1 Introduction

Wind is a highly variable phenomenon over all time scales, from gusts lasting seconds, to long-period variations spanning decades (e.g. Watson, 2014). Harnessing the wind resource for electricity production is a rapidly-developing field, with many challenges for engineering, energy systems design, national-scale energy policy and meteorological forecast systems (e.g. Wiser et al, 2011) Short-term wind variability is critically important to the day-to-day management of a wind farm, and efficient running depends on having high quality wind speed forecasts (e.g. Foley et al. 2012; Jung and Broadwater, 2014). However, the impact of long-term, decadal-scale variations in the wind climate is less well understood.

This is partly due to a historical lack of data. Typically, when a site is considered for wind farm development, developers are often restricted to using statistical techniques to relate observational records from nearby stations to the site in question. Homogeneous data from any single station will usually only span a few years to a decade, but can be supplemented by data from a dedicated meteorological mast positioned on-site for a limited period of time such as 1–3 years (Petersen and Troen 2012; Liléo et al. 2013; Carta et al. 2013). In the absence of long-term data sets of wind speed itself, studies of long-term wind variability typically use pressure-based metrics as proxies for the wind (e.g. Palutikof et al, 1992), often combined with complex statistical procedures to relate to the wind speed at a site (e.g. Kirchner-Bossi et al. 2013, 2014). Around Europe, indices based on the North Atlantic Oscillation (NAO) have often been used Boccard (2009). Standard NAO indices correlate well with winter wind speeds in northern/western parts of Europe. However, this is not true more generally, such as at other times of the year or in other locations (Hurrell et al. 2003), and alternative indices must be used in these cases (e.g. Folland et al. 2009). Regardless of definition, the NAO does not capture the full variability seen in wind speeds. Thus, there is scope for improvement over all these techniques.

Within the past decade, reanalysis data products have been able to extend such site assessment studies, allowing a description of a reasonable climatological period of around 30 years. The two main global reanalysis data sets used for this are the ECMWF Footnote 1 Re-Analysis Interim product (ERA-Interim, hereafter ERAI; Dee et al. 2011), and NASA’s Modern Era Retrospective-analysis for Research and Applications (MERRA, Rienecker et al. 2011), which both cover the ‘satellite era’ (1979 onwards). Such data sets are necessarily produced at relatively low spatial resolution (e.g. grid sizes ∼0.7°), and cannot, on their own, be used to determine the likely wind speeds at a site. In combination with other techniques however, from simple rescaling, detailed statistical modelling or even full dynamical downscaling, reanalysis data can be a key source for obtaining a representative wind climatology for a specific site (Kiss et al. 2009; Petersen and Troen 2012; Kubik et al. 2013; Badger et al. 2014).

Most recently, attempts at producing century-scale reanalyses have yielded results: the NOAAFootnote 2 Twentieth Century Reanalysis (hereafter 20CR, Compo et al. 2011) and ECMWF’s ERA-20C (Poli et al. 2013; Dee et al. 2013) data sets provide ensemble realisations of the atmospheric state spanning over 100 years. However, as they are at even lower resolution (e.g. 1–2 °), and their early data is subject to substantial uncertainty, care must be taken when considering how to interpret their results in the context of wind farms.

Concerns within the wind industry about the possible impacts of future climate change, along with greater availability of larger data sets, have motivated various studies resulting in a greater awareness of the risks of climate variability (whether anthropogenic or natural). In fact, unlike the situation for temperature, there is little evidence of any long-term trend in globally-averaged wind speeds—see, e.g. the Fourth and Fifth Assessment Reports (AR4/AR5 respectively) of the IPCC’sFootnote 3 Working Group I, Trenberth et al. (2007) and Hartmann et al. (2013). The low confidence in such assessments is due in part to difficulties with the historical observational record, coupled with the highly-variable nature of winds in both space and time. For example, various data sets have suggested a positive trend in wind speeds over the oceans, with significant regional variability (Tokinaga and Xie 2011; Young et al. 2011a; Young et al. 2011b; Wentz and Ricciardulli 2011; Young et al. 2012). Over land however, the situation is different: an apparent reduction in surface wind speeds (nicknamed ‘global stilling’) has been seen in recent decades in some data sets (McVicar et al. 2012, 2013), with studies suggesting that it could be due in part to anthropogenic factors, such as changes in land-use increasing the surface roughness (Vautard et al. 2010; Wever 2012), or aerosol emissions locally changing the thermal structure of the atmosphere (Bichet et al. 2012). It is important to note that stilling is not seen in reanalysis data, which use climatological aerosol levels and do not include land-use change. Over both the land and oceans, opposing trends in different regions and times of year will act to reduce any globally averaged trend signal. While further and better data is required to settle questions on the true scale, causes and interrelationships of changes in wind speeds over oceans and land, it is important to note that these observed trends are always much smaller than interannual variability.

