Skillful seasonal prediction of wind energy resources in the contiguous United States

A key challenge with the wind energy utilization is that winds, and thus wind power, are highly variable on seasonal to interannual timescales because of atmospheric variability. There is a growing need of skillful seasonal wind energy prediction for energy system planning and operation. Here we demonstrate model ’ s capability in producing skillful seasonal wind energy prediction over the U.S. Great Plains during peak energy seasons (winter and spring), using seasonal prediction products from a climate model. The dominant source of that skillful prediction mainly comes from year-to-year variations of El Niño-Southern Oscillation in the tropical Paci ﬁ c, which alters large-scale wind and storm track patterns over the United States. In the Southern Great Plains, the model can predict strong year-to-year wind energy changes with high skill multiple months in advance. Thus, this seasonal wind energy prediction capability offers potential bene ﬁ ts for optimizing wind energy utilization during peak energy production seasons.

A key challenge with the wind energy utilization is that winds, and thus wind power, are highly variable on seasonal to interannual timescales because of atmospheric variability.There is a growing need of skillful seasonal wind energy prediction for energy system planning and operation.Here we demonstrate model's capability in producing skillful seasonal wind energy prediction over the U.S. Great Plains during peak energy seasons (winter and spring), using seasonal prediction products from a climate model.The dominant source of that skillful prediction mainly comes from year-to-year variations of El Niño-Southern Oscillation in the tropical Pacific, which alters large-scale wind and storm track patterns over the United States.In the Southern Great Plains, the model can predict strong year-to-year wind energy changes with high skill multiple months in advance.Thus, this seasonal wind energy prediction capability offers potential benefits for optimizing wind energy utilization during peak energy production seasons.
Wind energy provides a renewable and clean energy source that does not directly produce greenhouse gas emissions or air pollutants, so it plays a crucial role in the transition to a sustainable and low-carbon energy system and helps mitigate climate change by reducing the dependence on fossil fuels 1 .One challenge that remains, however, is that wind power availability is highly variable on multiple time scales ranging from day-to-day weather patterns [2][3][4][5] , seasonal-interannual large-scale modes of variability [6][7][8][9][10] , and up to centennial climate changes 11,12 .In the United States, with the steady increase of wind energy production over the last 20 years 13 , the latest U.S. Wind Turbine Database up to May 2023 contains 72,732 turbines with a total rated capacity of 142,435 megawatts 14 .Wind energy was the source of about 10.2% of total U.S. utility-scale electricity generation and accounted for 47.6% of electricity generation from renewable sources in 2022.The daily wind-powered electricity first surpassed both coal-fired and nuclear electricity generations and ranked as the second-largest source of U.S. electricity generation on March 29, 2022 15 .Therefore, there is a growing need of skillful wind energy prediction for energy system production, operation, and management.
The improved weather forecasts of wind speed have been shown to substantially increase economic activity by efficiently using wind-generated electricity in the U.S. electricity sector 16 .Beyond short-range weather forecasts of wind energy, seasonal climate prediction provides a new source of climate information for the long-range management of wind energy resources 17 .Previous studies have shown skillful seasonal predictions of wind energy several months in advance using statistical methods or dynamical models [18][19][20] .However, research on seasonal wind energy prediction over the contiguous United States (CONUS) using the state-of-theart seasonal prediction system has not been reported yet.Large-scale climate phenomena such as El Niño-Southern Oscillation (ENSO) 6,7,[21][22][23] , the North Atlantic Oscillation (NAO) 8 , or the Arctic Oscillation (AO) 20 can influence jet stream and wind patterns on regional and global scales.These climate patterns can contribute to seasonal variations in wind energy by altering atmospheric circulation and wind speed patterns, thus producing potential predictability sources of wind energy.Skillful seasonal predictions of jet stream and extratropical storm tracks, which strongly modulate interannual variability of wind energy resources over CONUS 3,6,7 , have been achieved mainly via the ENSO teleconnection in state-of-the-art dynamical seasonal prediction system multiple months in advance [22][23][24][25] .Thus, there may exist emerging opportunities in seasonal prediction of wind energy over CONUS.Here, we use the seasonal retrospective forecasts (SRF) from the Geophysical Fluid Dynamics Laboratory (GFDL)'s Seamless System for Prediction and EArth System Research (SPEAR) 26 to assess the seasonal prediction skill of wind energy resources over CONUS during 1991-2022 and ascertain the underlying physical drivers that contribute to the prediction skill using an advanced predictability analysis technique.

