1 Introduction

Compared with other atmospheric variables such as temperature or precipitation, wind speed near the surface has been less studied from a climatic perspective than, for instance, hydrological cycles, energy budgets or atmospheric circulation analysis (Stocker et al. 2013; Hartmann 2015). For wind speed, the recent increase of long-term research is being highly motivated by the need of wind resource assessment for the power industry, although it is also presents research interest in several science fields, due to its influence on ecosystems, vegetation, evapotranspiration, marine food chains, air pollution, forest fires or urban heat islands, heatwave studies (McVicar et al. 2012a, b; Kahru et al. 2010; Arain et al. 2007; Le Goff et al. 2009; Kong et al. 2021; Pyrgou et al. 2020) for example.

In order to analyse wind properties from a climate point of view, long-term data series are needed. However, well-spread observational wind databases are scarce in comparison to the ones for temperature or precipitation. This observational limitation can be partially overcome using reanalysis products (Ramon et al. 2019) or climate models (Rockel and Woth 2007; Hahmann et al. 2015; Tobin et al. 2015; Lorente-Plazas et al. 2015; Dörenkämper et al. 2020; Andres-Martin et al. 2023). They take advantage of the dynamical physical consistency when solving the main atmospheric evolution equations, which can improve local processes, and specifically wind features. Europe is a challenging region for wind studies, due to the presence of numerous areas of complex orography. Several studies (Kiss and Jánosi 2008; Swart et al. 2009; Bett et al. 2017; Ramon et al. 2019; Molina et al. 2021; Vautard et al. 2021) have analysed the basic wind speed statistics and have shown the importance of the spatial and temporal resolution of climate models for wind modelling, as can be seen in the analysis of coastal winds (Winterfeldt and Weisse 2009; Feser et al. 2011), or areas with orographic complexity (Obermann et al. 2018; Graf et al. 2019; Rodrigo et al. 2020; Dörenkämper et al. 2020; Molina et al. 2022).

Long-term wind speed studies have been focused mostly on mean fields, its variability, and measurement trends (such as the stilling phenomenon), studying large areas of the globe (Hartmann et al. 2013; Azorin-Molina et al. 2017; Deng et al. 2021), or with a more regional character (Lorente-Plazas et al. 2015; Molina et al. 2021), but they are still limited when compared with other atmospheric variables.

To fully characterize a magnitude from a climate perspective, an approach to its extreme values is also needed. Extremes are, by definition, events that occur with low frequency, as they lay on the distribution’s tail. However, their impact on the society could be extremely harmful, and so it would deserve more attention. Characterization of extreme climate conditions has been made with plenty of proposals (Zhang et al. 2011) and indices. Most of them are based on fixed or percentile-based thresholds, and are the base of several widely-studied extreme events, such as heatwaves (Perkins 2015) or dry spells/drought conditions (Sánchez et al. 2011; Heinrich and Gobiet 2012; Caloiero and Coscarelli 2020).

Research made on extreme wind events has been mainly related to high values (Palutikof et al. 1999; Nikulin et al. 2011; Kumar et al. 2015; Laurila et al. 2021), due to its harmful potential. Low or light-wind conditions, on the contrary, have received less attention, with a lack of clear definition of low-wind events so far (Deaves and Lines 1998), although with an increasing interest in recent years. Several relative thresholds have been proposed to define calm or weak wind days: 10th percentile (Bett and Thornton 2016; Tedesco et al. 2023), or first tercile (Bett et al. 2017), for example. Absolute values have also been employed: related to wind-measurement limitations (less than 5 knots = 2.57 m/s, Deaves and Lines 1998), light breezes (below 4 m/s, Jiang et al. 2010; Weber et al. 2019), air stagnation conditions (less than 3.2 m/s, Horton and Diffenbaugh 2012; Van Nieuwenhuyse et al. 2023), or calm periods (less than 1 m/s, Lucio-Eceiza et al. 2018), and others related to days below the cut-in threshold [lowest operational limit of wind turbines (Leahy and McKeogh 2013; Moemken et al. 2018; Alexander 2016; Santos et al. 2018; Ohlendorf and Schill 2020; Potisomporn and Vogel 2022)]. Additionally, the WMO (WMO 2018) observational guidelines (based on the Beaufort wind scale) state that calm wind speed means less than 0.2 m/s [0 m/s is even sometimes used to define calm periods (Dunn et al. 2022)], light air up to 1.5 m/s, or light breeze less than 3.3 m/s. A specific example of the increasing interest on these extreme values is the emerging concept of energy droughts and associated literature (see for instance, Lledó et al. 2018; Weber et al. 2019; Gangopadhyay et al. 2022), which are generally defined based on an energy deficiency and, thus, wind threshold (Carroll et al. 2018; Raynaud et al. 2018; de la Vara et al. 2020; Gutiérrez et al. 2021; Katzenstein et al. 2010). Low-wind characterization can be of high interest in relation to regional climate models, first to see their capability to properly describe them in present climate conditions, and second, to see how that conditions could be changed for future climate scenarios, as it is shown in Moemken et al. (2018) where several areas project an increase for low-wind values in future conditions.