Given the uncertainties in trends in the historical wind climate, it is not surprising that projections of future wind climates should also be treated with caution. The review of Pryor and Barthelmie (2010) concluded that wind speeds over Europe would continue to be dominated by natural variability, although by the end of the century some differences could have emerged—although even the sign of the change was uncertain. The IPCC’s Special Report on Renewable Energy Sources and Climate Change Mitigation (SRREN) came to a similar conclusion (Wiser et al. 2011), and the IPCC’s AR4 (Meehl et al. 2007; Christensen et al. 2007) and AR5 (Collins et al. 2013; Christensen et al. 2013) noted that there is low confidence in any projected changes. Consequently, Pryor and Schoof (2010) and Dobrynin et al. (2012) found that the choice of emission scenario or concentration pathway has relatively little impact overall on the resulting wind climate. It is important to note that simulations of the historical climate over the twentieth century (from both atmosphere-only and ocean-coupled models) do not reproduce the observed variability in atmospheric circulation (Scaife et al. 2005; Scaife et al. 2009), so the uncertainties in these climate projections do not preclude large multi-decadal variations in the future.

Overall, the effect of climate change on the annually-averaged wind resource is thought to be small, although the increased seasonality seen in some studies by 2100 could have a challenging impact on wind-dominated electricity networks (Hueging et al. 2012; Cradden et al. 2012).

Thus, when seeking to improve assessments of future wind speeds over the lifetime of a turbine, there is more to be gained from an increased understanding of historical long-term wind variability than through climate change model runs. Given this context, we show in this paper how the new class of century-scale reanalyses can be linked to the more widely-used satellite-era reanalyses, thus allowing for information on the long-term decadal-scale variability in wind speeds to be propagated through the model chain when performing a wind site assessment. In Section 2, we describe the two main data sets we use, including their limitations. We compare them in detail in Section 3, and describe our procedure for relating the two. Section 4 shows results for the wind speed distribution over Europe, including long-term averages, variabilities and changes in the shape of the distribution over time for selected regions. We discuss our conclusions in Section 5.

2 Data sources

Reanalyses represent the most convenient data sets for assessing the long-term historical wind climate, in the sense that they aim to provide an optimal combination of observations and numerical model: the data provided in a reanalysis aims to give the best estimate of the “true” situation at any given point, as well as being homogeneous in time (e.g. free of systematic shifts), and complete in both space and time. However, in reality, biases and uncertainties inherent in both raw observations (due to location, frequency, instrumentation, etc.) and models (due to resolution, parametrisation schemes, etc.) mean that such data sets must be used with caution.

This study primarily uses data from the Twentieth Century Reanalysis project (20CR), in conjunction with wind speeds from the ERA-Interim data set (ERAI) for validation and calibration of the 20CR data. We describe key aspects of these data sets in the following sections.

2.1 Data from the 20CR ensemble system

A full description of the ensemble reanalysis system used in the 20CR project is given in Compo et al. (2011). Here, we describe some key features that have important impacts on our analysis methods and results.

The 20CR assimilates sea-level pressure and surface pressure observations alone (from the International Surface Pressure Databank, incorporating the ACRE Footnote 4 project, Allan et al. 2011), using observational fields of sea-surface temperature and sea-ice concentration (HadISST1.1, Rayner et al. 2003) as boundary conditions. It uses the April 2008 experimental version of the NCEPFootnote 5 Global Forecast System (GFS), a coupled atmosphere–land model produced by the NOAA NCEP Environmental Modelling Centre.

The 20CR data assimilation system is based on an Ensemble Kalman Filter. The data are produced in a series of 5-yearFootnote 6 ‘streams’ (independent runs, to simplify parallelisation), with 56 members in each stream. A consequence of this system is that ensemble members only remain temporally continuous for the 5-year duration of each stream. This has implications for how variability is assessed over long time periods; we discuss this in more detail in Section 4.1.

As highlighted in Compo et al. (2011), when considering variability, it is important to use the ensemble members directly, rather than using the daily ensemble-mean time series alone. The increased uncertainty in the early period of the data leads to greater disagreement between the ensemble members, such that a time series of their mean will have much less variability than the members individually. This would lead to a spurious strong reduction in variability appearing at earlier times in the ensemble mean.