Model fidelity and prediction skill
The observed high wind energy resources (see Methods) associated with high wind speed are mainly located in the U.S. Great Plains and Great Lakes regions (Fig. 1a, c), in which air masses from north and south sweeping over the relatively flat and smooth terrain 27 , interacting with the Rocky Mountain terrain forcing 28 , seasonal jet stream 3,29,30 (Supplementary Fig. S1) and extratropical storm tracks (Supplementary Fig. S2), maintain the strong wind.SPEAR's SRF shows a high level of agreement with the fifth generation reanalysis from the European Centre for Medium-Range Weather Forecasts 31 (ERA5) in simulating the climatological surface "wind belt" with high onshore wind energy resources over the Great Plains extending to the Great Lakes (Fig. 1b, d).The model tends to overestimate the observed wind energy in the Midwest and western United States while underestimating observed values in the Great Plains (Supplementary Fig. S3).The wind energy resource over the CONUS shows substantial seasonal variations, and generally tends to peak during the boreal winter and spring seasons and is lower during the summer and fall seasons (Supplementary Fig. S4).More specifically, the observed wind resource in the Southern Great Plains (SGP, south of 40°N) shows larger seasonal variations (range of about ±40% relative to the annual mean) than those in the Northern Great Plains (NGP, north of 40°N, with a range of about ±20%) (Fig. 2a).Interestingly, the seasons with higher (lower) wind energy resources generally tend to show stronger (weaker) year-to-year variability (Fig. 2a, c).The strong interannual variability in wind energy resources during the peak seasons suggests the potential for producing high forecast benefit to energy planning via accurate and reliable seasonal predictions.SPEAR's SRF broadly captures the observed seasonal swings of wind energy and its interannual variability in the Great Plains (Fig. 2b, d).
The skill of the SPEAR system in predicting seasonal wind power and 100-m wind speed was assessed at all forecast lead times for all target seasons.The spatial distribution of seasonal wind speed skill and seasonal wind energy skill bears strong resemblance for all seasons (Fig. 3 and Supplementary Fig. S5), as higher wind speeds result in increased wind power output within the optimal wind speed range (See Methods).Therefore, the mean wind speed can provide a useful indication of the wind energy resource from a seasonal prediction perspective, and we will use the seasonal mean wind speed to diagnose the predictability sources of seasonal wind energy prediction.Interestingly, spring exhibits the highest skill of wind energy and wind speed predictions concentrated over the southern Great Plains across all seasons with anomaly correlation coefficient (ACC) exceeding 0.7 at 1-month lead, while the model shows moderate skill with significant ACC around 0.4-0.6 over the western Great Plains during winter.During summer, there exists significant skill sporadically distributed in northern California, Oregon, eastern Colorado, and western Nebraska.In contrast, the seasonal predictions show little seasonal prediction skill during fall (Supplementary Fig. S5).The first season prediction skill (initialized on the first day of the season) tends to be generally higher than the 1-month lead skill for both winter and spring due to the impact of atmospheric initialization with observations 23,25,32 (Supplementary Fig. S6).Although the prediction skill generally degrades with forecast lead time, the spatial pattern of significant skill over CONUS is retained up to 7 and 9 months in advance for spring and winter respectively (Supplementary Figs.S6, S7).
The high skill of wind energy prediction achieved by the model occurs in wind energy peak seasons (spring and winter), and geographically collocated with the regions over the Southern Great Plains with high wind energy capacity.According to the latest U.S. installed wind power data 33 , more than half of total U.S. wind capacity is located in the Southern Great Plains, and Texas alone accounts for almost a quarter of the total.Thus, SPEAR's wind energy prediction capability offers potential benefits for optimizing wind energy production and grid integration during the energy peak seasons.

