Interannual to millennial‐scale variability of River Ammer floods and its relationship with solar forcing

The relationship between River Ammer flood frequency variability, extreme summer climate over Europe, and solar forcing is investigated. First, we used observational data to evaluate extreme weather and climate anomaly patterns associated with flood and solar forcing as well as the possible dynamical mechanisms behind them. Then, the annual resolution flood layer record from the Lake Ammer sediments is analysed to evaluate millennial‐scale variability of floods and possible related extreme climate patterns back to 5,500 years BP. A composite analysis reveals that observed River Ammer flood frequency variability at interannual to multidecadal time scales is connected to large‐scale extreme precipitation and temperature patterns. From a synoptic‐scale perspective, the extreme precipitation pattern associated with floods is related to an increase in the frequency of high upper‐level potential vorticity (PV) events over western Europe and a decrease over eastern Europe and western Russia. Increased (decreased) frequency of upper‐level high PV events is related to more (less) surface extreme precipitation occurrence. Furthermore, we show that increased frequency of upper‐level high PV events over western Europe is associated with enhanced blocking activity over eastern Europe. Therefore, the out of phase interannual to millennial‐scale variations of River Ammer flood frequency and solar irradiance, as presented in previous studies, can be explained by a solar modulation of eastern European‐western Russia summer blocking and associated upstream upper‐level wave breaking activity. In addition, we identify two distinct quasi‐periodic signals in both frequency of Lake Ammer flood layer and solar irradiance records with periods of ~900 years and ~2,300 years. We argue that similar cycles should dominate millennial‐scale variations of blocking activity in eastern Europe‐western Russia as well as extreme precipitation and flood frequency variability over central and western Europe during the last ~5,500 years.


| INTRODUCTION
Over the past decades, Europe has experienced heavy floods with major socioeconomic consequences. One of these cases is the summer 2013 flood in Central Europe (Ionita et al., 2015), emphasizing the need for improved forecast methods of extreme hydrologic events and a better understanding of the underlying climatic processes. In particular, understanding past changes of floods on short and long timescales is crucial for anticipating the evolution of these events in response to climate change.
A focus of current climate research is on mean temperature fluctuations and less on regional changes in extreme climate events, particularly on extreme floods. Understanding the physical mechanisms behind flood variability is important for anticipating extreme climate anomalies at different spatial and temporal scales. Observational data permit the investigation of flood variability at short timescales. To study extreme precipitation and flood variability at longer timescales proxy records for extreme precipitation and floods should be used. By employing historical documents and natural archives, we can extend our knowledge back through the Holocene period or beyond. Integrating instrumental and proxy records can provide valuable information about longterm flood trends, at very high precision (Wilhelm et al., 2018).
The drivers of European floods are, usually, associated with specific atmospheric circulation patterns like zonal westerly or meandering regimes or VB cyclone tracks (e.g., Swierczynski et al., 2012). However, such circulation regimes are related not only to local extreme precipitation and floods, but could also be associated with extreme weather phenomena in more distant regions. Here, we combine instrumental River Ammer discharge data back to 1926 with the seasonally resolved flood layer time series from varved sediments of the downstream Lake Ammer covering the last 5,500 years, as well as meteorological data to investigate the mechanisms behind interannual to millennial flood variability. Detecting such features can improve the interpretation of the flood layer record from Lake Ammer sediments (Czymzik et al., 2010), in terms of extreme weather and climate variations. The main goal of this paper is to relate River Ammer flood frequency variability from the discharge and lake sediment records with extreme climate anomaly patterns as well as to identify the dominant forcing of flood variability on up to millennial timescales.
Previous studies have shown that extreme precipitation phenomena are associated with upper-level atmospheric circulation patterns (e.g., Schlemmer et al., 2010;Barton et al., 2016). Due to conservation of potential vorticity (PV), significant features that are related to synoptic-scale weather systems, responsible for extreme precipitation, can be identified and followed in space and in time. River Ammer floods are related to specific upperlevel PV patterns (Rimbu et al., 2016). Here we investigate the possible role of solar forcing on River Ammer flood frequency variability through such upper-level PV patterns.
