Global assessment of spatiotemporal changes of frequency of terrestrial wind speed

Wind energy, an important component of clean energy, is highly dictated by the disposable wind speed within the working regime of wind turbines (typically between 3 and 25 m s−1 at the hub height). Following a continuous reduction (‘stilling’) of global annual mean surface wind speed (SWS) since the 1960s, recently, researchers have reported a ‘reversal’ since 2011. However, little attention has been paid to the evolution of the effective wind speed for wind turbines. Since wind speed at hub height increases with SWS through power law, we focus on the wind speed frequency variations at various ranges of SWS through hourly in-situ observations and quantify their contributions to the average SWS changes over 1981–2021. We found that during the stilling period (here 1981–2010), the strong SWS (⩾ 5.0 m s−1, the 80th of global SWS) with decreasing frequency contributed 220.37% to the continuous weakening of mean SWS. During the reversal period of SWS (here 2011–2021), slight wind (0 m s−1 < SWS < 2.9 m s−1) contributed 64.07% to a strengthening of SWS. The strengthened strong wind (⩾ 5.0 m s−1) contributed 73.38% to the trend change of SWS from decrease to increase in 2010. Based on the synthetic capacity factor series calculated by considering commercial wind turbines (General Electric GE 2.5-120 model with rated power 2.5 MW) at the locations of the meteorological stations, the frequency changes resulted in a reduction of wind power energy (−10.02 TWh yr−1, p < 0.001) from 1981 to 2010 and relatively weak recovery (2.67 TWh yr−1, p < 0.05) during 2011–2021.


Introduction
Wind energy is a key component of the energy market and a potential way for climate mitigation (IEA 2020). In 2021, the global wind industry reached 94 GW power capacity addition, mainly driven by China, Europe and the United States (Global Wind Energy Council 2022). Yet, the current installation rates suggest that it will still be challenging to meet the 1.5 • C mitigation goal (Global Wind Energy Council 2022). To promote wind energy expansion, understanding the efficiency of wind power generation is necessary.
Wind power generation is particularly sensitive to changes in wind speed as wind power is proportional to the cubic of wind speed (McElroy et al 2009, Sohoni et al 2016, Eurek et al 2017, Pryor et al 2020. Global annual mean near-surface wind speed (SWS) continuously declined over the past five decades before 2010, known as the period of 'stilling' (Roderick et al 2007, Vautard et al 2010, McVicar et al 2012, with a decrease rate of −0.08 m s −1 decade −1 during 1978-2010 (Zeng et al 2019). But during the past ten years (i.e. 2011 to ∼2021), such stilling phenomenon has been replaced by a 'reversal' , with an increasing annual mean SWS of 0.24 m s −1 decade −1 since (Zeng et al 2019). However, how these SWS changes govern wind power generation is uncertain.
Average SWS changes can be insufficient for accurately assessing the wind power generation change relating to the stilling and reversal periods, given that wind power generation on a global scale depends on the effective SWS characterized by its range, frequency, and distribution. Generally, wind speed ranging from 3 to 25 m s −1 at the hub height is effective in wind power generation. Specifically, light winds may fail to rotate the turbine blades, while strong winds force wind turbines to shut down to prevent damage (Lydia et al 2014). Moreover, most wind power is produced by the SWS within the upper half of the wind speed frequency distribution (Pryor and Barthelmie 2010), which is typically positively skewed (Jung and Schindler et al 2019a). To quantify the portion of effective SWS evolution affecting generating wind power generation, wind frequency must be considered. However, previous studies assessing wind frequency change often ignored the statistical distribution of SWS (e.g. Vautard et al 2010, Zha et al 2017, leading to unrealistic assessments of its influence on wind power generation. To fill these gaps, here we use the hourly SWS data from Hadley Centre Integrated Surface Database (HadISD, Dunn et al 2014 to derive global and continental wind speed trends, to perform a comprehensive analysis of SWS frequency change over 1981 to 2021. SWS was divided into nine ranges (see details in section 2.2) to analyze the year-to-year SWS frequency variations and quantify the influence of frequency variations on the annual average SWS. We also used the power law to extrapolate the SWS to the wind speed at the hub height of a commercial wind turbine to perform a power assessment and evaluate the effect of SWS frequency changes on wind power generation. Our research proposes a new method to quantify the influence of frequency changes in average SWS changes. We revealed that the weakening of strong wind was the main cause of global 'stilling' and the slight winds are major parts of the SWS reversal.