Besides, persistence of low-wind conditions has been quantified using local (percentiles) thresholds (Cradden et al. 2017), fixed values (typically related to wind energy power operational limits) (Leahy and McKeogh 2013; Handschy et al. 2017; Patlakas et al. 2017; Weber et al. 2019; Frank et al. 2020; Potisomporn and Vogel 2022), small percentages of total wind production (Henckes et al. 2018), or consecutive hours in which the aggregated capacity factors are constantly below a threshold (Ohlendorf and Schill 2020).

A general picture for a better understanding of low-wind behaviour on climatic scales over large regions is relevant for the above-mentioned energy purposes and other scientific areas (Arain et al. 2007; Le Goff et al. 2009; McVicar et al. 2012a, b; Kahru et al. 2010; Kong et al. 2021; Pyrgou et al. 2020) as knowledge on the whole wind speed statistical distribution can be relevant. Besides, climate change is likely to modify also low-wind conditions (Perera et al. 2020; Rapella et al. 2023). Therefore, the more accurate characterization of low-wind for present conditions, the better future changes due to anthropogenic climate change projections could be analyzed.

The objective of this study is to present an overall description of low-wind conditions over Europe (both land and oceanic regions, including Atlantic Sea areas close to the continent and the Mediterranean basin), using 40 years (1979–2018) of hourly wind field from ERA5 reanalysis (0.25\(^{\circ }\) horizontal resolution). Low-wind thresholds will be inspected, and special focus will be made on time variability, and on how these conditions could remain in time.

The structure of the study is as follows: first, the data and proposals to characterize low-wind conditions will be introduced. Then, main statistics, spatial distribution and other relevant features over the whole continent will be shown. Finally, the description of persistence of low-wind speed conditions will be inspected and discussed. The main aim is to contribute to a systematization of low-wind conditions characterization on climatic scales.

2 Data and methods

Fig. 1
figure 1

Situation in the map of each meteorological station. The colour scale represents the range of heights of each station, used in Fig. 2. Blue/red boxes make reference to the sea/land regions. Land regions are Iberian Peninsula (IP), British Isles (BI), France (FR), Mid-Europe (ME), Scandinavia (SC), Alps (AL) and Eastern Europe (EA), as described in Christensen and Christensen (2007), together with five oceanic ones (North Sea area (NS), three Mediterranean Sea parts (MDW, MDC, MDE), as in Romera et al. (2017), and one in front of Portuguese coasts (PTOC))

2.1 Data

Wind observations of 245 weather stations (those with at least 90% of the data) from the Met Office Hadley Centre’s Integrated Surface Database, HadISD (Dunn et al. 2016) are used for validation of wind speed from ERA5 reanalysis (C3S 2017; Hersbach et al. 2020). The locations of meteorological stations from the HadISD dataset are represented in Fig. 1. ERA5 is one of the more recent and widely used reanalysis products, and has been validated to reasonably describe plenty wind characteristics and features (Olauson 2018; Molina et al. 2021; Laurila et al. 2021). Reanalysis allows for a consistent representation of the atmospheric fields, as it solves the main dynamical evolution equations, assimilating and including observational information, including satellite data during the numerical modelling process (Hersbach et al. 2020). Once that validation process is performed, it is widely used as a good observational approximation, over a regular grid for the whole atmospheric volume, with plenty of available atmospheric magnitudes. Nevertheless, this modelling representation of atmospheric fields presents some limitations, mainly due to the employed resolution and parametrizations. These issues prevents a fully accurate description of wind speed flows, in particular related to the small scale processes, such as over areas with orographic heterogeneity or with land complexities. This limitations are seen when dealing with extreme values or distribution tails (Molina et al. 2020; Soares et al. 2020; Campos et al. 2022; Jung and Schindler 2022). It is also important to consider that wind measurements from HadISD shows some numerical resolution limitations, as stated in Dunn et al. (2019), related to transcription, rounding, conversion and truncation on the recording process. This issue can be potentially more relevant for close-to-zero winds (Dunn et al. 2022), when also wind direction becomes unreliable.

