ArticlePDF Available

Influence of solar activity changes on European rainfall

  • Hochschule für Technik und Wirtschaft des Saarlandes (retired)
  • Institute for Hydrography, Geoecology and Climate Sciences


European hydroclimate shows a high degree of variability on every time scale. The variability is controlled by natural processes such as Atlantic ocean cycles, changes in solar activity, volcanic eruptions and anthropogenic factors. This contribution concentrates on the solar influence on European precipitation, a relationship which has been documented by a large body of published case studies. Here we are concentrating on the period 1901–2015 for which we compare sunspot data with monthly precipitation series of 39 European countries by calculating Pearson correlation coefficients for a multi-year cross-correlation window. The coefficients have been mapped out across Europe with the aim to identify areas in which solar activity may have influenced precipitation. Results show that February precipitation in Central and Western Europe yields the strongest solar response with coefficients reaching up to +0.61. Rainfall in June–July is equally co-driven by solar activity changes, whereby the solar-influenced zone of rainfall shifts from the British Isles towards Eastern Europe during the course of summer. Other months with noteworthy solar responses are April, May and December. On a decadal scale, the correlation between precipitation and solar activity in central Europe appears to be mostly positive, both statistically and by visual curve comparison. Yet, best positive correlations coefficients of February, June, July and December are typically reached when the solar signal lags rainfall by 1.5–2 years. Taking into account cause and effect, it is suspected that increases in Central European rainfall are actually triggered by the solar minimum some 3–4 years before the rainfall month, rather than the lagging solar maximum. Similar lags of a few years occur between solar activity and the solar-synchronized North Atlantic Oscillation (NAO) due to memory effects in the Atlantic. The literature review demonstrates that most multidecadal studies from Central Europe encountered a negative correlation between solar activity and rainfall, probably because short time lags of a few years are negligible on timescales beyond the 11 year solar Schwabe cycle. Flood frequency typically increases during times of low solar activity associated with NAO- conditions and more frequent blocking.
Influence of solar activity changes on European rainfall
Ludger Laurenza, Horst-Joachim Ludeckeb, Sebastian Luningc,1
a Independent Researcher, Münster, Germany
b University of Applied Sciences HTW, Saarbrücken, Germany
c Institute for Hydrography, Geoecology and Climate Sciences, Hauptstraße 47, 6315, Ägeri, Switzerland
Non layout-version of Laurenz et al., 2019, Journal of Atmospheric and Solar-Terrestrial
Physics 185 (2019) 29-42
European hydroclimate shows a high degree of variability on every time scale. The variability is controlled by
natural processes such as Atlantic ocean cycles, changes in solar activity, volcanic eruptions and
anthropogenicfactors. This contribution concentrates on the solar influence on European precipitation, a
relationship which has been documented by a large body of published case studies. Here we are concentrating
on the period 19012015 for which we compare sunspot data with monthly precipitation series of 39 European
countries by calculating Pearson correlation coefficients for a multi-year cross-correlation window. The
coefficients have been mapped out across Europe with the aim to identify areas in which solar activity may
have influenced precipitation. Results show that February precipitation in Central and Western Europe yields
the strongest solar response with coefficients reaching up to +0.61. Rainfall in JuneJuly is equally co-driven by
solar activity changes, whereby the solar-influenced zone of rainfall shifts from the British Isles towards Eastern
Europe during the course of summer. Other months with noteworthy solar responses are April, May and
December. On a decadal scale, the correlation between precipitation and solar activity in central Europe
appears to be mostly positive, both statistically and by visual curve comparison. Yet, best positive correlations
coefficients of February, June, July and December are typically reached when the solar signal lags rainfall by
1.52 years. Taking into account cause and effect, it is suspected that increases in Central European rainfall are
actually triggered by the solar minimum some 34 years before the rainfall month, rather than the lagging solar
maximum. Similar lags of a few years occur between solar activity and the solar-synchronized North Atlantic
Oscillation (NAO) due to memory effects in the Atlantic. The literature review demonstrates that most
multidecadal studies from Central Europe encountered a negative correlation between solar activity and
rainfall, probably because short time lags of a few years are negligible on timescales beyond the 11 year solar
Schwabe cycle. Flood frequency typically increases during times of low solar activity associated with NAO-
conditions and more frequent blocking.
1. Introduction
European hydroclimate shows a high degree of variability on diverse time scales, reaching from daily
to millennial (e.g. Linderholm et al., 2018; Magny, 2004; Markonis et al., 2018; Zveryaev and Allan,
2010). This variability in rainfall, floods and droughts is thought to be controlled by natural processes
such as Atlantic ocean cycles (e.g. Hurrell and van Loon, 1997; Trigo et al., 2004), changes in solar
activity (e.g. Czymzik et al., 2016b) and volcanic eruptions (e.g. Rao et al., 2017), as well as by
anthropogenic factors (e.g. Maraun, 2013). A robust understanding of natural precipitation drivers is
necessary in order to reliably distinguish their effects from anthropogenic influences. This is
particularly important for climate models which need to take all possible forcing factors qualitatively
1 Corresponding author. E-mail addresses: (H.-J. Ludecke), (S. Luning).
and quantitatively into account in order to continuously improve their hindcast and forecast
performances (Bothe et al., 2018; DeAngelis et al., 2015; Hoerling et al., 2009). In this contribution
we are concentrating on the potential influence of solar activity changes on European rainfall. In the
first part, we are reviewing the existing literature on the subject, focussing on regional trends, time
lags and methodologies. In the second part of this paper we are comparing regional European rainfall
series of the past 115 years with solar activity indices by means of statistical analyses. The objective
is to test for possible correlations on yearly, seasonal and monthly resolutions.
2. Solar influence on European rainfall
Various papers have suggested a solar influence on European rainfall. Here we are reviewing this
evidence, regionally grouped for western, northern, eastern and southern Europe. The studies use
modern rainfall and river discharge data, as well as palaeoclimate proxies for wetlands humidity and
river floods. Time scales reach from the solar Schwabe cycle (11 years) to the solar Hallstatt cycle
(2300 years).
2.1. Western Europe
The solar Schwabe cycle appears to play a major role for summer flooding in the European Alps. The
flood frequency of River Ammer in the Bavarian Alpine Foreland typically increases during intervals of
reduced solar activity. Significant correlations have been identified between late spring/summer
discharge data of the last 90 years and solar activity (Czymzik et al., 2016b). Interestingly, the solar
influence on hydroclimate appears somewhat delayed, as the flood record lags the solar signal by 2
3 years. The 11 years solar cycle was also found in a cross-spectral analysis of summer floods in
Switzerland of the past 200 years (Peña et al., 2015). As in River Ammer, flooding was more frequent
during solar activity minima. Nonlinear spectral analysis of Holocene varves in a Westeifel crater lake
of Holzmaar (western Germany) also yielded a Schwabe cycle periodicity (Negendank et al., 1997;
Vos et al., 1997, 2004), even though it is unclear whether hydroclimate or temperature changes are
the main climatic driver. Solar-driven changes in discharge of river Rhine at Basel were suggested by
Franke and Bechteler (1969) involving alternating phase shifts and 23 years time lags. Vines (1985)
proposed various periodicities for European rainfall, including Schwabe and Hale (22 years) cyclicity.
Solar influence on European hydroclimate has been also reported on a centennial to multi-
centennial scale comprising of the Gleissberg (80100 years) and Suess de Vries (210 years) solar
cycles. In the northern and central Alps, multidecadal summer flood-prone periods typically occurred
when solar activity was reduced. Varve studies in the Bavarian Lake Ammersee for the past 450 years
document an increase in spring and summer floods during the Sporer, Maunder, and Dalton solar
minima of the Little Ice Age (LIA) (Czymzik et al., 2010). Holocene summer flood frequency in the
Central Alps is pulsed by Gleissberg and Suess de Vries solar periodicities, as evidenced in lake
sedimentary cores in Switzerland and northern Italy (Rabadan and Schulte, 2014; Schulte et al., 2015;
Wirth et al., 2013b). In an analysis of historical floods in Switzerland of the past 200 years, Peña et al.
(2015) identified a clear Gleissberg cyclicity. All Swiss studies agree that summer flood frequency was
higher during solar activity minima. Nevertheless, regional differences between the Northern and
Southern Alps have been observed and need to be taken into account (Pena et al., 2015; Wirth et al.,
2013b). Gleissberg and Suess-de Vries solar periodicities have been documented in Holocene
hydroclimate reconstructions studying lake and wetlands cores in Germany (Czymzik et al., 2016a;
Negendank et al., 1997; Vos et al., 1997), the Netherlands (Blaauw et al., 2004), UK (Macklin et al.,
2005; Mauquoy et al., 2002, 2004; Swindles et al., 2007b, 2012) and Ireland (Blackford and
Chambers, 1995; Stolze et al., 2013). In most cases, wet periods fall into low solar activity phases. In
contrast, Nurtaev (2015) suggested a positive correlation between sunspots and river Rhine
discharge for the past 100 years.
Solar activity appears to also play a role for rainfall in Western Europe on even longer time scales,
namely through the solar cycles of 500 years and the millennial-scale 1000 years (Eddy) and 2300
years (Hallstatt) periodicities. These cycles were documented for flood histories in southern Germany
(Czymzik et al., 2013) and Switzerland (Schulte et al., 2009; Wirth et al., 2013b), lake levels in
Switzerland and France (Magny, 1993, 2004), and wetlands humidity changes in the UK and Denmark
(Mauquoy et al., 2008; Swindles et al., 2007b, 2010, 2012). Time lags for full hydroclimate response
of up to 50 years have been reported by Mauquoy et al. (2008). More humid conditions typically
prevailed during phases of low solar activity. A particularly wet and cold episode occurred in Western
Europe during the so-called 2.8 kyr BP event, the Homeric Minimum, a phase of low solar activity
that took place around 2800 years ago and persisted for more than 150 years (e.g. Bond et al., 2001).
The associated dramatic increase in humidity has been documented in Germany (Martin-Puertas et
al., 2012), the Netherlands (Kilian et al., 1995; van Geel et al., 2014; van Geel and Mauquoy, 2010;
Van Geel et al., 1997) and the UK (Swindles et al., 2007a).
Solar activity also affects wind regimes in Central Europe. Schwander et al. (2017) analysed
weather types for the past 250 years and found fewer days with westerly and west south-westerly
flow over Central Europe under low solar activity, hereby northerly and easterly flow types increased.
The blocking frequency between Iceland and Scandinavia increases during solar minima and Central
European temperatures cool. Notably, model simulations are still not able to reproduce this imprint
of the 11-year solar cycle on the tropospheric weather of the region (Schwander et al., 2017).
2.2. Northern Europe
The phase relationship between solar activity and precipitation appears to be regionally
differentiated in northern Europe. Studies from southern and central Sweden document a marked
increase in precipitation and floods during the 2.8 kyr BP grand solar minimum (Labuhn et al., 2018;
Mellstrom et al., 2015). In northern Sweden, however, summer rainfall increases in high solar activity
phases, as documented by Kokfelt and Muscheler (2013) for the past 1000 years in a lake
sedimentary core. Rainfall was reduced during the Wolf, Sporer and Maunder solar minima. Kokfelt
and Muscheler (2013) also compared the sunspot cycle with a long instrumental series of summer
precipitation at the Abisko Scientific Research Station in northern Sweden for the past 100 years.
Whilst the first half of the series 19201960 lacked a robust link, the second half 19602000 yielded
statistically significant correlations. As in the multi-centennial reconstruction, the amount of summer
precipitation increased during periods with higher solar activity. In Latvia, Hajian and Movahed
(2010) presented a comparison of sunspots and discharge of the river Daugava. The authors
identified a cyclical element in the river flow that showed some similarities with solar activity
although with a periodicity closer to the solar Hale cycle (22 years).