Predictability source analysis
To ascertain the predictability sources for the skillful wind energy predictions, we apply the average predictability time (APT) analysis [34][35][36] (see Methods) to the seasonal wind power over CONUS in SPEAR's SRF for winter and spring respectively (Supplementary Fig. S8).Both leading predictable components (PrC1) in winter and spring show a similar spatial pattern with a strong trend-like time series (Supplementary Figs.S9-10).The observed trend amplitude of PrC1 is only about a quarter of the predicted trend in winter, although the correlation skill of PrC1 is significant with ACC around 0.5 at all lead times.The leading trend component in spring is not significantly predicted in observations.Therefore, the leading predictable component with a strong trend does not provide a pivotal role in the skillful wind energy predictions for winter and spring.This discrepancy in the trend between the model and ERA5 data may be partially ascribed to the inherent trend uncertainty within ERA5 37 .Note that the trend Fig. 1 | Spatial distributions of 100-m wind speed and wind power resources.The climatological annual 100-m wind speed (shading, units in m s −1 ) over the period 1991-2022 from (a) ERA5 data and (b) SPEAR's SRF.The same as (a) and (b) but for the annual wind energy power capacity shown in (c) and (d) respectively.The wind power is expressed by the normalized capacity factor calculated using Eq. ( 1) with 100-m wind speed (see Methods).The annual mean wind power is calculated from 6-hourly wind power data for both ERA5 and SPEAR.The black outlines denote the states in the U.S. Great Plains.The spatial pattern of the second predictable component (PrC2) in winter, shown in Fig. 4, is characterized by an overall reduction of wind power in most of CONUS except the coastal regions of the southeast United States and California.The time series of PrC2 is highly correlated with the observed Niño 3.4 index (NINO3.4)(see Methods) with the correlation coefficient above 0.9, suggesting that this pattern is mainly driven by ENSO.The December-February (DJF) NINO3.4 is highly predictable by the model with ACC above 0.7 up to 7 months ahead.Consequently, the correlation skill of PrC2 remains high with ACC ranging from 0.5 to 0.8 up to 7 months in advance, and then decreases slightly at lead of 8-9 months, largely following the evolution of NINO3.4 skill over lead times.The strong signal of PrC2 appears to be located in the Northwest, Great Plains, and Great Lakes regions, collocating well with the high-skill zone of wind power prediction (Figs. 3 and 4).The spatial pattern of PrC2 in spring also exhibits an overall reduction of wind power over most of CONUS in its positive phase, but in comparison with the winter pattern, the strong signal, which corresponds well with the high skill zone (Figs. 3 and 5), tends to shift towards the southern Plains.The temporal variability of PrC2 in spring shows a similar strong linkage with ENSO as in winter, and the skill in spring remains high with ACC around 0.6 up to 6 months in advance, although it is slightly lower than that in winter at lead of 8-9 months.Note that the PrC2 in winter (spring) explains about 24% (17%) of total variance, which is about four times of that by PrC1 in winter (spring) (Supplementary Fig. S8), indicating the dominant role of ENSO-related PrC2 in the skillful wind energy predictions.Therefore, the high spatial alignment between PrC2 and the highskill zone, and the strong temporal connection between PrC2 and ENSO support that ENSO is a primary driver of the prediction skill of wind energy over CONUS during the peak seasons.
To further quantify the relationship between large-scale circulation and wind energy associated with ENSO, we show in Fig. 6 the observed and predicted regression patterns of the DJF 100-m wind speed, 700-hPa horizontal winds, and geopotential height onto the observed NINO3.4.During El Niño years, the 100-m wind speed values tend to be reduced over the entire central United States 7 , in association with two contrasting There is a tendency for the predicted maximum teleconnections in Canada (USA) to be shifted westward (eastward) relative to observations (Fig. 6c, d).Consequently, the predicted surface wind pattern tends to be shifted westward relative to observations, and thus the prediction skill in the eastern Great Plains is degraded (Figs.3a and 7).
The observed large-scale wind pattern associated with ENSO in spring is predominantly an overall weakening of wind speed over most of CONUS with the maximum signal in the southern Great Plains 7 (Fig. 7).This wind pattern generally responds to an anomalous geopotential dipole with a high in western Canada and an elongated low extending from the eastern North Pacific towards the U.S. Southeast.This geopotential dipole weakens the equator-to-pole pressure gradients over the central United States and generates the easterly wind anomalies against the prevailing climatological westerlies, thus reducing the wind speeds.Unlike the apparent teleconnection shift bias in winter, the model well predicts the observed ENSO teleconnections of both wind speeds and circulations in spring.This may explain the higher prediction skill of wind energy in spring than winter over the Great Plains.The regression analysis indicates that a significant reduction of wind energy resources is expected in most of CONUS during wind peak seasons for El Niño and vice versa for La Niña.The ENSO teleconnection is also characterized by strong transient eddy-mean flow interactions in the extratropics 21,38 , so further insights into underlying dynamics of wind energy variations associated with ENSO can be gained by considering the dynamic interplay between large-scale wind flow changes and accompanying storm track variations [38][39][40][41][42][43][44][45][46] .The observed ENSO teleconnection patterns of the seasonal 100-m eddy kinetic energy (EKE, see Methods) coincide well with the seasonal mean 100-m wind patterns during winter and spring (Figs.6-8).The decreased 100-m EKE and wind speed over the central USA and the increased counterparts over a curved band covering the northeast Pacific, the Gulf of Mexico and the southwest North Atlantic are dynamically consistent with the ENSOinduced equatorward shift of upper-level jet and storm tracks 22,23,44 (Supplementary Fig. S12).The spatial coincidence among the 100-m EKE, wind speed, and upper-level jet supports the dynamical reinforcement between storm track variations and large-scale mean circulation changes associated with ENSO.The seasonal 100-m EKE is highly correlated with the wind power over the central USA (Supplementary Fig. S13), indicating that the stronger winds associated with stronger extratropical storm tracks 22,47 tend to produce higher wind energy 6 .The model well predicts the observed dynamical interplay between storm track variations and large-scale circulation changes associated with ENSO during winter and spring, thus the storm track-induced winds substantially contribute to the skillful seasonal wind energy prediction over CONUS.
In addition to the skillful predictions of ENSO-related wind patterns over multiple lead months, the accuracy of near-term seasonal predictions over CONUS can be further enhanced by skillfully forecasting prominent  atmospheric large-scale teleconnection patterns, notably including the NAO 32 and the North Pacific Oscillation (NPO) 25 .The first season prediction largely captures the observed decrease in 100-m wind speed associated with the positive phase of NAO during spring in the southern Great Plains (Supplementary Fig. S14).The decrease in wind speed across the southern Great Plains primarily stems from the NAO-induced abnormal easterly winds that counter the usual westerlies, aligned with the positive geopotential height anomalies in the central US 48 .The model well predicts the observed increase in 100-m wind speed associated with the positive phase of NPO during spring in the northern Great Plains and Great Lakes states (Supplementary Fig. S15).During the positive phase of NAO in winter, the model only reproduces the observed decrease of wind speed in the northeast US and the increase of wind speed in the northwestern Great Plains, while showing no consensus elsewhere across CONUS (Supplementary Fig. S16).The modeled wind speed pattern associated with the positive phase of NPO during winter largely resembles that of ERA5.However, the maximum signals across CONUS exhibit a westward shift relative to observations, corresponding to the westward shift of the geopotential low in Canada relative to observations (Supplementary Fig. S17).Note that the model exhibits significant skill at 0-lead month in predicting the spring NAO (NPO) index with ACC of 0.64 (0.61), and for the winter NAO (NPO) index with ACC of 0.52 (0.64) (Supplementary Fig. S18), but the skill significantly drops at longer lead months.
Forecast refinement and potential regional seasonal outlook For the potential utilization of seasonal wind energy forecasts, we provide a complete survey of prediction skills over all seasons with a focus over the U.S. Great Plains.The northern Great Plains exhibit significant skill starting from November-January (NDJ) to February-April (FMA) for all lead months with a peak in FMA and a rapid drop of skill starting from spring to fall (Fig. 9a).In contrast, the southern Great Plains shows significant skill from winter (DJF) to May-July (MJJ) at least over 7 lead months with a peak in spring and no skill from late summer to fall (Fig. 9b).The skill pattern over lead months and target seasons corresponds well to the associated signal-to-noise ratio (SNR, see Methods) pattern, i.e., higher skill with higher SNR and consistent higher SNR in SGP than NGP (Supplementary Fig. S19a, b).Most forecasts with lead time longer than 1 month exhibit a low predictable signal with SNR less than 0.5, thus posing a great challenge to the wind energy prediction.To enhance SNR, we refine the forecasts using the top 5 predictable components from APT by filtering out the forecast noise while retaining the forecast signal (see Methods).The refined forecasts greatly enhance the signal over the raw forecasts with at least doubled SNR for all target seasons and lead months (Supplementary Fig. S19c, d).Consequently, the forecast skill is coherently improved during the winter and spring seasons (Fig. 9c, d).Interestingly, both refined and raw forecasts show forecast skill barriers in the summer and fall seasons.This skill barrier might be related to the relatively weaker interannual variations of wind energy (Fig. 2).Nevertheless, the robust skill during the energy peak seasons indicates that the model's seasonal outlooks can potentially enable better planning and decision-making of wind energy production on the seasonal timescales.
To leverage the seasonal wind outlooks for the potential wind energy resource planning at regional scales, we showcase time series of forecasted spring wind power averaged over SGP, in which more than half of total U.S. wind capacity is located (Fig. 10a).The observed wind power in SGP shows a strong interannual variation with a large range from about 75% to 120% of its climatological value, indicating the importance of accurate wind energy prediction for ensuring a reliable energy supply.Remarkably, the model well predicted the interannual range changes with a high skill (ACC = 0.76) at 0-month lead.Consistent with high loadings of the ENSO regression patterns of wind power over SGP (Figs. 5 and 7), the predicted time series over SGP shows strong links to ENSO with a significant correlation coefficient of −0.69.The model also can provide a robust state-level wind energy outlook with a correlation skill reaching 0.81 for Texas at 0-month lead (Fig. 10b), which alone accounts for almost a quarter of the total U.S. wind capacity.The model retains its capability to achieve "useful" forecast accuracy (ACC > 0.6) 49 for wind power over SGP and Texas up to 4 months in advance (Fig. 9).Therefore, the skillful seasonal wind energy outlooks at the regional scale or state level can provide useful predictable information over the U.S. Great Plains for coping with year-to-year variations and optimizing energy production.