Instantaneous hourly wind components at 10 m from the period 1979-2018 are considered from observations (Dunn et al. 2016) and reanalysis and then wind speed is computed from their components. ERA5 netcdf reanalysis data have been downloaded through the EU-funded Copernicus Climate Change Service (C3S, https://cds.climate.copernicus.eu/). HadISD observational database values were obtained from https://www.metoffice.gov.uk/hadobs/hadisd/ web page.

Some of the analysis is performed over several subregions of the European domain, shown on Fig. 1. Validation of reanalysis against land observational stations is made over seven land regions, following (Christensen and Christensen 2007), as they roughly correspond with homogeneous climatic areas: Iberian Peninsula (IP), British Isles (BI), France (FR), Mid-Europe (ME), Scandinavia (SC), Alps (AL) and Eastern Europe (EA). Five more regions over the ocean are included when the analysis is just performed with ERA5: one covers the North Sea area (NS), the Mediterranean Sea is separated in three parts (West, Central and East: MDW, MDC, MDE), as in Romera et al. (2017), and finally one in front of Portuguese coasts (named also Portugal Ocean, PTOC), to inspect also that oceanic region.

2.2 Methods

The proposed wind speed absolute thresholds for light and low-wind conditions are 1.5 and 3.3 m/s, respectively (where the first one is the limit for light air category and the second one is the limit for light breeze category in the Beaufort scale). Although in the first stages of the analysis both 1.5 and 3.3 m/s will be studied, “low-wind” expression will be used to define the overall analysis. Basic statistical analysis from hourly data is made with mean values and 10th percentile as a measure of lowest wind speeds.

Interannual variability is analyzed using the coefficient of variation (CV = \(s/\overline{x}\), being s the standard deviation over the 40 years, and \(\overline{x}\) the annual mean), and the annual cycle by using seasonal means, averaged over the 40 years.

Finally, low-wind events (those events that could remain in time), hereafter named as low-wind spells, are quantified through their frequency and intensity, as both aspects are needed to fully characterize these episodes. A low-wind spell event is considered when at least two consecutive hours are below the considered threshold. First, the longest annual low-wind spell from hourly and daily time frequencies is computed. Any daily magnitude is obtained from the daily average of hourly wind speeds. Such an index gives an idea of how extreme are the low-wind episodes. Using hourly wind speed, the mean length of such spells and the total number of spells (all averaged for the whole 40 years period) at each grid cell of the European domain were studied. The complete frequency distribution of the spells’ length was also inspected for each of the subregions described above.

These computations were made with the free software R (R Core Team 2022). From R-base package, the function rls (run length encoding) was employed. The Pearson correlation coefficient in scatterplots and maps was obtained from the corrr package (Kuhn et al. 2020). Graphical representation was made from several packages (Hijmans 2020; Bivand and Lewin-Koh 2020; Perpiñán and Hijmans 2021).

3 Results

3.1 Low-wind conditions comparison between ERA5 and observations

Figure 2 represents values from the 245 HadISD weather stations against the ERA5 reanalysis corresponding cells. The first row shows the mean wind speed, the second row the number of hours below the low-wind speed threshold (3.3 m/s) and third row the number of hours below light-wind threshold (1.5 m/s). In addition, each column represents observations from a specific height interval, with the aim to obtain some detail on the observational validation related to the height of the stations. The first column shows meteorological stations below 50 m height, the second column shows the meteorological stations between 50 and 150 m height and the third column shows meteorological stations above 150 m. Results are also averaged over the seven main land climatic regions (from Christensen and Christensen (2007)), and are presented with different colors. The spatial correlation coefficient (Pearson) between reanalysis and observations is computed for each scatter plot.

Fig. 2
figure 2

Scatterplot of annual values from the observational stations against corresponding ERA5 land cells, averaged for 1979–2018 period. The first row shows the mean hourly wind speed (m/s); second row the low-wind threshold hours per year (3.3 m/s); third row the light-wind threshold hours per year (1.5 m/s). First column show stations below 50 m height, the second column observational stations between 50 and 150 m height and the third column observational stations above 150 m height. Colors distinguish each of the seven land regions covering Europe. Correlation coefficients (Pearson) are shown on each top-right corner

The representation of mean values shows a general good agreement between ERA5 and observations. However, there is a larger spread for higher mean wind speed values and a slight underestimation in areas where the observed mean wind speed is lower. This underestimation is clearer for those stations above 150 m. These results are consistent and in agreement with the several ERA5 wind statistics, mainly on monthly scales, that were already validated against HadISD in previous works (Molina et al. 2021).

