52157538
Temporal organization of magnetospheric fluctuations unveiled by recurrence patterns in the Dst index.
Magnetic storms constitute the most remarkable large-scale phenomena of nonlinear magnetospheric dynamics. Studying the dynamical organization of macroscopic variability in terms of geomagnetic activity index data by means of complexity measures provides a promising approach for identifying the underlying processes and associated time scales. Here, we apply a suite of characteristics from recurrence quantification analysis (RQA) and recurrence network analysis (RNA) in order to unveil some key nonlinear features of the hourly Disturbance storm-time (Dst) index during periods with magnetic storms and such of normal variability. Our results demonstrate that recurrence-based measures can serve as excellent tracers for changes in the dynamical complexity along non-stationary records of geomagnetic activity. In particular, trapping time (characterizing the typical length of "laminar phases" in the observed dynamics) and recurrence network transitivity (associated with the number of the system's effective dynamical degrees of freedom) allow for a very good discrimination between magnetic storm and quiescence phases. In general, some RQA and RNA characteristics distinguish between storm and non-storm times equally well or even better than other previously considered nonlinear characteristics like Hurst exponent or symbolic dynamics based entropy concepts. Our results point to future potentials of recurrence characteristics for unveiling temporal changes in the dynamical complexity of the magnetosphere.
122334280
The effects of geomagnetic disturbances on electrical systems at the earth's surface
Abstract Geomagnetic disturbances have affected electrical systems on the ground for over 150 years. The first effects were noted on the early telegraph in the 1840s and in this century magnetic storms have caused power system blackouts and phone system outages. Affected systems include all those that use electrical conductors: whether for transmission of power or signals or where the conducting properties are incidental to their use such as with pipelines and railway tracks. In power systems geomagnetically induced currents cause partial saturation of power transformers producing transformer heating and distortion of the ac waveform leading to misoperation of relays and other equipment. On pipelines, induced currents may contribute to corrosion but also present a problem with the electrical surveys of the pipe performed to monitor the corrosion prevention systems. Severity of these effects depends on disturbance size, proximity to the auroral zone, and the conductivity structure of the Earth. Also significant are system parameters such as the use of higher resistance coatings on pipelines and the linking of power systems into larger networks. In this paper we have attempted to catalogue all the published reports of geomagnetic effects on electrical systems and show their occurrence in the context of the solar cycle and geomagnetic activity variations for the years 1844 to 1996.
109030396
GIC observations and studies in the Hydro-Quebec power system
Abstract On March 13, 1989, at 7 h 45 UT, Hydro-Quebec experienced a complete black-out of its system due to a severe geomagnetic storm. Consequently, service was interrupted for many hours and overvoltages resulting from line openings cost 6.5 M$ in material damages alone among a total of 13.2 M$. In 1991, geomagnetically induced currents (GIC) produced some effects and damages on the Radisson–Sandy Pond HVDC link. On March 24, at 21 h 55 UT, GIC larger than 110 A were measured in one of two transformers in parallel (presumably, giving a total of 220 A) at Radisson substation which led to the loss of the HVDC link. The same thing happened on October 28, but this time with material damages to equipment. From these events, short-term studies led to the upgrading of operational processes, modifications of opening thresholds of Static Var Compensators and modifications of some filters at Radisson. Also an agreement was concluded with Geological Survey of Canada (GSC) for sending a warning alert to the Network Control Centre (CCR) before any anticipated severe geomagnetic storms. Among more long-term studies, in collaboration with GSC, we have installed 5 acquisition substations along a 250-km long copper telephone line in Abitibi, a site typical of Hydro-Quebec facilities, and from 1992 to 1994 measured ground voltages and magnetic fields every 10 s . The highest ground voltage measured at Louvicourt substation was ∼1.70 V/km for 20 s . Asymmetry measurement of line voltages, based on techniques developed at IREQ in the 1980s, have been upgraded, the number of installations has been increased (from 4 to 8) and functions like harmonic measurement have been added. Voltage asymmetries over a fixed threshold produce an alarm at the CCR, which reacts by taking security measures in network operation. During March 1989 and 1991 events, voltage asymmetry grew to 9.6% and 15.5%, respectively, at the Arnaud substation. A major change, for needs of network stability during short circuit or other contingencies, has been the installation of series compensation in 1996 into the Hydro-Quebec 735-kV network. Since capacitors block DC current, the observed asymmetry has remained about 20% of that observed before. So, now, we are confident that our network would survive the anticipated worst case GIC.