Discussion
Wind energy resources across the CONUS typically exhibit strong year-toyear variability during peak seasons, presenting challenges for effective energy planning.We have demonstrated SPEAR's ability to provide accurate seasonal predictions of wind energy resources several months in advance, particularly during wind energy peak seasons (spring and winter) across the U.S. Great Plains.Hence, these accurate seasonal wind energy forecasts hold the potential to yield significant benefits in optimizing the production, distribution, and allocation of wind energy resources, ultimately contributing to the enhancement of a sustainable and reliable energy supply.Within the extended multi-month forecast window, the primary factor for accurate wind energy predictions stems from the teleconnection patterns of wind energy linked to ENSO over the CONUS.For the first season predictions, the accuracy is additionally influenced by prominent atmospheric large-scale teleconnection patterns, including NAO and NPO.Therefore, enhancing the model's representation of the teleconnections associated with those large-scale climate modes is pivotal for advancing the accuracy of seasonal wind energy prediction.
The study further enhances our understanding of how storm-track induced winds substantially contributing to the skillfull wind energy prediction.This is achieved through the dynamical interaction between storm track variations and large-scale circulation changes associated with ENSO during the winter and spring seasons.In addition to the skillful seasonal predictions of extratropical storm tracks and winter temperature swings by dynamic models 22,25 , this study underscores the importance of the eddymean flow interaction perspective in comprehending the seasonal climate predictability in the extratropics.
The model exhibits bias in wind patterns associated with ENSO and NPO, which degrades the skill of wind energy predictions in the Northern Great Plains, particularly during winter, suggesting that future model development to better represent these teleconnections has the potential to improve the regional wind energy forecasts.Reconciling the discrepancy between the predicted and observed trends in surface winds has the potential to improve forecast skill, particularly in regions where the skill of detrended forecasts exceeds that of complete forecasts (Supplementary Fig. S20).Forecasting wind energy resources during low resource seasons such as summer and fall is crucial for effective energy storage planning.The limited skill in predicting wind patterns during summer and fall suggests that certain influential drivers may not be well represented in the model 50 , underscoring the necessity for further investigation.The reliability of wind energy forecast skill over the Rocky Mountains needs further validation since ERA5 exhibits significant biases in estimating wind speed over the complex terrains 51 , possibly attributable to the imperfect gust wind parametrization within ERA5 52 .While this study has utilized spatially varying and seasonal varying power law exponents for wind power calculations, it neglects short-term fluctuations in these exponents due to small-scale changes in atmospheric stability.To improve the accuracy of wind energy predictions and minimize errors linked to the power-law wind speed extrapolation method, it is advisable to enable instantaneous model output of wind speed at two layers (e.g., 10 m and 100 m) for calculating wind speed at turbine hub height.