Regarding the comparison for the low-wind threshold (Fig. 2 second row), ERA5 generally overestimates the hours below 3.3 m/s compared with the corresponding observational points. The overestimation is more clear for stations above 150 m and over IP, EA and AL regions. A similar behaviour can be seen for the light-wind comparison (Fig. 2 third row). These results show in each case a relatively high correlation between reanalysis and observations in spite of the above mentioned limitations: 0.82–0.85 for mean wind speed (top row), 0.63–0.81 for low-wind hours (middle row), and down to 0.38–0.74 for light-wind hours (bottom row).

A reasonable overall ERA5 mean values behaviour is obtained, with a decrease in their performance as wind speed values decrease. In the case of light-wind threshold for stations below 50 m, anomalously low correlation values are present, probably mainly due to some strong outliers.

Low-wind hours average 3000–4000 h per year for cells up to 150 m, being larger for higher elevations. When light hours are inspected, these numbers do not reach 1000 h per year, being also more spread when stations above 150 m are analyzed.

Regional differences are also of interest, in the ERA5 wind speed spatial representation. It can be seen that the Alpine region (AL, pink color) presents the lowest mean values, with an overall ERA5 underestimation, together with the larger overestimated low and light-wind hours. This result could be related to the difficulties for modelled wind to accurately describe the atmospheric dynamics over these mountainous areas, where the steep orography is misrepresented by the limited resolution of the reanalysis, leading to inaccurate wind channelling characterization over valleys and peaks (Graf et al. 2019; Dörenkämper et al. 2020). Such biased results could be reduced when using higher resolution (Molina et al. 2022), but model parameterizations seem to play also a significant role (Van Nieuwenhuyse et al. 2023). For the rest of the regions, a better correspondence between ERA5 and observations with respect to mean values is observed. However, some differences can be seen for low and light-wind hours. When looking at subregions it can be seen that ME and BI present the best performance, EA shows a large spread and a clear overestimation in low-wind hours. The same behaviour is also observed for SC or the IP.

Fig. 3
figure 3

Boxplots of averaged seasonal values (above) and hourly (below) comparing all the observational stations on each boxplot against the corresponding ERA5 land cells, averaged for 1979–2018 period of low-wind events, in hours per year, using the 3.3 m/s threshold

When low-wind hours are computed on different time scales averages (seasonally and hourly) for each cell, and then represented through boxplots (Fig. 3), the spread among all the points for both observations and reanalysis and how they evolve on both time cycles can be studied. A similar analysis was already performed for mean wind values and their annual cycle in (Molina et al. 2021). Results are quite similar when comparing both time cycles for ERA5 and observations. Hourly values range from around 200 h in the night to 150 h in the middle of the day, as expected due to the smaller average wind speed when the sun is absent. A relatively homogeneous distribution throughout the year of around 1100 h per season is also obtained for both ERA5 and observations averaged cells. These rough statistics point to the capability of ERA5 to reasonably describe the global low-wind observed features for the whole region and at different time scales.

3.2 Low-wind spatial and temporal variability

3.2.1 Spatial analysis

The spatial distribution of mean hourly wind speed over Europe for the 40 years period is shown in Fig. 4 (top-left). Values of mean wind speed over land regions are around 3 m/s on a latitudinal band around 55\(^{\circ }\)N (British Isles, Central and North-Eastern Europe), as a result of the typical atmospheric westerly circulation (Bartoszek 2017). On southern regions, like the Mediterranean basin and surrounding land areas, wind speed mean values are around 2 m/s, with a more heterogeneous distribution, strongly related to the complex orography of the surrounding mountain chains. This is in agreement with the aforementioned difficulties to properly describe wind values over mountains, as it is the case also over Scandinavian region. Values over oceanic regions are larger, near 10 m/s on the Atlantic ocean above 50\({^\circ }\)N, and over 6–8 m/s on the southern Atlantic and most of the Mediterranean Sea. These results are expected due to the absence of orographic barriers or complexities in marine areas that could reduce or significantly alter the wind flow.

