Sweden shows an overall topographic feature of being low in the southeast with hills and coastlines and high in the northwest with Scandinavian mountains (Fig. 1). Sweden consists of three main climatic zones: a mild oceanic climate in the south, a humid continental climate in the middle, and a cold sub-Arctic climate in the north (Chen and Chen, 2013). Early measurements of wind speed and direction in Sweden prior to the 1950–1960s were previously recorded only in paper journals held by SMHI, which are not accessible for researchers and stakeholders but hold information about early WS change and variability. Since that period, the popularization and use of automatic observation instruments heralded a change to digital storage of WS and other meteorological variables. To allow the community to easily access these century-long series, following the WMO guidelines, the first work package of the WINDGUST project utilized a dedicated scanner and digitization method to rescue the early paper-based measurements of wind speed and direction at the 13 stations in Sweden (Fig. 1). Initial quality controls including the identification of outliers and erroneous data points have been conducted by SMHI (Engström et al., 2022).

The rescued raw hourly WS series were averaged into daily values and then monthly values. To reduce sampling artifacts and include as much data as possible, months having fewer than 10 daily observations per month were excluded in the study, and this applied to 0.3 % of the months. Note that if this threshold increases to 25 d per month, it will remove only 1 % of the months. Finally, a total of more than 10 000 months from 1925 to the present (i.e., 2021) at the 13 stations were used. Different stations own different durations of available data. The monthly values were converted into monthly anomalies relative to the mean of the entire data period.

It is crucial to find a reliable reference series for detecting and adjusting discontinuities in the long-term time series of climate variables. The main reason for this is that a good reference series can effectively remove most of the background climate variations from the raw time series, before subsequent homogenization. This enhances the non-climatic signal, enabling statistical detection and reasonable removal of artificial change points contained in the raw time series. A good reference series should be homogeneous and able to describe the real background climate variations in the time series. Therefore, we aimed to find the best possible reference series for WS in this study by examining and comparing the homogeneity and correlation (with the candidate series) of various potential reference datasets. Based on the previous related experience in monthly series homogenization (Minola et al., 2016; Azorin-Molina et al., 2019; Gillespie et al., 2021; Zhou et al., 2021b), the geostrophic wind speed data (geowind) and three current climate reanalyses were selected into the potential pool of reference series for the century-long series homogenization. Nearby station series were not chosen as reference series in this study because of the sparse distribution of weather stations prior to the 1960s (Fig. 1).

Geowind was calculated based on surface air pressure, air temperature, and latitude information triangles formed by three weather stations (Fig. 1). Geowind data are available from 1900 on triangles 1–2 and from 1940 on triangles 3–9. Geowind was considered homogenous (Wern and Bärring, 2011) and has been used as a reference series to homogenize the WS series from automatic measurements since the 1960s in Sweden (Minola et al., 2016).

Three climate reanalysis products were considered as potential reference series: NOAA-20CRv3 (the Twentieth Century Reanalysis version 3 from National Oceanic and Atmospheric Administration) (Slivinski et al., 2019), ERA-20C (the 20th Century Reanalysis from the European Centre for Medium-Range Weather Forecasts, ECMWF) (Poli et al., 2016), and CERA-20C (ECMWF Coupled Ocean-Atmosphere Reanalysis of the 20th Century) (Laloyaux et al., 2018). This choice is based on their performance documented by prior studies (Zhou et al., 2018; Gillespie et al., 2021) and their characteristics of long-term data availability, potential physical homogeneity, statistical homogeneity, and ability to capture the background climate variations (see below). NOAA-20CRv3, ERA-20C, and CERA-20C are available for the periods of 1836–2015, 1900–2010, and 1901–2010, respectively. The three reanalysis products focus on the representation of low-frequency climate variability and assimilate only surface pressure from ISPD (the International Surface Pressure Databank) and ICOADS (International Comprehensive Ocean-Atmosphere Data Set) datasets and surface marine winds from ICOADS (Zhou et al., 2018). Thus, the WS series from the three reanalysis products should be homogeneous (in theory) since they did not assimilate the WS measurements over land.

The reanalysis data of 3-hourly zonal and meridional wind components were downloaded to calculate 3-hourly WS values and then integrate into monthly anomalies. Following Zhou et al. (2021b), we also assessed homogeneities of the reference series by applying the penalized maximal F (PMF) test (Wang, 2008) at a significance level of 0.05 to the WS series at each grid box collocated with the 13 stations in Sweden. This process revealed no detectable change points, further validating their homogeneities and suitability as reference series for WS at these Swedish stations. Furthermore, we examined the correlations of monthly WS anomalies between the rescued dataset and the four potential reference series datasets and found that CERA-20C best reflects the background climate variations (median correlation coefficient 0.72) (Fig. 2). The same procedure was applied to ERA5 from 1979 to 2021 (ECMWF's Reanalysis version 5) (Hersbach et al., 2020). Even though ERA5 assimilates most of the routine observations, it also does not assimilate the WS measurements over land (Hersbach et al., 2020). No change point was detected in the ERA5 WS series at those grids, and the median correlation is 0.71 (Fig. 2). Therefore, ERA5 can be used to extend the reference series to 2021, by using linear regression between the series during their mutual overlap period to eliminate their systematic biases. In summary, CERA-20C during 1925–2010 with an extension from ERA5 during 2011–2021 was chosen to construct the monthly difference series, which removes most of the background climate variations in the rescued WS series during the subsequent homogenization.