We use the updated release of the 20CRv2 data (hereafter simply 20CR), spanning 142 years from 1st Jan 1871 to 31st Dec 2012. While it was produced on a T62 spectral grid with 28 vertical levels, we use the output data provided on a regular latitude–longitude grid with cell size 2°, at the the near-surface pressure level at σ:=P/P surface = 0.995 (around 40 m height). The σ = 0.995 level is a reasonable choice for turbines whose rotor hubs are expected to be some tens of metres above the surface; typical hub heights are between 40 and 100 m, but vary greatly (Wiser et al. 2011); we do not expect our conclusions to be qualitatively affected by the precise height above ground. More details on our choice of levels can be found in Appendix A. We use daily-mean wind speeds U, which we calculate by averaging the wind speed magnitudes from the 6-hourly u (zonal, i.e. westerly) and v (meridional, i.e. southerly) component fields. We are not considering sub-daily variability, as this is likely to be poorly represented with only four timesteps per day, in addition to the low horizontal resolution. Using daily means significantly reduces the amount of data that we need to analyse. However, calculating daily means using only four snapshots is likely to lead to some underestimation, as the wind distributions we are sampling tend to be positively skewed. Using daily means also has an impact on the form of the resulting wind speed distribution, and on Weibull fits in particular; we discuss this in the Supplementary Information.

Some recent studies have highlighted potential problems with the 20CR data set. Ferguson and Villarini (2012, 2014) have performed a detailed analysis of change points in the 20CR data, finding that, while these are in fact common in the data set overall, there are many areas, especially in the northern hemisphere, where the 20CR remains largely homogeneous for many decades. Their results emphasize that users of the 20CR data must be aware of possible—indeed, probable—inhomogeneities in the data, and the potential impact this could have on their analyses. Stickler and Brönnimann (2011) found very significant differences between 20CR winds and pilot balloon measurements in the West African Monsoon region over 1940–1957, and Liléo et al. (2013), using the 20CR to study interannual wind variability over Scandinavia, had to discard 20CR data prior to 1920 due to suspicious behaviour in some grid cells. Finally, there has been some debate on the consistency of long-term trends in storminess and extreme winds found in 20CR compared to observations (Donat et al 2011, Brönnimann et al 2012, Wang et al. 2013, 2014), and Krueger et al. (2014, 2013). These studies serve to emphasize the importance of being extremely careful with methodology when comparing reanalysis data with observations, and when identifying trends.

2.2 Data fromERA-Interim

The second source of data we use is the 60 m wind speed fields from the ERAI data set (Dee et al. 2011). This uses the ECMWF Integrated Forecasting System model (IFS), and assimilates observational data of many types, mostly coming from satellites. The atmospheric fields of ERA-Interim were calculated on a T255 spectral grid, with surface fields calculated on a reduced Gaussian grid. We use the 6-hourly wind speed data available on the regular latitude–longitude grid of cell-size 0.75°, and calculate daily-mean wind speeds as for the 20CR. A comparison of ERAI data at 60 and 10 m with the 20CR levels can be found in Appendix A. The reanalysis starts in 1979 and continues to the present; we use the data up to the end of 2013. Further details are available in Dee et al. (2011) and references therein, and the ERA-Interim Archive report (Berrisford et al. 2011).

Stopa and Cheung (2014) compared ERAI wind speeds with those measured from buoys and satellite data, finding that the reanalysis performs very well in terms of homogeneity, but with a small negative bias and reduced variability compared to the observations. Szczypta et al. (2011) found that ERA-Interim tended to overestimate wind speeds over most of France, but underestimated it in mountainous areas, compared to the SAFRAN high resolution (8 km) reanalysis data set—although the authors note that the SAFRAN wind speed data is known to be biased low.

As already discussed, it is known that reanalysis data sets including ERA-Interim do not exhibit the observed large-scale trends in wind speeds (see, e.g. McVicar et al. 2013, Mears 2013 and references therein), and the relatively low resolution of ERAI (and similar data sets) prevents it from being used directly as a proxy for observations at the scale of a wind farm (Kiss et al. 2009; Kubik et al. 2013). We will instead be using ERAI as an example of the kind of data currently used for providing a climatological basis for wind farm site assessments, the first link in the ‘model chain’ of dynamical and statistical downscaling for such studies: reanalyses are connected to mesoscale dynamical models, then in turn to microscale models and computational fluid dynamics (CFD) at the scale of a wind farm itself (Petersen and Troen 2012).

3 Linking the reanalyses

While the strength of the 20CR is its characterisation of real-world variability on long time scales, the ERA-Interim data set provides wind speeds that are at much higher spatial resolution, and are more tightly-constrained by observations. ERA-Interim is therefore much better suited for developing a climatology of wind speeds over small (sub-national) regions, or, in conjunction with additional dynamical or statistical downscaling techniques, at a point location. However, as it only spans ∼30 years, it cannot give a good indication of climate variability on multi-decadal timescales. In this section, we describe how we calibrate the 20CR wind speed data to produce a data set that has the same distribution of wind speeds in time as ERA-Interim (over their overlapping period), but with the long-term variability of 20CR.

3.1 Comparison of the reanalyses

We focus our study on Europe, and consider several small sub-regions for more detailed examination. To aid comparison, we regrid the ERAI data by area-averaging onto the 20CR’s native 2° grid.

