The last two winters in central Europe were relatively cold [Cattiaux et al., 2010; Guirguis et al., 2011], major rivers like the Rhine were near to freezing, and smaller rivers froze down to the riverbed. Synoptic analyses of these two winters have shown that the cold temperatures in Europe were caused by anomalous atmospheric circulation patterns [Cattiaux et al., 2010; Guirguis et al., 2011], in particular the persistent negative phase of the Arctic Oscillation (AO) and the North Atlantic Oscillation (NAO). This negative NAO phase implies a reduced pressure gradient between Iceland and the Azores, and is associated with the occurrence of blockings in the eastern North Atlantic, which induces a northerly flow over Europe. The influence of low pressure systems, which can transport warmer, maritime air from the west towards the continent, is reduced, leading to cold winter conditions in Europe [Guirguis et al., 2011; Sillmann and Croci-Maspoli, 2009]. These last two winters occurred during a long and pronounced sunspot minimum. The sunspot cycle has long been known to affect stratospheric chemistry and temperature [Labitzke and van Loon, 1992; Haigh, 1996]. Evidence for a connection of variations in solar activity with European tropospheric weather was more recently documented in modern meteorological data from the last approximately 50 years [Bochnicek and Hejda, 2005; Barriopedro et al., 2008; Lockwood et al., 2010; Lockwood, 2012; Gray et al., 2010; Woollings et al., 2010]. The most likely physical mechanism behind it has been demonstrated in several modelling studies [Shindell et al., 2001; Ineson et al., 2011; Matthes et al., 2006], which indicate that the solar influence on the stratosphere may propagate downwards and lead also to tropospheric circulation anomalies. Low sunspot activity is, according to these studies, related to a more negative phase of AO and NAO, associated with cold winter conditions in central Europe.
 However, meteorological time series of only a few decades are often not long enough for studying the solar forcing with a periodicity of 11 years in a statistically robust way. Moreover, the increase in global surface temperature during the last 50 years may further complicate an investigation of the natural forcing of European winter climate. There are only a few studies that investigated the solar influence on European climate from direct observations [Lockwood et al., 2010]. Proxy reconstructions from historical data have been used to understand the severe winter coldness during the maximum of the Little Ice Age from 1675–1704, which can be best explained by a combination of weak solar insolation and interaction with North Atlantic sea surface temperatures [Wanner et al., 1995; Luterbacher et al., 2001]. To bridge the gap between these two lines of evidence we use a historical time series spanning the last 230 years, the freezing of a large river in Germany, which represents a robust and easily detectable climate signal (see Figure 1). This signal is best documented for the river Rhine, which has been used for ship cargo transport since its regulation at the end of the 18th century.
 Table 1 (see also the auxiliary material) lists 14 freezing events from 1780 until 1963, when the Rhine was frozen to an extent that people could walk on the ice (Figure 1), or there is clear evidence for freezing at multiple places along the Rhine between Mainz and Düsseldorf. Local freezing, which is only documented by one single source or is not associated with walkable ice, is not taken into account. Figure 2 shows these freezing events as a time series plotted together with the time series of sunspot activity. A visual comparison of the two records already indicates a connection between freezing events and sunspot minima. Quantitatively, a freezing event is associated with a minimum in solar activity if it occurred during the 4 winters adjacent to a local minimum in this sunspot curve (e.g., Rhine freezing during the winters 1876/77, 1877/78, 1878/79 or 1879/80 would be associated with the sunspot minimum in 1878). According to this definition, 10 of the 14 freezing events are associated with a solar minimum and are plotted as green lines in Figure 2a (the remaining 4 events are plotted in red). To test the statistically significance of this relationship we apply a bootstrap method. 14 randomly chosen winters within the period 1770 to 1970 are compared with the sunspot curve, and the number of matches is counted. This experiment is repeated 10,000 times, resulting in a statistical distribution of matching numbers, which can then be compared to the number of matches obtained for the freezing events. If less then 5% (1%) of the random allocations lead to a number of matches equal to or larger than the freezing events, the relationship between solar forcing and river freezing is assumed to be statistically (highly) significant at the 95% (99%) confidence level. According to this test, our empirical observation of 10 freezing events occurring in the 4 winters adjacent to a sunspot minimum is statistically highly significant at the 99% level. Thus, it is highly unlikely that the relationship between historical freezing events and the solar forcing described here is one of chance.