Fig. 4
figure 4

Annual averages (1979–2018 period) of hourly mean wind speed (m/s) (top-left figure), 10th percentile wind speed (m/s) (top-right figure), number of hours below light-wind threshold (h/year) (bottom-left figure), number of hours below low-wind threshold (h/year) (bottom-right figure)

The mean values and the spatial distribution are consistent with results already shown with other reanalyses, (ERA40 Kiss and Jánosi 2008; Swart et al. 2009), multi-reanalysis (Ramon et al. 2019), regional climate models (Jerez et al. 2015; Moemken et al. 2018; Vautard et al. 2020), or ERA5 at 100 m height (Dörenkämper et al. 2020).

As a first approach to quantify low-wind features, the 10th percentile (P10) of hourly wind field is inspected (Fig. 4, top-right). P10 can be seen as a rough approach of the low-wind extremes or the lower tail of wind distribution, as it is the value that is not exceeded during 10\(\%\) of the time (876 h per year). The 10th percentile map closely resembles mean wind features (0.98 of spatial correlation between both), roughly with half of the values. The 10th percentile ranges between 0.5 and 2.5 m/s over land regions. Northern continental Europe exhibit higher and more spatially homogeneous values, while the Mediterranean land regions present smaller P10 due to the more complex spatial features. Over the marine areas, the Mediterranean Sea has generally values around 2–2.5 m/s, whereas results over the Atlantic Ocean show the highest P10 values of the domain (up to 5 m/s).

Assessing the spatial extent of thresholds on the 10th percentile map, over the 24.8\(\%\) of the domain the P10 is smaller than 1.5 m/s (light-wind), increasing up to 79\(\%\) for the low-wind threshold (3.3 m/s). Therefore, low-wind threshold does seem to be quite usual over Europe, specially over land areas. This is consistent with, for example, the European Environmental Agency Swart et al. (2009) report. Using 2000–2005 ERA40 reanalysis (0.25\(^{\circ }\) resolution, 6-h averages), annual 10 m wind speeds larger than 4 m/s were obtained just across 13.5% of the European land surface area. Light (left) and low (right) wind speed hours per year (averaged over the 40 years) are shown on the bottom panels of Fig. 4. Values over 4300 h/year (bottom-right), that is, roughly half of the year, are found for most of the continental areas, with much larger values over mountain chains. These values are obtained over most of the northern half of Europe, including the British Isles, but also at the Iberian Peninsula plateaus, over non-mountainous areas over the Balkans and at the Scandinavian Peninsula out of their mountains. Therefore, the numbers indicate that, the P10 was strongly below the low-wind threshold. When looking at results over oceanic areas, on the contrary, less than 500 h over the Atlantic region, for example, are obtained. This is consistent with the higher values of mean wind, due to the absence of obstacles and the pressure conditions that lead to stronger and more regular atmospheric flows. Over the Mediterranean Sea results are similar to the ones seen over Central Europe.

The spatial structure of light-wind threshold hours (Fig. 4, bottom-left) and low-wind hours (Fig. 4, bottom-right) are quite similar, with a correlation coefficient of 0.85. Obtained light-wind values are typically around 900 h, and close to 3300 h for low-wind threshold. Due to these obtained similarities, the study will be focused from here just on low-wind features analysis. Low-wind magnitude can be seen, from the results already obtained, not a representation of very small wind or calms, but a description of the lower part of wind speed distribution.

3.2.2 Time variability

The annual cycle (showing the average over each of the four seasons) of low-wind is described in Fig. 5, computing boxplots for each season, and over the seven land regions, together with another five regions over oceanic areas, as indicated in the methods section (one of the oceanic regions at the North Sea, three in the Mediterranean, and one in front of the Portuguese coasts). Several remarkable features can be seen from the seasonal cycle perspective. A cycle with a maximum during summer (JJA) and a minimum during winter (DJF) is found for almost all the regions. This annual cycle is in opposition to the mean wind speed annual cycle already described in the literature (Jung and Schindler 2020; Molina et al. 2021), and is due to the fact that the larger the wind speed, the smaller the amount of hours below the low-wind threshold. The only exception is over the eastern Mediterranean, where summer season does presents such maximum on low-wind hours, which is related to the Etesian winds (Tyrlis and Lelieveld 2013), that occur from May to September.