The 20CR and ERAI data do not exhibit the same climatology in wind speeds over their period of intersection (1979–2012, 34 years). This is due to a number of factors. These include the structural differences (NWP model, data assimilation and reanalysis procedure), spatial resolution and the amount of orographic complexity resolved, the amount and type of observational data assimilated and the mismatch between vertical levels available for comparison.

In this section, we denote ensemble-mean daily-mean wind speeds from 20CR (at its σ = 0.995 vertical level) and from ERAI (at its 60 m model level on the 20CR grid), by U 20CR and U ERAI respectively. As we are focusing on the later period of the 20CR data set for our calibration procedure, the ensemble spread is small, so it is acceptable to use the ensemble mean series in this case (this is not generally true for all time periods, or regions of the globe with fewer observations; see Compo et al. 2011). We consider the ‘bias’ between the 20CR and ERAI data in terms of the simple difference in wind speeds,

$$ \beta := U^{\mathrm{20CR}} - U^{\text{ERAI}}, $$

and the day-to-day relative difference compared to ERAI,

$$ \beta_{\text{rel}} := \left( U^{\mathrm{20CR}}-U^{\text{ERAI}}\right) / U^{\text{ERAI}}. $$

In Fig. 1, we showFootnote 7 the 34-year mean bias 〈β〉 and the mean of the day-to-day relative bias 〈β rel〉. The bias maps are all rather noisy, but over most of the land surface the bias is negative (i.e. U 20CR<U ERAI), with differences of up to ∼20 % of the ERAI wind speeds in many areas. There are some notable exceptions to this however, with positive biases (i.e. U 20CR>U ERAI): for example over Britain, wind speeds are up to 20 % higher in the 20CR data. Some areas have particularly strong negative bias, such as around the Czech Republic. The Strait of Gibraltar is particularly affected by the low spatial resolution, resulting in the lowest 20CR wind speeds compared to ERAI. We have used a t test to assess whether the data is consistent with 〈β〉=0 (i.e. no bias) at the 1 % level. When it is not consistent with zero, we say there is a significant bias; this is the case for most areas according to this test.

Fig. 1
figure 1

Maps of the difference between wind speeds from 20CR and ERA-Interim; details as given in the panels. Crosshatched areas in the top panel are not significantly different from zero at the 1 % level, according to a t test

In addition to the spatial variability, it is important to bear in mind that the difference between 20CR and ERAI does not have to be constant in time. Figure 2 shows the day-to day variability of β rel in terms of its standard deviation σ. There is a suggestion in the data of increased β rel around coastal regions, such as in large parts of the Mediterranean, as well as Norway and Britain. The relative-bias variability is generally around 15–30 %, which is a similar magnitude to the mean relative bias 〈β rel〉 shown in Fig. 1.

Fig. 2
figure 2

Map of the variability of the daily relative ‘bias’ β rel between 20CR and ERAI wind speeds, in terms of its standard deviation

Finally, we show the correlation between the daily wind speeds of the 20CR and ERAI in Fig. 3. The data are well-correlated in most places, but the correlation is particularly strong (≥0.9) in the Atlantic and northern Europe, including the British Isles.

Fig. 3
figure 3

Map of the Pearson correlation between daily-mean wind speeds in 20CR and ERA-Interim.

3.2 Procedure for calibration

The goal of our calibration procedure is to generate a wind speed data set that retains the fluctuation patterns of the 20CR data over time, and between ensemble members, but whose probability density functions (PDFs) of the ensemble-mean wind speed in each grid cell match those of the ERA-Interim data during their overlapping time period. In particular, the PDFs do not have to match over other periods (e.g. if comparing the distribution over 142 years from 20CR to the 35 years from ERAI), the time series do not have to match in detail (although we have shown that they do tend to be well-correlated), and individual ensemble members do not need to match ERAI data—thus retaining the 20CR’s important measure of uncertainty. We illustrate our procedure for the case of a particular grid cell in Fig. 4.

Fig. 4
figure 4

Illustrating the calibration procedure, in terms of daily-mean wind speed probability distributions, for the single grid cell covering north-western Germany (centre: 8° E, 52° N); for the 20CR, the ensemble mean is used throughout for clarity. Top left: Daily-mean wind speed distributions for ERAI and 20CR over their intersecting time period. Top right: A visualisation of the conditional probability matrix P(U iERAI|U j20CR), such that each row j is a PDF of ERAI wind speeds, given a particular 20CR wind speed \(U^{\mathrm {20CR}}_{j}\) (i.e. the values along each row have the same sum). Darker colours indicate higher frequencies in each ERAI PDF. Bottom left: Wind speed distributions over the full 142 years. Bottom-right: The cumulative distribution function derived from the PDF histograms shown to the left. The dotted lines and arrows illustrate the interpolation in the quantile-matching procedure used to convert wind speeds from the original 20CR data to their calibrated counterparts. Here, a high wind speed for this cell from the original 20CR is transformed to its higher counterpart at the same level in the calibrated distribution