56345842
Space weather events in July 1982 and October 2003 and the effects of geomagnetically induced currents on Swedish technical systems
Abstract. In this paper, we analyse in detail two famous space weather events; a railway problem on 13–14 July 1982 and a power blackout on 30 October 2003. Both occurred in Sweden during very intensive space weather storms and each of them a few years after the sunspot maximum. This paper provides a description of the conditions on the Sun and in the solar wind leading to the two GIC events on the ground. By applying modelling techniques introduced and developed in our previous paper, we also calculate the horizontal geoelectric field at the Earth's surface in southern Sweden during the two storms as well as GIC flowing in the southern Swedish 400 kV power grid during the event in October 2003. The results from the calculations agree with all measured data available. In the July-1982 storm, the geomagnetic field variation, ΔBx, reached values up to ~2500 nT/min and the geoelectric field reached values in the order of several volts per kilometer. In the October-2003 storm, the geomagnetic field fluctuations were smaller. However, GIC of some hundreds of amperes flowed in the power grid during the October-2003 event. Technological issues related to the railway signalling in July 1982 and to the power network equipment in October 2003 are also discussed.
122168519
Solar wind drivers of geomagnetic storms over more than four solar cycles
Using a classification of near-Earth solar wind flows into corotating high-speed streams, slow interstream solar wind, and transients originating with coronal mass ejections at the Sun, we determine the drivers of geomagnetic storms of various sizes from 1964 to 2011 based on the Kp index, encompassing more than four solar cycles. We also briefly discuss storm occurrence rates since the beginning of Kp in 1932.
117317421
Nonlinear Dynamics in the Earth’s Magnetosphere
Observational evidence and numerical modeling demonstrate that substorms are a global, coherent set of processes within the magnetosphere and ionosphere. This knowledge supports the view that magnetospheric substorms are a configurational instability of the coupled global system. The magnetosphere progresses through a specific sequence of energy-loading and stress-developing states until the entire system suddenly reconfigures. The energy loading-unloading sequence is the basis of nonlinear dynamics models that have been successful in describing the essential behavior of substorms without invoking detailed treatments of the internal substorm instability mechanism. Recent results in data analysis and modeling show that powerful concepts in statistical physics and applied mathematics can be incorporated into space plasma physical research. A number of methods for modeling complex systems, data assimilation, system estimation, and predictive methods have been applied to the recent wealth of ionospheric and magnetospheric data. Nonlinear prediction schemes, for example, have greatly improved space weather forecasting and in most instances they remain more accurate and faster than physics-based models. From the standpoint of basic physical understanding, self-organized criticality recently has been used to describe scale-free avalanching phenomena observed in space plasma domains such as the plasma sheet and its low-altitude extension in the ionosphere. Self-organized criticality arises in the bursty transport of magnetic energy (flux) from the tail lobes, through the plasma sheet, and out of the mid-tail region where reconnection occurs. Multi-point measurement techniques and missions are being developed to determine the spatial and temporal development of the global phenomena that constitute energy dissipation within the magnetosphere.
140590921
Introduction to Space Weather
Adverse space weather is one of the principal threats to modern human technology. Solar coronal mass ejections, large solar flares, and high-speed solar wind streams often lead to sequences of damaging disturbances within the Earth’s magnetosphere, in the atmosphere, and even on the Earth’s surface. Powerful and long-lasting geomagnetic storms can develop following solar disturbances and enhancements of the highly relativistic electron populations throughout the outer terrestrial radiation zone can also result. High-energy protons and heavier ions arriving in near-earth space – or trapped in the magnetosphere and having clearest effect in the South Atlantic Anomaly (SAA) – can damage satellite solar power panels, confuse optical trackers, and deposit harmful charges into sensitive electronic components. Recent international space science programs have made a concerted effort to study activity on the Sun, the propagation of energy bursts from the Sun to near-Earth space, energy coupling into the magnetosphere, and its redistribution and deposition in the upper and middle atmosphere. Extreme solar, geomagnetic and solar wind conditions can be observed by a large array of international satellites and ground-based sensors. Many types of space weather-related problems have been identified in recent years. This chapter presents examples of space weather-induced anomalies and failures and discusses community efforts to propose technical and operational solutions to space weather problems now and in
121155063
Investigating dynamic coupling in geospace through the combined use of modeling, simulations and data analysis
Comprehensive understanding of the dynamics of the coupled solar wind-magnetosphere-ionosphere system is of utmost interest, both from the perspective of solar system astrophysics and geophysics research and from the perspective of space applications. The physical processes involved in the dynamical evolution of this complex coupled system are pertinent not only for the Sun-Earth connection, but also for major phenomena in other astrophysical systems. Furthermore, the conditions in geospace collectively termed space weather affect the ever increasing technological assets of mankind in space and therefore need to be understood, quantified and efficiently forecasted. The present collaborative paper communicates recent advances in geospace dynamic coupling research through modeling, simulations and data analysis and discusses future directions.