The amplitude of the seasonal cycle for the median values is above 300 h for most of the regions, ranging, for example, from around 930 h to 1350 h in France, from 1420 to 1680 h over the Iberian Peninsula, from 620 to 900 h at the British Isles. Oceanic regions exhibit smaller values throughout the year for the five regions and shows smaller amplitude on their seasonal cycle. Interestingly, a different behaviour is obtained for the Mediterranean subregions with larger and more spread values compared to the North Sea and the Portuguese coastal area. On both marine areas with very low amplitude of the seasonal cycle and values from 150 to 200 h among seasons, and very small interquartile seasonal spread of values.

Fig. 5
figure 5

Seasonal (winter (December–January–February: DJF); spring (March–April–May: MAM); summer (June–July–August: JJA); autumn (September–October–November: SON)) boxplots of 1979–2018 averaged low-wind hours at each cell for 12 regions covering Europe: seven over land and five over the ocean (as described in methods section). Outliers (values larger than \(Q3+1.5 \cdot (Q3-Q1)\) or \(Q1-1.5 \cdot (Q3-Q1))\) are not shown (to ease the view of the main boxplot features)

The interannual time variability of the amount of hours below the low-wind threshold is represented by the coefficient of variation CV, defined as \({s\over \overline{x}}\), where s is the standard deviation along the years and \(\overline{x}\) the 40-years average. It is represented in Fig. 6 for the twelve regions under study. There is no clear or systematic difference that can be attributed to land/sea position of the regions. IP, SC and ME continental areas CV boxplots present very low values (0.05 or less). The oceanic regions with lower values (NS, MDW and PTOC) are around 0.10. As these ocean regions present smaller low-wind hours than the land regions, that means that such land regions present, proportionally, smaller interannual standard deviation variations. It is interesting to notice also that, the three Mediterranean regions behave differently in terms of their CV, being the Western Mediterranean (MDW) the one with smaller values (around 0.07), and the Eastern one with the largest (0.15), without overlapping when including whiskers of the boxplot. Not only mean values, but also spread distribution values of CV present differences among regions. EA is the one with larger spread in their values, probably due to the heterogeneity of spatial region covered, being also the case for FR or AL. When looking at the five oceanic regions CV spread is smaller than those land regions with larger spread, but similar to some other land regions, such as ME or SC.

Fig. 6
figure 6

Coefficient of variation (CV) (CV = \(s/\overline{x}\), standard deviation (s) divided by mean annual value (\(\overline{x}\)) over 40 years) for each cell of the domain, grouped as boxplots for each of the regions defined in the methods section. As in Fig. 5, outliers are not shown. Land regions are shown in red colors, ocean regions in blue colors

3.3 Low-wind spells characterization

Low-wind features are further explored by analyzing how these conditions could remain in time. As a simple measure of the limits of such events the longest annual episodes are shown first. Then, an overall characterization of low-wind spells is presented through the annual averages of frequency, intensity and extension, using both the mean length and the number of spells. Finally, for further insight on the relative contribution of large and short events, the whole frequency distribution of spells over the subregions is inspected.

3.3.1 Longest low-wind annual spells

The longest annual spell is a standard feature when describing heat/cold waves, or dry spell events. It can be seen as a measure of how extreme these events can be. Figure 7 presents the longest spells from both hourly and daily mean values, averaged annually over the 1979–2018 period.

Fig. 7
figure 7

Longest annual low-wind spell (days/year), averaged over the 40 years period. Left figure is obtained using wind daily means, right figure from hourly wind values (also expressed in days/year, that is, multiplying by 24 the consecutive hours for the spells)

Some high values in Fig. 7.left (from daily wind speed means) are out of the color scale (more than 90 consecutive days) over the mountains. As mean wind speed is there clearly underestimated, low-wind threshold values are obtained during most of the time, and so the longest spell could last even for the whole year. For the rest of the domain, around the main mountain chains, longest daily wind spells can last around 30 days over the Iberian Peninsula plateaus, Sweden, Southern France or several Central Europe countries. The northern part of the continent belt, around the Baltic Sea, presents spells around 10–15 days/year.