Our method proceeds in two stages, and is performed on each grid cell independently. Firstly, a transfer matrix is obtained as the conditional probability density of ERAI wind speeds, given bins of 20CR ensemble mean, daily mean wind speeds for the overlapping period:

$$ \mathcal{P}_{ij} := P(U^{\text{ERAI}}_{i}|U^{\mathrm{20CR}}_{j}), $$

where i and j index bins in wind speed for the data sets indicated. We use bins of 0.5 m s −1 covering the range 0–40 m s −1. This transfer matrix is applied to the full 142-year 20CR PDF, to obtain a calibrated PDF of 20CR wind speeds spanning 1871–2012:

$$ P\left( U^{\mathrm{20CRc}}_{i}\right) = \sum\limits_{j} \mathcal{P}_{ij} P\left( U^{\mathrm{20CR}}_{j}\right). $$

Secondly, calibrated daily time series of wind speeds, U 20CRc(t), from all ensemble members, are obtained by quantile matching (e.g. Panofsky and Brier 1968): the cumulative distribution function (CDF) of the calibrated 20CR ensemble mean wind speeds is interpolated at the quantiles of each ensemble member’s wind speed (see bottom-left panel in Fig. 4). Using the individual ensemble members in this step rather than the ensemble mean allows the ensemble spread to be transferred to the calibrated climatology.

In some cases, there can be wind speeds present in the 142-year 20CR data that were greater than any in the 34-year period common with ERAI. This means that such wind speeds have no corresponding frequency in ERAI that we can calibrate to: the CDF corresponding to \(P\left (U^{\mathrm {20CRc}}_{i}\right )\) reaches its maximumFootnote 8 below that wind speed, so quantile matching by interpolating the CDF will fail. In this case, we instead perform a linear regression on the relationship between original and corrected winds up to this point (i.e. U 20CRc(U 20CR)=a U 20CR+b). We then extrapolate this model to obtain corrected wind speeds for the final few high wind days.

We demonstrate our procedure for the case of a grid cell in north-western Germany in Fig. 4. This shows the different PDFs in question, the transfer matrix and the quantile matching. It is clear that in this case the ERAI wind climate largely represents a shift to higher wind speeds compared to 20CR (i.e. the 20CR winds are low compared to ERAI), and the calibrated 20CR reproduces this well. The PDFs of both the ERAI and 20CR wind speeds appear somewhat truncated at lower wind speeds, rather than reducing smoothly towards U = 0 m s −1. This is due to the daily averaging of the 6-hourly wind speeds, and has implications when attempting to fit Weibull functions to the wind speed distribution; we discuss this issue in detail in the Supplementary Information.

It is important to note that the method we describe here is not unique. Many other techniques for calibrating one data set with another have been developed and used in climatological studies. These are usually designed to compare reanalysis or model data with observations, or climate model data at different spatial scales, such as a global run with regional model output; see (Teutschbein and Seibert 2012), Watanabe et al. (2012), Lafon et al. (2013) and references therein for recent reviews of methods. Compromises are reached between statistical complexity, data volumes, direct numerical simulation and time available. In our case, we have chosen a relatively simple statistical procedure.

3.3 Results of calibration procedure

Time series of annual mean wind speeds from both the original and calibrated 20CR data, and from ERA-Interim, are shown in Fig. 5 for a region covering Denmark and Northern Germany (using area-weighted averaging over the region). The calibrated data retains the interannual variability of the original 20CR wind speeds, but with a climatology matching that of ERA-Interim over 1979–2012.

Fig. 5
figure 5

Time series of annual mean wind speeds for a region covering 9° E– 15° E and 53° N– 57° N, showing the original 20CR data (purple), ERA-Interim (red) and calibrated 20CR (green). For the 20CR data, the ensemble members are plotted in paler colours, with the ensemble means of the annual mean data plotted in darker colours. Long-term averages are plotted as horizontal dashed lines

We map the bias remaining after our procedure in Fig. 6. This can be compared to the original bias maps in Fig. 1—note that here the values are much smaller. The mean bias 〈β〉=〈U 20CRcU ERAI〉 is consistent with zero almost everywhere (using a t test at a 1 % significance level, as before). An exception is a residual positive bias east of Gibraltar: we expect this area to be heavily affected by differences in how well the complex orography here is resolved between ERAI and 20CR. Two further exceptions occur in the central and eastern Mediterranean, which correspond to anomalies seen in other aspects of the 20CR data (see later sections), and which we discuss in more detail in Appendix C.