120363211
On the Earth’s magnetospheric dynamics: Nonequilibrium evolution and the fluctuation theorem
[1] The Earth’s magnetosphere evolves as an out-of-equilibrium system due to the continuous coupling with the solar wind and the Earth’s ionosphere. We test the validity of the symmetries implied in the Fluctuation Theorem for the magnetospheric dynamics by investigating the long-term evolution of the Earth’s magnetospheric ring current, as monitored by the geomagnetic Dst index. We find that the symmetries implied by the Fluctuation Theorem are all verified, thus providing a proof of the existence of a steady state far from equilibrium for the Earth’s magnetosphere. A possible link between the Dst index and the entropy production rate is also proposed and discussed.
38183550
Testing the SOC hypothesis for the magnetosphere
As noted by Chang, the hypothesis of self-organised criticality provides a theoretical framework in which the low dimensionality seen in magnetospheric indices can be combined with the scaling seen in their power spectra and with observed plasma bursty bulk flows. As such, it has considerable appeal, describing the aspects of the magnetospheric fuelling:storage:release cycle which are generic to slowly-driven, interaction-dominated, thresholded systems rather than unique to the magnetosphere. In consequence, several recent numerical “sandpile” algorithms have been used with a view to comparison with magnetospheric observables. However, demonstration of SOC in the magnetosphere will require further work in the definition of a set of observable properties which are the unique “fingerprint” of SOC. This is because, for example, a scale-free power spectrum admits several possible explanations other than SOC. A more subtle problem is important for both simulations and data analysis when dealing with multiscale and hence broad-band phenomena such as SOC. This is that finite length systems such as the magnetosphere or magnetotail will by definition give information over a small range of orders of magnitude, and so scaling will tend to be narrow band. Here we develop a simple framework in which previous descriptions of magnetospheric dynamics can be described and contrasted. We then review existing observations which are indicative of SOC, and ask if they are sufficient to demonstrate it unambiguously, and if not, what new observations need to be made?
39003598
Low-dimensional chaos in magnetospheric activity from AE time series
The magnetospheric response to the solar-wind input, as represented by the time-series measurements of the auroral electrojet (AE) index, has been examined using phase-space reconstruction techniques. The system was found to behave as a low-dimensional chaotic system with a fractal dimension of 3.6 and has Kolmogorov entropy less than 0.2/min. These indicate that the dynamics of the system can be adequately described by four independent variables, and that the corresponding intrinsic time scale is of the order of 5 min. The relevance of the results to magnetospheric modeling is discussed.
128627334
Properties of AE data and bicolored noise
A detailed analysis has been made of 13 periods of 20 days of the AE data. The average correlation dimension is found to be 3.4, and the calculated dimension is found to depend on the magnetospheric activity such that more active periods have smaller dimensions. This apparent correlation dimension does not, however, imply that the magnetospheric system behind the AE data is low-dimensional. On the contrary, bicolored noise is shown to share many properties with the AE data. The AE time series is also found to be self-affine such that the scaling exponent changes at the time scale of about 2 hours. This same time scale is suggested to appear as a spectral break at about 1/(5 hours) in the power spectrum of the AE data.
