Nevertheless this analysis highlights the need for further studies designed to decompose the IAV of AEP into the root causes of wind climate variability, curtailment, WT availability and WT performance degradation with age.

Understanding the spatial scales of coherence at which wind speed variability on different timescales is manifest is important to the integration of wind-energy-generated electricity into the grid. Over much of the US, the variability of wind speeds on seasonal to interannual timescales is determined by the frequency and tracking of midlatitude cyclones as dictated by the phase of internal climate modes (Schoof and Pryor, 2014). The timing of the occurrence of the rolling 12-month period of minimum and maximum AEP as computed from the WRF simulations exhibits relatively complex spatial patterns (Fig. 7). This indicates that at least at the annual scale, the geographic dispersal of wind turbine deployments is such that it extends beyond regions of high coherence in gross AEP. However, there are also regions of coherence consistent with the importance of large-scale climate modes in dictating wind speed anomalies over the contiguous USA (Schoof and Pryor, 2014). Minimum AEP over the upper Midwest (i.e., over Minnesota, Michigan, Illinois, Indiana and Ohio) occurred during 2011 (and early 2012; Fig. 7a) during a weak La Niña period (i.e., negative ONI; see Fig. 7c), while in the lower Central Plains (Fig. 7a) the timing of this minimum was more strongly focused on 2015–2016 during a relatively strong El Niño event (i.e., positive ONI; Fig. 7c). Conversely, the upper Central Great Plains and parts of the southeast exhibit the lowest values for a 12-month period starting in mid-2008 (during a weak la Niña, Fig. 7). The timing of maximum AEP is also consistent across the upper Midwest states and is focused on 2007 (Fig. 7b). Much of the Central Plains indicate maximum AEP for a period centered on 2011, while estimated AEP in the northeastern states is highest close to the start of the simulation period in 2001–2002. Analysis of the years that differ most from the bootstrapped mean AEP from the three sample grid cells (IA, TX and NY; see Table 2) reemphasizes the findings of the analysis presented in Fig. 7. Both indicate that different regions within the eastern USA differ in terms of 12-month period that has the lowest AEP and thus when viewed system-wide (i.e., spatially) there are important compensating variations in the wind climate and derived AEP. For example, although 2010 is indicated as a year of relatively low electricity production in Iowa, it is associated with higher than average AEP from WTs in New York state. Figure 7 further illustrates that the IAV of AEP (and wind speeds) and the occurrence of higher than normal values is a complex function of the state of multiple climate modes (Schoof and Pryor, 2014). For example, late 2006 saw a weak positive ONI and positive PNA and NAO and was associated with relatively high AEP over much of the Midwest, but late 2009 when ONI was also positive but NAO was negative and PNA was closest to zero was not associated with high estimated AEP over the Midwest.