Fig. 6
figure 6

Map of the remaining ‘bias’ after calibration. This can be compared to the map of the original bias in Fig. 1; note the colour scale covers much smaller values here. Crosshatched areas are not significantly different from zero at the 1 % level, using a t test

The mean of the relative bias 〈β rel〉 (not shown) is ≤5 % almost everywhere. Finally, we note that the correlations between 20CR and ERAI after calibration (not shown) remain almost identical to those shown previously in Fig. 3.

4 Analysis and results

In this section, we use the 20CRc data to analyse the distribution of wind speeds over Europe in various complementary ways.

4.1 The European context: maps of the long-term average, variability and trends

The map of the 142-year mean wind speed in Fig. 7 gives an overview of the geographic distribution of wind speeds over Europe. There is a noticeable land–sea contrast, although it is the mountainous regions that have the lowest mean wind speed, just as is seen in the uncorrected 20CR data (Bett et al. 2013), and is inconsistent with observations. This erroneous behaviour is a known consequence of the orographic drag schemes in atmospheric models (Howard and Clark 2007), and is particularly apparent when (as here) the orographic variability is on a much smaller horizontal scale than the model grid cells. The spatial pattern in fact agrees very well with that derived by Kiss and Jánosi (2008) from the 10 m wind speeds covering 1958–2002 in the ERA-40 reanalysis (Uppala et al. 2005), although since they used winds at a lower level their mean values are correspondingly smaller.

Fig. 7
figure 7

Long-term mean wind speed over Europe from the 20CRc data

It is important to note that the wind speeds shown here apply to the particular spatial scale of this data set, which implies a certain amount of smoothing compared to values measured at a specific site. For example, Kirchner-Bossi et al. (2013) use a complex statistical procedure to relate sea-level pressure from 20CR to wind speed observations at a range of meteorological stations in Spain. Because they are statistically downscaling to this local scale, the mean wind speed they find is 2–3 m s −1 higher than we show in Fig. 7.

We map the wind variability in terms of its standard deviation. The structure of the data set makes the calculation of the long-term standard deviation non-trivial: simply considering the ensemble-mean daily time series would result in a standard deviation that was negatively biased. Furthermore, the ensemble members’ time series are only continuous in 5-year chunks, and using them as if they were continuous throughout could potentially inflate the apparent variability at the discontinuities (although in practice the impact of this is likely to be very small). To avoid such spurious signals and trends, we calculate the mean and standard deviation of daily wind speeds in each 5-year stream for each ensemble member, then take ensemble means for each period. We then combine these 5-yearly ensemble-mean standard deviations into single aggregate values for the full 142-year period, for each grid cell; see Appendix B for details.

Since the standard deviation of wind speeds tends to correlate with the mean, we show in Fig. 8 the wind variability in terms of the coefficient of variation, the ratio of the standard deviation to the mean. This shows that, in most areas, the wind speed standard deviation is ∼40 % of the mean. The central Mediterranean has proportionally higher variability, with Greece, Turkey and the Alps (whose orography will be extremely poorly represented) showing lower variability.

Fig. 8
figure 8

Map of the wind speed variability in terms of the coefficient of variation, i.e. the ratio of the standard deviation to the long-term mean

The presence of any long-term trends in the mean or variability of wind speeds could have important consequences for wind farms, in terms of their future deployment, energy yield and maintenance requirements. Figure 9 maps the trends in both the ensemble-mean annual mean wind speed and the ensemble-mean annual standard deviation of daily wind speeds. The trends are found from the ensemble-mean annual time series using the Theil–Sen estimator (Theil 1950; Sen 1968). This is the median of the slopes between all pairs of points in the data set, and is more robust against outliers than simple linear regression, making it more suited to skew-distributed data such as wind speed.

Fig. 9
figure 9

Map of the linear trend in the time series of ensemble-annual-mean wind speeds in each grid cell (top), and the ensemble-mean of the annual standard deviation of daily wind speeds (bottom), over 1871–2012. Crosshatched areas indicate where the trend is not significant at the 0.1 % level (see text for details)

We test the significance of these trends at the 0.1 % level, using a Mann–Kendall test (Mann 1945; Kendall 1975) modified using the method of Hamed and Rao (1998) to account for autocorrelation in the data (following Sousa et al. 2011); as is the case with much meteorological data, we expect adjacent timesteps to be correlated. As with all significance tests, the result says whether the measured trend was unlikely, given the assumption of there being no true underlying physical trend. If the probability of measuring the trend we did was below 0.1 %, then we describe the trend as ‘significant’, otherwise we regard it as consistent with zero. We chose the particularly stringent threshold of 0.1 % to guard against detection of spurious trends; we only want to highlight trends we are very sure are present in the data.