Methods
Model GFDL's Seamless SPEAR 26 has been used for subseasonal 53 , seasonal 54 to decadal 55 climate predictions and future climate projections.One configuration of SPEAR, called SPEAR_MED, is used for the seasonal prediction with about 1°horizontal resolution in the ocean and sea ice components (telescoping to 0.33°meridional spacing near the equator) and 75 layers in the ocean component.SPEAR_MED uses an atmosphere/land resolution of ~50 km with 33 vertical levels.SPEAR_MED is currently used for GFDL's real-time seasonal forecasts delivered each month to the NOAA National Centers for Environmental Prediction through the North American Multimodel Ensemble (NMME) project 56 .
SPEAR's seasonal retrospective forecasts (SRF) were initialized with SPEAR's ocean data assimilation in combination with a separate set of SPEAR_MED's ensemble coupled simulations, in which the atmosphere state and sea surface temperature (SST) are nudged towards observations.The 15 ensemble members of SRF were initialized on the first day of each month and integrated for 12 months from 1991 to 2022.SPEAR's SRF has shown skillful seasonal predictions for a wide range of essential climate variability and extremes, including but not limited to ENSO, surface air temperature over land, midlatitude baroclinic waves, atmospheric rivers over western North America, Antarctic/Arctic sea ice, Kuroshio extension sea surface height, North American summertime/wintertime temperature extremes and winter temperature swings 54,[57][58][59][60][61][62][63] .
Another 15-member SPEAR_MED ensemble simulations with historical radiative forcing (hereafter called HIST) were used to isolate the predictability source from the radiative forcings.Ensemble members of HIST were initialized from conditions in a long 1850 control simulation with atmospheric composition fixed at levels representative of calendar year 1850.In HIST, the time-varying historical natural and anthropogenic forcings were applied before 2014, while projections for the Shared Socioeconomic Pathway 5-8.5 (SSP5-8.5) 64,65were applied for years after 2014.Note that the radiative forcing in SRF is identical to those in the HIST simulations.