This article is organized as follows. Data and methods are presented in Section 2. The results are presented in Section 3. The relationship between observed daily River Ammer floods with extreme climate and upper-level atmospheric circulation is discussed in Section 3.1. In Section 3.2, the possible role of atmospheric blocking on the observed solar forcing-flood relationship is discussed. Section 3.3 discusses the millennial-scale variability of flood layer frequencies in the Lake Ammer sediments and its possible implications for extreme climate variability throughout the last 5,500 years. A summary and the main conclusions are given in Section 4.

| DATA AND METHODS
The main quantity analysed here is daily mean River Ammer runoff recorded at Gauge Weilheim (Bayerisches Landesamt für Umwelt, 2007) covering the period 1926 to 2015. River Ammer rises in the Bavarian Alps and flows northward for about 80 km to Lake Ammer (48.01 N; 11.12 E). Details about River Ammer and its catchment can be found in Ludwig et al. (2013) and Petrow and Merz (2009). Here we examine the observed daily discharge of River Ammer during summer (June, July, August), the main flood season in the River Ammer region (Czymzik et al., 2010(Czymzik et al., , 2013. We combine the measured discharge data with the 5,500-year flood layer record from varved Lake Ammer sediments, a proxy for River Ammer flood frequency in spring and summer (Czymzik et al., 2010). A daily River Ammer discharge, greater than 125m 3 /s is associated with a flood, since above this threshold the deposition of a flood layer in the investigated lake Ammer sediments is very likely (Czymzik et al., 2010). Millennial-scale variability in the lake sediment record, a proxy for River Ammer floods during the last 5,500 years  is analysed in connection with solar forcing. The flood layer time series is available at the environmental database PANGAEA (https://doi.pangaea.de/10.1594/PANGAEA. 803368).
The R20mm index describes the number of days in summer with total daily precipitation higher than 20 mm (e.g., Zhang et al., 2011). It is analysed in connection with observed River Ammer flood variability. As a measure of extreme temperature we have used the summer day (SU) index, defined as the number of days in summer with a maximum daily temperature (TX) above 25 C. These indices are calculated based on daily precipitation and maximum daily temperatures from the E-OBS data set (e.g., Cornes et al., 2018).
Previous studies (Browning, 1997;Schlemmer et al., 2010) have emphasized a strong relationship between upper-level potential vorticity (PV) anomalies and precipitation extremes. Southern intrusions of air with relatively high PV in the upper troposphere or lower stratosphere are commonly accompanied by a local lowering of the dynamic tropopause, intense vertical motions, high vertically integrated water vapour transport, rapid cyclogenesis, intense convection and heavy rainfall (e.g., Krichak et al., 2014). The height of the dynamic tropopause is commonly defined as the level at which PV equals 2.0 PV units (PVU). In the troposphere, PV is ordinarily below this value and relatively uniform, but in the stratosphere, it is much higher due to increased stability. PV gradients are large in polar regions, where a particular isentropic surface lies in the stratosphere, but are weak further southward. Usually, the 2 PVU contour on an isentropic surface that lies in the stratosphere in the polar region is noticeably contorted showing long tongues of high PV air extended outward. Such PV streamers are associated with extreme mid-latitude weather (e.g., Schlemmer et al., 2010). Cutoff lows, which appears as small regions of high PV air totally encircled by low PV air, are also related to extreme surface precipitation and floods. Here, we investigate the relationship between River Ammer floods and PV patterns on the 330 K isentropic surface. We look also at the relationship between the frequency of high upper-level PV days, that is, PV on 330 K surface greater than 2.0 PVU, and solar irradiance forcing. The PV patterns remain qualitatively the same if the analysis is performed on isentropic surfaces varying from 320 K to 340 K. PV on the 330 K isentropic surface is calculated using temperature and horizontal wind field from NCEP1 reanalysis (Kalnay et al., 1996) for 1948 to 2015 summers. The same quantity, i.e. PV on the 330 K surface, covering the 1836-2015 period, was extracted from the 20CR V3 data set (Slivinski et al., 2019) and used to derive flood and solar-related PV patterns at interannual to multidecadal timescales.