In contrast to ERA-20C, the successor CERA-20C adopts an Earth system approach to climate reanalysis, which leads to a more balanced system for better representations of atmosphere–ocean heat fluxes and of mean sea level pressure (Laloyaux et al., 2018). To account for key uncertainties in the assimilated observations (by adding pseudorandom errors) and simulated model errors (by using a stochastic physics scheme) for producing a long-term climate reanalysis, CERA-20C and ERA5 provide 10-member ensembles of climate reanalysis through a variant of the four-dimensional variational ensemble assimilation technique (Isaksen et al., 2010; Poli et al., 2013; Laloyaux et al., 2018; Zhou et al., 2018; Hersbach et al., 2020). Thus, the 10-member ensembles enable us, for the first time, to investigate the uncertainty associated with using reanalysis as a reference series in the homogenized WS data series.

Several statistical homogenization methods with associated software, for example, the standard normal homogeneity test (SNHT) (Alexandersson and Moberg, 1997), multiple analysis of series for homogenization (MASH) (Szentimrey, 1999), penalized maximal T test (PMT) (Wang et al., 2007), and penalized maximal F test (PMF) (Wang, 2008), have been widely compared and employed for various climate variables including temperature, precipitation, humidity, and WS (Domonkos, 2011; Minola et al., 2016; Zhou et al., 2017, 2021b; Yosef et al., 2018; Azorin-Molina et al., 2019). Compared to the SNHT, the PMT and PMF tests are revealed to more reliably detect all the change points, by incorporating a penalized empirical correction that accounts for greater likelihood of detecting change points at the beginning and end of time series (Wang et al., 2007; Wang, 2008). Both tests consider the effect of series autocorrelation in the detection of change points (Wang et al., 2007; Wang, 2008; Zhou et al., 2021b). In addition, compared with the PMT, the PMF can preserve linear trends for most segments split by the detected change points through visual inspection, especially for long-term time series with apparent climate fluctuations (Wang et al., 2007; Wang, 2008; Zhou et al., 2021b). Thus, the PMF test was chosen to homogenize the century-long WS series in this study.

The homogenization procedure comprises four steps: construction of the difference series with a reference series, detection of change points, adjustment of the discontinuities, and the final creation of the homogenized series. Firstly, we constructed the monthly difference series (WSraw–WSrea) of the raw rescued wind speed (WSraw) minus the reanalysis wind speed (WSrea, from CERA-20C and ERA5) by linear regression. The linear regression can eliminate systematic errors in the reanalysis and the effect of the station-versus-grid difference. Secondly, we applied the PMF test at a significance level of 0.05 to the WSraw–WSrea series, for statistically detecting possible change-point dates. For comparison, the PMT test at a significance level of 0.01 was also applied and yielded the same results (details in Sect. 3.3). A significance level of 0.05 for the PMT test was also tried but unreasonably generated too many short (2–3-year) segments. Thirdly, after obtaining the change-point dates, the mean-matching algorithm was applied to the WSraw–WSrea series to adjust the detected spurious discontinuities. Up to 5 years of data from the segments before and after each change point were used to adjust the discontinuities, with the last segment as the baseline. Finally, the homogenized series was added back onto the WSrea series to obtain the final homogenized wind speed anomaly series (WSadj). The above procedure was also conducted on individual months and yielded similar results.

The PMF test at a significance level of 0.05 was applied to the WSraw–WSrea series to detect spurious change points. Results identified 71 change points in total for all the 13 stations, with a mean segment length of approximately 11.3 years. A histogram of years with detected change points shows three peaks, i.e., 1935–1944, 1956–1964, and around 1985 (Fig. 3).

We collected all available metadata from the SMHI archive and tried to validate the detected change points to the extent that these incomplete records permit. Approximately 38 % of our detected change points are confirmed by the known events recorded in the metadata. Because of the incompleteness of the metadata record, this value was calculated as the ratio of the number of change points with one or more metadata events recorded within 1 year of the change point to the number of change points within 5 years of the metadata event record. This calculation is to cover those periods with available metadata for different stations well, that is, to exclude those periods or stations without metadata records, such as Malmslätt station (Fig. 4). Events recorded by the metadata include changes in the observatory, measurement instrument, and surrounding environment. For example, at the Bjuröklubb stations, two change points detected in 1942 and 1949 are verified by changes in the observatory, whereas a change point in 1978 has no metadata record to verify it (Fig. 4a). Additionally, the changes in the observatory from 1965 to 1975 may not have caused any discontinuities, or the discontinuities were indistinguishable from the background climate variability by the statistical homogenization method. Note that ∼24 % of the detected change points based on the PMT test at a significance level of 0.01 are confirmed by the metadata event changes.