2.3. Eastern Europe
A shift towards a wetter and colder climate in association with the 2.8 kyr solar minimum was
described by Speranza et al. (2003) for the Czech Republic. Discharge of Elbe River at Děčin in the
northern Czech Republic shows alternating correlations with sunspots during the period 18501960
(Franke and Bechteler, 1969). Nurtaev (2015) compared Danube River discharge with solar activity
for the past 100 years and found an inverse correlation, with higher flow rates during weak solar
phases. Ducic et al. (2007) tested various combinations of solar and lower Danube discharge
parameters in the Romanian-Serbian segment and found the best correlations between flow index
and latitude of sunspots. Mares et al. (2016) studied the same lower Danube discharge data and
found maximum spring and summer flow rates about 2–3 years after solar Schwabe minima. The
geomagnetic index aa as solar proxy produced the best results. Dobrica et al. (2017) analysed the
power spectrum of the lower Danube discharge and identified periods that are linked to the solar
Schwabe and Hale cycles and their multiples. Lamy et al. (2006) studied the Holocene discharge
history of Sakarya River which represents Anatolia's longest river. Maximum discharge was found to
be associated with periods of reduced solar activity, similar as in the case of the Danube.
2.4. Southern Europe
Variability in Italian precipitation and floods is controlled by the North Atlantic Oscillation (NAO) and
solar activity (Brunetti et al., 2000; Wirth et al., 2013a). Zanchettin et al. (2008) analysed Po River
discharge and northern Italian regional precipitation data and found that wet and dry periods
alternate in accordance with polarized sunspot cycles, i.e. solar Hale cycles. Solar forcing is assumed
to take place via the solar-forced NAO. Positive (negative) NAO anomalies are associated with
comparatively lower (higher) Po River discharges (Zanchettin et al., 2008). The strength of solar
activity is thought to modulate the connection between the NAO and Po River discharges.
Landscheidt (2000) in response to Tomasino and Valle (2000) pointed to phase shifts in the solar
influence on Po River discharge over the past 100 years. Based on the observed patterns, Tomasino
et al. (2004) suggested that Po River discharge may be predictable based on solar activity
periodicities. Periodicities associated with the Schwabe solar cycle and the NAO have also been
reported from sedimentary cores in the Gulf of Taranto located at the distal end of the Po-river
discharge plume (Chen et al., 2011; Cini Castagnoli et al., 2002). Notably, Summer precipitation
trends have been anti-correlated in northern and southern Italy during the past 150 years (Brunetti
et al., 2000).
Climate reconstructions for the past 2000 years in Lake Ledro in the Italian Southern Alps found an
increase in flooding during phases of low solar activity, namely in the Dalton, Sporer, Maunder, and
Wolf Minima (Vanniere et al., 2013; Wirth et al., 2013a). The northern Italian rivers Tiber, Adige and
Po show a maximum in flooding frequency during the Sporer Minimum (Camuffo and Enzi, 1995;
Glaser et al., 2010). Tiber and Adige experienced another flooding maximum at the onset of the
Maunder Minimum (Glaser et al., 2010). In Iberia, the relationship between floods and solar activity
is opposite to that in Italy. Reconstructions from Spain for the last 1000 years show a decrease of
flood frequency during solar minima in late summer and autumn (Barrera-Escoda and Llasat, 2015;
Corella et al., 2014; Glaser et al., 2010; Moreno et al., 2008; Vaquero, 2004). Smith et al. (2016)
documented millennial-scale hydroclimatic cycles from a northern Spanish cave which appear to be
linked to a cyclicity that Bond et al. (2001) associated with solar activity changes.
2.5. Complexity of the solar signal
The literature review shows that the solar influence on European precipitation follows certain
patterns, yet in a complex way. The correlation coefficients between hydroclimate and solar activity
keep changing on regional and temporal scales (Le Mouel et al., 2009). Regional differences occur
and reflect the dominance of different atmospheric regimes resulting in opposite solar effects.
Typical time lags of a few years point to delayed climatic response due to the inertia of the oceans
which play an important additional role for variability in European rainfall. Once fully understood, the
lags may offer seasonal rain forecasts. Solar effects on precipitation have been observed on time
scales ranging from Schwabe (11 years) to Hallstatt (2300 years) cycles and also differ for separate
seasons and months. The coupling between solar activity and rainfall is variable and includes periods
with stronger and other periods with weaker correlation.
3. Material and methods
3.1. Data
In order to test for possible correlations between rainfall and solar activity, monthly precipitation
data for 39 European countries covering the period 19012015 was downloaded from the Climate
Change Knowledge Portal which is operated by the World Bank Group
( This gridded historical dataset is derived from
observational data and has been produced by the Climatic Research Unit (CRU) of the University of
East Anglia, reformatted by the International Water Management Institute. The CRU dataset shows
reasonably consistent interannual variability compared to other gauge-based precipitation datasets,
namely those from the Global Precipitation Climatology Centre (GPCC) and the University of
Delaware (UDEL), even though with deviations in magnitudes of up to about 100mm (Sun et al.,
2018). In order to extend the rainfall record into the 19th and 18th centuries, three additional long
term data series were included in the analysis. The Stockholm data set reaches back to 1786 and was
sourced from the Swedish Meteorological and Hydrological Institute (http://opendata-download- A historical precipitation series from Paris covers the period 18041919,
kindly provided by Meteo-France. This series contained minor (< 2%) data gaps which were filled by
interpolation. The Edinburgh series covers the period 17852002 and was sourced from the UK Met
Office National Meteorological Archive. The sunspot data is based on Sunspot Number Version 2.0
from the Royal Observatory of Belgium in Brussels, Sunspot Index and Long-term Solar Observations
(, (Clette et al., 2015).
3.2. Statistical processing
Both the monthly precipitation and sunspot data were smoothed using a Savitzky-Golay Filter (SGF).
the SGF is a method of filtering thedata for increasing the signal-to-noise ratio. The fundamental
method is mathematical convolution (Riley et al., 2006) by fitting successive sub sets of close-by data
points with a polynomial by the linear least squares method (Luo et al., 2005; Savitzky and Golay,
1964). In most cases, SGF gives better results than smoothing by a simple moving average (SMA).
Supplement Figs. S2021 visualize the SGF applied on a graph of this paper by comparing it with the
unfiltered data and with a simple moving average of width 3 (SMA). The SGF used here, generally,
has a frame size of 11 and a polynom order of 5 for both precipitation and sunspots.
Monthly precipitation per country and sunspots were compared by calculating Pearson correlation
coefficients. In order to allow for lead/lag relationships, a cross correlation window of −120 to +24
months was chosen. While the rainfall was kept stable, the solar signal preceding the rainfall by up to
120 months (negative solar lag, i.e. lead) or postdating the rainfall by up to 24 months (positive solar
lag) was shifted onto the rain series. The coefficient of the most positive correlation in this window
was recorded, together with the solar lag in full months (Table 1 and S1; see illustrated time series
for all countries in Supplement Figs. S1 and S2). In a parallel exercise, the most negative correlation
coefficients and their respective lag were recorded for a slightly shortened cross correlation window
of −80 and + 24 months (Tables S2 and S3). Window shortening was empirically found necessary in
order to obtain more consistent results. Selected rainfall series were studied by means of wavelet
analysis (Grinsted et al., 2004).
In order to ascertain the statistical confidence of the Pearson correlation r between precipitation
and Sunspot time series over 1901 to 2015, we assumed the null hypothesis that r is caused by
chance. We evaluated this assumption by Monte Carlo simulation (MC) (Mazhdrakov et al., 2018)
based on surrogate records of the same Hurst exponent H as the European precipitation time series.
We evaluated H by the detrended fluctuation analysis of the European country precipitations
(Kantelhardt et al., 2001) with the result of H≈0.6, which means only weak autocorrelation (white
noise as H=0.5). H≈0.6 was also found by J. W. Kantelhardt for worldwide precipitation time series
(Kantelhardt, 2004). In the MC simulation 10,000 surrogates replaced the real monthly precipitation
time series. Both for the surrogates and the sunspot number series the same Savitzky-Golay filter of
frame size 11 and polynom order 5 was used. The surrogates were generated by a standard method
(Turcotte, 1997). As a result, we found the following probabilities p for the null hypothesis: For values
of |r|>0.45 p < 0.001, for |r|>0.35 p < 0.01, and for |r|>0.25 p < 0.05.
4. Results
The correlation between monthly precipitation and sunspots of the period 19012015 shows
significant regional and seasonal variability (Tables 1 and S2). Pearson coefficients vary from 0.61
(Liechtenstein, February) to −0.53 (Estonia, February), representing correlations ranging from
moderate positive to moderate negative. The best positive correlations occur during February when
7 out of the 39 countries achieve coefficients of 0.50 or better (Tables 1 and 2). February also shows
the best negative correlations, although with slightly weaker strength than the positive correlations
(Tables 2 and S2). Significant parts of Europe yield moderate to low positive correlations during the
months of April, June, July and December (Tables 1 and 2). The month of May differs because the
best coefficients are negative correlations, with 9 countries showing r values of −0.35 and better
(Tables 2 and S2). The remaining six months (January, March, August, September, October,
November) show weaker coefficients, suggesting somewhat reduced solar influence on precipitation
during these times. The results of all months were mapped out in order to see if regional patterns
can be identified. The months with the best results are illustrated here in the main paper (Figs. 3, 4,
6–8), and the remaining months are contained in the Supplement (Figs. S3S9).
4.1. January
January precipitation variability is only weakly correlated with solar activity. Regions with low
correlation strengths are scattered across Europe, namely eastern Scandinavia, the southern North
Sea countries, Spain, Switzerland and parts of the Balkans (Fig. S3).
4.2. February
Of all months, February yields the best correlations between precipitation and solar activity.
Germany, Luxemburg, Belgium, Liechtenstein, Switzerland, Estonia and Sweden all show coefficients
of 0.510.61 suggesting moderate correlation. Visual inspection of the temporal development (Fig. 1,
S1, S2) suggests that the 11 year Schwabe solar cycle is well represented in the variability of
precipitation. This is particular the case during the period from the mid 1920s to the mid 2000s for
which the Pearson correlation values would be even higher.
A wavelet analysis of Germany's February precipitation confirms the presence of a 1 1 ye ar cy cl e
period from the mid 1920s to the mid 2000s (Fig. 2). The cycle appears to be weaker in the 1-2
decades before and after this period.
The February correlation sweetspot forms part of a southwest- northeast trending belt stretching
from Switzerland to Sweden, characterized by moderate correlation strength (Fig. 3). Slightly weaker
but still significant correlations occur in SW and NW Europe as well as in parts of the Balkans.
February precipitation in a northeast-trending corridor from the Adriatic Sea to Belarus appears to
lack solar influence as Pearson coefficients are statistically insignificant (Fig. 3). Notably, the lag of
the optimum correlations changes across Europe. Optimum lag values are +20 months in central
Western Europe, −105 months in Sweden and Estonia, and −65 months on the Balkans (Fig. 3),
illustrating systematic phase shifts across the continent.
4.3. March
March precipitation shows a significant solar response in a belt reaching from Austria to Scandinavia
where a low to moderate correlation strength with r values of 0.360.43 is achieved (Fig. S4).
Southern Europe, France and the British Isles lack any indication for solar influence on rainfall. The
best coefficients are reached at solar lags of 100 to −110.
4.4. April
During the month of April, low to moderate correlations are developed in parts of Central Europe,
SW Europe and Greece (Fig. S5). Low correlations are identified in a N-S corridor stretching from Italy
to Scandinavia. About half of Europe lacks evidence for solar influence on April rain, which includes
for example the British Isles, France, Finland and central Eastern Europe.
4.5. May
The month of May differs from most other months because the best correlations are characterized
by negative coefficients. The best coefficients are reached in a belt from the Czech Republic to
Belarus with r values of up to −0.48 (Fig. 4). Significant correlations also exist in neighbouring
countries, although slightly weaker. The lag of the best correlations is +15 months, indicating a
general anticorrelation of May rain solar activity in this region, which is also confirmed by visual
inspection of the development of the Belarus times series (no lag version, Fig. 5).
4.6. June
The best June correlations occur in NW Europe with r values of 0.50 and better in Ireland and Iceland
(Fig. 6). Moderate to low Pearson coefficients are also recorded in a belt reaching from the UK
westwards into central Eastern Europe, with a typical solar lag of about −90 months, i.e. the sun
leading rainfall by 7.5 years for a positive correlation. Rainfall in southern Europe and eastern
Scandinavia appears to generally lack solar influence in June.