Skill assessment
For the skill assessment and diagnosis for SPEAR's SRF, the seasonal forecast anomalies of each variable were obtained by subtracting out the climatology from forecasts at each lead time individually, which effectively removes the climate drift assuming that the climate drift is systematic as a function of forecast lead time.The anomaly correlation coefficient (ACC) between ensemble mean forecast anomalies and observational anomalies is used for skill assessment.The signal-to-noise ratio (SNR) is calculated as the ratio between the ensemble mean-variance and the ensemble noise variance in the forecasts.

Data
The skill verification data is obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis-ERA5 31 , as it provides reliable estimates of wind speed at wind turbine heights, validated against observations from meteorological towers and sodars across the United States 51 .The observed SST is the monthly SST data from NOAA's Optimum Interpolation Sea Surface Temperature (OISST) V2 66 .The Niño 3.4 index (NINO3.4)is calculated as the area-averaged SST anomalies over 5°S-5°N and 170°-120°W.The NAO index 67 is the station-based index calculated as the difference of normalized SLP between Lisbon, Portugal, and Stykkisholmur/Reykjavik, Iceland.The North Pacific Oscillation (NPO) index 68 is calculated as the difference of the area-averaged SLP anomalies between a high-latitude North Pacific box (55°-72.5°N;180°-140°W) and a subtropical North Pacific box (15°-27.5°N;175°E-147.5°W).

Wind power calculation
The wind power is calculated using a generic power curve equation 4 as follows: where power is the normalized power capacity values (or production as percentage of capacity) for different wind speeds, S is the wind speed in ms −1 , and C 0 to C 7 are estimated coefficients (Supplementary Fig. S21).This generic power curve was created by Underwriters Laboratories Renewables and represents a composite of several different manufacturers' International Electrotechnical Commission (IEC) Class II turbines.This power curve has been used for wind energy forecast assessment from weather 16 to seasonal 18 wind energy forecasts.The wind power is calculated using wind speed at hub height of wind turbines.Modern turbines have hub heights in the range of 80-120 m, so a fixed hub height of 100 m is assumed here without loss of generality.Since model outputs only provide 10-m winds, we use the power law to estimate hub height wind speed at 100 m from 10-m wind speed as: A constant value with α = 0.143 has been widely used for land 5,18,69,70 .The constant power exponent of 0.143, assuming neutral stability conditions 69 , typically results in a biased estimation of both 100-m wind speed and wind energy 71 .To reduce the bias due to the constant power exponent, seasonally dependent and spatially explicit power law exponents are derived from ERA5 data.Following Jung and Schindler 71 , the 6-hourly power exponent at each grid point is calculated by: where t is the time step, 100-m and 10-m wind speed values are taken from ERA5.The seasonally varying power exponent is calculated as the mean of α t for each calendar month over 1991-2020 as follows: where M is the calendar month, N is the total sample size for month M. Consistent with Jung and Schindler 71 , the estimated power exponent exhibits strong spatial and seasonal variability over CONUS (Supplementary Fig. S22).The notable underestimation of wind power capacity, resulting from the constant power law exponent of 0.143, is substantially improved over CONUS when employing the spatially and seasonally varying power exponents (Supplementary Fig. S23).The 6-hourly 10-m wind speed is first adjusted to 100-m wind speed using (2) with α M from (4), and the 6-hourly wind power is calculated using (1) for the model and observations respectively.The seasonal mean wind power is calculated as the 3-month average of 6-hourly wind power.