Daily 500 hPa geopotential height (Z500) data from the NCEP1 reanalysis (Kalnay et al., 1996) is used to construct blocking frequency for the period 1950-2015. We calculate the two-dimensional blocking index as described by Scherer et al. (2006), which is an extension of the classical one-dimensional blocking index of Tibaldi and Molteni (1990). As the horizontal resolution of Z500 field is 2.5 longitude × 2.5 latitude, a latitudinal gradient of 15 north and south is taken around each grid point from 35 N to 75 N to calculate the Z500 gradients. A grid point is considered as blocked if the northern Z500 gradient is less than −10 m/(deg. latitude) and the southern Z500 gradient is positive. The time persistence threshold, considered here, is one day. Therefore, this index captures blocking like circulations or instantaneous blocking, as it is often referred to in the literature (e.g., Davini et al., 2012). The blocking pattern associated with low solar forcing is calculated as the average blocking frequency anomaly maps for all summers characterized by a solar activity index smaller than minus one standard deviation.
Two solar activity reconstructions are used in this study. The first is the open solar flux (Lockwood et al., 2009) derived from geomagnetic measurements. It exhibits stronger correlations with atmospheric circulation variations than conventionally used measures of solar activity (Woolings et al., 2010). Open solar flux data at annual resolution are available at the KNMI webpage (www.knmi.nl). Based on this record, we construct the blocking frequency as well as upper PV patterns associated with low solar activity during the observational period. The second is the Holocene total solar irradiance (TSI) reconstruction of Steinhilber et al. (2009), which is used to analyse the relationship between millennial-scale TSI variability and frequency of flood layer in the Lake Ammer sediments during the last~5,500 years . Singular spectrum analysis (SSA) (e.g., Ghil et al., 2002) was applied to search for quasiperiodic signals in the TSI and flood layer records.

| RESULTS
3.1 | Extreme climate patterns associated with River Ammer floods during the observational period Based on daily River Ammer discharge we identify flood years, that is, years with at least one day of River Ammer discharge above 125m 3 /s. The frequency of flood years ( Figure 1) is relatively high from 1950 to 1981 and 2000 to 2015. No flood days are recorded during summers from 1982 to 1999 ( Figure 1). Interestingly, during this period solar activity was relatively high. 8(5) out of 13 flood years occur during summers with a solar irradiance activity below the mean (minus one standard deviation). Note also that the River Ammer flood in summer 2010, when enhanced blocking activity was recorded in the Eastern Europe (Drouard and Woolings, 2018), is associated with very low solar irradiance (Figure 1).
River Ammer floods are related to heavy rain in the catchment area during spring and summer (e.g., Czymzik et al., 2010). We address the question of the spatial extension of the extreme precipitation anomalies causing River Ammer floods during summer. The composite map of the R20mm index shows that River Ammer floods are associated with more frequent extreme rainfalls over parts of central, western, and southern Europe (Figure 2a). The pattern is consistent with enhanced precipitation in the Ammer region 1 day before the onset of each daily River Ammer flood from 1950 to 2015 period ( Figure S1). Similar patterns are obtained for other extreme precipitation indices, like R10mm, Rx5day and R95PTOT (not shown). The composite map of the SU index ( Figure 2b) shows a decrease (increase) in the frequency of summer days over western, central, and southern Europe (southwestern Europe, northeastern Europe and western Russia) during flood years relative to the climatology. Both patterns are consistent with the precipitation and temperature anomaly patterns associated with observed River Ammer floods (Rimbu et al., 2016). We conclude that River Ammer floods are associated with large scale extreme precipitation and temperature patterns.