4.7. July
The zone of solar-influenced rainfall mapped for June gradually weakens during the course of
summer. In July, only the eastern European sector shows moderate to low coefficients while the
western sector loses its solar influence altogether (Fig. 7). 4.8. August to October During the months
of August to October, correlations of low and occasionally low to moderate strengths occur in
Scandinavia and the Baltic states as well as in SW Europe and France (Figs. S6S8). The majority of
Central and Eastern Europe lack any solar influence. Lags differ between the regions. 4.9. November
and December Compared to previous months, the regional correlation patterns fully change during
November. The best correlations are now achieved in the eastern Balkans and western Black Sea
regions with r values 0.35 (Fig. S9). In subsequent December, solar influence further strengthens
and regionally expands across many parts of Europe. Besides the Balkans, coefficients of moderate to
low strengths also occur in Iceland, Sweden, Germany, Benelux and Portugal (Fig. 8).
4.10. Historical precipitation series
Analysis of the gridded historical CRU dataset covers the past 115 years and shows that solar
influence on European rainfall affects certain regions during certain months during certain
multidecadal time periods. In the case of February and central Europe, it was shown that the solar
signature is only distinctly present from the mid 1920s to the mid 2000s. In order to verify if the solar
influence on precipitation also existed during the 19th century, long time series of individual stations
or station composites are needed, as European gridded data are not available. Observational
precipitation data are available e.g. for Edinburgh, Stockholm and Paris. The historical Edinburgh
rainfall series 17852002 reaches its best correlation during the month of February with a Pearson r
value of +0.35 and a lag of −103 months (Table S4). This matches quite well with the r value of +0.40
calculated for the UK rainfall series 19012015 (Table 1). Visual inspection of the historical Edinburgh
time series (Fig. S16) as well as the wavelet graphs (Fig. S19) shows that the series contains particular
periods in which the correlation breaks down such as in the early and mid 19th Century, apparently
partly associated with phase shifts. A better coupling between February rain in Edinburgh and solar
activity is observed during the second half of the 19th Century and most of the 20th Century.
Similar discontinuous relationships are seen in the historical precipitation series of Paris and
Stockholm (Figs. S17S19) which demonstrates the complexity of the long term development.
4.11. Time lags
In order to identify the best positive and negative correlation coefficients, the sunspot series is
progressively shifted against the precipitation series, the latter being kept stable. The cross
correlation window encompasses −120 to +24 months, i.e. the solar signal precedes the rainfall by up
to 120 months (negative solar lag, i.e. lead) or postdates the rainfall by up to 24 months. When
plotting the r values against the solar lag for individual monthly country precipitation series, the
result is an oscillating curve, with the extreme values represented by the most positive and most
negative correlation coefficients. The period of the oscillation corresponds to one 11 year Schwabe
solar cycle, whilst the minimum and maximum values are offset by about half a Schwabe cycle. Fig. 9
shows such a plot of r against sun lag for February rain in Germany. The best positive r values are
achieved at solar lag times of 110 to −95 and again at +10 to +20 months. The maxima are about
one solar Schwabe cycle apart from each other (11 years = 132 months). The most negative Pearson r
values plot in the range of −50 to −35 months, representing a lead time for the solar minimum of 50
to 35 months (=34 years) before an increase in rainfall occurs. In the case of February precipitation
of Germany, the best positive correlations (r +0.54, lag +17 months) are numerically better than the
best negative correlations (r −0.35, lag −37 months) (Tables 1, S1-S3). Notably, in other cases, the
reverse is true. February rain in the UK for example has a best positive correlation of r = +0.40 (lag
+16 months), whilst the most negative correlation of r = −0.47 (lag −53 months) indicates a better
correlation strength (Figs. 3 and S11; Tables 1, S1-S3). Another good example is February rain of
Estonia in which the best positive correlation (r = +0.52, lag −108 months) is very similar to the best
negative correlation (r = −0.53, lag −41) (Fig. S11, Tables 1, S1-S3). Notably, the best positive
correlation in Estonia is not achieved at low positive lags (like in Germany and the UK) but one solar
cycle back, with the solar peak leading rainfall by 9 years (Table S1). The solar minimum leads peak
February rainfall in Estonia by about three and a half years. The solar lag of the best correlations was
schematically mapped in Figs. 3, 4, 6-8, S3-S9. Specific regions consisting of clusters of several
countries typically share a similar lag. Systematic shifts in the lag occur across the European
continent. Taking the example of February rain, the region stretching from the British Isles across
Central Europe to the Baltic Sea area shares a similar lag (Fig. 3). The recorded lag values of 105 and
+ 20 months both correspond to the same relationship, i.e. they refer to successive maxima in the ‘r
against solar lag’ plot. The two maxima are offset by one solar Schwabe cycle, whereby the best
positive coefficients are mathematically reached in some cases in the high negative and sometimes in
the low positive peak, without any greater statistical difference. In contrast, the solar lag for the best
positive correlations on the Balkans is around −65 months (Fig. 3), therefore is phase-shifted against
the lag in northern Europe by 40 months (3 years) (Fig. S10). Negative r values of February
precipitation in Greece (r=−0.43, lag −1 month; Tables S2 and S3) document better correlation
strength than the positive coefficients (r = +0.30, lag −57 months; Tables 1 and S1). This implies a
classical inverse relationship between solar activity and February rain in Greece and some other parts
of the Balkans.
5. Discussion
The 11 year solar Schwabe “heartbeat” is clearly identifiable in the European precipitation series
during certain months, as already suggested by Vines (1985). Regions, strength and solar leads/lags
of optimum correlations change across Europe throughout the course of the year, pointing to a
complex relationship of solar effects on European precipitation. A better empirical and genetic
understanding of these relationships opens up the chance for valuable predictions of precipitation on
a regional and seasonal basis.
5.1. February
The best Pearson coefficients of precipitation and sunspots occur in central Western Europe, Sweden
and Estonia with r values of ≥0.50. The respective solar lags are +20 and −105 months, which are
separated by about one solar Schwabe cycle (~132 months), therefore corresponding to the same
solar phase. It is clear that positive solar lags do not make any logical sense, because rainfall cannot
influence solar activity. Therefore, the only real possibility for a positive link between solar activity
and precipitation would be a lag of −105 months. This would mean that a solar maximum would
trigger a precipitation maximum nearly 9 years later. It is unclear how such a long delay could be
explained and transported in the climate system, even though it is not entirely impossible. We
therefore favour the possibility that actually the solar minimum triggers the precipitation maximum
in this region during February. The solar lags for the most negative r values is −50 to 35 months,
meaning that the inverse rainfall effect would take place about 4-3 years after the solar trigger.
This would also explain why most studies from Western and Central Europe on various time scales
have found generally higher rainfall and flood activity associated with low (rather than high) solar
(e.g. Czymzik et al., 2016a; Mauquoy et al., 2004; Negendank et al., 1997; Swindles et al., 2012; Vos
et al., 1997). Other authors have already noted such lead/lag relationships in which the solar trigger
led hydroclimate by a few years (e.g. Czymzik et al., 2016b; Franke and Bechteler, 1969; Mares et al.,
2016; Schwander et al., 2017). This may be particularly noteworthy for multidecdal flood maxima
which may be best explained by the more abundant blocking events during phases of low solar
activity (Czymzik et al., 2016a; Rimbu et al., 2017; Schwander et al., 2017). A similar time lag was
described for the quasi-decadal NAO variability which is synchronized by the solar Schwabe cycle
(Thieblemont et al., 2015). NAO+ (NAO-) typically lags the solar maximum (minimum) by a few years,
possibly due to accumulation and memory effects in the Atlantic (Andrews et al., 2015; Gray et al.,
2013, 2016; Ma et al., 2018; Roy et al., 2016; Scaife et al., 2013; Sfică et al., 2015; Sjolte et al., 2018;
Thieblemont et al., 2015; Zhou et al., 2014). Processes in the atmosphere are too fast-paced and
cannot provide significant time lags (Andrews et al., 2015). Regardless of the exact trigger
mechanisms, visual inspection of the unshifted times series of sunspots and February precipitation in
Germany and neighbouring countries suggests a generally positive relationship between the two
parameters (Figs. 1 and S1). This is because the zero time lag line in the r-against-lag diagram plots
closer to the Pearson r maximum than to the minimum (Fig. 9). Empirically, this means more
precipitation during times of higher solar activity, even though peak precipitation occurs 20 months
before the Schwabe maximum. The area of maximum solar influence on precipitation is located in
central and western Europe which is significantly affected by the westerlies that typically transport
rain to the region. During low solar activity winters, westerlies are reported to be weaker and occur
less often in central Europe (Ineson et al., 2011; Schwander et al., 2017), because intense and long
lasting winter blocking events become more frequent, disrupting the westerly winds (Barriopedro et
al., 2008; Lockwood et al., 2010). The solar effect may fade out towards Eastern Europe because cold
continental arctic conditions prevail here in winter (Fig. 3). During times of high solar activity, the
westerlies are stronger, more persistent and less interrupted by blockings, bringing increased
amounts of rain to central Europe. Long-term trends of solar activity and the North Atlantic
Oscillation (NAO) were mostly in-phase since 1940, implying that low and high solar activity were
typically associated with NAO- and NAO + conditions, respectively (Gray et al., 2013; Scaife et al.,
2013; Thieblemont et al., 2015). During NAO- conditions, the westerly storm belt typically shifts
southwards to southern Europe, leading to increased amounts of rain there, whilst resulting in
reduced precipitation in central Europe (Morley et al., 2014; Wirth et al., 2013b). Correspondingly,
the westerly storm belt hits central Europe during NAO + conditions, bringing increased amounts of
rain there. The phase relationship between solar and precipitation maxima is not entirely stable. In
the case of central Europe, the best correlations exist from the 1920s to the mid 2000s (Figs. 1 and
2). Phase shifts occur before and after this interval. This interval of best correlations corresponds
generally to the maximum of the solar Gleissberg cycle (70100 years) when multidecadal trends of
NAO and solar activity run in parallel and are positively correlated (van Loon et al., 2012) (Fig. S22).
During Gleissberg Minima, however, the two trends are opposite and are negatively correlated. The
reasons for these phase reversals in correlation are still unclear and may be due to equator to pole
temperature gradients (van Loon et al., 2012), or in the solar dynamo fields (Georgieva et al., 2012).
The variable relationship between solar forcing and NAO has also been discussed by Sjolte et al.
(2018). As the detailed processes involved in solar forcing of European hydroclimate are still poorly
understood, the influence of the solar magnetic and geomagnetic fields has to be included in the
lead/lag considerations. Notably, cosmic ray variations seen by neutron monitors lag sunspot number
variations by up to 14 months in odd numbered cycles, whilst only by 2 months in even numbered
cycles (Hathaway, 2015). The search for cause-effect is further complicated by the fact that some
hydrological processes, e.g. European extreme precipitation, are influenced by the preceding
wintertime NAO with time lags of one, two and three seasons (Tabari and Willems, 2018). This points
to multiyear chains of coupled lags, linking the solar signal with ocean cycles and subsequently with
the final hydroclimatic effect.
5.2. May
May rainfall responds very differently to the solar signal than in the preceding and subsequent
months (February–July). The best Pearson r values are negative and occur in northeastern Europe
(Czech Republic, Poland, Belarus) with a typical solar lag of +15 months (Fig. S13). High solar activity
commonly results in low precipitation, a relationship that is well illustrated in the unshifted and
shifted May time series of e.g. Belarus (Figs. 5 and S2). The exact meteorological reasons for this
shortterm phase shift in May are unclear.
5.3. Summer months
June and July are typically the wettest months in Central Europe. As the summer develops, the area
of solar influence on precipitation gradually migrates from the British Isles southeastwards via
Germany into SE Central Europe (Figs. 6 and 7). High solar activity appears to push rain-bearing
westerlies gradually deeper into Eastern Europe. By August, the solar-influenced rain belt reaches its
most easterly position and is restricted to Belarus (r=0.35) and Moldova (r=0.32) (Table 1, Fig. S6).
Drought conditions in June/July 2018 in Germany support the observed relationship. Rainfall reached
only 5060% of the long term normal, coinciding with a solar activity minimum regime of solar cycle
24. Likewise, June 2018 in England and Wales ranked within the top five driest Junes on record with
figures dating back to 1910.
