The Sun is both an element and a climate forcing. Therefore, solar cycles
presented in the dendrochronological series will be re-analyzed because many
periods found in these series may be possibly due to a combination of solar
cycle harmonics. As for example, the periods of ∼ 17 to ∼ 18 years (Saros
cycle) and ∼ 30 to ∼ 35 years (Brückner cycle) can also be found in the
climatological series. Moreover, discussed that the
climatic variations are forced oscillations driven by solar forcing, and
consequently, it implies the existence of intrinsic climatic oscillations
related to solar activity. As aforementioned, the main focus of this paper is
to study the nonlinear behavior of the solar activity and their correlation
with the variability of climate conditions. Due to this fact, we will divide
Sect. into two subsections: solar influences and climate
influences.
Solar influences
The amplitude spectra for each tree-ring thickness time series using the
ARIST at a confidence level of 95 % are shown in Fig. . These
spectra are related to the tree-ring thickness time series shown in
Fig. .
It is possible to see the presence of some well-known periodicities related
to the solar activity. The solar activity presents several sub-intervals
including the Schwabe cycle which corresponds to a period bandwidth of
8–13 years, the cycle of ∼ 11 years related to the sunspot number
variability, and the Hale cycle of 20–29 years related to the magnetic solar
cycle of 22 years. The Gleissberg cycle of
70–90 years can also been seen . This spectral analysis of each
tree individual sample related to the solar activity was not done by
.
Several authors (e.g., ; ;
; ;
; ) applied different analysis techniques (Fourier analysis,
maximum entropy, and multitaper method) to determine the spectral content of
the sunspot number time series. Their main results include a low period cycle
of 5.5 years; a variable solar cycle of 11 years, which may appear with lower
or higher periods between ∼ 8 and ∼ 13 years depending upon on
the decadal time interval used in the analysis; and a cycle of
∼ 90 years, which is also frequently present in the sunspot number
series . Considering the solar cycles from 11 to 22, an
average period of 9.67 years can be found; therefore, it explains why the
period may vary between 9 and 11 years .
In dendrochronological series, similar results were found by many authors
. analyzed tree-ring time series
obtained in Australia and Taiwan and found periods related to the solar cycle
of 11 years between 9.3 and 13.3 years, and between 11.1 and 13.6 years,
respectively. In the South Brazil region, studied tree
rings collected in Concórdia, and they found periods of 10.6 and
83.4 years, which corresponds to the solar cycle of 11 years and the
Gleissberg cycle of ∼ 80 years, respectively.
performed a study using tree-ring chronology obtained in Brazil and Chile.
The Brazilian tree samples showed periodicities of 79, 51.3, 23.7, and
10.5 years relating to solar activity, while the tree-ring samples collected
in Chile showed periodicities of 197, 89.6, 50.3, 11.8, and 10.5 years.
Another study using Araucaria angustifolia samples collected in
General Carneiro, Irani, and Fazenda Rio Grande in South Brazil was performed
by . In this study, periodicities related to solar cycle
of 11 years, 22 years, and longer periods such as the Gleissberg cycle were found.
studied tree-ring growth using 391-year-old
cedar samples collected in
Japan, and they found periodicities of 25 and 12 years. These authors
concluded that tree growth rate can be influenced by solar activity.
Periodicities between 20 and 28 years were also found by
in Araucaria columnaris samples from New
Caledonia. found periodicities around 204, 73,
20.5, 11.2–11.1, and 5.3–5.1 years performing spectral analysis using
samples from the mountains of Tibet, which correspond to Suess, Gleissberg,
Hale cycle and second harmonic of the Schwabe cycle, respectively.
In , the periodicities found in the tree rings
collected in Passo Fundo were also mainly attributed to the solar
variability. The periods between 8.1 and 12.4 years were related to solar
cycle of 11 years, while the period of 23.0 year was related to the Hale
cycle. They suggested that the period of 55.7 years might be related to the
fourth harmonic of the Suess cycle as discussed by . On the
other hand, they suggested that the period of 73.1 years was attributed to
the Gleissberg cycle, and the period of 188.6 years was attributed to the
Suess cycle of 200 years. In the bottom panel of Fig. , all the
aforementioned periodicities related to solar activity can be observed, in
addition to each of the 12 dendrochronological series obtained in Passo
Fundo, although they are not so evident as in their average series.