To understand how floods are related to extreme temperature and precipitation ( Figure 2) we look first at atmospheric circulation patterns associated with daily River Ammer floods, that is, daily discharge higher than 125 m 3 /s. Correlation analysis reveals that River Ammer daily discharge and local daily precipitation are maximally correlated at one-day time lag (not shown). Therefore, we look at the upper level PV maps, 1 day before the onset of a daily River Ammer flood. Most of the observed daily floods from the 1950 to 2015 period are associated with high PV values (PV > 2PVU) in the Ammer region ( Figure S2). The PV patterns have various spatial structures, including streamers, cutoffs, or troughs. For most of the flood events relatively low PV values are recorded over southwestern Europe and eastern Europe-western Russia ( Figure S2).
The composite map for upper-level circulation during all River Ammer flood days ( Figure 3a) shows a pronounced trough over western Europe, consistent with previous studies (Rimbu et al., 2016). However, this trough is part of a large-scale wave pattern that extends downstream over the Atlantic. The wave-structure is clearly emphasized on the PV distribution on the 330 K potential temperature surface (Figure 3b). This wave, which shows an increasing amplitude over the North Atlantic, breaks over western Europe. The relatively high (low) PV values prevail over the region with an increased (decreased) frequency of extreme precipitation (Figure 2a), consistent with the strong connection between upper-level PV anomalies and surface extreme precipitation (Schlemmer et al., 2010;Krichak et al., 2014). A similar analysis of 20CRV3 PV data, going back to 1926, reveals that daily River Ammer floods are associated with a hemispheric scale pattern with wave-number 6 ( Figure S3). Similar patterns were related to the dramatic increase in recent Northern Hemisphere summer extreme temperature and precipitations through the quasistationary resonance (QRA) mechanism (Petoukhov et al., 2013;Kornhuber et al., 2016).

| The role of atmospheric blocking
Atmospheric blocking plays a central role in generating extreme precipitation and temperature anomalies (e.g., Woolings et al., 2018). Here we investigate the relationship between summer blocking, River Ammer floods, and solar forcing during the 1950-2015 summers.
The 2D instantaneous blocking frequency climatology for the Atlantic-European region is displayed in Figure 4.
It shows a relatively high blocking frequency (9-13% of all days) over the Scandinavian region. Another highfrequency centre (9-11% of all days) is recorded over northwestern Russia, near Novaya Zemlya. The position of the high blocking frequency band is connected with the position of the jet stream during summer (Masato et al., 2013). Previous studies of two-dimensional summer blocking frequency (Masato et al., 2013;Woolings et al., 2018) reveal similar blocking patterns over this region.
The composite map of blocking frequency anomalies for observed summer River Ammer floods (Figure 5a) (a) (b) F I G U R E 3 Composite map of daily (a) Z500 (contour) and Z500 anomalies (shaded) and (b) potential vorticity on 330 K potential temperature surface for observed daily River Ammer floods during summers from 1950 to 2015. Filled black circles depict the location of the Ammer region. Units: m and potential vorticity units (PVU) F I G U R E 4 Summer blocking frequency climatology. The period is 1950-2015. Units: percent of blocked days from total number of summer days E648 depicts positive anomalies over northern and northeastern Europe. In these regions, positive Z500 anomalies are recorded during daily floods (Figure 3a). Interestingly, a similar blocking pattern is associated with low solar irradiance summers during the same period (Figure 5b). This is consistent with an increased flood frequency during low solar irradiance summers as shown in Figure 1.