5.4. December
Increased solar activity appears to mildly stimulate precipitation in a southwest-northeast trending
corridor reaching from Iberia to Belarus (Fig. 8). This effect could be related to rain-bearing
southwesterly winds from the Atlantic, which may be stronger when the sun is more active. Notably
for Iberia, the December effect at first sight appears to deviate from the general link of reduced solar
activity, negative NAO and increased precipitation which dominates for most of the rest of the cold
season in Iberia (Hurrell et al., 2003; Vicente-Serrano et al., 2011). Considering that the NAO lags the
solar Schwabe signal by up to half a solar cycle, the relationship may in fact be true here as well. The
solar influence on the Balkan in December is still poorly understood and may be unrelated to the
5.5. Mid-term forecasting potential
The near-cyclical nature of the 11 year s solar Schwabe cycle and the empirically identified lead/lag
relationships with precipitation open up opportunities for improved mid-term prognoses that could
be valuable for agricultural purposes, flood risk preparedness and other fields of human activity. An
example is the anomalously low precipitation recorded in Germany during February 2018 (17.8 mm),
representing only 36% of the long term average (DWD, 2018). The anomaly occurred exactly four
years after an early 2014 activity spike in solar activity, associated with the maximum of the 24th
solar cycle (Fig. S14). A closer look at the development 20002018 points to a possible pattern. For
example, a similar solar activity spike during 2011 was followed by another very dry February in
Germany (2015), again a delay of 4 years (Fig. S14). In contrast, the very wet year 2016 was preceded
by relatively lower solar activity in 2012. The observations fit with the hypothesis of a negative
correlation between solar activity and February rain in Central Europe, whereby the precipitation
effect is delayed by up to 50 months (solar lag=−50). It may also be worth experimenting with rolling
averages of solar activity rather than specific monthly values, in order to adjust for significant solar
variability in certain years. Whilst February yields the best correlation coefficients in Europe,
precipitation of other months also shows a clear link to solar variability, even though of weaker
coupling. In Central Europe and parts of Scandinavia, the months of March, April, June and July show
a correlation and phase pattern that has similarities with February. As these months comprise a
significant part of the agricultural growing season, which in Germany lasts from March to October,
any forecasting potential has economic significance. In Iberia, the months of February, April, August
and December show noteworthy correlations that could be used to develop mid-term forecasts. On
the Balkans, the months of February, April, November and December look most promising. The
negative r coefficient of r=−0.43 for Greece with a negligible lag (Tables S2 and S3) suggests an
inverse relationship between February rain and solar activity in that country. If the empirically
identified relationship stays stable, February precipitation in Greece is expected to be reduced during
20192023 because of the expected development of the solar minimum associated with the
transition between solar cycles 24 and 25. In this contribution we focus on the link between solar
activity and precipitation. Nevertheless, other important mechanisms play a major role in controlling
variability of European hydroclimate. Future research will have to fully integrate the solar results
with the known influence of the NAO and the Atlantic Multidecadal Oscillation (AMO). Despite the
temporal and spatial complexity, some systematic patterns begin to emerge that may help to
eventually understand the meteorological mechanisms behind these hydroclimatic changes. Non-
linear responses and phase shifts complicate the picture. Considering that large amounts of
observational data are now available, it may be worth considering artificial intelligence and machine
learning techniques (e.g. Jones, 2017) to get a full view of the dependencies and possible processes
included in the variability of European precipitation.
6. Conclusions
European hydroclimate shows a high degree of variability on every time scale. The variability is
controlled by natural processes such as Atlantic ocean cycles, changes in solar activity, volcanic
activity and anthropogenic factors. This contribution concentrates on the solar influence on
European precipitation, which has been documented by a large body of published case studies. We
are concentrating on the period 19012015 for which we compare monthly precipitation series of 39
European countries with sunspot data by calculating Pearson correlation coefficients for a multi-year
cross-correlation window. The results have been mapped out across the continent in order to
identify areas in which solar activity may have influenced precipitation. February precipitation in
Central and Western Europe shows the strongest solar response with coefficients reaching up to
+0.61. Rainfall in JuneJuly is also co-driven by solar activity changes, whereby the solar-influenced
zone of rainfall gradually migrates from the British Isles southeastwards via Germany into SE Central
Europe. On a decadal scale, the correlation between precipitation and solar activity in central Europe
during these months appears to be positive, both statistically and by visual curve comparison. Yet,
best positive correlations coefficients of February, June, July and December are typically reached
when the solar signal lags rainfall by 1.52 years. Honouring cause and effect, it is suspected that
increases in rainfall are actually triggered by the solar minimum some 34 years before the rainfall
month. Lags of a few years also occur between solar activity and the solar-synchronized-NAO,
possibly due to memory effects in the Atlantic. A lag in rainfall relative to the solar signal may open
up new possibilities for forecasts, likely with enormous economic significance. The literature review
demonstrates that most multidecadal studies from Central Europe encountered a negative
correlation between solar activity and rainfall, probably because short time lags of a few years are
negligible on timescales beyond the 11 year solar Schwabe cycle. Flood frequency typically increases
during times of low solar activity associated with negative NAO conditions and more frequent
blocking. The Alps form the southern limit of the Central European solar-driven rainfall region
because solar/rain relationships in the southern Alps appear to flip (Pena et al., 2015; Rabadan and
Schulte, 2014). Future research on the solar influence on European rainfall may also have to consider
possible effects of the 22 year solar Hale cycle, which represents a full magnetic cycle after two
Schwabe magnetic polarity reversals (Dobrica et al., 2017; Zanchettin et al., 2008).
We thank Josef Kowatsch, Steven Michelbach and Frank Bosse for valuable discussions. We are
grateful to Denis Fourgassie (Meteo-France), Mark Beswick (Met Office National Meteorological
Archive) and Hans Bengtsson (Swedish Meteorological and Hydrological Institute, SMHI) for providing
long historical rainfall series for Paris, Edinburgh and Stockholm. The vectorised Europe base map in
this paper was sourced from, a useful service for which we are thankful. We are
extremely grateful to the anonymous reviewers whose valuable comments stimulated us to expand
our study and include some important additional aspects.
Appendix A. Supplementary data
Supplementary data to this article can be found online at
Andrews, M.B., Knight, J.R., Gray, L.J., 2015. A simulated lagged response of the North Atlantic Oscillation to the solar cycle
over the period 19602009. Environ. Res. Lett. 10 (5), 054022.
Barrera-Escoda, A., Llasat, M.C., 2015. Evolving flood patterns in a Mediterranean region (1301–2012) and climatic factors
the case of Catalonia. Hydrol. Earth Syst. Sci. 19 (1), 465–483.
Barriopedro, D., Garcia-Herrera, R., Huth, R., 2008. Solar modulation of Northern Hemisphere winter blocking. J. Geophys.
Res.: Atmosphere 113, D14.
Blaauw, M., van Geel, B., van der Plicht, J., 2004. Solar forcing of climatic change during the mid-Holocene: indications from
raised bogs in The Netherlands. Holocene 14 (1), 35–44.
Blackford, J.J., Chambers, F.M., 1995. Proxy climate record for the last 1000 years from Irish blanket peat and a possible link
to solar variability. Earth Planet. Sci. Lett. 133 (1), 145–150.
Bond, G., Kromer, B., Beer, J., Muscheler, R., Evans, M.N., Showers, W., Hoffmann, S., Lotti-Bond, R., Hajdas, I., Bonani, G.,
2001. Persistent solar influence on North Atlantic climate during the Holocene. Science 294, 2130–2136.
Bothe, O., Wagner, S., Zorita, E., 2018. Inconsistencies between observed, reconstructed, and simulated precipitation over
the British Isles during the last 350 years. Clim. Past Discuss 128 2018.
Brunetti, M., Maugeri, M., Nanni, T., 2000. Variations of temperature and precipitation in Italy from 1866 to 1995. Theor.
Appl. Climatol. 65 (3), 165–174.
Camuffo, D., Enzi, S., 1995. Climatic features during the Sporer and Maunda minima. In: Frenzel, B. (Ed.), Solar Output and
Climate during the Holocene, Paleoclimate Research, Special Issue 16. Fischer Verlag, Stuttgart, pp. 105–125.
Chen, L., Zonneveld, K.A.F., Versteegh, G.J.M., 2011. Short term climate variability during “Roman classical period” in the
eastern mediterranean. Quat. Sci. Rev. 30 (27–28), 3880–3891.
Cini Castagnoli, G., Bonino, G., Taricco, C., Bernasconi, S.M., 2002. Solar radiation variability in the last 1400 years recorded
in the carbon isotope ratio of a mediterranean sea core. Adv. Space Res. 29 (12), 1989–1994.
Clette, F., Svalgaard, L., Vaquero, J.M., Cliver, E.W., 2015. Revisiting the sunspot number. In: Balogh, A., Hudson, H.,
Petrovay, K., von Steiger, R. (Eds.), The Solar Activity Cycle: Physical Causes and Consequences. Springer, New York, NY, pp.
35–103 New York.
Corella, J.P., Benito, G., Rodriguez-Lloveras, X., Brauer, A., Valero-Garces, B.L., 2014. Annually-resolved lake record of
extreme hydro-meteorological events since AD 1347 in NE Iberian Peninsula. Quat. Sci. Rev. 93, 77–90.
Czymzik, M., Brauer, A., Dulski, P., Plessen, B., Naumann, R., von Grafenstein, U., Scheffler, R., 2013. Orbital and solar
forcing of shifts in Mid- to Late Holocene flood intensity from varved sediments of pre-alpine Lake Ammersee (southern
Germany). Quat. Sci. Rev. 61, 96–110.
Czymzik, M., Dreibrodt, S., Feeser, I., Adolphi, F., Brauer, A., 2016a. Mid-Holocene humid periods reconstructed from calcite
varves of the Lake Woserin sediment record (north-eastern Germany). Holocene 26 (6), 935–946.
Czymzik, M., Dulski, P., Plessen, B., von Grafenstein, U., Naumann, R., Brauer, A., 2010. A 450 year record of spring-summer
flood layers in annually laminated sediments from Lake Ammersee (southern Germany). Water Resour. Res. 46 (11).
Czymzik, M., Muscheler, R., Brauer, A., 2016b. Solar modulation of flood frequency in central Europe during spring and
summer on interannual to multi-centennial timescales. Clim. Past 12 (3), 799–805.
DeAngelis, A.M., Qu, X., Zelinka, M.D., Hall, A., 2015. An observational radiative constraint on hydrologic cycle
intensification. Nature 528, 249.
Dobrica, V., Demetrescu, C., Mares, I., Mares, C., 2017. Long-term Evolution of the Lower Danube Discharge and
Corresponding Climate Variations: Solar Signature Imprint: Theoretical and Applied Climatology.
Ducic, V., Lukovic, J., Nikolova, N., 2007. Possible connection between Danube river discharge variability and solar activity.
Bull. Serbian Geograph. Soc. 1, 31–38.
DWD, 2018. The weather in Germany in February 2018.
Franke, P.G., Bechteler, W., 1969. Relation between Sunspots and Discharge: the Use of Analog and Digital Computers in
Hydrology: Proceedings of the Tucson Symposium. pp. 527–530.
Georgieva, K., Kirov, B., Koucka Knižova, P., Mošna, Z., Kouba, D., Asenovska, Y., 2012. Solar influences on atmospheric
circulation. J. Atmos. Sol. Terr. Phys. 9091, 15–25.
Glaser, R., Riemann, D., Schonbein, J., Barriendos, M., Brazdil, R., Bertolin, C., Camuffo, D., Deutsch, M., Dobrovolny, P., van
Engelen, A., Enzi, S., Haličkova, M., Koenig, S.J., Kotyza, O., Limanowka, D., Mackova, J., Sghedoni, M., Martin, B.,
Himmelsbach, I., 2010. The variability of European floods since AD 1500. Climatic Change 101 (1), 235–256.
Gray, L.J., Scaife, A.A., Mitchell, D.M., Osprey, S., Ineson, S., Hardiman, S., Butchart, N., Knight, J., Sutton, R., Kodera, K.,
2013. A lagged response to the 11 year solar cycle in observed winter Atlantic/European weather patterns. 13. J. Geophys.