Dataset
We use the hourly SWS data provided by HadISD (Dunn et al 2014(Dunn et al , 2016, which is a subset of the station data from the Integrated Surface Database (ISD, Smith et al 2011). These data were subject to a series of quality control procedures, including duplicate checks, neighbor outliers and distribution gap checks, to eliminate bad data and maintain data continuity (Dunn et al 2016). The HadISD has been used for the annual monitoring of wind in the Bulletin of the America Meteorological Society State in recent years (Dunn et al 2016) and has been widely used in previous studies (Woolway et al 2019, Zhou et al 2021, Millstein et al 2022. It is noteworthy that Dunn et al (2022a) reported on erroneously missing calm winds (SWS = 0 m s −1 ) in the ISD and hence the HadISD since May 2013 for many stations outside of North America, which has an impact on the magnitude of the reversal in winds occurring approximately at the same time (see text S1 and figure S1 in the supplementary information for more detail, Dunn et al 2022a). A simple correction was applied for the HadISD in version v3.3.0.202201p and later, which recovers many of the missing observations, and our analyses are based on this corrected version (v.3.3.0.202202p).

Homogenization and resample of SWS data
To ensure the continuity of the long-term decadal analysis of SWS frequency, we implemented strict selection criteria for SWS time series to use a final subset of qualified stations. The final subset of stations is required to meet the following standards: (1) each final station needs to have continuous monthly records over 1981-2021; (2) each month should have more than 15 d of records; (3) the daily values must have at least four observations. After the data selection, the final subset of stations includes 1511 stations in version (v3.3.0.202202p, see figure S1(c) for station locations).
To obtain the frequency of SWS, we resampled the time series data to address the issue that the observations have inconstant observation intervals. According to appendix figures S2 and S3, the observation intervals vary from 8 h to 1 h for most stations, and some stations have shorter observation intervals since 1990; the standard deviation of the observation intervals is greater than 0.8 h for about 40% of the stations, implying variable observation intervals in one year. Uneven observation intervals introduce biases when counting frequencies of SWS on the annual scale. Therefore, it becomes necessary to transform SWS into equally time-spaced data. Here, we fill the time gap by repeating the later value in the time gap. The biases caused by this resampling method will be discussed in supplementary text S2 and figures S4 and 5.

Wind speed classification criteria
Cut-in and cut-out wind speeds are considered to decide the classification criteria for categorizing the SWS in power generation. The cut-in wind speed, denoted as v i ' , refers to the minimum wind speed that results in the turbine to commencing rotating and generating electricity. The cut-out wind speed, marked as v f ' , is the maximum wind speed to generate usable power. The cut-in and cut-out wind speeds refer to the wind speed at the hub height of the wind turbine. Here we use the parameters of the General Electric GE 2.5-120 wind turbine model (2.5 MW, 120 m diameter, hub height at of 25.0 m s −1 (https://en.wind-turbine-models.com/ turbines/310-ge-general-electric-ge-2.5-120).
The exponential wind profile power-law relation is applied to transform v i ' and v f ' at 110 m height from the 10 m wind speed records. The power-law relationship can be expressed as follows: where u tb and u s represent wind speed at height z tb (110 m) and z s (10 m), and α is a nondimensional parameter usually assumed to be constant 1/7, which is broadly applicable to low surface roughness and adopted by some studies involving wind power assessment (Islam et al 2011, Wang et al 2016, Liu et al 2019. The cut-in (v i ) and cut-out (v f ) wind speeds at 10 m above the ground surface transformed from the wind profile power law are 2.2 m s −1 and 17.7 m s −1 . Thus, the classification criteria of SWS are based on two aspects: (1) the cut-in and cut-out wind speeds defining the range of efficient SWS used in power generation; (2) the incrementing percentiles of SWS among efficient SWS. The incrementing percentiles refer to the values of 50th, 60th, 70th, 80th, and 90th corresponding to 2.9 m s −1 , 3.5 m s −1 , 4.1 m s −1 , 5.0 m s −1 , and 6.2 m s −1 . These values are obtained by averaging values for 41 years and over global stations aiming to set a uniform standard of categorization. At the same time, we consider zero SWS into one separate group to verify the result of data correction (Dunn et al 2022a) and describe small wind speeds more accurately. Then SWS data was divided into nine ranges to show the changes in the SWS frequency at different ranges (table 1). We denote SWS in specific range i as class i (i = 1,2…9, table 1). Here, SWS of class 3-8 is efficient wind speed.