For a paleoclimatic study, used fossil trees of
∼ 70 000 years old (380 rings) and ∼ 12 000 years old
(120 rings). Using the fossil of ∼ 70 000 years old, the researchers
found periodicities of 8–10, 20–22, and 100–120 years that correspond
to Schwabe, Hale, and Gleissberg cycles, respectively. Using a
∼ 12 000-year-old fossil, periodicities of 4, 9–12 (Schwabe cycle), 17
(lunar cycle), and 31–34 years (Brückner cycle) were found.
Fossil trees of ∼ 50 000 years and living trees obtained in
Chile were analyzed by . They found similar spectral
periodicities between these two data sets, such as 136–153, 81–94, and 47–53
years and periods of 35, 24, 17.8, 11.8, 6.6, 5.1, 4.58, 4.3, 3.7, 3.2, and
2.77 years. This indicates that similar factors may affect the radial growth
of these trees since the end of the Pleistocene. These authors related the
periods of 81–94, 24, and 11.8 years to the solar modulation.
However, the cycles of 7 and 8 years found in the tree-ring chronological
series could be related to two beating solar/climatic cycles as discussed by
. It is well known that a combination of wave oscillation patterns between
various forcing frequencies can be obtained as a response of the
nonlinearity interactions as discussed by . The
nonlinearity wave oscillation patterns are the response to additive and multiplicative periodic
forcing fo, so they are composed of the harmonic of the forcing
fh and their combination, for example
fo+fh, fo-fh, and
fo+2fh, among many others.
For , the Brückner cycle is a result of
solar activity nonlinear effects in the terrestrial environment. They found
that the combination of the Gleissberg cycle (∼ 90 years) and the Hale
cycle (22 years) may result in the Brückner cycle ((1/22)-(1/90)≅1/30) or in the Saros lunar cycle ((1/90)+(1/22)≅1/17). Therefore,
concluded that the periods of between ∼ 17 and ∼ 18
and ∼ 30 and ∼ 35 years might also be a result of solar activity nonlinear
effect in atmospheric processes. showed that the
combinations of two periods of 12.6 and 17.1 year could generate periods of
7.3 and 47.9 years as mathematical described by the following equations:
(1/12.6)+(1/17.1)≅1/7.3, and (1/12.6)-(1/17.1)≅1/47.9.
Once more, in the average chronology obtained in Passo
Fundo (bottom panel of Fig. ), we observe that the period of 6.6 and 35 years
may be the beat period (the rate of alternation between constructive and destructive wave interference) results from the periods of 11 and 16.2 years,
[(1/11)+(1/16.2)≅1/6.6] and [(1/11)-(1/16.2)≅1/35],
respectively, as discussed by . In the same
way, the periods of 17.5 and 33.5 years may also be a result from the
beat period
of 23 and 73.1 years, [(1/23)+(1/73.1)≅1/17.5] and [(1/23)-(1/73.1)≅1/33.5], respectively.
Moreover, analyzed the natural climatic oscillations driven
by solar activity. The author verified that variations in climatic parameters do not
always occur synchronously with the corresponding 11- and 22-year solar
cycles. Based on this analysis, we apply a period bandwidth filter of
8–13 years in the tree-ring width average and in the sunspot number series,
as shown in Fig. . We observe that the phase shift between
tree rings and sunspot variations is variable, and it changes with time from
0 to 180∘. The phase shift occurs when there is a significant change
in the sunspot number amplitude, as can be observed in Dalton minimum
(1794–1824). Therefore, our result of tree-ring width and solar variation
analysis behaves in the same way as reported by .
Signals filtered of the mean width of tree-ring series and sunspot
number between 8 and 13 years.
In addition, and showed that the profile
features between climatic parameters and sunspot number can be reproduced by
a forced oscillation equation using a driving force term that describes the
variation of the sunspot number with a period varying from 16 to 70 years.
This forced oscillation equation also describes the presence of natural
climatic oscillations with periods above 30 years, which possibly correspond
to the Brückner cycle usually observed in the variations of some climatic
parameters such as precipitation and temperature.