Res.: Atmosphere 118 (24), 405413 420.
Gray, L.J., Woollings, T.J., Andrews, M., Knight, J., 2016. Eleven-year solar cycle signal in the NAO and Atlantic/European
blocking. Q. J. R. Meteorol. Soc. 142 (698), 1890–1903.
Grinsted, A., Moore, J.C., Jevrejeva, S., 2004. Application of the cross wavelet transform and wavelet coherence to
geophysical time series. Nonlinear Process Geophys. 11 (5/6), 561–566.
Hajian, S., Movahed, M.S., 2010. Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow
fluctuations. Phys. Stat. Mech. Appl. 389 (21), 4942–4957.
Hathaway, D.H., 2015. The solar cycle. Living Rev. Sol. Phys. 12 (1), 4.
Hoerling, M., Eischeid, J., Perlwitz, J., 2009. Regional precipitation trends: distinguishing natural variability from
anthropogenic forcing. J. Clim. 23 (8), 2131–2145.
Hurrell, J.W., Kushnir, Y., Ottersen, G., Visbek, M., 2003. An overview of the north Atlantic oscillation. In: In: Hurrell, J.W.,
Kushnir, Y., Ottersen, G., Visbeck, M. (Eds.), The North Atlantic Oscillation: Climatic Significance and Environmental Impact,
vol 134. American Geophysical Union, Geophysical Monograph Series, pp. 1–35.
Hurrell, J.W., van Loon, H., 1997. Decadal variations in climate associated with the north Atlantic oscillation. Climatic
Change 36 (3), 301–326.
Ineson, S., Scaife, A.A., Knight, J.R., Manners, J.C., Dunstone, N.J., Gray, L.J., Haigh, J.D., 2011. Solar forcing of winter climate
variability in the Northern Hemisphere. Nat. Geosci. 4, 753–757.
Jones, N., 2017. How machine learning could help to improve climate forecasts. Nature 548, 379–380.
Kantelhardt, J.W., 2004. Fluktuationen in Komplexen Systemen. Habilitation Thesis. Justus-Liebig-University Giesen, pp. 217.
Kantelhardt, J.W., Koscielny-Bunde, E., Rego, H.H.A., Havlin, S., Bunde, A., 2001. Detecting long-range correlations with
detrended fluctuation analysis. Phys. Stat. Mech. Appl. 295 (3), 441–454.
Kilian, M.R., Van der Plicht, J., Van Geel, B., 1995. Dating raised bogs: new aspects of AMS 14C wiggle matching, a reservoir
effect and climatic change. Quat. Sci. Rev. 14 (10), 959–966.
Kokfelt, U., Muscheler, R., 2013. Solar forcing of climate during the last millennium recorded in lake sediments from
northern Sweden. Holocene 23 (3).
Labuhn, I., Hammarlund, D., Chapron, E., Czymzik, M., Dumoulin, J.-P., Nilsson, A., Regnier, E., Robygd, J., von Grafenstein,
U., 2018. Holocene hydroclimate variability in central Scandinavia inferred from flood layers in contourite drift deposits in
lake Storsjon. Quaternary 1 (1), 2.
Lamy, F., Arz, H.W., Bond, G.C., Bahr, A., Patzold, J., 2006. Multicentennial-scale hydrological changes in the Black Sea and
northern red sea during the Holocene and the arctic/North Atlantic oscillation. Paleoceanography 21 (1) n/a-n/a.
Landscheidt, T., 2000. River Po discharges and cycles of solar activity. Hydrol. Sci. J. 45 (3), 491–493.
Le Mouel, J.-L., Blanter, E., Shnirman, M., Courtillot, V., 2009. Evidence for solar forcing in variability of temperatures and
pressures in Europe. J. Atmos. Sol. Terr. Phys. 71 (12), 1309–1321.
Linderholm, H.W., Nicolle, M., Francus, P., Gajewski, K., Helama, S., Korhola, A., Solomina, O., Yu, Z., Zhang, P., D'Andrea,
W.J., Debret, M., Divine, D.V., Gunnarson, B.E., Loader, N.J., Massei, N., Seftigen, K., Thomas, E.K., Werner, J., Andersson, S.,
Berntsson, A., Luoto, T.P., Nevalainen, L., Saarni, S., Valiranta, M., 2018. Arctic hydroclimate variability during the last 2000
years: current understanding and research challenges. Clim. Past 14 (4), 473–514.
Lockwood, M., Harrison, R.G., Woollings, T., Solanki, S.K., 2010. Are cold winters in Europe associated with low solar
activity? Environ. Res. Lett. 5, 1–7.
Luo, J., Ying, K., He, P., Bai, J., 2005. Properties of Savitzkygolay digital differentiators. Digit. Signal Process. 15 (2), 122–
Ma, H., Chen, H., Gray, L., Zhou, L., Li, X., Wang, R., Zhu, S., 2018. Changing response of the North Atlantic/European winter
climate to the 11 year solar cycle. Environ. Res. Lett. 13 (3), 034007.
Macklin, M.G., Johnstone, E., Lewin, J., 2005. Pervasive and long-term forcing of Holocene river instability and flooding in
Great Britain by centennial-scale climate change. Holocene 15 (7), 937–943.
Magny, M., 1993. Solar influences on Holocene climatic changes illustrated by correlations between past lake-level
fluctuations and the atmospheric 14C record. Quat. Res. 40, 1–9.
Magny, M., 2004. Holocene climate variability as reflected by mid-European lake-level fluctuations andits probable impact
on prehistoric human settlements. Quat. Int. 113, 65–79.
Maraun, D., 2013. When will trends in European mean and heavy daily precipitation emerge? Environ. Res. Lett. 8 (1),
Mares, I., Dobrica, V., Demetrescu, C., Mares, C., 2016. Hydrological response in the Danube lower basin to some internal
and external climate forcing factors: Hydrol. Earth Syst. Sci. Data 124 2016.
Markonis, Y., Hanel, M., Maca, P., Kysely, J., Cook, E.R., 2018. Persistent multi-scale fluctuations shift European
hydroclimate to its millennial boundaries. Nat. Commun. 9 (1), 1767.
Martin-Puertas, C., Matthes, K., Brauer, A., Muscheler, R., Hansen, F., Petrick, C., Aldahan, A., Possnert, G., Geel, B. v., 2012.
Regional atmospheric circulation shifts induced by a grand solar minimum. Nat. Geosci.
Mauquoy, D., Engelkes, T., Groot, M.H.M., Markesteijn, F., Oudejans, M.G., van der Plicht, J., van Geel, B., 2002. High-
resolution records of late-Holocene climate change and carbon accumulation in two north-west European ombrotrophic
peat bogs. Palaeogeogr. Palaeoclimatol. Palaeoecol. 186 (3), 275–310.
Mauquoy, D., van Geel, B., Blaauw, M., Speranza, A., van der Plicht, J., 2004. Changes in solar activity and Holocene climatic
shifts derived from 14C wiggle-match dated peat deposits. Holocene 14 (1), 45–52.
Mauquoy, D., Yeloff, D., Van Geel, B., Charman, D.J., Blundell, A., 2008. Two decadally resolved records from north-west
European peat bogs show rapid climate changes associated with solar variability during the midlate Holocene. J. Quat. Sci.
23 (8), 745–763.
Mazhdrakov, M., Benov, D., Valkanov, N., 2018. The Monte Carlo Method: Engineering Applications. ACMO Academic Press,
Sofia, pp. 235.
Mellstrom, A., van der Putten, N., Muscheler, R., de Jong, R., Bjorck, S., 2015. A shift towards wetter and windier conditions
in southern Sweden around the prominent solar minimum 2750 cal a BP. J. Quat. Sci. 30 (3), 235–244.
Moreno, A., Valero-Garces, B.L., Gonzalez-Samperiz, P., Rico, M., 2008. Flood response to rainfall variability during the last
2000 years inferred from the Taravilla Lake record (Central Iberian Range, Spain). J. Paleolimnol. 40 (3), 943–961.
Morley, A., Rosenthal, Y., deMenocal, P., 2014. Ocean-atmosphere climate shift during the mid-to-late Holocene transition.
Earth Planet. Sci. Lett. 388, 18–26.
Negendank, J.F.W., Zolitschka, B., Rein, B., Brauer, A., Bruchmann, C., Sanchez, A., Vos, H., 1997. Varve chronology and solar
variability in lake Holzmaar (eifel, Germany), Bulletin de la Societe belge de Geologie 106, 5361.
Nurtaev, B., 2015. Influence of climate variability on large rivers runoff. Proc. IAHS 371, 211–214.
Peña, J.C., Schulte, L., Badoux, A., Barriendos, M., Barrera-Escoda, A., 2015. Influence of solar forcing, climate variability and
modes of low-frequency atmospheric variability on summer floods in Switzerland: Hydrol. Earth Syst. Sci. 19 (9), 3807–3827.
Rabadan, J.C.P., Schulte, L., 2014. Effects of solar activity and climate variability on large floods in Switzerland. Boletin de la
Asociacion de Geografos Espanoles 65, 469–475.
Rao, M.P., Cook, B.I., Cook, E.R., D'Arrigo, R.D., Krusic, P.J., Anchukaitis, K.J., LeGrande, A.N., Buckley, B.M., Davi, N.K.,
Leland, C., Griffin, K.L., 2017. European and Mediterranean hydroclimate responses to tropical volcanic forcing over the last
millennium. Geophys. Res. Lett. 44 (10), 5104–5112.
Riley, K.F., Hobson, M.P., Bence, S.J., 2006. Mathematical Methods for Physics and Engineering: A Comprehensive Guide.
Cambridge University Press, Cambridge.
Rimbu, N., Ionita, M., Czymzik, M., Brauer, A., Lohmann, G., 2017. Patterns of extreme weather associated with observed
and proxy River Ammer flood records. Clim. Past Discuss 127 2017.
Roy, I., Asikainen, T., Maliniemi, V., Mursula, K., 2016. Comparing the influence of sunspot activity and geomagnetic activity
on winter surface climate. J. Atmos. Sol. Terr. Phys. 149, 167–179.
Savitzky, A., Golay, M.J.E., 1964. Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem.
36 (8), 1627–1639.
Scaife, A.A., Ineson, S., Knight, J.R., Gray, L., Kodera, K., Smith, D.M., 2013. A mechanism for lagged North Atlantic climate
response to solar variability. Geophys. Res. Lett. 40 (2), 434–439.
Schulte, L., Pena, J.C., Carvalho, F., Schmidt, T., Julia, R., Llorca, J., Veit, H., 2015. A 2600-year history of floods in the
Bernese Alps, Switzerland: frequencies, mechanisms and climate forcing: Hydrol. Earth Syst. Sci. 19 (7), 3047–3072.
Schulte, L., Veit, H., Burjachs, F., Julia, R., 2009. Lutschine fan delta response to climate variability and land use in the
Bernese Alps during the last 2400 years. Geomorphology 108 (1), 107–121.
Schwander, M., Rohrer, M., Bronnimann, S., Malik, A., 2017. Influence of solar variability on the occurrence of central
European weather types from 1763 to 2009. Clim. Past 13 (9), 1199–1212.
Sfică, L., Voiculescu, M., Huth, R., 2015. The influence of solar activity on action centres of atmospheric circulation in North
Atlantic. Ann. Geophys. 33 (2), 207–215.
Sjolte, J., Sturm, C., Adolphi, F., Vinther, B.M., Werner, M., Lohmann, G., Muscheler, R., 2018. Solar and volcanic forcing of
North Atlantic climate inferred from a processbased reconstruction. Clim. Past Discuss 122 2018.
Smith, A.C., Wynn, P.M., Barker, P.A., Leng, M.J., Noble, S.R., Tych, W., 2016. North Atlantic forcing of moisture delivery to
Europe throughout the Holocene. Sci. Rep. 6, 24745.
Speranza, A., van Geel, B., van der Plicht, J., 2003. Evidence for solar forcing of climate change at ca. 850 cal BC from a
Czech peat sequence. Glob. Planet. Chang. 35 (1), 51–65.