When the longest spell is computed from hourly values (Fig. 7 right), numbers are much smaller. This may be expected, as in this case every of the 24 hourly data must meet the criteria and not just the daily average. Outside the largest mountain chains, values obtained can be close to 10 days (that is, 240 consecutive hours) over many areas of the southern half of Europe. Central European latitudes (around the 55\(^{\circ }\)N belt) present their largest annual hourly spell around 4–5 days (120 h), values that can be compared with the ones of Ohlendorf and Schill (2020), from a 5-years period over Germany, although there just 3–6 h frequencies of wind speed at 50 m from MERRA2 reanalysis are used. Both hourly and daily figures are closely correlated, with a Pearson correlation coefficient of 0.82. Hereafter, and for consistency with the analysis already presented, based on hourly data, the rest of the spells results will be just focused on hourly wind values. Other studies at specific locations (Leahy and McKeogh 2013; Potisomporn and Vogel 2022) are also roughly consistent with these results.

3.3.2 Average low-wind spells features

When all the spells are considered, both the number (as a measure of frequency) and the mean length (as a measure of intensity) are needed to characterize these events. Figure 8 presents both, considering a spell when wind is below the threshold at least for two consecutive hours.

Fig. 8
figure 8

Mean spell length (left) and number of low-wind spells (right), averaged over the 40 years. A spell is defined when at least two consecutive hours are below the 3.3 m/s threshold

The mean length (Fig. 8.left) is larger over the mountain areas of the continent, even out of scale, above 60 h/year averaged for the whole period. The northern European (50–55\(^{\circ }\)N belt) land region exhibit a relatively homogeneous pattern, with values around 15–20 h/year. The Mediterranean land regions patterns resembles what is seen for the longest spells in Fig. 7, with more complex and heterogeneous mean value patterns than over northern Europe that range from 15 to 30 h/year. Most oceanic areas present mean spell values below 5 h/year with some exception on the Mediterranean.

The spatial structure of the spells’ frequency, is presented in Fig. 8.right. This magnitude is more homogeneous over Northern Europe, with more than 200 episodes, and more spatially complex over the southern half of continental Europe, ranging from 200 to 300 events. A small number of events are obtained over oceanic regions, as already seen in de la Vara et al. (2020) for a Mediterranean islands analysis, where the larger mean wind leads to this small number of episodes. Over the mountain chains, also a small number of events is obtained, but for opposite reasons. There, the underestimation of the wind on the mountains causes few and long low-wind spells, as shown also in Frank et al. (2020). It is interesting also to notice results over the oceanic regions, where the Mediterranean areas present more complex features compared with the Atlantic ones, related to the channelling wind flow behaviour due to the distribution of islands over that sea, as already pointed in de la Vara et al. (2020), for example, at the strait of Bonifacio between Sardinia and Corse. These results are comparable, in the spatial distribution, to de la Vara et al. (2020), based on wind energy droughts over the Mediterranean islands, using the deficiency index method of Raynaud et al. (2018). It is interesting to notice that the differences between the Mediterranean basin and the Atlantic Ocean results already seen when looking at time variability on both seasonal and interannual scales are also obtained when looking at low-wind spells.

3.3.3 Low-wind spells frequency distribution

Figure 9 represents distributions of low-wind spells at each land and ocean region, averaged over the 40 years. Note that the Y axis in the figure is presented in logarithmic scale. The frequency of low-wind spells decreases exponentially (and so linearly with the logarithmic Y axis) as their length increases, as it seems to be reasonable for persistence statistics (Weber et al. 2019), for continental regions until a spell length of around 10 h. After that, some different behaviour is found depending on the region. The number of the shortest events (2 h) range from 30 to 20 over land on average. Differences on the shape of the mean curve show some with a more pronounced decrease in frequency for shorter spells, which is the case of Eastern Europe or British Isles. They present a higher slope at the beginning compared to other regions like France. It can also be noticed how for spells from 14 to 20 h length, some regions present a local maximum in frequency, being the Iberian Peninsula the region where it can be seen more clearly. Mean values for the shortest spells range from more than 20 h/year over the Iberian Peninsula, the Alps, France or Eastern Europe, to around 10 h/year over the British Isles. Similar low-wind persistence figures are obtained in the UK (Potisomporn and Vogel 2022) when studying offshore wind energy production over that region.

Results for the oceanic regions of Fig. 9 show that the shortest events on the Atlantic and North Sea region occur around 10–15 times a year, but around 25–30 events in the Mediterranean areas. When looking at the largest spell lengths shaded areas (bottom-right part of the figures), a large spread is obtained. This is due to the low frequency and the large standard deviation at such values, that is magnified on a logarithmic scale as the lower band of the shaded area values (annual mean low-wind spell lengths minus the interannual standard deviation) are close to zero in absolute numbers, and so much longer when logarithm is computed. As stated before, this different behaviour reinforces the fact that low-wind characteristics over the Mediterranean basin are strongly affected by wind processes that do not occur over the North Sea or the Portuguese coast.