The PV composite map associated with observed daily River Ammer floods ( Figure 3b) suggests a possible upper-level atmospheric forcing on flood variability. We consider the number of days in a summer with high upper level (i.e., 330 K surface) PV values (PV > 2PVU) as a measure of upper-level atmospheric forcing on extreme surface precipitation and floods. Positive anomalies of this index can be linked to more frequent upperlevel high PV structures, like streamers or cutoffs. Such PV patterns increase the probability of extreme surface precipitation and floods (e.g., Krichak et al., 2014). Consistent with the PV structures during individual daily floods ( Figure S2), more (less) frequent high PV days at upper levels are recorded over western Europe (eastern Europe and western Russia) during River Ammer flood summers (Figure 6a). A similar pattern is associated with low solar irradiance summers (Figure 6b). Overall, there are some inconsistencies between the blocking ( Figure 5) and PV (Figure 6) corresponding patterns. These can be related to the relatively short time-span covered by the NCEP1 data as well as to the characteristics of the applied blocking and PV indices.
To better assess and confirm the relationship between solar forcing and upper-level PV, as shown in Figure 6b, we used the 20CRV3 PV data (Slivinski et al., 2019) to extend the analysis back to 1836. The time series of a regional index (RPV), defined as the average of PV indices described above in all grid points within the (30-60 E; 40-55 N), and solar irradiance ( Figure S4a) are significant (95% level) positively correlated (r = .24). Negative values of RPV are associated with more frequent blocking days in this region. Correlations between this index and R20mm extreme precipitation indices over central and western Europe during 1950-2015 are predominantly negative ( Figure S4b). On synoptic scales, a blocking over northeastern Europe favours the occurrence of wave breaking and heavy precipitation over western Europe (e.g., Barton et al., 2016). We propose the same mechanism to explain the solar-flood connection described above. More frequent blocking events over eastern Europe-western Russia during low solar irradiance summers lead to more frequent wave breaking events over western Europe, a less stable vertical atmosphere, and more frequent floods. Anomaly patterns of our PV index, i.e. the number of days with PV higher than 2PVU, linked to solar forcing resemble each other on interannual and multidecadal time scales ( Figure S5). This similarity suggests that solar irradiance changes modulate extreme precipitation and flood variability over western and central Europe through the same mechanism on interannual and multidecadal timescales.

| Flood layer variability during the last millennia
The frequency of flood layers of Lake Ammer sediments shows strong interannual to millennial variability during the last 5,500 years (Figure 7). Periods with low flood frequency lasting from several decades to centuries occur often during this period. High flood frequency is recorded during 3,400 BC-3,200 BC, immediately before the Piora Oscillation (BPO) or Piora Cold Period (Figure 7). The Piora Oscillation, named after the Piora Valley in Switzerland, was an abrupt cold and wet period in the Alpine region dated to about 3,200 BC-2900 BC (e.g., Wick and Tinner, 1997). Another period with high flood frequency is the Homeric Minimum (HM) (Figure 7). The HM is a grand solar minimum that took place between 800 BC and 600 BC (e.g., Martin-Puertas et al., 2012). During this period wet conditions were recorded over western Europe, while dry conditions prevailed over eastern Europe, consistent with extreme precipitation patterns associated with River Ammer floods during the observational period (Figure 2a).
More frequent flood layers occur during the Little Ice Age (LIA;~1,300 AD-1850 AD), a period characterized by low temperatures over Europe (e.g., Kaniewski et al., 2016) (Figure 7). Low frequency of flood layers is recorded during warm periods like the Roman Warm Period (RWP;~250 BC-400 AD) or Medieval Warm Period (MWP;~900 AD-1,300 AD). The variability in the frequency of observed flood years is not unusual in the perspective of the last~5,500 years (Figure 7).