Eddy kinetic energy
The specific kinetic energy is defined as , and the synoptic eddy kinetic energy is defined as EKE ¼ 1 2 ðu 02 þ v 02 Þ, where u and v are the zonal and meridional winds respectively, overbar denotes seasonal mean and prime denotes synoptic eddy terms, calculated using a 24-h-difference filter 72 .The resulting statistical properties of extratropical storm tracks using the 24-h-difference filter are very similar to those obtained from other bandpass filters 73 .This method of measuring synoptic eddies has been widely used in previous studies from subseasonal 74 to seasonal 22,23,25 climate predictions and future projections 75 of extratropical storm tracks.EKE is employed here to examine the influence of extratropical storm track activity on the interannual variability of wind energy.

Average predictability time (APT) analysis
To diagnose the predictability source of wind energy prediction, we apply the APT analysis 34,35 to the ensemble forecasts for each individual season.APT has been widely used for identifying the timescale-aware predictable components in seasonal to decadal climate predictions 22,36,62,63,76 .Briefly, the method is to maximize APT, which is defined as the integral over lead time of the "signal to total" variance ratio of a forecast model: where σ 2 signal is the signal variance at fixed lead time τ, and σ 2 total is the corresponding total variance.Within ensemble forecasts, the signal and total covariance can be approximated by their corresponding ensemble covariances.Maximizing APT in ensemble forecasts leads to the generalized eigenvalue problem 2 where L is the maximum forecast lead time, q is the desired projection vector, e Σ signal ðτÞ is the ensemble mean covariance matrix at the forecast lead time τ and e Σ total is the total ensemble covariance matrix.The eigenvalues of (6) give APT values, and each eigenvector q corresponds to a component.The eigenvectors provide the basis for decomposing the ensemble forecasts into a complete, uncorrelated set of components ordered such that the first maximizes APT, the second maximizes APT subject to being uncorrelated with the first, and so on.This decomposition based on APT is analogous to empirical orthogonal function analysis, except that we decompose predictability instead of decomposing variance.APT has units of time and measures the decay time scale of predictability 77 .In general, components that are persistent or oscillate over narrow frequencies have large APT values 36 .
Let x τ,i,e be the state vector of ensemble forecast anomalies at fixed lead time τ, forecast event i, and ensemble member e.The ensemble mean and total covariances at lead time τ are respectively given by: e Σ signal τ ð Þ ¼ x τ;i;e x τ;i;e and e Σ total ¼ ½½x τ;i;e x T τ;i;e ; ð8Þ where the overlines denote the average over ensemble members, the angle brackets denote the average over all forecast events, and the double brackets denote the grand mean over all forecast events and ensemble members, and the superscript T denotes the transpose operation.The spatial pattern P associated with each component is obtained by regressing the time series q T x τ;i;e with x τ;i;e , which gives p ¼ e Σ total q.For solving the APT optimization problem (6) in practice, the data are first projected onto the leading principal components (PCs).Following ref. 76, we choose 20 PCs for the APT analysis of the seasonal wind power over the contiguous USA.Here the maximum forecast lead time L is 10 months for each season.
APT is capable of decomposing raw hindcasts into predictable components and unpredictable components, so we can reconstruct hindcasts based upon the predictable components while filtering out unpredictable components following previous studies 22,62,63 .Here, we generate a reconstructed model using 5 leading predictable components with their corresponding APT values statistically significant at the 5% significance level (Supplementary Fig. S8).www.cpc.ncep.noaa.gov/products/NMME/).Other SPEAR simulations are available from the corresponding author upon request and with the permission of NOAA.The data for figures are available online at https:// doi.org/10.5281/zenodo.10823524.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material.If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2024 https://doi.org/10.1038/s43247-024-01457-wSkillful seasonal prediction of wind energy resources in the contiguous United States Check for updates Xiaosong Yang 1 , Thomas L. Delworth 1 , Liwei Jia 1 , Nathaniel C. Johnson 1 , Feiyu Lu 1,2 & Colleen McHugh 3 component is highly predictable in the historical forced experiment (see Methods) with ACC larger than 0.95 for both seasons (green lines in Supplementary Figs.S9-10), indicating that the trend component is mainly due to changes in external radiative forcing.

