Wind speeds come from the full set of current 20th century reanalyses and are provided by two different centers: the European Centre for Medium-Range Weather Forecasts (ECMWF) and the National Oceanic and Atmospheric Administration (NOAA) from the USA. NOAA provided the first 20th century reanalysis named 20CR . 20CR is an atmospheric reanalysis that assimilates sea-level pressure observations only. In this study, we use the ensemble mean wind speeds from version 20CRv2c, which has 58 ensemble members. ECMWF followed a different approach and assimilates both sea-level pressure and marine wind observations. This difference in approaches yields substantial disagreement with respect to long-term wind speed trends but, as we show, there is large agreement regarding seasonal to multidecadal variability after subtraction of the linear trends. ECMWF provides an atmosphere ERA20C; and a coupled atmosphere–ocean 20th century reanalysis CERA20C;. ERA20C is deterministic (i.e., has only 1 member) and CERA20C comes with a 10-member ensemble. Unless otherwise stated, we report the CERA20C ensemble mean as the spread is usually very limited. Our analysis is based on 10 m wind speeds. In contrast to higher-altitude wind speeds, they are available for all 20th century reanalyses allowing us to apply the same methodology to all datasets and thereby ensuring comparability. We validate the approach in Sect. 3.

The longer temporal coverage comes at the cost of reduced spatial resolution as compared with modern reanalyses such as ERAINT , MERRA/MERRA2 or ERA5 . ERA20C and CERA20C have a spatial resolution of 1.125∘×1.125∘ and the 20CR resolution is even coarser (1.875∘×1.875∘). While the datasets are thus clearly not well suited for site-specific assessments, they are sufficiently detailed for country-level assessments (see also Fig. ). Temporal resolution is 3 h for all datasets and hence allows us to capture intraday effects.

There is a demonstrated disagreement in the 20th century reanalyses in terms of wind speed trends, which originate from the assimilation of marine winds by ECMWF . We thus remove the long-term (1901–2010) trends by subtraction of the zero-mean trend that is obtained via least-squares fitting of a linear fit function and subsequent subtraction of the trends mean: 1G(t)=Graw(t)-Gtrend(t)-〈Gtrend(t)〉, where Graw(t) denotes the raw annual or seasonal time series, Gtrend(t) denotes the linear fit and 〈Gtrend(t)〉 is its mean value.

We focus on the long-term evolution of 20-year generation averages because 20 years is a typical lifetime for wind parks. Moreover, the averaging smooths the pronounced interannual variability, which has already been extensively studied elsewhere. Both energy system planning and wind park investment are forward procedures in the sense that infrastructure built today will be operated under the weather conditions of the future. We therefore decided to compute 20-year forward running means of wind power generation G20 as 2G20(t)=120∑t′=tt+20yrG(t′), where G(t′) denotes the annual wind power generation in year t′. To study the evolution in different seasons (winter DJF, spring MAM, summer JJA, autumn SON), we similarly compute the seasonal 20-year means as 3G20season(t)=120∑t′=tt+20yrG(t′)season, where G(t′)season denotes the wind power generation in the respective season of year t′. Note that G20(t) and G20season(t) are ill defined at the end of the dataset when 20 years are not available. We thus only compute them up to 1990. We generally report normalized lifetime generation or normalized seasonal lifetime generation, which is obtained by division of G20(t) or G20season(t) with the 1901–2010 mean 〈G(t)〉 or 〈G(t)〉season, respectively.

We test significance of low-frequency components in the annual and seasonal wind generation time series using the multitaper method MTM;. Classical approaches, such as Fourier spectral analysis, suffer from spectral leakage when applied to relatively short time series, hindering reliable assessments. MTM provides an alternative in that it calculates tapers that are designed to minimize leakage. We use K=3 tapers with a bandwidth of p=2 years as suggested by for a comparable time series. Eigentapers are weighted based on their eigenvalues and the computation is performed via the Python package spectrum .