It is also possible that the correlation and the phase shift between
tree-ring width and the sunspot number series can be due to the modulation of
the cloudiness . This modulation can be caused by the
cosmic ray ionization, which increases the diffuse radiation, and
consequently, makes the photosynthetic production more efficient
seeand references therein.
showed that the tree growth is greater when it is not under extremely shady
conditions compared to full daylight conditions. Their study
was based on the daily photosynthetic production of each plant using
Araucaria angustifolia specimen in the juvenile stage. However, the
ratio of the strength between the effect of cosmic rays and the climate (UV
light) may be about 1 : 10, and therefore the effect of cosmic rays is
minor.
Amplitude spectra of the (a) annual mean temperature
anomaly between 24 and 44∘ S; (b) SOI. The significance level is 95 %.
Climate influences
Other period intervals observed in Fig. may also be related to
the climate influences, such as the El Niño and La Niña phenomena, which
correspond to a period bandwidth of 2–7 years in each tree-ring amplitude
spectrum. This phenomenon modifies global climate activity; however
it does not have well-defined regularity .
For this reason, spectral analysis using the ARIST is performed, in order
to verify a possible cause–effect relationship between the periods found in
the annual mean temperature and the SOI series, as shown in Fig. .
The periods between 8.2 and 10.1 years in the temperature data may be related
to solar cycle of 11 years, while the period of 20.3 years may be related to
the Hale cycle. The period of 158.1 years may be related to the second harmonic
of the 328 years found by in the sunspot number data.
The lower periods of 4.2, 6.7, and 7.6 years in the temperature data can be
attributed to the effects of the El Niño events because they are related
to the periods of 4.2, 6.4, and 7.4 years in the SOI data. These results agree with
the El Niño model discussed by . In that paper, the El Niño
model is assessed in terms of the two modes: first – the sea surface
temperature mode, which implies low-amplitude El Niño events with a frequency of
2–3 years; second – the thermocline mode, which involves
the western Pacific circulation, and consequently, implies large-amplitude
El Niño events with a frequency of 4–5 years.
Morlet cross-wavelet map between the annual mean temperature
anomaly, between 24 and 44∘ S, and the tree-ring average chronology.
The contour plot represents the significance levels for 95 %.
Panel (b) presents
the global wavelet spectrum, which is defined as the wavelet coefficients
power average for each scale, i.e., it corresponds to a Fourier
spectrum.
(a) Signals filtered of the mean width of tree-ring series
and annual mean temperature anomaly (from 24 to 44∘ S);
(b) annual mean temperature anomaly (from 24 to 44∘ S) and
sunspot number, between 20 and 23 years.
As discussed by , it is possible to quantify every
frequency detected (Pi) in the signal by obtaining a power fraction
(fP, where
fP=Pi∑Pi) of this frequency related to the total spectrum
(sum of all powers found). Therefore, Table presents the power
fraction of every frequency signal found in relation to the total signal
spectrum for both the annual mean temperature and the SOI presented in
Fig. . We observe that 25 % of the fP of the annual
mean temperature (between 4.2 and 7.6 years) is related to the SOI
periodicities (between 2.9 and 7.4 years). In other words, the El Niño
phenomenon represents a total of 25 % of the spectral temperature signal.
This result is consistent with the study on
trees 391-year-old trees in Japan of , who found lower periods
than the solar cycles and related them to ENSO events.
Power fraction of the frequency found in the mean width of tree-ring
series and annual mean temperature anomaly and SOI signals.
Temperature
SOI
period
power
total
period
power
total
(year)
fraction
(%)
(year)
fraction
(%)
158.1
0.27
27
45.9
0.07
7
20.3
0.15
15
13.6
0.08
16
14.7
0.14
33
9.0
0.08
10.1
0.10
7.4
0.07
77
8.2
0.09
6.4
0.10
7.6
0.07
25
5.7
0.09
6.7
0.09
5.2
0.06
4.2
0.09
4.8
0.08
4.2
0.06
3.6
0.06
3.5
0.10
3.4
0.09
2.9
0.06
Morlet cross-wavelet map between tree-ring average chronology
collected in Passo Fundo and the SOI. The contour
plot represents the significance levels for 95 %. Panel (b)
presents the global wavelet spectrum, which is defined as the wavelet
coefficients power average for each scale, i.e., it corresponds to a Fourier
spectrum.