17722579
Analysis of the geomagnetic activity of the D st index and self-affine fractals using wavelet transforms
Abstract. The geomagnetic activity of the Dst index is analyzed using wavelet transforms and it is shown that the Dst index possesses properties associated with self-affine fractals. For example, the power spectral density obeys a power-law dependence on frequency, and therefore the Dst index can be viewed as a self-affine fractal dynamic process. In fact, the behaviour of the Dst index, with a Hurst exponent H≈0.5 (power-law exponent β≈2) at high frequency, is similar to that of Brownian motion. Therefore, the dynamical invariants of the Dst index may be described by a potential Brownian motion model. Characterization of the geomagnetic activity has been studied by analysing the geomagnetic field using a wavelet covariance technique. The wavelet covariance exponent provides a direct effective measure of the strength of persistence of the Dst index. One of the advantages of wavelet analysis is that many inherent problems encountered in Fourier transform methods, such as windowing and detrending, are not necessary.
13092835
Phase transition‐like behavior of magnetospheric substorms: Global MHD simulation results
[1] Using nonlinear dynamical techniques, we statistically investigate whether the simulated substorms from global magnetohydrodynamic (MHD) models have a combination of global and multiscale features, revealed in substorm dynamics by Sitnov et al. [2000] and featured the phase transition-like behavior. We simulate seven intervals of total duration of 280 hours from the data set used in the above works [Bargatze et al., 1985]. We analyze the input–output (vBs–pseudo AL index) system obtained from the global MHD model and compare the results to those inferred from the original set (vBs–observed AL index). The analysis of the coupled vBs–pseudo AL index system shows the first-order phase transition map, which is consistent with the map obtained for the vBs–observed AL index system. Although the comparison between observations and global MHD simulations for individual events may vary, the overall global transition pattern during the substorm cycle revealed by singular spectrum analysis (SSA) is statistically consistent between simulations and observations. The coupled vBs–pseudo AL index system also shows multiscale behavior (scale-invariant power law dependence) in SSA power spectrum. Besides, we find the critical exponent of the nonequilibrium transitions in the magnetosphere, which reflects the multiscale aspect of the substorm activity, different from power law frequency of autonomous systems. The exponent relates input and output parameters of the magnetosphere. We also discuss the limitations of the global MHD model in reproducing the multiscale behavior when compared to the real system.
56051757
Global and multiscale features of the magnetosphere: data-derived and global MHD modeling
The Earth's magnetosphere exhibits global features such as plasmoid formation and release, and multiscale behavior, e. g., turbulence, bursty bulk flows, current disruption, etc. It is essential to model these features properly in order to forecast them accurately and efficiently. The global behavior has clear dynamical behavior and can be predicted using dynamical models. The multiscale features on the other hand has a power law behavior and can not be modeled in the dynamical sense and can be described/modeled in terms of statistical properties. These properties of the magnetosphere are modeled using correlated data of the solar wind - magnetosphere coupling and global MHD simulations. The data-derived models yield forecasts of the global behavior from a mean-field model and the statistical limits of predictability from the multiscale features. The disturbances originating at the sun can lead to many hazardous effects in the geospace environment, and the development of predictive models of these is one of the key objectives of the International Living With a Star (ILWS) program. The chain of physical processes at the sun and their coupling to the solar wind, the magnetosphere, the ionosphere and the thermosphere, span a wide range of space and time scales and consequently it is at present a challenge to develop a single comprehensive model in which all these processes are directly represented. The present models, such as MHD (global, two-fluid and Hall), hybrid and particle-in- cell simulations each cover a part of the spectrum of processes and new multiscale simulation approaches are needed to cover the global and multiscale phenomena. The solar wind-magnetosphere coupling has been studied extensively using data from many space missions and modeling approaches. The coupling of the solar wind mass, momentum and energy to the magnetosphere is enhanced when the interplanetary magnetic field (IMF) turns southward, leading to geospace storms and substorms. The magnetosphere is a highly dynamic system under these conditions and its main component, the magnetospheric substorms, are disturbances with a typical time scale of an hour. When the IMF remains southward for an extended interval, the ring current grows under the influence of the solar wind variations, leading to geospace storms with typical time scales of days and are characterized by strong variations in the magnetic field on the ground. Along with the storms and substorms there are a number of processes, e. g., turbulence, bursty bulk flows, current disruption, etc., that contribute to the multiscale phenomena. The Earth's magnetosphere is a non-autonomous dynamical system, driven by the solar wind. Studies of the magnetospheric dynamics using models derived from the correlated data of the solar wind - magnetosphere system have enhanced our understanding of the complex behavior of the magnetosphere. The advantage of this approach is the ability to yield the dynamical behavior of the system, inherent in observational data, independent of modeling assumptions. There has been considerable progress in the modeling and forecasting of the solar wind-magnetosphere coupling as an input-output system using techniques of nonlinear dynamics and complexity (Sharma et al., 2005). These data-derived models are based on the correlated data of the input time series I(t) (usually the solar wind convective electric field VBz) and the output time series O(t) (the geomagnetic activity index AE or AL for substorms and the Dst index for storms).