|20th century||December 1962 / January 1963|
|December 1946–February 1947|
|December 1941–February 1942|
|19th century||January 1891|
|December 1844–March 1845|
|January / February 1830|
|January / February 1823|
|18th century||December 1783–February 1784|
 The relative time of the freezing with respect to the nearest sunspot minimum is plotted as a histogram in Figure 3 and shows that the historical freezing events occurred at about the same numbers in the two years before and after the sunspot minimum. Before we discuss a possible explanation for this observation, we will evaluate another relevant factor. Toniazzo and Scaife  have shown that moderate El Niño events are related to a more negative NAO and thereby colder winter temperatures in central Europe. In order to test if this relation is also visible in our Rhine freezing time series, the winters with a moderate or strong El Niño in the period 1870–1970 identified by these authors are compared to the Rhine freezing events (Figure 4). Only during one winter, 1913/14, there is a match between the events.
 To identify the atmospheric circulation anomalies in the North Atlantic and European region associated with cold winters during solar minima, Figure 5a shows the difference in the geopotential height fields at 500 hPa (Z500) between the winters directly following a year with a sunspot minimum and the remainder of the period 1871 to 2008, obtained from the 20th Century Reanalysis dataset [Compo et al., 2011]. A strong, statistically significant positive anomaly occurs over the eastern North Atlantic in the region of Iceland, while negative anomalies are found over the Iberian peninsula and over north-eastern Europe (the latter being not significant). These Z500 anomalies are associated with an enhanced northerly flow and cold air advection from the Arctic and Scandinavia towards central Europe, leading to significantly negative temperature anomalies over England, France and western Germany (Figure 5b). The centre of the cooling is in the region of southern England, the Benelux countries and western Germany down to middle Rhine area. Eastern and southern Germany are not affected as much as the above region. Accordingly, it is only the Rhine and possible some Dutch rivers that provide the possibility to reconstruct this specific temperature anomaly pattern, which corresponds to an anomalously negative NAO and a preference for blockings over the eastern North Atlantic. The statistically significant anomalies of Z500 are mainly restricted to the North Atlantic region, and no larger-scale pattern resampling a negative AO is found, in contrast to, e.g., the model results ofIneson et al.  (not shown). The high geopotential anomaly southeast of Greenland (Figure 5a) is stronger in the upper than in the lower troposphere indicating a downward propagation of the solar signal from the stratosphere. The Z500 and corresponding temperature anomalies from the 20th Century Reanalysis are similar to the patterns found in previous studies based on other reanalysis data sets covering only the more recent decades [Barriopedro et al., 2008; Woollings et al., 2010]. Regional differences, e.g., related to the extent of the cold anomaly over Eastern Europe, might also be due to differences in details of the methodology.
 In agreement with the 20th Century Reanalysis central European temperature observations from the CRUTEM3 dataset [Brohan et al., 2006] from winters directly following a sunspot minimum are also significantly lower than the average temperature during the remaining winter seasons (Figure 6a). The relation between cold winter conditions and sunspot activity is thus not specific to rivers alone (which could also be affected by a number of additional factors, for example warm water from the numerous powerplants constructed along the river). The strong variations of the time series in Figure 6a, which are largely independent of the sunspot cycle, show the important role of internal, stochastic variability of the atmosphere for European winter temperatures. The relation shown above holds true only for central European temperatures. When the CRUTEM3 winter temperature data are averaged over the whole Northern Hemisphere, no relation to the solar minima is found. This is indicated in Figure 6b and has the reason that the circulation anomalies associated with sunspot minima only redistribute warm and cold air masses, leading to a cold anomaly over Europe, but also to warm anomalies, e.g., over Greenland and parts of Asia (see again Figure 5b) [Lockwood et al., 2010].
 Accordingly, anomalously cold winters in central Europe occurred in the last 2 years, the last 50 years, the last 230 years and the Little Ice Age frequently during times of low sunspot numbers and thus weak solar irradiance. This holds true even for the 21th century, when winters are undoubtedly warmer than during the 20th century, but still, the coldest winters are connected with weak solar activity.