Quantification of the influence of the SWS frequency variation
To validate the categorization, we use the Pearson correlation coefficient to compare the SWS from in-situ data and weighted-average speed calculated by the following formula: wherev is the climatological mean of SWS of the corresponding wind speed category over 41 years (all the subscripts indicated the wind speed range), Weighted v (t) and f i (t) are the wind speed and frequency of year t accordingly.
To estimate the contribution of SWS frequency changes of each class to the wind speed trend, we keep the multiplication of frequency and mean SWS in a specific class of SWS to be a constant value as the 41 year climatology mean value, denoted asν i f i , to calculate the fixed weighted-average SWS (Fixed v i ) within class i: The difference (Diff v i ) between the weightedaverage speed (Weighted v ) and fixed weightedaverage SWS (Fixed v i ) representing the influence of the certain range of SWS to the weighted-average wind speed, as shown in formula (4): We calculate the ratio of the trend of Diff v i to the trend of Weighted v according to the following formula (5) representing the contributions of changes of frequency in each class to the general changes of weighted-average SWS: The trend of weighted SWS is the sum of the trends of the nine classes of Diff v i , thus having little chance to be close to zero as the denominator. The trend of Diff v i is dependent on the only variable frequency f i (t). In this way, for SWS at each class i, the trend of Diff v i ends up to be a proportion of the trend of Weighted v .

Wind power assessment
The theoretical power assessment of wind turbines requires complex parameters such as air density and turbine parameters, which introduces vast complexity to set influencing parameters properly (Sohoni et al 2016), especially when considering the global spatial extent of our study. The power curve of wind turbines is helpful for wind energy forecasting without further technical details of wind power operating conditions (Lydia et al 2014). It is widely used in wind power assessment (Wang et al 2016, Pryor et al 2020, Millstein et al 2022. We assume the wind turbine GE 2.5-120 was installed around each observation site and use its power curve to derive the wind power output under the wind regime at observation sites. Wind turbines at higher hub heights tend to experience better wind regimes with stronger wind and generate more energy . In this research, we considered hub heights of 110 m and 139 m to ensure that the results are comprehensive and convincing. Yearly wind power generation (Energy, unit: GW·h) is calculated by combining the global wind turbine installations and the capacity factor based on formula (6), that is, the ratio of wind power output (P real , unit: MW) to rated power (P rated = 2.5 MW) multiplied by the installed capacity (837 GW). Installed capacity data is from the Global Wind Energy Council (2022),

Wind speed changes
We On the other hand, SWS in South America, Africa, and Australia did not show the first weakening and then reversing trend. The SWS in South America has a nonsignificant trend before 1990 (p > 0.05), then following a continuous increasing trend with a rate of 0.14 m s −1 decade −1 (p < 0.05) till 2021 ( figure 1(e)). Yet, neither an increase nor decrease trend of SWS is found in Africa (p > 0.05, figure 1(f)). The SWS in Australia first increases at a rate of 0.39 m s −1 decade −1 (p < 0.05) during 1981-1998, then such increase slows down after 1998 with a rate of 0.12 m s −1 decade −1 (p < 0.05, figure 1(g)). The SWS trend from in-situ observations in the Southern Hemisphere remains highly uncertain, which may be due to the lack of enough long-term observations, relocation of in-situ stations or changes in the observational practices (Lucas 2010, Wu et al 2018.