Stolze, S., Muscheler, R., Dorfler, W., Nelle, O., 2013. Solar influence on climate variability and human development during
the Neolithic: evidence from a high-resolution multi-proxy record from Templevanny Lough, County Sligo, Ireland. Quat. Sci.
Rev. 67, 138–159.
Sun, Q., Miao, C., Duan, Q., Ashouri, H., Sorooshian, S., Hsu, K.-L., 2018. A review of global precipitation data sets: data
sources, estimation, and intercomparisons. Rev. Geophys. 56 (1), 79–107.
Swindles, G.T., Blundell, A., Roe, H.M., Hall, V.A., 2010. A 4500-year proxy climate record from peatlands in the North of
Ireland: the identification of widespread summer ‘drought phases’? Quat. Sci. Rev. 29 (13), 1577–1589.
Swindles, G.T., Patterson, R.T., Roe, H.M., Galloway, J.M., 2012. Evaluating periodicities in peat-based climate proxy
records. Quat. Sci. Rev. 41 (0), 94–103.
Swindles, G.T., Plunkett, G., Roe, H.M., 2007a. A delayed climatic response to solar forcing at 2800 cal. BP: multiproxy
evidence from three Irish peatlands. Holocene 17 (2), 177–182.
Swindles, G.T., Plunkett, G., Roe, H.M., 2007b. A multiproxy climate record from a raised bog in County Fermanagh,
Northern Ireland: a critical examination of the link between bog surface wetness and solar variability. J. Quat. Sci. 22 (7),
Tabari, H., Willems, P., 2018. Lagged influence of Atlantic and Pacific climate patterns on European extreme precipitation.
Sci. Rep. 8 (1), 5748.
Thieblemont, R., Matthes, K., Omrani, N.-E., Kodera, K., Hansen, F., 2015. Solar forcing synchronizes decadal North Atlantic
climate variability. Nat. Commun. 6, 8268.
Tomasino, M., Valle, F.D., 2000. Natural climatic changes and solar cycles: an analysis of hydrological time series. Hydrol.
Sci. J. 45 (3), 477–489.
Tomasino, M., Zanchettin, D., Traverso, P., 2004. Long-range forecasts of River Po discharges based on predictable solar
activity and a fuzzy neural network model/Previsions a long terme des debits du Fleuve Po basees sur l’activite solaire
previsible et sur un modele de reseau de neurones flou. Hydrol. Sci. J. 49 (4), null–684.
Trigo, R.M., Pozo-Vazquez, D., Osborn, T.J., Castro-Diez, Y., Gamiz-Fortis, S., Esteban-Parra, M.J., 2004. North Atlantic
oscillation influence on precipitation, river flow and water resources in the Iberian Peninsula. Int. J. Climatol. 24 (8), 925–
Turcotte, D.L., 1997. Fractals and Chaos in Geology and Geophysics. Cambridge University Press, Cambridge.
Van Geel, B., Heijnis, H., Charman, D.J., Thompson, G., Engels, S., 2014. Bog burst in the eastern Netherlands triggered by
the 2.8 kyr BP climate event. Holocene 24 (11), 1465–1477.
van Geel, B., Mauquoy, D., 2010. Peatland Records of Solar Activity: PAGES News, vol. 18. pp. 1112.
Van Geel, B., Van Der Plicht, J., Kilian, M.R., Klaver, E.R., Kouwenberg, J.H.M., Renssen, H., Reynaud-Farrera, I., Waterbolk,
H.T., 1997. The sharp rise of Δ14C ca. 800 cal BC: possible causes, related climatic teleconnections and the impact on
human environments. Radiocarbon 40 (1), 535–550.
Van Loon, H., Brown, J., Milliff, R.F., 2012. Trends in sunspots and North Atlantic sea level pressure. J. Geophys. Res. 117
(D7), D07106.
Vanniere, B., Magny, M., Joannin, S., Simonneau, A., Wirth, S.B., Hamann, Y., Chapron, E., Gilli, A., Desmet, M., Anselmetti,
F.S., 2013. Orbital changes, variation in solar activity and increased anthropogenic activities: controls on the Holocene flood
frequency in the Lake Ledro area. Northern Italy: Clim. Past 9 (3), 1193–1209.
Vaquero, J.M., 2004. Solar signal in the number of floods recorded for the tagus river basin over the last millennium.
Climatic Change 66 (1), 23–26.
Vicente-Serrano, S.M., Trigo, R.M., Lopez-Moreno, J.I., Liberato, M.L.R., Lorenzo-Lacruz, J., Begueria, S., Moran-Tejeda, E., El
Kenawy, A., 2011. Extreme winter precipitation in the Iberian Peninsula in 2010: anomalies, driving mechanisms and future
projections. Clim. Res. 46 (1), 51–65.
Vines, R.G., 1985. European rainfall patterns. J. Climatol. 5 (6), 607–616.
Vos, H., Bruchmann, C., Lucke, A., Negendank, J.F.W., Schleser, G.H., Zolitschka, B., 2004. Phase stability of the solar
Schwabe cycle in lake Holzmaar, Germany, and GISP2, Greenland, between 10,000 and 9,000 cal. BP. In: Fischer, H., Kumke,
T., Lohmann, G., Floser, G., Miller, H., von Storch, H., Negendank, J.F.W. (Eds.), The Climate in Historical Times: towards a
Synthesis of Holocene Proxy Data and Climate Models. Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 293–317.
Vos, H., Sanchez, A., Zolitschka, B., Brauer, A., Negendank, J.F.W., 1997. Solar activity variations recorded in varved
sediments from the Crater Lake of Holzmaar - a Maar Lake in the Westeifel volcanic field, Germany. Surv. Geophys. 18 (2),
Wirth, S.B., Gilli, A., Simonneau, A., Ariztegui, D., Vanniere, B., Glur, L., Chapron, E.,Magny, M., Anselmetti, F.S., 2013a. A
2000 year long seasonal record of floods in the southern European Alps. Geophys. Res. Lett. 40 (15), 4025–4029.
Wirth, S.B., Glur, L., Gilli, A., Anselmetti, F.S., 2013b. Holocene flood frequency across the Central Alps solar forcing and
evidence for variations in North Atlantic atmospheric circulation. Quat. Sci. Rev. 80, 112–128.
Zanchettin, D., Rubino, A., Traverso, P., Tomasino, M., 2008. Impact of variations in solar activity on hydrological decadal
patterns in northern Italy. J. Geophys. Res. 113, D12102.
Zhou, L., Tinsley, B., Huang, J., 2014. Effects on winter circulation of short and long term solar wind changes. Adv. Space
Res. 54 (12), 2478–2490.
Zveryaev, I.I., Allan, R.P., 2010. Summertime precipitation variability over Europe and its links to atmospheric dynamics and
evaporation. J. Geophys. Res.: Atmosphere 115, D12.
... The largest contribution comes from solar activity, which has been documented by a large body of published case studies. For a long-term multi-year forecast, the authors of the article recommend an approach based on the research outlined in the article by Laurenz et al. [16]. The methodology is based on the fact that the amount of precipitation in a particular region correlates quite well with the 11-year solar cycle of Schwabe. ...
... Thus, the original T*M dimensional optimization task (11)-(13) splits into T/2 (for even T and (T − 1)/2 for odd) subtasks of type (14)- (16), which can be solved independently from each other, hence one can use the multitask and multiprocessor computer modes. Such a decomposition of the optimization task into T/2 independently solvable subtasks allows using the multitasking mode of the operating system (Windows) and the multiprocessor mode of supercomputer, which can significantly reduce the optimization time (practically by several tens of times). ...
... 1. We construct a predicted long-term hydrological series of inflows P f for the last 40-50 years of observed inflows with a duration of T f years, using the method described in Sections 2.1 and 3.1 or other methods [16]. ...
Full-text available
In the second half of the twentieth century, a cascade of reservoirs was constructed along the Angara: Irkutskoe, Bratskoe, Ust-Ilimskoe and Boguchanskoe, which were intended for producing renewable hydroelectric energy for providing transportation through the Angara and Yenisei Rivers, and for avoiding floods. The upper reservoir (Irkutsk Dam) is used to regulate the level of Baikal Lake. The cascade of Angarsk reservoirs is managed using the dispatch schedules developed in 1988. This article contains a multi-criteria analysis of the “Lake Baikal–Irkutsk Reservoir” operating modes in a changing climate, based on statistical summaries of performance criteria: reliability, resilience, vulnerability. Studies have shown that dispatch schedules need to be developed on the historical series of recent years, updated more often and optimization methods should be used for real-time management. This article discusses mathematical methods, algorithms and their implementations for the formation of reservoir operation modes based on dispatch schedules (DS) and optimization methods. Furthermore, mathematical methods, algorithms and programs have been developed for the formation of reservoir operation modes in real time, based on optimization approaches and long-term series of observed inflows, taking into account a given hierarchy of priorities of water users’ requirements. To solve the integer nonlinear large-dimensional task of performing water resource calculations, a special optimization algorithm was developed that allows decomposition of the task into a series of two-year dimensional independent subtasks.
... More recently, Leamon et al. (2021) have stressed the need of accounting for solar activity changes in short term climate variability. The influence of SS minimum counts has even reported to affect rain season in Central Europe (Laurenz et al., 2019) with a lag of 3-4 years. Yamakawa et al. (2016) have reported that solar impacts in terms of SS numbers not only affect the troposphere but also the sea surface, even though SS abundance is only a partial measure of solar activity (Scafetta, 2014). ...
Full-text available
The sea surface temperature (SST), anomalies (SSTA), Oceanic Niño Index (ONI), and Multivariate ENSO (MEI) index in El Niño 1 + 2 and El Niño 3.4 regions, Pacific Decadal Oscillation (PDO) and Atlantic Multidecadal Oscillation (AMO), as well as the meteorological parameter Southern Oscillation Index (SOI) were cross correlated to sunspot counts (SS) from cycles 19 to 24 (1954–2019). Over the 1954–2019 period, the SS or Schwabe cycles did not show strong cross-correlation coefficients (cc-ρ) with values falling between 0.063 and 0.100 (p < 0.05). It seems that the Total Solar Irradiation (TSI) constant variability (±0.1%, ±1.361 W m⁻²) due to the SS cycles balanced out throughout the whole period. The cc-ρ coefficients for SST and SSTA versus each individual SS cycles were between 0.100 and 0.200 with lag times between maxima of each being from a few to 48 months. The ONI showed a cc-ρ < 0.1, while MEI reached up to 0.2 through all SS cycles. The slope of the cc-ρ changed from negative to positive over 6–12 months periods, with peaks in slope change occurring somewhere between 2 and 3 years. The SOI cc-ρ varied by around 0.200 through cycles 19–21, but for SS 22–24 it was not noticeable. Interdecadal indexes PDO and AMO showed cc-ρ of up to 0.283; with a possible association of 8%, with a lag time of 1–3 years. During the ascending and descending phases of each SS cycle, the cc-ρ were 0.288 and − 0.233, respectively for SST in El Niño 3.4 region, but in El Niño 1 + 2 were negligible. The ONI and MEI showed cc-ρ up to 0.448 and 0.480 respectively with lag times of 1–15 months in ascending phase of the SS cycle. The SS vs SOI had cc- ρ up to +0.420 to −0.567 in the ascending phases, while PDO and AMO registered cc-ρ up to 0.417 and − 0.491. AMO appeared systematically associated with SS cycles from 10.0 to 30.2% during descending and ascending phases, respectively. Compiled SS counts for all the ascending and descending phases of the SS cycles, gave a clear spectral coherence (quasi sine-function distribution); for SST and SSTA, lag times of 9–48 months were observed with inverse and direct linear relationship, and peaks of −0.38 and 0.39, respectively. The ONI and MEI with SS counts have similar cc-ρ values: 0.245 and 0.387. Around 6–15% of the ONI and MEI can be explained by SS during ascending and < 4% in descending phases. It seems that over the relatively short time scales of SS cycles, either on their initial ascending or final descending phases, the studied indexes seem to be influenced. Even though it was difficult to elucidate the physics behind the observed cross-correlations, these results can be used to help improve understanding and aid the predictions of ENSO, PDO and AMO oceanographic events in the Pacific and Atlantic oceans.