Fig. 2 |Fig. 3 |
Fig. 2 | The normalized annual cycle of seasonal wind power.The normalized climatology of zonally averaged seasonal wind power over the U.S. Great Plains (110°W-90°W) during 1992-2022 from (a) ERA5 data and (b) SPEAR's seasonal retrospective forecasts (SRF).The same in (c) and (d) as in (a) and (b) but for the normalized standard deviation of seasonal wind power.The normalization is with respect to the climatological annual mean value for ERA5 and SPEAR respectively.

Fig. 4 |Fig. 5 |
Fig. 4 | The spatial pattern and time series of predictable components in winter.a The spatial structure of the 2nd predictable component (PrC2, color shading) in the seasonal retrospective forecasts for the DJF season.b The anomaly correlation coefficients (ACC) between forecasts and observations (red squares) and associated 95% error bars as a function of initial month for PrC2.The green line denotes the ACC for the Niño-3.4index.c The ensemble mean time series of PrC2 averaged over lead time 0-4 months (red) and 5-9 months (blue) as a function of time; the time series of the ERA5 data projected onto PrC2 (black) and the Niño-3.4index (green) from 1991 to 2022.The black outlines in (a) denote the states in the U.S. Great Plains.

Fig. 6 |
Fig.6| ENSO regression patterns for winter largescale atmospheric circulation.The regression coefficients of the DJF 100-m wind speed (units in m s −1 ) onto the normalized NINO3.4 index during 1992-2022 calculated from (a) ERA5 reanalysis and (b) the ensemble members of SPEAR's SRF.Each member corresponds to its respective NINO3.4 index in the regression analysis conducted in SRF.The regression coefficients calculated in the same way but for the DJF geopotential height (shading, units in m) and horizontal winds (vectors) at 700 hPa (c) ERA5 reanalysis and (d) the ensemble members of SPEAR's SRF.The stippling indicates regression coefficients of wind speed and geopotential height significant at 5% level.SPEAR's SRF initialized on 1st November each year.

Fig. 7 |
Fig. 7 | ENSO regression patterns for spring largescale atmospheric circulation.The regression pattern onto the normalized NINO3.4 index for the MAM 100-m wind speed (units in m s −1 ) from (a) ERA5 reanalysis and (b) the ensemble members of SPEAR's SRF during 1992-2022.Each member corresponds to its respective NINO3.4 index in the regression analysis conducted in SRF.The regression pattern calculated in the same way for the MAM geopotential height (shading, units in m) and horizontal winds (vectors) at 700 hPa from (c) ERA5 reanalysis and (d) the ensemble members of SPEAR's SRF.The stippling indicates regression coefficients of wind speed and geopotential height significant at 5% level.SPEAR's SRF initialized on 1st February each year.

Fig. 8 |a
Fig. 8 | ENSO regression patterns for 100-m EKE.The regression pattern onto the normalized NINO3.4 index for the DJF 100-m eddy kinetic energy (EKE) (units in m 2 s −2 ) during 1992-2022 from (a) ERA5 reanalysis and (b) the ensemble members of SPEAR's SRF.Each member corresponds to its respective NINO3.4 index in the regression analysis conducted in SRF.The regression patterns calculated in the same way as in (a) and (b) but for MAM in (c) and (d) respectively.The stippling indicates regression coefficients significant at 5% level.SPEAR's SRF initialized on 1st November each year for DJF and 1st February each year for MAM.

Fig. 9 |
Fig. 9 | Forecast skill in raw and refined forecasts.Anomaly correlation coefficients (ACCs) between model and observations for each lead month (x-axis) and target season (y-axis).ACC is calculated from the raw forecasts for wind power area-averaged over the Northern Great Plains (NGP) (40°-50°N, 100°-110°W) in (a) and the Southern Great Plains (SGP) (30°-40°N, 95°-107°W) in (b).The same as in (a) and (b) but for the refined forecasts using a few predictable components from APT in (c) and (d) respectively.Cross markers in (c) and (d) indicate ACCs in the refined forecasts exceeding those in the corresponding raw forecasts.

Fig. 10 |
Fig. 10 | Wind power seasonal outlook potential over the Southern Great Plains and Texas.a Time series of normalized observations (black squares), ensemble mean (red dots), and spread (shading) from SPEAR's SRF averaged over the Southern Great Plains (30°-40°N, 95°-107°W) during 1992-2022 for the spring (MAM) wind power.b The same as in (a) for the spring wind power averaged over Texas.The observations and model results are both normalized by their mean over 1992-2022.SPEAR's SRF initialized on 1st March each year.