Frequency changes of global and regional SWS
Wind speed trends are closely associated with frequency. We found that the wind speed distribution had changed during the past decades ( figure 2(a)), implying the frequency change at different SWS categories. Notably, 90th SWS has been decreased from 6.6 m s −1 to 6.2 m s −1 from 1982 to 2021, indicating that the SWS frequency tends to increase and centralize in relatively small winds from 1 to 3 m s −1 (figure 2(a)). Moreover, the peak of the wind speed distribution shifts towards smaller values as time passes (figure 2(a)), implying an increase in the skewness in SWS frequency. A similar increase of skewness and kurtosis of SWS distribution was found during 2006-2019, as was predicted in 2020-2099 under the representative concentration pathway RCP8.5 (Jung and Schindler 2019a).
After the SWS resampling, resampled SWS was divided into nine ranges based on the positive-skewed wind speed distribution and contribution to wind energy generation (see section 2.2). To validate the categorization of SWS, the weighted-average SWS calculated from formula (2) was compared with the observed mean SWS after resampling ( figure 2(b)). The Pearson correlation coefficient of weightedaverage SWS and the observed average was 0.998 (p < 0.01; figure S7), implying that the classification criteria of SWS categorization were rather satisfying. Notice, however, that there was a slight deviation between the weighted-average SWS and the observed SWS. This was because we used the climatological mean value of SWS to multiply the changing frequency when calculating weighted-average SWS.
The change in SWS frequency during the past decades is shown in figure 3. Calm wind frequency decreased (−2.61% decade −1 , p < 0.001) for the past 41 years (figure 3(a)). An increase with a rate of 3.47% decade −1 (p < 0.001) was found in class 2 (0.1-2.1 m s −1 ) wind frequency ( figure 4(b)). However, the class 2 wind was smaller than the cut-in wind speed and thus did not contribute to the wind power generation. The frequency of class 9 (> 17.7 m s −1 ) wind was so small that the decrease rate was only −0.01% decade −1 (p < 0.001). Up to 60% of wind speed records fall in class 3-8 that can be used for wind power generation (figures 3(c)-(h)). Among them, SWS frequency at class 3 and class 5 increased at a rate of 0.18% decade −1 and 0.37% decade −1 (both p < 0.001, figures 3(c) and (e)), while SWS frequency at class 7 and class 8 decreased at a rate of −0.71% decade −1 and −0.68% decade −1 (both p < 0.001, figures 3(g) and (h)). increase in wind speed frequency mainly occurred for relatively low winds, we suggest that the reversal of global SWS was attributed to the decreasing frequency of calm winds and the increasing frequency of light winds. However, light winds are generally smaller than v i (2.2 m s −1 ), which has a limited effect on promoting wind power generation (Pryor and Barthelmie 2010).
The decreasing frequency of relatively strong wind is noteworthy because a majority of wind power generation depends on the strong SWS (Tian et al 2019). To quantify the influence of the changing SWS frequency on wind speed trend, we combined the frequency with climatological mean SWS at each class. Regarding a significant turning point around 2010, the trend of Diff v is analyzed separately in 1981-2010. During 1981-2010, a substantial change is found in class 2, class 7, and class 8 ( figure 4(a)). The Diff v at class 2 had significantly increased at a rate of 5.82% m s −1 decade −1 (p < 0.001), meaning that the increase in class 2 wind contributes 99.94% to offset part of the global wind stilling trend ( figure 4(b), table 2). Nevertheless, the Diff v at class 7 and class 8 decreased by −4.90% m s −1 decade −1 and −6.85% m s −1 decade −1 (p < 0.001), respectively, meaning that the decrease in class 7 and class 8 winds contributed 89.00% and 124.52% to the wind stilling ( figure 4(b), table 2). After 2011, almost SWS in all classes has positive contribution to wind speed reversal, but the contribution of slight wind (class 2-3) are larger, accounting for 33.17%, 30.90% respectively for class 2, 3. Since the strong winds of class 7 and class 8 had an apparent trend change from −11.50% m s −1 yr −1 (p < 0.001, 1981-2010) to an increased rate of 3.00% m s −1 yr −1 (p < 0.001, 2011-2020), they had the largest contribution (i.e. 73.38%) to the trend changes of average SWS from stilling state to reversal state. The substantial decrease of strong Regionally, the calm wind frequency in Asia and South America decreased from over 25% to below 10% from 1990 to 2010 ( figure 5(a)). The decrease was smaller for Africa, Australia and Europe  Positive (negative) values indicate the specific classes of fixed weighted-average SWS increases (decreases). The star represents that the trend is significant with p value < 0.05. The symbol 'n.s.' means the trend is not significant. Error bars show the standard error of the slope in simple linear regression. Table 2. The rate of Diffv and the contribution to weighted-average SWS changes. The rate of Diffv is calculated before 2010 (i.e. 1980-2010) and after 2011 (i.e. 2011-2021) for each wind speed class. The trend of Diffv at class 1 is not shown due to that class 1 only contains SWS = 0 m s −1 , resulting in Diffv is always zero though the frequency of calm wind changes. ( figure 5(a)). Calm wind frequency did not show a noticeable change in North America, instead having significant interannual variations. In Asia, most winds were found to be the light wind of class 2, and the frequency of class 2 wind reached over 50% in 2005-2021 ( figure 5(b)). South America and Europe has the largest increment in the frequency of moderate wind (class 3-6), which increased form 29.48% and 29.44% in 1981 to 41.46% and 42.37% in 2021 (figures 5 (c)-(f)). The frequency of moderate wind has no apparent change in North America and Europe for 41 years. Australia is an exception for  the observed increasing frequency of strong wind at classes 6-8, yet this is obtained by only 26 stations (figures 5(f)-(h)). As for the class 9 wind frequency, a consistent decrease is found in nearly all continents (figure 5(i)). This rapid decrease in strong wind concords with a series of earlier regional studies conducted in America (Pryor et al 2007(Pryor et al , 2009