... Compared to the six other drivers tested, the SSC exhibited long-standing, stationary relationships with all extreme temperature and precipitation records across all regions studied, and accounts for many of the quasi-decadal periodicities observed in spectral and CWT analyses. The strength of the interaction between the SSC and extreme weather across all three regions parallels that reported elsewhere in North America (Currie, 1993;Currie & O'Brien, 1988;Mendoza et al., 2001;Vines, 1977;Vines, 1984;Walsh & Patterson, 2022) and globally (Currie & Vines, 1996;Du et al., 2017;Laurenz et al., 2019;Lockwood, 2012;Maliniemi et al., 2014;Sfîcă et al., 2018;van Loon & Shea, 1999;van Loon et al., 2004;Vines, 1977Vines, , 1980, though much of the literature does not discuss this relationship in reference to extreme weather, but rather in regards to average climate records. ...
Full-text available
Instrumental weather records (1880–2020s) from eastern North America were analyzed to characterize the regional patterns and drivers of seasonal extreme weather (snow, rain, high and low temperatures). Using agglomerative hierarchical clustering of extreme weather data, the region was divided into three subregions that are influenced by coastal‐marine gradients and latitudinal factors. Subsequent analyses were performed on high‐quality stations from each subregion and results compared between one another. Long‐term locally weighted linear regressions delineated long‐term changes in extreme weather, and a combination of spectral analysis, continuous wavelet transforms, and cross wavelet transforms were used to identify periodic components in the data. Regional extreme weather is generally periodic, composed of interannual to interdecadal‐scale oscillations and driven by several natural climatic oscillations. The most important such oscillation is the 11‐year Schwabe Solar Cycle, which has a strong and continuous effect on regional extreme weather. The Pacific Decadal Oscillation and Quasi Biennial Oscillation also show considerable influence, but intermittently. The El Niño Southern Oscillation, the Arctic Oscillation, and the North Atlantic Oscillation all have a weaker but interrelated influence. While the Atlantic Multidecadal Oscillation showed the weakest overall influence on regional extreme weather, it demonstrated a clear spatial gradient across the region, unlike the aforementioned oscillations. Long‐term changes in regional extreme weather are not generally important, in that a sustained increase or decrease in extreme weather events is not usually characteristic of the weather records. The primary exception to this result is for extreme minimum temperature events, whose frequency has slightly decreased since the 1880s.
... [122] and [123] also attributed the occurrence of observed 10-11 years cycles in eastern North American precipitation and temperature records to the SSC. Several other relations between the SSC and extreme temperature and precipitation records have been made regionally around the world, including North America and western Europe [5,6,[124][125][126][127][128][129][130][131]. ...
Full-text available
Patterns in historical climate data were analyzed for Ottawa, Ontario, Canada, for the interval 1890–2019. Variables analyzed included records of annual, seasonal, and extreme temperature and precipitation, diurnal temperature range, and various environmental responses. Using LOWESS regressions, it was found that annual and seasonal temperatures in Ottawa have generally increased through this interval, precipitation has shifted to a less snowy, rainier regime, and diurnal temperature variation has decreased. Furthermore, the annual growing season has lengthened by 23 days to ~163 days, and the annual number of frost-free days increased by 13 days to ~215 days. Despite these substantial climatic shifts, some variables (e.g., extreme weather events per year) have remained largely stable through the interval. Time-series analyses (including multitaper spectral analysis and continuous and cross wavelet transforms) have revealed the presence of several strong cyclical patterns in the instrumental record attributable to known natural climate phenomena. The strongest such influence on Ottawa’s climate has been the 11-year solar cycle, while the influence of the El Niño-Southern Oscillation, Arctic Oscillation, North Atlantic Oscillation, and Quasi-Biennial Oscillation were also observed and linked with the trends in annual, seasonal, and extreme weather. The results of this study, particularly the observed linkages between temperature and precipitation variables and cyclic climate drivers, will be of considerable use to policymakers for the planning, development, and maintenance of city infrastructure as Ottawa continues to rapidly grow under a warmer, wetter climate regime.
... More recently, Leamon et al. (2021) have stressed the need of accounting for solar activity changes in short term climate variability. The influence of SS minimum counts has even reported to affect rain season in Central Europe (Laurenz et al., 2019) with a lag of 3-4 years. Yamakawa et al. (2016) have reported that solar impacts in terms of SS numbers not only affect the troposphere but also the sea surface, even though SS abundance is only a partial measure of solar activity (Scafetta, 2014). ...
... It is clear that this additional independent way for reconstructing the GSN can be beneficial for a comparison and contrast with all the various intensive efforts of reconstructing an accurate GSN record. This effort would add to the understanding of the underlying solar magnetism and, perhaps also, the study of the solar activity variation in connection to the Earth's climate (see, e.g., Hoyt and Schatten, 1997;Soon and Yaskell, 2003;Soon et al., 2014;Laurenz, Lüdecke, and Lüning, 2019;Courtillot, 2019, 2020;Connolly et al., 2021). ...
Full-text available
Historical sunspot records and the construction of a comprehensive database are among the most sought after research activities in solar physics. Here, we revisit the issues and remaining questions on the reconstruction of the so-called group sunspot numbers (GSN) that was pioneered by D. Hoyt and colleagues. We use the modern tools of artificial intelligence (AI) by applying various algorithms based on machine learning (ML) to GSN records. The goal is to offer a new vision in the reconstruction of sunspot activity variations, i.e. a Bayesian reconstruction, in order to obtain a complete probabilistic GSN record from 1610 to 2020. This new GSN reconstruction is consistent with the historical GSN records. In addition, we perform a comparison between our new probabilistic GSN record and the most recent GSN reconstructions produced by several solar researchers under various assumptions and constraints. Our AI algorithms are able to reveal various new underlying patterns and channels of variations that can fully account for the complete GSN time variability, including intervals with extremely low or weak sunspot activity like the Maunder Minimum from 1645 – 1715. Our results show that the GSN records are not strictly represented by the 11-year cycles alone, but that other important timescales for a fuller reconstruction of GSN activity history are the 5.5-year, 22-year, 30-year, 60-year, and 120-year oscillations. The comprehensive GSN reconstruction by AI/ML is able to shed new insights on the nature and characteristics of not only the underlying 11-year-like sunspot cycles but also on the 22-year Hale’s polarity cycles during the Maunder Minimum, among other results previously hidden so far. In the early 1850s, Wolf multiplied his original sunspot number reconstruction by a factor of 1.25 to arrive at the canonical Wolf sunspot numbers (WSN). Removing this multiplicative factor, we find that the GSN and WSN differ by only a few percent for the period 1700 to 1879. In a comparison to the international sunspot number (ISN) recently recommended by Clette et al. (Space Sci. Rev. 186, 35, 2014), several differences are found and discussed. More sunspot observations are still required. Our article points to observers that are not yet included in the GSN database.
In this work, we study the periodicities of annual rainfall over Kerala, India, and sunspot number over the time interval 1871–2016, and analyze their potential relationship. The periodicity analysis is done using Fourier and wavelet techniques. The results of the Fourier analysis and the wavelet analysis are in agreement. Wavelet power in the two time series shows common features at 8–16 years with varying significance, indicating a relationship between them. An analysis of the temporal relationship between sunspot number and rainfall using cross-wavelet transform revealed high cross-power around 8–16 years. A wavelet-coherence analysis is used to determine the correlation between them, and weak coherence has been found with varying degrees of significance over time.
In this work, we investigate the periodicities of rainfall over Kerala, India, and sunspot number (1871–2016) and their possible association. Fourier and wavelet transform were performed on the rainfall and sunspot number time series to determine dominant periods. Both the data were considered on an annual scale, as well as on a seasonal scale by grouping into winter, pre-monsoon, monsoon, and post-monsoon seasons. Fourier analysis showed short periods between 2-12 years for all the seasonal rainfall and a prominent 10.7-year period for sunspot number. Further, the wavelet spectrum of rainfall over Kerala showed the most significant periodicities around 2-10 years but with intermittent character and 8-12 years for sunspot number. The periodicity of sunspot number and rainfall estimated by Fourier analysis was in agreement with wavelet analysis. Wavelet analysis gave common spectral powers with varying significance for winter and monsoon seasons around 2-3 years. Common features in the wavelet power of the two time series were visible at 8-12 years with varying significance, suggesting a relationship between them. The cross-wavelet transform, employed to study the temporal relationship, indicated high cross-power around 8-12 years, during all the seasons. The relationship between sunspot number and rainfall over Kerala during varying levels of solar activity was examined using wavelet coherence. Results showed higher coherence during the high solar activity period than during low solar activity, mainly during winter, monsoon, and post-monsoon seasons. Coherence studies were also performed to check whether the influence of solar activity on rainfall completely diminished after the onset of global warming. Results showed persistence of solar influence in different seasons during the whole period of study.
Full-text available
The available ice out (the date of disappearance of ice from a water body) records were analyzed from four relatively closely spaced lakes in southwestern New Brunswick (Harvey, Oromocto, Skiff) and eastern Maine (West Grand Lake), with the longest set of available observations being for Oromocto Lake starting in 1876. Results of a coherence analysis carried out on the ice out data from the four lakes indicates that there is regional coherence and correspondingly, that regional drivers influence ice out. These results also indicate that ice out dates for lakes from the region where records have not been kept can also be interpolated from these results. As the ice out record was coherent, further analysis was done for only Oromocto Lake on the basis of it having the longest ice out record. Cross-wavelet analysis was carried out between the ice out record and a variety of cyclic climate teleconnections and the sunspot record to identify which phenomena best explain the observed ice out trends. The most important observed contributors to ice out were the North Atlantic Oscillation (NAO) and the El Niño Southern Oscillation (ENSO), with observed periodicities at the interannual scale. At the decadal scale the Pacific Decadal Oscillation (PDO) and the 11-year solar cycle were the only patterns observed to significantly contribute to ice out.
Rainfall erosivity is one of the key dynamic factors leading to water erosion, which causes widespread soil erosion worldwide. This study calculated the rainfall erosivity from 1965 to 2019, based on daily precipitation data, for 17 watersheds on the Loess Plateau. The data were also used to analyze the temporal and spatial variation of rainfall erosivity, and assess the impact of rainfall erosivity changes on sediment load in these typical watersheds. The possible causes of rainfall erosivity and sediment load changes are also discussed. The results of the study revealed that on different time scales, the spatial distribution of rainfall erosivity showed a pattern of decreasing from southeast to northwest in the Loess Plateau. Moreover, the rainfall erosivity measured by some weather stations increased significantly in May, June, and September (p < 0.05). Additionally, the changes brought on by ENSO and sunspots had a specific influence on the changes of rainfall erosivity in the Loess Plateau. Furthermore, the sediment load in the typical watersheds of the Loess Plateau showed a significant decreasing trend in yearly and monthly time scales (p < 0.05). Before 1980, the change in rainfall erosivity was an important reason for the change of sediment load and the construction of backbone check dams also intercepted a large amount of sediment. However, from 1980 to 1998, the interception effect of backbone check dams and the increase in vegetation together caused sediment load changes. After 1999, the restoration of vegetation was the main factor instigating a further reduction in sediment load. Studying the changes in the rainfall erosivity will provide a useful reference for future ecological construction and soil erosion control in the Loess Plateau.
Full-text available
The scarcity of long instrumental records, uncertainty in reconstructions, and insufficient skill in model simulations hamper assessing how regional precipitation changed over past centuries. Here, we use standardised precipitation data to compare global and regional climate simulations and reconstructions and long observational records of seasonal mean precipitation in England and Wales over the past 350 years. The effect of the external forcing on the precipitation records appears very weak. Internal variability dominates all records. Even the relatively strong exogenous forcing history of the late 18th and early 19th century shows only little effect in synchronizing the different records. Multi-model simulations do not agree on the changes over this period. Precipitation estimates are also not consistent among reconstructions, simulations, and instrumental observations regarding the probability distributions’ changes in the quantiles for severe and extreme dry or wet conditions and in the standard deviations. We have also investigated the possible link between precipitation and temperature variations in the various data sets. This relationship is also not consistent across the data sets. Thus, one cannot reach any clear conclusions about precipitation changes in warmer or colder background climates during the past centuries. Our results emphasize the complexity of changes in the hydroclimate during the most recent historical period and stress the necessity of a thorough understanding of the processes affecting forced and unforced precipitation variability.