Some key points about long-term trends in European winds are immediately apparent from Fig. 9. Firstly, they are only on the order of a few centimetres per second per decade; and secondly, that in most areas of the continent, the trend is not significantly different from zero. The trends in standard deviation show a similar spatial pattern, although at an even lower magnitude.

There are three areas of apparently significant trend in annual wind speed that merit looking at in more detail: the areas of positive trend in the Atlantic Ocean to the north and west of the British Isles, and the eastern Mediterranean around Crete; and the negative trend in an area of the central Mediterranean around the Italian peninsula and Sicily. The Mediterranean regions were also anomalous in terms of their bias with respect to ERA-Interim (see previous section). We look at the behaviour of wind speeds in these regions in more detail in Appendix C.

Bett et al. (2013) used the same significance threshold for analysing trends in the uncorrected 20CR data, but measured trends using simple linear regression and t tests to establish significance. While we consider the present technique to be more robust, the magnitude and spatial patterns of the trends are similar, and similar regions are highlighted as significant, pointing to genuine features in the underlying 20CR data.

As already discussed in the context of the mean wind speed, it is important to realise that these trends are those seen at the large scales of the 20CR data, and detailed physical or statistical modelling is required to downscale to a specific location. Considering again the example of Kirchner-Bossi et al. (2013), they find that the site in Spain they describe has a statistically significant negative trend in wind speed of around −0.01 m s −1 decade −1. In our results, the corresponding grid cell has a trend of around +0.01 m s−1 decade−1, and is consistent with zero according to our test.

4.2 Wind distribution time series

We use a region covering England and Wales to to give an example of how wind speed distributions can vary with time. The time series of the area-averaged data from this region are shown in Fig. 10. The annual mean wind speed (panel a) shows both large interannual variability, and (when smoothed with a 5-year boxcar window) strong decadal-scale variation. For example, the smoothed series shows a clear increasing trend from around 1970 to a peak in the mid-1990s, followed by a return to near-average values after 2000. When seen in the 142-year context however, these recent variations are not exceptional, and the year-to-year variability is always much greater. Note that, for this region, the year 2010 is the extreme low-wind year. This is linked to exceptionally cold months at the start and end of that calendar year, and a strongly negative NAO index in the 2009–2010 winter (Cattiaux et al. 2010; Osborn 2011; Brayshaw et al. 2012; Fereday et al. 2012; Maidens et al. 2013; Earl et al. 2013). The peak in wind speeds that occurs in the 1990s is another important feature in this region, and is also seen clearly in the observational record of wind speeds (Earl et al. 2013), in studies using geostrophic winds derived from pressure observations (Palutikof et al. 1992; Alexandersson et al. 2000; Wang et al. 2009), and is consistent with the large positive NAO in these years (e.g. Scaife et al. 2005, and references therein). Indeed, much of the variability of wind speeds in this region is likely to be related to modes of climate variability such as the NAO and Atlantic Multidecadal Oscillation (AMO, e.g. Knight 2006); further consideration of this requires careful seasonal breakdowns of both wind speed and these climate indices however, and is beyond the scope of this paper.

Fig. 10
figure 10

Time series of the wind speed distribution for a region covering 5° W– 1° E and 51° N– 55° N. In panels a–c, annual statistics are shown in light colours/shading, with darker lines showing the data smoothed with a 5-year boxcar window. Panel a: Ensemble-mean annual mean wind speed. Individual years are shown with shading indicating the 10th/90th percentiles of the ensemble spread in the annual means. Panel b: Ensemble means of the deciles of the daily wind speed distribution each year (i.e. the 10th to 90th percentiles). Panel c: Distribution half-widths, i.e. half the difference between symmetric decile pairs (as labelled); the standard deviation σ is also plotted, with its trend shown as a thin black dashed line. Panel d: The annual mean of the day-to-day standard deviation between ensemble members, as a fraction of the ensemble-mean annual mean wind speed

Our results bear a remarkable qualitative resemblance to those produced over 20 years ago by Palutikof et al. (1992) using geostrophic wind speeds (1881–1989) adjusted to match wind speed observations from a station in England over 1975–1984. A key purpose of that study was to illustrate the long-term variability present in wind speeds, as it could have important implications for wind power production. With the advent of larger datasets and greater computational capacity, we are able to re-emphasize their conclusions and consider the decadal-scale behaviour of the wind more robustly and in greater detail.

Considering the time series of the distribution as a whole (panel b), we can see that it follows the same decadal trends as the mean (panel a). The distribution width (panel c) highlights that while the outer reaches of the distribution are subject to much variability, with the distribution width growing and shrinking over decades, the inner parts of the distribution are much more constant. The standard deviation shown in that panel has a small but statistically significant positive trend, of 0.016 m s −1 decade −1.