Significance testing is based on the null hypothesis of red noise. The underlying process that creates a red-noise spectrum is referred to as a autoregressive model of first order or AR(1). The parameters of the red-noise spectrum, SR(f), are fitted to minimize the mismatch between the median smoothed real and the red-noise spectrum as suggested by . A peak in the real spectrum S(f) at frequency f′ is considered significant at the 90 % level if 6S(f′)>SR(f′)⋅χ2(90%,2K), again following . χ2(90%,2K) denotes the chi-squared distribution with 2 K degrees of freedom at a 90 % confidence level. White noise is a special case of red noise and is characterized by a constant spectrum (i.e., SW(f)=S0, where S0 is a real positive number). White noise is generated by an autoregressive model of zeroth order, AR(0).

In an investment decision, the installation and operational costs of an asset have to be compared with expected revenues. Taking into account risks and alternative investments, an investment is made if the expected revenues exceed the total costs by some amount. The expected revenue may be substantially flawed if it is based on only a couple of years of wind data. In contrast, decision makers that are aware of all modes of wind variability gain an advantage through more reliable revenue estimates.

To quantify this impact of low-frequency wind variability on wind park investments, we calculate the discounted lifetime cash inflows as 7Cin(t)=c⋅∑t′=tt+τ1(1+γ+Δη)t′-tG(t′), where γ=5.5 % yr-1 is the discount rate, Δη≈1.5 % yr-1 accounts for the decline in turbine performance , τ=20 years is the conservatively assumed lifetime, c is the revenue per generated unit of electricity and G is wind power generation. We set c to be constant because the German system is still designed to guarantee prices for wind park operators. Prior to the recent shift towards auctions, the price was determined politically. Since the latest reform of the renewable energy act in 2017, the price is determined via auctions but is still guaranteed over 20 years . Both for old and new wind parks it is thus justified to use constant prices, albeit the price will differ depending on the date of construction and the auction outcome.

To gain more insight into the coevolution of wind generation variability and the general circulation of the atmosphere, we include the North Atlantic Oscillation (NAO). The NAO is the leading pattern of climate variability in the North Atlantic sector affecting weather and climate over Europe, particularly in winter . It is here defined as the first principle component of sea-level pressure over the area 20–80∘ N and 90∘ W–40∘ E as detailed in . Our NAO index is computed from sea-level pressure data from the Hadley Center over the winter months December, January and February.

We find ERA20C and CERA20C to feature statistically highly significant trends (see Table ). In both datasets, the trends are strong: ERA20C reports 28 % higher wind power generation at the end of the 20th century as compared to its beginning. The corresponding increase in CERA20C is substantial (16 % increase in a hundred years) but roughly half as large. In contrast, there is no significant trend in 20CR.

The existence of these trends comes as no surprise given strong long-term trends in (C)ERA20C surface wind speeds over large parts of the world . In our previous publication, we showed that the trends originate from the assimilated marine wind speeds that also feature very strong long-term trends. They are likely spurious and caused by the evolving measurement technique. In addition to wind speed trends, ERA20C also features trends in marine sea-level pressure gradients that are not in line with observations . All following analyses are therefore based on detrended time series.

After subtraction of the trends, there is large agreement among the datasets regarding multidecadal variability in normalized lifetime generation (see Fig. ). Maxima and minima of annual and seasonal time series coincide for ERA20C, CERA20C and 20CR. The amplitude of variability is also comparable among the datasets for all seasons and the annual values. Only in September–October–November (SON) is there disagreement from 1960 onwards as 20CR reports values that are 5 % to 10 % off the (C)ERA20C values. Generally, there is stronger variability in seasonal compared to annual generation, hinting at compensating effects between seasons. In June–July–August (JJA), for example, the maximum to minimum difference is around 15 %. This compares to 5 % to 10 % maximum to minimum difference for the annual values.

German annual generation is dominated by winter generation due to generally stronger winds in winter. This winter dependence explains the high similarity between the annual and wintertime series (compare Fig. a with c) and also the high correlation of r=0.71 between them (see Fig. b). On the timescales considered here, there is also a weak anticorrelation between the annual and the summer values (r=-0.39) and between the summer and autumn values (r=-0.46).

The ratio of winter to summer generation (i.e., seasonality) is characterized by strong multidecadal variability. While the maximum 20-year seasonality is between 110 % and almost 120 % (dependent on the dataset), the minimum lies between 80 % and 90 % (see Fig. g). If an extended definition of seasonality is applied, the amplitude of the variability is reduced, but the maximum to minimum difference still ranges around 15 % to 20 % (see Fig. h).