To remove the detected discontinuities in the WSraw–WSrea series, we employed a mean-matching adjustment using up to 5 years of data before and after each detected change point, as widely done in previous studies (Minola et al., 2016; Zhou et al., 2018, 2021b; Ma et al., 2022). The most recent segment was chosen as the reference segment since it was usually measured by the most advanced instrument and thus probably most reliable. Starting from the last change point, the mean difference of the WSraw–WSrea segments over up to 5 years around the change point was estimated to adjust the entire segment before the change point, and this process repeated backward in time for the remaining change points. After the adjustments, the artificial discontinuities around the change points disappear (Fig. 4). Such a mean-matching adjustment implies that the mean shift estimated using the WSraw–WSrea segments over up to 5 years around a change point is due to non-climatic changes. This highlights the critical importance of minimizing the natural variations in the WSraw–WSrea series. The WSrea series preserves most of the natural variations so that the adjustment using the WSraw–WSrea series rather than the WSraw series is less affected by the natural variations.

Two examples of the mean adjustment are presented in Fig. 4, demonstrating the clear improvements in the long-term homogeneity of the series. Two apparent positive WS biases around the 1950s (due to the station relocations), and one apparent negative WS bias in 1978, at Bjuröklubb station are largely removed after the adjustment (Fig. 4a). The adjustments removed most of the apparent discontinuities and decreased the linear trend during 1926–1997 from 0.30 to -0.06 m s-1 per decade at Bjuröklubb station (Fig. 4a). Two apparent negative biases in the 1960s and 1990s were substantially adjusted, significantly turning the century-long trend from a negative trend (-0.01 m s-1 per decade) to positive (0.04 m s-1 per decade) at Malmslätt station (Fig. 4b). Overall, the adjustments make the WS series more homogeneous.

Figure 5 compares the raw and homogenized WS series at the 13 stations in Sweden. One can see that many apparent adjustments were made at Bjuröklubb, Härnösand, Landsort, Malmslätt, Ölands norra udde, Hoburg, and Kalmar stations (cf. left versus right panels in Fig. 5). These substantial adjustments are concentrated in the 1930s, 1950s, 1960s, 1980s, and 2000s and significantly alter the long-term trends in WS (Fig. 5). For example, wind stilling was enhanced from -0.08 to -0.20 m s-1 per decade at Landsort station but was weakened from -0.41 to -0.03 m s-1 per decade at Kalmar station. The sign of the WS trend changed from positive to negative at Bjuröklubb station but from negative to positive at Torslanda and Malmslätt stations (Fig. 5). Thus, reducing the discontinuities in the rescued WS series is important for increasing our confidence in the detection of WS changes.

The mean adjustment to the monthly anomaly series can significantly alter the long-term trend. Figure 6 compares raw and homogenized WS anomaly series averaged at the 13 stations from 1925 to 2021. Note that the average of the nine stations excluding Väderöbod, Torslanda, Visby, and Kalmar stations due to short data availability also yields similar results as shown below. Despite there being no change in the century-long trends (-0.03 m s-1 per decade, p<0.05) before and after adjustment, the signs and amplitudes of the multidecadal trends changed significantly (Fig. 6). A 15-point Lanczos filter with a 10-year cutoff was applied to show the decadal changes in the raw and adjusted WS anomaly series (Fig. 6). The raw WS series fluctuated steadily before the 1970s, declined rapidly during the 1970s–2000s, and reversed swiftly thereafter, while the homogenized WS series exhibited clear periodic fluctuations after 1925 (Fig. 6). Decadal correlation between the North Atlantic Oscillation (NAO) and WS series increased from 0.29 to 0.54 (p<0.05) before and after adjustment (Fig. 6).

It is useful to analyze the trend differences for subperiods. In particular, during the 1960s to the 1990s, the homogenized WS shows an increasing trend of 0.09 m s-1 per decade (p<0.05), whereas the raw WS presents a non-significant trend (p>0.05, Fig. 6). This change mainly results from adjustments during the 1850s–1980s as mentioned in Sect. 3.2. The raw WS anomaly series peaks around 1975, where the homogenized WS has a local maximum around 1990, which matches that of the NAO (Fig. 6). During the period from 1990 to 2005, the magnitude of the wind stilling trend decreased by 25 %, to -0.35 m s-1 per decade (p<0.05), after adjustments (Fig. 6). Considering the uncertainty of the homogenized data, this decrease after adjustments is significant during this period. An early stilling was observed during the 1930s–1960s. Uncertainty in the homogenized WS series is evident for the periods before 1945 and after 1990 (see the shading in Fig. 6), and stems from the uncertainty associated with using the century-long reference reanalysis series. It is worth noting that the homogenized data based on the PMT test are consistent with the above results based on the PMF test (Fig. 6). Overall, we find that adjustments of the discontinuities with consideration of the homogenization uncertainty for the century-long WS series are vital in studies of the detection and attribution of recent global stilling and recovery.