Previous studies (e.g., Czymzik et al., 2016) show that River Ammer flood frequency is significantly negatively correlated with total solar irradiance (TSI) on decadal to centennial timescales. Here, we focus on millennial-scale variations of the flood layer record and its relationship with the TSI reconstruction of Steinhilber et al. (2009) throughout the last 5,500 years. The analysis is based on the frequency of flood layers and TSI anomalies in a nonoverlapping 100-year moving window for the common period which is 3,500 BC-1999 AD. A simple visual inspection of the flood frequency and anomaly TSI time series (Figure 8) reveals that periods of high flood activity are associated with low solar irradiance. For example, relatively high flood frequency is recorded during 3,400 BC-3200 BC, when TSI was relatively low. A similar relationship is present during the LIA (Figure 8). Less flood activity is recorded during high solar irradiance periods like RWP or MWP (Figure 8).
An SSA (Ghil et al., 2002) isolates two distinct millennial-scale cycles in flood frequency between 3,500 BP and 1999 AD. The first cycle has a period of~2,300 years and the second~900 years. Together they describe~60% of the centennial to millennial-scale flood frequency variability (Figure 8a). A similar SSA of the TSI time series identifies two cycles with similar periods (Figure 8b). The reconstructed flood and TSI signals from these two cycles during the last 5,500 years are broadly anti-phased ( Figure 8). Most of the warm or cold Holocene periods are associated with maxima or minima of the signal reconstructed from these two cycles.

| DISCUSSION AND CONCLUSIONS
In this study, we investigated the observed and proxy River Ammer flood variability and its relationship to solar irradiance forcing during summer. It was shown that atmospheric blocking occurs with a higher probability over eastern Europe-western Russia during summers characterized by low solar activity. Increased blocking frequency in this region is associated with positive anomalies of extreme precipitation indices over central and western Europe, including the Alpine region. This explains, from a synoptic-scale perspective, the out-ofphase variations of solar irradiance and River Ammer flood frequency, as reported in previous studies (e.g., Czymzik et al., 2016). Recently, Drouard and Woolings (2018) investigated the processes that initiate blocking events over western, central, and eastern Europe-western Russia during summer. They showed that blocking over eastern Europe-western Russia is preceded by significant low-frequency, large-scale wave trains (their Figure 1c) that resemble the Northern Hemisphere atmospheric circulation pattern associated with River Ammer floods, presented in this paper ( Figure S3). Similar patterns are related to the significant increase in extreme summer temperature and precipitation during recent decades (Petoukhov et al., 2013;Kornhuber et al., 2016). We argue that this pattern, which favours enhanced blocking activity in eastern Europe (Drouard and Woolings, 2018), could be enhanced during low solar irradiance summers. Enhanced blocking activity in this region increases the probability of upper-level wavebreaking and surface extreme precipitation over western Europe (Barton et al., 2016). However, the relationship between solar irradiance and other forcing on wave breaking across the western Europe, like ridges over the central Atlantic or extra-tropical transition events over the western Atlantic and North America (e.g., Barton et al., 2016), should also be investigated.
The influence of solar activity on weather and climate variability has received significant scientific attention for winter but less for summer. Significant modulation of solar forcing on the frequency of synoptic types winter atmospheric circulations was reported (e.g., Huth et al., 2008). The solar irradiance forcing can modulate the frequency of extreme precipitation and floods through modulation of the frequency of the related atmospheric circulation types. Furthermore, statistical analysis of long-term instrumental, historical, and proxy data sets reveals that large-scale teleconnection patterns are associated with decadal to multidecadal solar irradiance forcing . Various dynamical mechanisms have been proposed to explain the solar influence on winter surface climate, such as the downward propagation of polar vortex anomalies (Ineson et al., 2011), synoptic-scale Rossby wave breaking (Lu et al., 2013), or eddy momentum fluxes (Simpson et al., 2009). Using modelling experiments, Haigh (1999) reported a weakening and broadening of the tropical Hadley cells accompanied by polewards moving of the sub-tropical jets and mid-latitude Ferrel cells during high solar irradiance years. This causes sub-tropical warming and a characteristic vertical banding of mid-latitudes temperature changes in both the summer and winter hemispheres. The enhanced summer blocking over eastern Europe during low solar irradiance summers reported here could be related to a direct impact of Sun on summer climate or could be a result of persistence of winter anomalies induced by the Sun through the subsequent summer (e.g., Ogi et al., 2003). Also, blocking over eastern Europe could be amplified through diabatic processes associated with weather systems that generate heavy precipitation (Pfahl et al., 2015). Furthermore, the possibility that solar irradiance forcing to set the conditions to increase the probability of occurrence of QRA events, a pattern responsible for summer extremes (e.g., Kornhuber et al., 2016) should also be investigated.