In winter there is also a good connection between 20-year mean anomalies of the North Atlantic Oscillation (NAO) and normalized lifetime generation as highlighted by correlation coefficients between them that range from r=0.7 to r=0.76 for the different datasets (see Fig. a). This relation is consistent with the NAO being the dominant pattern of wintertime climate variability in the North Atlantic sector . The agreement is strongest on multidecadal timescales and it is particularly high since 1960. However, a peak in normalized lifetime wind generation around mid-century is not paralleled by a similar feature in the NAO.

Modern reanalyses, such as ERAINT, are too short to capture these modes of low-frequency variability (see blue arrows in Fig. ). Unfortunately, ERAINT not only fails to capture these effects but also provides biased high estimates in some cases. For example, the seasonality reported by ERAINT, coincides with above-average values of seasonality and is hence not representative in general (see Fig. g). The same is true for annual and winter generation. Moreover, ERAINT begins at a time of maximum normalized lifetime wind generation. ERAINT-based trend assessments can thus misidentify the downward part of reoccurring cycles as trends (as discussed in Sect. ). Similarly, the decline of autumn generation since the 1970s could be falsely interpreted as a trend.

We perform multitaper spectral analysis for detrended annual and seasonal German wind power generation over the period 1901–2010 (Fig. ). No prior smoothing or filtering is applied. A focus is given to the low-frequency part of the spectrum with frequencies of less than 0.1 yr-1, which corresponds to at least 10-year periods. There are statistically significant low-frequency peaks in all seasons with different levels of agreement among reanalyses. All reanalyses feature a significant peak in MAM (f≈0.04 yr-1 or f-1≈25 yr) and JJA (f≈0.03 yr-1 or f-1≈33 yr), and the latter is also clearly visible in the time series (see Fig. e). In SON, CERA20C and ERA20C report a clearly significant peak that is also almost significant in 20CR (f≈0.02 yr-1 or f-1≈50 yr). In winter there is a spectral peak with a period of around 50 years (f≈0.02 yr-1) that is related to the NAO (see Fig. b). This connection to a physical pattern of climate variability suggests that the peak is not a statistical artifact, despite its low statistical significance. The generally high agreement among the reanalyses adds confidence to the existence of multidecadal periodicities during the historical period.

Spectral peaks generally do not exist at the same frequencies in different seasons. This implies that the relevant processes vary by season. While the winter NAO explains a large share of the winter variability, similar explanations can currently not be given for the other seasons.

Interestingly, the AR(1) fit to the median-smoothed spectra does not reveal red noise but white noise (except for MAM), in agreement with the understanding of atmospheric variability as a process that is white to first order . This can be seen by the thin solid lines in Fig. , which display the fitted AR(1) spectra: they are virtually flat, i.e., virtually independent of the frequency. For example, in JJA (Fig. d), the power of the AR(1) fit is 100 (GWh/GWh)2 for all frequencies. White noise implies that the system does not have relevant memory from one year to the next but rather behaves erratically on year-to-year timescales.

In addition to the relevance of low-frequency variability for system design, the long lifetime of wind parks makes returns on individual investment susceptible to low-frequency variability, and not taking this susceptibility into account has substantial economic implications. The effect is illustrated in Fig.  where the discounted lifetime cash inflow of a wind park that follows the German mean wind generation is shown. The values are normalized such that 100 % refers to the 1901–2010 mean. This graph shows variability in a wind park's cash inflow between a maximum of 104 % to 107 % and a minimum of 95 % to 97 % dependent on the phase of low-frequency climate variability at the commissioning date. In other words, a wind park created in 1955 would produce 7 %–12 % less revenue than one created in 1975. Recall that we abstract from technology innovations throughout the entire article. Dependent on the individual project characteristics, most notably the ratio of the investment to the expected lifetime cash inflows, a few per cent more or less on the income side can turn an average project into a very profitable one or might leave a slightly profitable project unprofitable. Roughly between 1960 and 1975, there was a linear increase in cash inflows, which has been followed by a decrease since 1980. Assessments based on ERAINT may tend to overestimate discounted lifetime cash inflows as ERAINT coincides with a period of high wind generation.