In this work, the Sun–Earth–climate relationship is studied using tree
growth rings of

In Brazil, dendrochronological/dendroclimatic studies are still incipient

However, the study of solar variations related to the energy flux entering the Earth's atmosphere is predominantly observational, and it has also only recently been undertaken. This fact limits understanding their effects on climate, and the possibility of long-term climate prediction. For these reasons, it is necessary to understand the solar variations, and other geophysical phenomena in the distant past to try to predict the future.

Tree-ring time series are witnesses of the environment and climate that
influenced their growth in the past

Tree-ring data have been used to reconstruct the climate

In the city of Passo Fundo located in South Brazil (52

The dendrochronological series are used in the present work for study the
Sun–Earth-climate relationship. These series are obtained from trees located
in the region of South Brazil. The tree samples from

All the

Mean time series of growth ring thickness of trees from Passo Fundo, Rio Grande do Sul, after removing their long trend curves.

The time series were obtained using a tree-ring measuring table (Lintab III)
with an accuracy of 0.01 mm. In the first step, the growth-rings were
identified and demarcated. In this part of the laboratory procedure, the
tree rings were properly indicated, i.e., without any false or missing rings
being considered. In the second step as previously explained by

Moreover, the tree-sample ages were determined by the ring-counting. As the
samples were collected from live trees in 2005, the last year of ring
formation is 2004. In samples of

We also used the most recent continuous series from climate drivers. In
Fig.

An iterative regression method (ARIST) is used to search for periodicities
embedded in tree growth ring time series, and it was used successfully by

Every periodicity embedded in the time series corresponds to a set of three
parameter values, where the periodicity is determined by applying the
iterative process to the original time series with the limiting condition of
maintaining the angular frequency

The advantage of this method over the Fourier method is that it is able to find periodicities associated with long trends. In other words, it fits senoidal functions in the signal. In addition, if only a segment of a sine function fits the original signal, it is possible to determine the period of this trend using ARIST. On the other hand, in the Fourier method, long trends are bounded by the finite length of the time series.

The wavelet transform is an useful tool for non-stationary signal analysis.
It permits the local identification of spectral content of a certain time
series in time and in space

The continuous wavelet transform (CWT) of a time series is defined as the convolution between the series and the scaled and translated version of the chosen wavelet function. By varying the wavelet timescale and translating the scaled versions of the wavelet mother, it is possible to build a two-dimensional spectrogram showing the time versus frequency (period), and how they vary with time.

The CWT of a time series

In this work, we used an updated version of the CWT algorithm of

The wavelet cross-correlation is also used because the wavelet cross power
indicates the scale of high correlation between two time series with indices
1 and 2

The wavelet cross-correlation will allow us to check the interaction between two sets of dendrochronological data for each considered timescale.

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

Amplitude spectra for each tree-ring thickness sample at a confidence of 95 % from S01 to S12 (top 12 panels) and the average of them (bottom panel).

The amplitude spectra for each tree-ring thickness time series using the
ARIST at a confidence level of 95 % are 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

Several authors (e.g.,

In dendrochronological series, similar results were found by many authors

In

For a paleoclimatic study,

Fossil trees of

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

For

Once more, in the average chronology obtained in Passo
Fundo (bottom panel of Fig.

Moreover,

Signals filtered of the mean width of tree-ring series and sunspot number between 8 and 13 years.

In addition,

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

Amplitude spectra of the

Other period intervals observed in Fig.

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.

Morlet cross-wavelet map between the annual mean temperature
anomaly, between 24 and 44

As discussed by

Power fraction of the frequency found in the mean width of tree-ring series and annual mean temperature anomaly and SOI signals.

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

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

Similar to the analysis done in Fig.

The time series of tree-ring growth from Passo Fundo, the SOI, and the
temperature anomaly (from 24 to 44

Figure

Comparing the SOI to the temperature anomaly (black and blue curve in
Fig.

In this paper,

There is evidence of the solar cycle influence related to the
cycles of Schwabe (

The cycles of

There is evidence in the temperature and in the SOI analysis that some of their natural climatic oscillation may be driven by solar activity.

In total, 25 % of the temperature spectral content is related to the
periodicities between

A 20–23-year bandwidth period is found in the dendrochronological
series, and it is well correlated with the temperature anomaly (from 24 to
44

In addition, the rainfall and the temperature variability in Passo Fundo seem to also be related to the SOI variation (sometimes in phase or in anti-phase) for the bandwidth corresponding to the El Niño/La Niña phenomena.

The annual mean temperature was obtained from Goddard
Institute for Space Studies (GISS), NASA,

The authors declare that they have no conflict of interest.

This article is part of the special issue “Space weather
connections to near-Earth space and the atmosphere”. It is a result of the
6

A. Prestes was supported by FAPESP (2009/02907-8) and CNPq (301441/2013-8). Virginia Klausner wishes to thank CNPq for the financial support for her postdoctoral research (grant 165873/2015-9). The authors express their appreciation to the late Nivaor Rodolfo Rigozo and the late Daniel Jean Roger Nordemann, whose contributions to this work were of great significance. Furthermore, the authors would like to thank GISS and CRU for the data sets used in this work. The topical editor, Alisson Dal Lago, thanks Maurício Bolzan and one anonymous referee for help in evaluating this paper.