In order to correlate the influence of the temperature on the tree-ring width
growth, the Morlet cross-wavelet transform was performed in the annual mean
temperature anomaly (from 24 to 44∘ S) and tree-ring average
chronology was collected in Passo Fundo (Fig. ). The results show
lower periods, between 4 and 8 years, occurring during 1910–1935,
and the period of ∼ 12 years appears between 1944 and 1974, while the period
of ∼ 22 years is present during the entire data interval. Some studies
showed that the periodicities of 11, 22, and 90 years found in temperature
time series are related to the solar activity
. Moreover, we observe the
strong relationship between the temperature and tree-ring growth in
∼ 1917, when the lowest temperature value is observed. This decrease in
temperature is also followed by a decrease of the tree-ring growth.
(a) Signals filtered of the mean width of tree-ring series
and annual mean temperature anomaly (from 24 to 44∘ S);
(b) annual mean temperature anomaly (from 24 to 44∘ S) and
sunspot number, between 5 and 7 years.
Similar to the analysis done in Fig. , Fig. shows the
tree-ring time series, the annual mean temperature anomaly (from 24 to
44∘ S) series, and the sunspot number series filtered using a period
bandwidth of 20 to 23 years. A lag of 3 years between the
tree-ring growth and the temperature during 1880 to 2004 is observed, whereas between the
temperature and the sunspot, the phase variably
shifts with time, changing from 4 years to 0 along the
interval studied. The reverse behavior is observed between the tree rings and the sunspot
number which corresponds to the red line and blue line in Fig. ,
respectively. We can see that the phase shifts with time from
0 to 4 years. The results of the Morlet cross-wavelet scalogram of SOI and
tree-ring chronology obtained in Passo Fundo are shown in Fig. .
These results indicate mainly a presence of periods between 4 and 8 years
during the time interval of ∼ 1910 to ∼ 1925, ∼ 1930 to ∼ 1955, and
∼ 1965 to ∼ 1975; and a period of ∼ 17 years during
∼ 1945 to ∼ 1985. The same kind of result was found by
using wavelet techniques. They studied the
periodicities of ENSO presented in the tree rings in the region of South Brazil,
and they found periods between 2 and 8 years in their data showing
non-stationary behavior.
The time series of tree-ring growth from Passo Fundo, the SOI, and the
temperature anomaly (from 24 to 44∘ S) are usually filtered in the
interval of 5–7 years, in order to find better correlations in their global
wavelet spectrum and cross-wavelet analysis. This interval is chosen because
it may be related to the El Niño/La Niña events. It is well known that
during the occurrence of El Niño events, an excess of precipitation occurs
in the South Brazil region, and the northern parts of Argentina and Uruguay.
In contrast, the lowest level of precipitation takes place during the
occurrence of La Niña .
Figure a shows the tree-ring and the SOI series filtered between 5
and 7 years, while Fig. b shows the tree-ring and the temperature
anomaly series filtered by the same bandwidth filter. The series of tree-ring
growth and SOI show a phase and anti-phase shift throughout the years of 1866
and 2004. In the intervals of 1866–1900 and 1959–1982, these series are in
phase, whereas in the intervals of 1900–1930 and 1982–2004, they are in
anti-phase. In the interval of 1930–1959, there is a lag of one year between
these two series. Similar behavior is observed between the series of
tree-ring growth and temperature anomaly. These series of tree-ring growth
and temperature anomaly are in anti-phase during the intervals of 1880–1906
and 1937–1950, and in phase during the intervals of 1906–1937 and
1950–2004.
Comparing the SOI to the temperature anomaly (black and blue curve in
Fig. a and b, respectively), we observe that in the interval
1880–1930, both series are in anti-phase. This fact indicates that during
the El Niño events (SOI negative) there is an increasing temperature
tendency due to the highest precipitation levels.
showed that the rainfall and the temperature variability in Santa Maria, RS
(29∘41′ S, 53∘48′ W) is related to the SOI variation,
especially during El Niño events. also found that
the precipitation at Pelotas, RS (31∘46′19′′ S,
52∘20′33′′ W) is strongly influenced by the ENSO phenomenon. In
summary, analyzing both graphs in Fig. , we observe that both
the SOI and the temperature have strong influence on the araucaria growth
in this region of Brazil, mainly when the temperature anomaly presents its
greatest amplitude as shown in the interval of 1906–1937.