The spatial variability of distributions, represented in Fig. 9 by the color shading, presents differences across regions, being larger for those with more orographic complexity, like the AL region or the IP. Their width (and so interannual spread or variability) at smaller lengths is also quite different among regions, ranging from 20 spells/year for IP, to 10 over SC or around 5 at NS or PTOC.

Fig. 9
figure 9

Frequency of low-wind spells (of at least two consecutive hours) against its length (h). Y axis uses logarithmic scale, to ease the inspection of long period probabilities. Panels show the mean number with a solid line (averaged for the 40 years and over all the cells of each region) and the shaded area represents the interannual range of variability (\(\overline{x}\pm s\), with \(\overline{x}\) the annual low-wind spell length mean and s the interannual standard deviation) for each region. Red colour refers to the continental regions and blue to the oceanic regions

4 Conclusions

An overall climatological description of low-wind conditions over Europe, using ERA5 reanalysis has been presented. ERA5 presents a reasonable statistical agreement with low-wind observational features, considering the small amount of available observations. Thus, apart from mean wind speed statistical features described in Molina et al. (2021), low-wind and light-wind hours present a strong correlation between at different heights, together with diurnal or seasonal time cycles for most of the continental locations. However, some clear exceptions on this agreement, in particular over higher mountain chains, is also obtained, so results there should be taken with a lot of care. Anticyclonic patterns (Patlakas et al. 2017; Weber et al. 2019), SST and large scale variability (Lledó et al. 2018) can help to explain, from a global perspective, persistence of these low-wind events, although a detailed analysis of such mechanisms is out of scope of this work. Two main big continental areas can be distinguished in terms of hourly mean wind speed values and so the amount of hours of low-wind conditions. One is the northern region above the 55\(^{\circ }\)N latitude belt over land and the other, the southern region around the Mediterranean, where topography and coastal processes are playing a relevant role. Most of the land areas exhibit, on annual average, low-wind values around half of the hours of the year. On the contrary, oceanic regions, with larger mean values, present typically around 1000 h per year of low-wind. Nevertheless, some differences are seen in the results when comparing the Mediterranean and the Atlantic regions. The former present higher amount of low-wind hours and spatial variability inside the basin, where western and eastern sides behave slightly different.

When looking at seasonal variability of low-wind, summer maximum and winter minimum seems to be a clear common feature for all the regions. Changes up to 300–400 h on the median values, from summer maximum to winter minimum over several continental regions (France, Mid-Europe, for example) are obtained, but other regions present smaller annual cycle. This cycle is also obtained over oceanic areas but with smaller values. A different behaviour is found in the eastern Mediterranean, with a decrease in low-wind conditions in summer, compared to other adjacent regions, as a result of a reinforcement of the Etesian. Those results are in line with previous energy drought analysis (de la Vara et al. 2020) over the Mediterranean islands.

The analysis of low-wind spells reveals that the longest annual values based on daily wind speed can last up to 30 days (for the 40 years average) over many land areas of the Iberian Peninsula, southern France or Scandinavia. Half of that numbers (10–15 days) are obtained over the northern 55\(^{\circ }\)N degrees belt. When hourly data is used, similar spatial patterns are obtained, with, logically much smaller values (around consecutive 5 days or 120 h over that belt). Statistical low-wind spells features distribution (mean length and frequency) present oceanic areas with small and short mean lengths events and land areas with a more heterogeneous behaviour.

The complete frequency distribution further highlights the differences between regions: a decreasing with different shapes (more regular or with mixed trends along the range of spells length) for low-wind spells duration over land regions, and a more regular and clear exponential decrease of values over the ocean, again with differences between the Atlantic and the Mediterranean region results. The shortest (2 h) and more frequent spell (averaged over each region and the whole period) presents values that range from 25–30 to less than 20 over the Atlantic regions.

The study presented here aims to serve as a first step towards a better understanding, quantification and standardization of low conditions with a climatological perspective. Reanalysis has been shown to be a good tool to perform such analysis with spatial and temporal consistency, allowing to describe differential features over the European continental areas and the main oceanic ones. Several elements of further research seem to be of high interest, such as low-wind spells analysis from the renewable energy perspective, a deeper analysis of smaller low-wind thresholds taking into account observational limitations, the capability of climate models to describe low-wind conditions and the potential impact of climate change on them.