Effect of wind speed frequency change on wind power potential
To understand the role of continuously decreasing strong winds in wind energy generation, we made an effort to quantify the above results in terms of wind power generation potential both at global and continental scales without considering the influence of technological improvement.  figure S8), which suggested that hub height has a little impact on trend changes of wind energy. The wind energy mentioned below is all based on hub height = 110 m. Compared to the reversal trend of SWS, the recovery of wind power is much slighter. Re-analysis data also report no noticeable changes in mean annual global wind energy generation (Jung et al 2019b). Wind power's reversal trend is relatively weak due to the decline in strong wind frequency.
The wind power changes are quite different from the trend of SWS in Asia and Africa. After a substantial decrease trend (−6.29 TWh yr −1 , p < 0.05), the wind power was still decrease (−0.79 TWh yr −1 , p < 0.05) after the turning year of SWS in Asia, since the rebound of SWS mainly driven by the small wind at class 2 ( figure 5(b)). Wind power in Africa also decreased in the past decade with a rate of −0.001 TWh yr −1 (p < 0.05, figure 7(e)). Tian et al (2019) also reported a decline in wind power potential in half of the stations in Africa. For other continents, the decreasing rates of wind power in America and Europe were −2.06 TWh yr −1 and −3.31 TWh yr −1 (p < 0.001) before turning years of SWS. After the turning years, the increasing rates were only 0.86 TWh yr −1 and 0.76 TWh yr −1 . Studies have also shown a slow increase in average wind energy in the United States over the last decades (Jung et al 2019b). Australia and South America still maintained increasing trends of wind power during 1981-2021, both with comparable rates of 0.11 TWh yr −1 after the turning years (figures 7(d) and (f)). Overall, the increase in wind power after the turning point of SWS was not as strong as the reversal of SWS in the recent decade for the reason that the weakening of strong winds hinders the upward trajectory of the global wind energy industry.
Other factors may affect our analysis of wind power assessment. The atmospheric stability and topography (e.g. mountainous and coastal regions) can affect wind power generation by shaping the main parameter α in the power law (Pryor et al 2020, Pacheco de Sá Sarmiento et al 2022, while we assume a constant and homogenous α in calculation. In addition, the wake effect in wind farms can also be an important factor. It has been suggested that the wake effect cause an average energy loss of around 5.8% in downwind wind farms (Wang et al 2022a(Wang et al , 2022b. Given our estimation does not consider the wake effects, thus our wind energy analysis may overestimate the global power potential. Although there are still uncertainties, this study offers a broad and worldwide estimate; meanwhile, more detailed regional assessments of wind energy help quantify the impact of continuing strong wind declines and benefit investment decisions.

Conclusion
We conducted a global spatiotemporal analysis on the variation of SWS trend and SWS frequency in recent decades (i.e. 1981-2021) and evaluated its impact on wind power generation. Analysis of wind speed frequencies emphasized that the decrease of strong wind frequency (SWS > 5.0 m s −1 ) is a dominant cause of wind stilling with a contribution of 215.96%. After the turning year of 2010, the continuous increase of the light wind (0.1 m s −1 < SWS < 2.9 m s −1 ) accompanying the decreasing calm wind mainly contributes 63.65% to wind speed reversal. Notably, the continuous increase in the frequency of light wind made a negligible contribution to wind power generation. Therefore, the rise in wind power potential was not as optimistic as subjectively estimated based on the reversal trend of average SWS. Global mean annual wind power potential only showed a slight increase at a rate of 2.67 TWh yr −1 (p < 0.05) from 2011 to 2021 (the 1981-2010 rate was −10.02 TWh yr −1 , p < 0.001) compared to the substantial reversal of mean SWS at 0.09 m s −1 decade −1 (p < 0.001) over 2011-2021 (the 1981-2010 rate is −0.08 m s −1 decade −1 , p < 0.001) of mean SWS.
Several issues deserve further research: firstly, synoptic phenomena like wind gusts (e.g. 3 s maximum wind speed) are not included in our results and discussions as the dataset used do not have the higher temporal resolution needed for their study. Secondly, the cause(s) of the continuously decreasing strong wind is yet to be fully explored and understood. Finally, finer-scale regional assessments of wind energy can help supplement the uncertainties associated with large-scale assessments, taking into account the effects of atmospheric stability and topography.

Data availability statement
The data that support the findings of this study are openly available at the following URL/DOI: www. metoffice.gov.uk/hadobs/hadisd/.