291916
Modeling substorm dynamics of the magnetosphere: from self-organization and self-organized criticality to nonequilibrium phase transitions.
Earth's magnetosphere during substorms exhibits a number of characteristic features such as the signatures of low effective dimension, hysteresis, and power-law spectra of fluctuations on different scales. The largest substorm phenomena are in reasonable agreement with low-dimensional magnetospheric models and in particular those of inverse bifurcation. However, deviations from the low-dimensional picture are also quite considerable, making the nonequilibrium phase transition more appropriate as a dynamical analog of the substorm activity. On the other hand, the multiscale magnetospheric dynamics cannot be limited to the features of self-organized criticality (SOC), which is based on a class of mathematical analogs of sandpiles. Like real sandpiles, during substorms the magnetosphere demonstrates features, that are distinct from SOC and are closer to those of conventional phase transitions. While the multiscale substorm activity resembles second-order phase transitions, the largest substorm avalanches are shown to reveal the features of first-order nonequilibrium transitions including hysteresis phenomena and a global structure of the type of a temperature-pressure-density diagram. Moreover, this diagram allows one to find a critical exponent, that reflects the multiscale aspect of the substorm activity, different from the power-law frequency and scale spectra of autonomous systems, although quite consistent with second-order phase transitions. In contrast to SOC exponents, this exponent relates input and output parameters of the magnetosphere. Using an analogy to the dynamical Ising model in the mean-field approximation, we show the connection between the data-derived exponent of nonequilibrium transitions in the magnetosphere and the standard critical exponent beta of equilibrium second-order phase transitions.
16311018
From pre-storm activity to magnetic storms: A transition described in terms of fractal dynamics
Abstract. We show that distinct changes in scaling parameters of the Dst index time series occur as an intense magnetic storm approaches, revealing a gradual reduction in complexity. The remarkable acceleration of energy release – manifested in the increase in susceptibility – couples to the transition from anti-persistent (negative feedback) to persistent (positive feedback) behavior and indicates that the occurence of an intense magnetic storm is imminent. The main driver of the Dst index, the VBSouth electric field component, does not reveal a similar transition to persistency prior to the storm. This indicates that while the magnetosphere is mostly driven by the solar wind the critical feature of persistency in the magnetosphere is the result of a combination of solar wind and internal magnetospheric activity rather than solar wind variations alone. Our results suggest that the development of an intense magnetic storm can be studied in terms of "intermittent criticality" that is of a more general character than the classical self-organized criticality phenomena, implying the predictability of the magnetosphere.
116335329
Recurrence quantification analysis : theory and best practices
Preface.- Mathematical and Computational Foundations of Recurrence.- Estimating Kolmogorov Entropy from Recurrence Plots.-Identifying Coupling Directions by Recurrences.- Complex Network Analysis of Recurrences.- Time Distortions and Other Oddities.- Dynamic Coupling between Respiratry and Cardiovascular System.- Application of Recurrence Quantification to the Analysis of Brain Electrical Activity.- Otoacoustic Emmission in Hearing Research.- Vibration Analysis in Cutting Materials.- Dynamical Patterns in Seismology.- Long Time-Scale Recurrences in Ecology: Detecting Relationships between Climate Dynamics and Biodiversity along a Latitudinal Gradient.- Recurrence Quantification and Recurrence Network Analysis of Global Photosynthetic Activity.- Recurrence Analysis Applications to Short-Term Road Traffic.- Interpersonal Couplings in Human Interactions.
6023633
Recurrences determine the dynamics.
