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Register a new userRecurrence Quantification Analysis of Two Solar Cycle Indices
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Solar activity affects the whole heliosphere and near-Earth space environment. It has been reported in the literature that the mechanism responsible for the solar activity modulation behaves like a low-dimensional chaotic system. Studying these kind of physical systems and, in particular, their temporal evolution requires non-linear analysis methods. To this regard, in this work we apply the recurrence quantification analysis (RQA) to the study of two of the most commonly used solar cycle indicators; i.e. the series of the sunspots number (SSN), and the radio flux 10.7 cm, with the aim of identifying possible dynamical transitions in the system. A task which is particularly suited to the RQA. The outcome of this analysis reveals the presence of large fluctuations of two RQA measures; namely the determinism and the laminarity. In addition, large differences are also seen between the evolution of the RQA measures of the SSN and the radio flux. That suggests the presence of transitions in the dynamics underlying the solar activity. Besides it also shows and quantifies the different nature of these two solar indices. Furthermore, in order to check whether our results are affected by data artifacts, we have also applied the RQA to both the recently recalibrated SSN series and the previous one, unveiling the main differences between the two data sets. The results are discussed in light of the recent literature on the subject.
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Wavelet analysis of different solar activity indices, sunspot numbers, sunspot areas, flare index, magnetic fields, etc., allows us to investigate the time evolution of some specific features of the solar activity and the underlying dynamo mechanism. The main aim of this work is the analysis of the time-frequency behavior of some magnetic strengtht indices currently taken at the Mt. Wilson Observatory 150-Foot Solar Tower. In particular, we analyzed both the long time series (Jan 19, 1970 - Jan 22, 2013) of the Magnetic Plage Strength Index (MPSI) values and of the Mt. Wilson Sunspot Index (MWSI) values, covering the descending phase of cycle 20, the full solar cycles 21-23 and the current part of the 24 solar cycle. This study is a further contribution to detect the changes in the multiscale quasiperiodic variations in the integrated magnetic solar activity with a comparison between past solar cycles and the current one, which is one of the weaker recorded in the past 100 years. Indeed, it is well known that an unusual and deep solar minimum occurred between solar cycles 23 and 24 and the time-frequency behavior of some magnetic strengtht indices can help to better interpret the responsible mechanisms.
The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on the concept of information entropy, in which the probabilities are associated to microstates defined from the recurrence phase space. Recurrence properties can properly be studied using recurrence plots, a methodology based on binary matrices where trajec- tories in phase space of dynamical systems are evaluated against other embedded trajectory. Our novel entropy methodology has several advantages compared to the traditional recurrence entropy defined in the literature, namely, the correct evaluation of the chaoticity level of the signal, the weak dependence on parameters, correct evaluation of periodic time series properties and more sensitivity to noise level of time series. Furthermore, the new entropy quantifier developed in this manuscript also fixes inconsistent results of the traditional recurrence entropy concept, reproducing classical results with novel insights.
A variety of indices have been proposed in order to represent the many different observables modulated by the solar cycle. Most of these indices are highly correlated with each other owing to their intrinsic link with the solar magnetism and the dominant eleven year cycle, but their variations may differ in fine details, as well as on short- and long-term trends. In this paper we present an overview of the indices that are often employed to describe the many features of the solar cycle, moving from the ones referring to direct observations of the inner solar atmosphere, the photosphere and chromosphere, to those deriving from measurements of the transition region and solar corona. For each index, we summarize existing measurements {bf and typical use}, and for those that quantify physical observables, we describe the underlying physics.
Context. The variations of solar activity over long time intervals using a solar activity reconstruction based on the cosmogenic radionuclide 10Be measured in polar ice cores are studied. Methods. By applying methods of nonlinear dynamics, the solar activity cycle is studied using solar activity proxies that have been reaching into the past for over 9300 years. The complexity of the system is expressed by several parameters of nonlinear dynamics, such as embedding dimension or false nearest neighbors, and the method of delay coordinates is applied to the time series. We also fit a damped random walk model, which accurately describes the variability of quasars, to the solar 10Be data and investigate the corresponding power spectral distribution. The periods in the data series were searched by the Fourier and wavelet analyses. The solar activity on the long-term scale is found to be on the edge of chaotic behavior. This can explain the observed intermittent period of longer lasting solar activity minima. Filtering the data by eliminating variations below a certain period (the periods of 380 yr and 57 yr were used) yields a far more regular behavior of solar activity. A comparison between the results for the 10Be data with the 14C data shows many similarities. Both cosmogenic isotopes are strongly correlated mutually and with solar activity. Finally, we find that a series of damped random walk models provides a good fit to the 10Be data with a fixed characteristic time scale of 1000 years, which is roughly consistent with the quasi-periods found by the Fourier and wavelet analyses.
Recurrence Quantification Analysis (RQA) can help to detect significant events and phase transitions of a dynamical system, but choosing a suitable set of parameters is crucial for the success. From recurrence plots different RQA variables can be obtained and analysed. Currently, most of the methods for RQA radius optimisation are focusing on a single RQA variable. In this work we are proposing two new methods for radius optimisation that look for an optimum in the higher dimensional space of the RQA variables, therefore synchronously optimising across several variables. We illustrate our approach using two case studies: a well known Lorenz dynamical system, and a time-series obtained from monitoring energy consumption of a small enterprise. Our case studies show that both methods result in plausible values and can be used to analyse energy data.
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