Full-text available
In recent years, there has been growing concern about the effect of global warming on water resources, especially at regional and continental scales. The last IPCC report on extremes states that there is medium confidence about an increase on European drought frequency during twentieth century. Here we use the Old World Drought Atlas palaeoclimatic reconstruction to show that when Europe's hydroclimate is examined under a millennial, multi-scale perspective, a significant decrease in dryness can be observed since 1920 over most of central and northern Europe. On the contrary, in the south, drying conditions have prevailed, creating an intense north-to-south dipole. In both cases, hydroclimatic conditions have shifted to, and in some regions exceeded, their millennial boundaries, remaining at these extreme levels for the longest period of the 1000-year-long record.
Full-text available
The risk of European extreme precipitation and flooding as an economic and humanitarian disaster is modulated by large-scale atmospheric processes that operate over (multi-)decadal periods and transport huge quantities of moisture inland from the oceans. Yet the previous studies for better understanding of extreme precipitation variability and its skillful seasonal prediction are far from comprehensive. Here we show that the winter North Atlantic Oscillation (NAO) and, to a lesser extent, winter ENSO signal have a controlling influence not only concurrently on European extreme precipitation anomaly in winter, but in a delayed way on the extremes in the following seasons. In a similar pattern, there is a strong footprint of summer atmospheric circulations over the Mediterranean Sea on summer extreme precipitation and with 1-, 2- and 3-season lags on the following autumn, winter and spring extremes. The combined influences of the different atmospheric circulation patterns mark a significant step forward for an improved predictability of European extreme precipitation in the state-of-the-art seasonal prediction systems.
Full-text available
Reanalysis data show an increasing trend in Arctic precipitation over the 20th century, but changes are not homogenous across seasons or space. The observed hydroclimate changes are expected to continue and possibly accelerate in the coming century, not only affecting pan-Arctic natural ecosystems and human activities, but also lower latitudes through the atmospheric and ocean circulations. However, a lack of spatiotemporal observational data makes reliable quantification of Arctic hydroclimate change difficult, especially in a long-term context. To understand Arctic hydroclimate and its variability prior to the instrumental record, climate proxy records are needed. The purpose of this review is to summarise the current understanding of Arctic hydroclimate during the past 2000 years. First, the paper reviews the main natural archives and proxies used to infer past hydroclimate variations in this remote region and outlines the difficulty of disentangling the moisture from the temperature signal in these records. Second, a comparison of two sets of hydroclimate records covering the Common Era from two data-rich regions, North America and Fennoscandia, reveals inter- and intra-regional differences. Third, building on earlier work, this paper shows the potential for providing a high-resolution hydroclimate reconstruction for the Arctic and a comparison with last-millennium simulations from fully coupled climate models. In general, hydroclimate proxies and simulations indicate that the Medieval Climate Anomaly tends to have been wetter than the Little Ice Age (LIA), but there are large regional differences. However, the regional coverage of the proxy data is inadequate, with distinct data gaps in most of Eurasia and parts of North America, making robust assessments for the whole Arctic impossible at present. To fully assess pan-Arctic hydroclimate variability for the last 2 millennia, additional proxy records are required.
Full-text available
External forcings are known to impact atmospheric circulation. However, the analysis of the role of external forcings based on observational data is hampered due to the short observational period, and the sensitivity of atmospheric circulation to external forcings as well as persistence the effects are debated. A positive phase of the North Atlantic Oscillation (NAO) has been observed the following winter after tropical volcanic eruptions. However, past major tropical eruptions exceeding the magnitude of eruptions during the instrumental era could have more lasting effects. Decadal NAO variability has been suggested to follow the 11-year solar cycle, and linkages has been made between grand solar minima and negative NAO. However, the solar link to NAO found by modeling studies is not unequivocally supported by reconstructions, and is not consistently present in observations for the 20th century. Here we present a reconstruction of atmospheric winter circulation for the North Atlantic region covering the period 1241–1970 CE. Based on seasonally resolved Greenland ice core records and a 1200-year long simulation with an isotope enabled climate model, we reconstruct sea level pressure and temperature by matching the spatio-temporal variability of the modeled isotopic composition to that of the ice cores. This method allows us to capture the primary and secondary modes of atmospheric circulation in the North Atlantic region, while, contrary to previous reconstructions, preserving the amplitude of observed year-to-year atmospheric variability. Our results show 5 winters of positive NAO on average following major tropical volcanic eruptions, which is more persistent than previously suggested. In response to decadal minima of solar activity we find a high-pressure anomaly over Northern Europe, while a reinforced opposite response in pressure emerges with a 5-year time lag. On longer time scales we observe a similar response in circulation as for the 5-year time-lagged response. This is likely due to an increase in blocking frequency and an associated weakening of the subpolar gyre. The long-term response of temperature to solar minima shows cooling across Greenland, Iceland and Western Europe, resembling the cooling pattern during the Little Ice Age. While our results show a clear link between solar forcing and the secondary circulation patterns, we find no consistent relationship between solar forcing and NAO.
Full-text available
Despite the societal importance of extreme hydroclimate events, few palaeoenvironmental studies of Scandinavian lake sediments have investigated flood occurrences. Here we present a flood history based on lithological, geochemical and mineral magnetic records of a Holocene sediment sequence collected from contourite drift deposits in Lake Storsjön (63.12◦ N, 14.37◦ E). After the last deglaciation, the lake began to form around 9800 cal yr BP, but glacial activity persisted in the catchment for ~250 years. Element concentrations and mineral magnetic properties of the sediments indicate relatively stable sedimentation conditions during the Holocene. However, human impact in the form of expanding agriculture is evident from about 1100 cal yr BP, and intensified in the 20th century. Black layers containing iron sulphide appear irregularly throughout the sequence. The increased influx of organic matter during flood events led to decomposition and oxygen consumption, and eventually to anoxic conditions in the interstitial water preserving these layers. Elevated frequencies of black layer occurrence between 3600 and 1800 cal yr BP reflect vegetation changes in the catchment as well as large-scale climatic change. Soil erosion during snowmelt flood events increased with a tree line descent since the onset of the neoglacial period (~4000 cal yr BP). The peak in black layer occurrence coincides with a prominent solar minimum ~2600 cal yr BP, which may have accentuated the observed pattern due to the prevalence of a negative NAO index, a longer snow accumulation period and consequently stronger snowmelt floods.
Full-text available
In this paper, we present a comprehensive review of the data sources and estimation methods of 30 currently available global precipitation datasets, including gauge-based, satellite-related, and reanalysis datasets. We analyzed the discrepancies between the datasets at daily to annual timescales and found large differences in both the magnitude and the variability of precipitation estimates. The magnitude of annual precipitation estimates over global land deviated by as much as 300 mm/yr among the products. Reanalysis datasets had a larger degree of variability than the other types of datasets. The degree of variability in precipitation estimates also varied by region. Large differences in annual and seasonal estimates were found in tropical oceans, complex mountain areas, northern Africa, and some high-latitude regions. Overall, the variability associated with extreme precipitation estimates was slightly greater at lower latitudes than at higher latitudes. The reliability of precipitation datasets is mainly limited by the number and spatial coverage of surface stations, the satellite algorithms, and the data assimilation models. The inconsistencies described limit the capability of the products for climate monitoring, attribution, and model validation.
Full-text available
Recent studies have presented conflicting results regarding the 11-year solar cycle (SC) influences on winter climate over the North Atlantic/European region. Analyses of only the most recent decades suggest a synchronized North Atlantic Oscillation (NAO)-like response pattern to the SC. Analyses of long-term climate data sets dating back to the late 19th century, however, suggest a mslp response that lags the SC by 2-4 years in the southern node of the NAO (i.e. Azores region). To understand the conflicting nature and cause of these time dependencies in the SC surface response, the present study employs a lead/lag multi-linear regression technique with a sliding window of 44-years over the period 1751-2016. Results confirm previous analyses, in which the average response for the whole time period features a statistically significant 2-4-year lagged mslp response centered over the Azores region. Overall, the lagged nature of Azores mslp response is generally consistent in time, with stronger and statistically significant SC signals tend to appear in the periods when the SC forcing amplitudes are relatively larger. Individual month analysis indicates the consistent lagged response in December-January-February average arises primarily from early winter months (i.e. December and January), which is associated with ocean feedback processes that involve reinforcement by anomalies from the previous winter. Additional analysis suggests that the synchronous NAO-like response in recent decades arises primarily from the late winter month (February), possibly reflecting a result of strong internal noise.
Full-text available
We investigate the relationship between the variability in the frequency of River Ammer floods (southern Germany) and temperature/precipitation extremes over Europe using observational River Ammer discharge data back to 1926 and the 5500-year-long flood layer record from varved Lake Ammersee sediments. We show that observed River Ammer flood frequency variability is not only related with local extreme precipitation, but also with large-scale temperature extreme anomalies. Less (more) extreme high temperatures over central and western (northeastern) Europe are recorded during periods of increased River Ammer flood frequency. We argue that changing radiative forcing due to cloudiness anomaly patterns associated with River Ammer floods induce these extreme temperature anomalies. Consistent patterns are obtained using observed discharge and proxy flood layer frequency data. Furthermore, a higher frequency of observed River Ammer floods and flood layers is associated with enhanced blocking activity over northeastern Europe. A blocking high over this region increases the probability of wave breaking and associated heavy precipitation over western Europe. A similar blocking pattern is associated with periods of reduced solar activity. Consequently, solar modulated changes in blocking frequency over northeastern Europe could explain the connection between River Ammer floods and solar activity, as also identified in previous studies. We argue that multi-decadal to millennial flood frequency variations in the Mid- to Late Holocene flood layer record from Lake Ammersee characterizes also the extreme temperatures in northeastern Europe.
”I look to the left… NOTHING? I look to the right… NOTHING? So, I say to myself: There is SOMETHING here…" From Burgas folklore sayings about Uncle Petyo Banderata One of mankind’s successful attempts to find out what that SOMETHING is the Monte Carlo Method. The method, as well as many of the achievements of mankind, was created for military purposes as part of the scientific tasks associated with the creation of the atomic bomb. The event was super secret and everything was encrypted. The code name of the method – Monte Carlo, has proved to be very successful and has survived in civilization (suck fate has the name of the armoured fighting vehicle – tank). The task was to create a method for modeling the behavior of a complex probability system. The classic solution is to present the phenomenon with one, two, etc. (but always a limited number) indicators. The new solution is the opposite – "artificially" increasing the number of input/output information. Currently, the Monte Carlo Method is effective, and in some cases – the only one, solution for a wide range of tasks from all areas of scientific knowledge. That is why we’ve decided to present yet another exposure of the foundations and some of the Monte Carlo applications. The monograph is divided in two parts. The first part returns the reader during the World War II. We follow the development of the idea of the method and the associated need for creating a powerful enough computer. The first publications are mentioned and are examined the scientific basics of the method and some basic algorithms. Described is application of the method for solving the classical task – calculating the number π and for two malicious problems – the phenomenon Black Swan and the functional literacy of the students. The second part contains applications of Monte Carlo method for solving tasks that can be characterized as "engineering". Without neglecting the concrete results obtained, we will point out that the described approaches for the practical application of the Monte Carlo method are of the greatest interest. The monograph includes tasks from the following areas: — quality management in extraction of underground resources – nonlinear optimization task solved in complex and dynamic conditions; — stability of opencast slopes in complex and underdeveloped environments; — assessment of the accuracy of mine surveying and geodetic measurements; — productivity of machinery in open pit mines; — emissions modeling; — urban acoustics. The present monograph is an attempt to examine the basic features of the Monte Carlo method, to systematize the results and conclusions of its application by authors and other researchers and, as a result, to help others using the method for solving a wide range of tasks in various engineering sciences. The authors believe that the monograph is of interest to specialists who work in the exploration and extraction of underground resources, environmental protection, urban planning and construction, mathematical modeling, and application development, engineering geology and geomechanics. We hope that the monograph will also be useful for students and PhD students from a significant number of professional fields. But the most useful monograph will be for those who are convinced that the world is probable and that's why life is so interesting.