We show that under suitable assumptions, Poincare recurrences of a dynamical system determine its topology in phase space. Therefore, dynamical systems with the same recurrences are dynamically equivalent. This conclusion can be drawn from a theorem proved in this paper which states that the recurrence matrix determines the topology of closed sets. The theorem states that if a set of points M is mapped onto another set N, such that two points in N are closer than some prescribed fixed distance if and only if the corresponding points in M are closer than some, in general different, prescribed fixed distance, then both sets are homeomorphic, i.e., identical up to a continuous change in the coordinate system. The theorem justifies a range of methods in nonlinear dynamics which are based on recurrence properties.
12143274
Recurrence-based time series analysis by means of complex network methods
Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related with the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches.
129650167
Investigating dynamical complexity in the magnetosphere using various entropy measures
[1] The complex system of the Earth's magnetosphere corresponds to an open spatially extended nonequilibrium (input-output) dynamical system. The nonextensive Tsallis entropy has been recently introduced as an appropriate information measure to investigate dynamical complexity in the magnetosphere. The method has been employed for analyzing Dst time series and gave promising results, detecting the complexity dissimilarity among different physiological and pathological magnetospheric states (i.e., prestorm activity and intense magnetic storms, respectively). This paper explores the applicability and effectiveness of a variety of computable entropy measures (e.g., block entropy, Kolmogorov entropy, T complexity, and approximate entropy) to the investigation of dynamical complexity in the magnetosphere. We show that as the magnetic storm approaches there is clear evidence of significant lower complexity in the magnetosphere. The observed higher degree of organization of the system agrees with that inferred previously, from an independent linear fractal spectral analysis based on wavelet transforms. This convergence between nonlinear and linear analyses provides a more reliable detection of the transition from the quiet time to the storm time magnetosphere, thus showing evidence that the occurrence of an intense magnetic storm is imminent. More precisely, we claim that our results suggest an important principle: significant complexity decrease and accession of persistency in Dst time series can be confirmed as the magnetic storm approaches, which can be used as diagnostic tools for the magnetospheric injury (global instability). Overall, approximate entropy and Tsallis entropy yield superior results for detecting dynamical complexity changes in the magnetosphere in comparison to the other entropy measures presented herein. Ultimately, the analysis tools developed in the course of this study for the treatment of Dst index can provide convenience for space weather applications.
16932984
Recurrence quantification analysis as a tool for nonlinear exploration of nonstationary cardiac signals.
The complexity, nonlinearity and nonstationarity of the cardiovascular system typically defy comprehensive and deterministic mathematical modeling, except from a statistical perspective. Living systems are governed by numerous, continuously changing, interacting variables in the presence of noise. Cardiovascular signals can be shown to be discontinuous alternations between deterministic trajectories and stochastic pauses (terminal dynamics). One promising approach for assessing such nondeterministic complexity is recurrence quantification analysis (RQA). As reviewed in this paper, strategies implementing quantification of recurrences have been successful in diagnosing changes in nonstationary cardiac signals not easily detected by traditional methods. It is concluded that recurrence quantification analysis is a powerful discriminatory tool which, when properly applied to cardiac signals, can provide objectivity regarding the degree of determinism characterizing the system, state changes, as well as degrees of complexity and/or randomness.
1923528
Brain signal analysis based on recurrences
The EEG is one of the most commonly used tools in brain research. Though of high relevance in research, the data obtained is very noisy and nonstationary. In the present article we investigate the applicability of a nonlinear data analysis method, the recurrence quantification analysis (RQA), to such data. The method solely rests on the natural property of recurrence which is a phenomenon inherent to complex systems, such as the brain. We show that this method is indeed suitable for the analysis of EEG data and that it might improve contemporary EEG analysis.
17404444
Identification of dynamical transitions in marine palaeoclimate records by recurrence network analysis
The analysis of palaeoclimate time series is usually affected by severe methodological problems, resulting primarily from non-equidistant sampling and uncertain age models. As an alternative to existing methods of time series analysis, in this paper we argue that the statistical properties of recurrence networks – a recently developed approach – are promising candidates for characterising the system's nonlinear dynamics and quantifying structural changes in its reconstructed phase space as time evolves. In a first order approximation, the results of recurrence network analysis are invariant to changes in the age model and are not directly affected by non-equidistant sampling of the data. Specifically, we investigate the behaviour of recurrence network measures for both paradigmatic model systems with non-stationary parameters and four marine records of long-term palaeoclimate variations. We show that the obtained results are qualitatively robust under changes of the relevant parameters of our method, including detrending, size of the running window used for analysis, and embedding delay. We demonstrate that recurrence network analysis is able to detect relevant regime shifts in synthetic data as well as in problematic geoscientific time series. This suggests its application as a general exploratory tool of time series analysis complementing existing methods.
