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Singular Spectrum Analysis (SSA) occupies a prominent place in the real signal analysis toolkit alongside Fourier and Wavelet analysis. In addition to the two aforementioned analyses, SSA allows the separation of patterns directly from the data space into the data space, with data that need not be strictly stationary, continuous, or even normally sampled. In most cases, SSA relies on a combination of Hankel or Toeplitz matrices and Singular Value Decomposition (SVD). Like Fourier and Wavelet analysis, SSA has its limitations. The main bottleneck of the method can be summarized in three points. The first is the diagonalization of the Hankel/Toeplitz matrix, which can become a major problem from a memory and/or computational point of view if the time series to be analyzed is very long or heavily sampled. The second point concerns the size of the analysis window, typically denoted as 'L', which will affect the detection of patterns in the time series as well as the dimensions of the Hankel/Toeplitz matrix. Finally, the third point concerns pattern reconstruction: how to easily identify in the eigenvector/eigenvalue space which patterns should be grouped. We propose to address each of these issues by describing a hopefully effective approach that we have been developing for over 10 years and that has yielded good results in our research work., Comment: 28 pages, 11 figures

What is certain is that surface temperatures around the globe vary considerably, regardless of the time scales or underlying causes. Since 1850, we have observed an average increase in global surface temperature anomalies of 1.2$^{\circ}$ and a median increase of 0.7$^{\circ}$: this overall difference masks significant regional differences. Nearly 60\% of the world's population now lives in urban areas, where vegetation cover has been significantly reduced, despite the paradoxical fact that vegetation plays an important role in regulating the thermal environment (\textit{eg} through the shading provided by tree canopies). Continuous electrical and thermal measurements of trees in a Parisian grove (France) show and quantify that canopies are not the only protectors against heat waves; we must also consider the role of tree trunks. It is clear that these trunks probably regulate themselves, possibly by modulating the uptake of groundwater, whose geothermal stability is well established at a depth of just one meter. This quantitative observation should not be overlooked in the urban planning of our cities., Comment: 15 pages, 6 figures

This book is intended for teaching Signal Analysis methods and Inverse Problems theory. It is completely open access and will remain free. It is currently illustrated with examples that we have actually encountered in geophysics, but will eventually evolve to address problems in biology. The main idea is to develop this material over time (probably every six months) and throughout our careers. Therefore, it is not yet complete and some minor points need to be corrected in this English version. It is also available in French ( https://www.dropbox.com/scl/fi/yx9le4tbwjg0ur7llp0fj/TheorieInfoTTS_vf.pdf?rlkey=uvc1ku8v4ihhogkcy0w2iixdf&st=gcddwegm&dl=0 ) and Portuguese ( https://www.dropbox.com/scl/fi/mx46mgn66ob3r1z9r0igq/TheorieInfoTTS_vp.pdf?rlkey=c8m9e8dmbwf1npu4bwfqkhblr&st=xveovcvs&dl=0 ). The MATLAB codes we used can be found at the following address: https://www.dropbox.com/scl/fi/6tedk1xyquswmh0vcekfi/matlab_book.zip?rlkey=cbj5ura63qy6u57ij2yzgggkw&st=8gp4gddd&dl=0, Comment: 334 pages, 97 figures

In this paper, we revisit old electrical measurements conducted on a poplar tree in 2003 (Gibert et al. 2006), which showed the presence of a diurnal electrical signal, attributed to an electrokinetic phenomenon correlated with sap flow, even in winter. We reanalyze these data using the singular spectrum analysis method and demonstrate that the electrical signal measured at various locations (roots, trunk, and branches) on the poplar tree can be decomposed to over 80\% into a sum of 7 pseudo-periods, all linked to luni-solar tides. The precision of the extracted periods exceeds that of models. To validate these old measurements, we have reproduced the 2003 protocol since 2018 at the Jardin des Plantes in Paris, on 3 oak trees and 3 hornbeams. The electrical signals today exhibit the same characteristics as those of 2003. Tidal forces could be a driving force of sap flow in trees., Comment: 22 pages, 7 figures

The trajectory of Earth about the Sun is perturbed by torques exerted by the Moon and Sun, and also the four giant planets. These provoke variations of insolation at Earth surface, known as kyr-long Milankovi\'c cycles. The concept has been extended to the shorter time scales of years to centuries, that are relevant to tree growth. This paper focuses on iSSA of results of the dendro-chronological study of a forest of long-lived Tibetan junipers. From this, we determine a median curve of tree growth rates, that is analyzed by iSSA. We obtain a rich set of (pseudo-) periods, from 3.3 yr up to more than 1000 years, that compare with the specific spectral signature found in the sunspot and length-of-day time series. We discuss in detail the record from a single tree that spans almost completely the 357-2000 AD interval. The 90 yr Gleissberg, 22 yr and 30 yr components are quite prominent. The Oort, Wolf, Sp\"orer, Maunder and Dalton climate extrema all correspond quite precisely to extrema of the Gleissberg cycle. The well-known Medieval Climate Optimum, Little Ice Age and Modern Climate Optimum all seem to be mainly forced by variations in the envelope of the Gleissberg cycle. The Gleissberg cycle is strongly modulated with a period of 500-600 years. The node near a small gap in the data is very close to the Medieval Climate Optimum. Observations in different parts of Earth are in favor of a global extension of the MCO. In the same way that the Milankovic mathematical theory of climate allows one to relate climate change and length of day, through changes in inclination of Earth's rotation axis and solar insolation, it is reasonable to propose that the set of pseudo-periods that are evidenced in the Tibetan tree ring growth rates simply corresponds to short period Milankovi\'c cycles. The Dulan forest could be considered as a good candidate for a continuous, global geophysical observatory., Comment: 26 pages, 15 figures