Analysing observational daily River Ammer discharge data revealed that during summer floods, extreme precipitation occurs with a higher probability over large areas of central and western Europe. Further empirical associations between flood frequency and solar activity in records from the Atlantic-European region support the larger spatial relevance of the flood signal from the River Ammer catchment . In our study, we describe the anomaly patterns of extreme precipitation and temperatures associated with River Ammer floods during the observational period and show that they are similar to the corresponding patterns associated with low solar irradiance. Furthermore, we argue that such patterns remain qualitatively the same for different timescales. Therefore, these patterns might be used to systematically search for a solar signature in different proxy records during the past. For example, during the period of the Spörer Minimum (SPM) in solar activity, that is, 1,400 AD-1,510 AD, major flood events were documented in the eastern part of the Carpathian basin, Bohemia, Austria and the Hungarian Kingdom (Camenisch et al., 2016 and references therein). In the same period River Ammer flood frequency was relatively high (Figure 7). This supports the hypothesis that particular flood records are related to large-scale extreme precipitation patterns and solar irradiance is a possible forcing. However, extreme climate conditions, like those during the early solar Spörer Minimum (SPM) around 1,430 AD are related not only to the solar irradiance forcing but to a superposition of internal and external factors (Camenisch et al., 2016).
Previous studies  identified significant low-frequency oscillations,with periods around 90 and 210 years, in the mid to late Holocene flood layer record from Lake Ammer sediments and connected with the solar Gleisberg and Suess cycles. Their analysis reveals also a dominantly anti-phase behaviour between frequency of flood layers and TSI at these time scales . Here, we show that about 60% of the centennial to millennial flood layer variability is described by two cycles with periods around 900 and 2,300 years. Kaniewski et al. (2016) identified persistent~900 and~2,300 year cycles in the records of storm surges, coastal flooding, and agricultural losses from the central Mediterranean. Comparable cycles were identified in Alpine paleoflood records by Wirth et al. (2013) and in the dominant mode of North Atlantic Holocene temperature variability . We identified similar cycles in the TSI reconstruction by Steinhilber et al. (2009), usually referred to as the Eddy (~900 years) and the Hallstatt (~2,300 years) cycle respectively. They are the longest studied direct tracers of solar activity. Both cycles were also found in the Solanki et al. (2004) solar irradiance reconstruction through a singular spectrum analysis (Dima and Lohmann, 2009). There are furthermore speculations that both cycles are of astronomical origin (Scafetta et al., 2016). Our analysis reveals that the atmospheric circulation patterns associated with flood frequency variability and low solar forcing are qualitatively the same for interannual to multidecadal timescales ( Figure S5). If they remain so also for centennial to millennial timescales, a hypothesis that should be confirmed through numerical model experiments, the corresponding precipitation and extreme temperature patterns associated with low solar forcing might be also independent on timescale, and, to a certain degree, be anticipated.
Our analysis reveals that flood frequency and solar variability are associated with distinct spatial and temporal patterns in blocking frequency, extreme temperature, and precipitation over Europe during summer. To date, however, the mechanistic explanation of Sun-climate connections focused on the winter season. Therefore, model experiments should be performed to assess the robustness of these summer patterns and test possible physical mechanisms behind them. This would have important implications for the predictability of extreme climate variability over Europe, especially at long timescales.