Finally, the bottom panel shows the relative uncertainty in the data, in terms of the annual mean of the day-to-day ensemble spread. As one looks further back, fewer observations are assimilated, and the ensemble members have more freedom to disagree with each other, resulting in increases in this measure of uncertainty. Two peaks are present that are related to the reduction in data from Atlantic shipping during the World Wars; these spikes in uncertainty are ubiquitous for near-Atlantic regions.

In Appendix C, we show similar plots for other regions that show particular features of interest, as already discussed.

Finally, we have given some consideration to the use of the Weibull (1951) distribution to concisely describe the wind speeds in our calibrated 20CR data. However, as already mentioned, our use of daily average wind speeds means that Weibull distributions tend to provide a poor description of the data. Nevertheless, the Weibull scale parameter, which is proportional to the mean of the distribution, does tend to behave in the same way as the mean wind speeds in terms of variability and trends. In particular, trends are of a similar magnitude and spatial pattern, and ‘anomalous’ regions in the central and eastern Mediterranean, noted in previous sections, are also present. Additional details and discussion are presented in the Supplementary Information.

5 Discussion and summary

In this paper, we have demonstrated how century-scale reanalyses—in particular, the Twentieth Century Reanalysis, 20CR—can be used for assessing the long-term trends and variability of near-surface wind speeds over Europe, through a calibration procedure to relate it to a higher-resolution satellite-era climatology (such as ERA-Interim), and subsequent careful analysis.

The long baseline of the 20CR means that it has great potential to inform wind speed assessments for the wind energy industry. In general, reanalysis data is used in conjunction with dynamical and/or statistical downscaling techniques in order to reach the spatial scale of wind farms, as part of the ‘model chain’ in such assessments. Often, it is the observation-rich and relatively high-resolution data sets of ERA-Interim and MERRA that provide that first reanalysis step. This limits any assessment of long-term variability, since they both only cover ∼3 decades. By calibrating the 20CR data to match the climatology of ERA-Interim over their period of overlap (1979–2012), this 142-year data set can be used in their place, providing a much more robust assessment of historic interannual and decadal variability in regions of Europe, and allowing the ‘short-term’ trends of the past 10–30 years to be put into the longer-term context.

To emphasise this point, we show in Fig. 11 the distribution of the 109 34-consecutive-year trendsFootnote 9 in annual mean wind speed for the England and Wales region described in the previous section. The full 1871–2012 trend is indicated and, as already shown, is near zero. The trend from ERA-Interim for the 34 years of overlap is also marked, with a negative trend driven by the general reduction in wind speeds since the early 1990s. It is clear that the strong multi-decadal variability in wind speeds means that attempting to estimate the long-term trend from a ∼30-year sample can lead to misleading results.

Fig. 11
figure 11

Distribution of trends for the England and Wales region. The 34-year trends in annual-mean wind speeds from the calibrated 20CR data are shown as the blue histogram), overplotted with the full 142-year trend (green arrow). The single 34-year trend from the overlapping period of ERA-Interim is shown as a red arrow

The 20CR data is a rich source of information on the large decadal-scale variability of wind speeds. However, it is not without limitations, and hence it does need to be analysed with care. For example, in areas of complex orography, near-surface wind speeds are strongly reduced at the spatial scale of the 20CR, making their variability more difficult to interpret.

As has been noted in other studies (Compo et al. 2011; Brönnimann et al. 2012), the ensemble nature of the 20CR needs to be taken into account when assessing long-term variability. Disagreement between ensemble members can be large, especially in the early period of the data. This leads to the daily ensemble-mean time series having less variability than the individual members, and can cause apparent trends in variability over time. Therefore, the daily ensemble-mean time series has little use in determining wind variability on long timescales, and the ensemble members should be used.

Assessment of trends over the full 142 years of the 20CR is complicated by the fact that the mid-point of the time series, and hence of a simple linear trend, is the 1940s. The reduction in ocean-based measurements during both the First and Second World Wars causes spikes in uncertainty, and in some cases systematic spikes in the wind speeds themselves (see Appendix C). Furthermore, the period after the Second World War corresponds to a large increase in national and international programmes collecting greater amounts of weather data. Taken together, the pre-1950s period is much more susceptible to greater random and systematic uncertainties. Measured trends in the 20CR data should therefore be treated with caution.

We have shown in fact that all trends in 20CR surface wind speeds over Europe are either consistent with zero (in most locations), so small to be of little practical relevance (e.g. possibly in the North Atlantic), or due to systematic problems with the data (e.g. in the central and eastern Mediterranean and possibly the North Atlantic; see Appendix C).

It is clear that, for most wind energy applications, interannual variability and the large decadal-scale variability are more important than the very small long-term trends in historical European wind speeds. Using century-scale reanalyses such as the 20CR allows wind resource assessment studies to incorporate more information on the historical decadal-scale variability at a site, which can reduce the uncertainties in the financial planning central to wind energy development.