17170544
Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution
Potential paleoclimatic driving mechanisms acting on human evolution present an open problem of cross-disciplinary scientific interest. The analysis of paleoclimate archives encoding the environmental variability in East Africa during the past 5 Ma has triggered an ongoing debate about possible candidate processes and evolutionary mechanisms. In this work, we apply a nonlinear statistical technique, recurrence network analysis, to three distinct marine records of terrigenous dust flux. Our method enables us to identify three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Middle Pliocene (3.35–3.15 Ma B.P.), (ii) Early Pleistocene (2.25–1.6 Ma B.P.), and (iii) Middle Pleistocene (1.1–0.7 Ma B.P.). A deeper examination of these transition periods reveals potential climatic drivers, including (i) large-scale changes in ocean currents due to a spatial shift of the Indonesian throughflow in combination with an intensification of Northern Hemisphere glaciation, (ii) a global reorganization of the atmospheric Walker circulation induced in the tropical Pacific and Indian Ocean, and (iii) shifts in the dominating temporal variability pattern of glacial activity during the Middle Pleistocene, respectively. A reexamination of the available fossil record demonstrates statistically significant coincidences between the detected transition periods and major steps in hominin evolution. This result suggests that the observed shifts between more regular and more erratic environmental variability may have acted as a trigger for rapid change in the development of humankind in Africa.
51822852
Correlation-based characterisation of time-varying dynamical complexity in the Earth's magnetosphere
Abstract. The dynamical behaviour of the magnetosphere is known to be a sensitive indicator for the response of the system to solar wind coupling. Since the solar activity commonly displays very interesting non-stationary and multi-scale dynamics, the magnetospheric response also exhibits a high degree of dynamical complexity associated with fundamentally different characteristics during periods of quiescence and magnetic storms. The resulting temporal complexity profile has been explored using several approaches from applied statistics, dynamical systems theory and statistical mechanics. Here, we propose an alternative way of looking at time-varying dynamical complexity of nonlinear geophysical time series utilising subtle but significant changes in the linear autocorrelation structure of the recorded data. Our approach is demonstrated to sensitively trace the dynamic signatures associated with intense magnetic storms, and to display reasonable skills in distinguishing between quiescence and storm periods. The potentials and methodological limitations of this new viewpoint are discussed in some detail.
12896555
Extracting qualitative dynamics from experimental data
Abstract We consider the notion of qualitative information and the practicalities of extracting it from experimental data. Our approach, based on a theorem of Takens, draws on ideas from the generalized theory of information known as singular system analysis due to Bertero, Pike and co-workers. We illustrate our technique with numerical data from the chaotic regime of the Lorenz model.
16503609
Recurrence Plots of Dynamical Systems
A new graphical tool for measuring the time constancy of dynamical systems is presented and illustrated with typical examples.
122890777
Embeddings and delays as derived from quantification of recurrence plots
Abstract Recurrence plots have been advocated as a useful diagnostic tool for the assessment of dynamical time series. We extend the usefulness of this tool by quantifying certain features of these plots which may be helpful in determining embeddings and delays.
23854540
Dynamical assessment of physiological systems and states using recurrence plot strategies.
Physiological systems are best characterized as complex dynamical processes that are continuously subjected to and updated by nonlinear feedforward and feedback inputs. System outputs usually exhibit wide varieties of behaviors due to dynamical interactions between system components, external noise perturbations, and physiological state changes. Complicated interactions occur at a variety of hierarchial levels and involve a number of interacting variables, many of which are unavailable for experimental measurement. In this paper we illustrate how recurrence plots can take single physiological measurements, project them into multidimensional space by embedding procedures, and identify time correlations (recurrences) that are not apparent in the one-dimensional time series. We extend the original description of recurrence plots by computing an array of specific recurrence variables that quantify the deterministic structure and complexity of the plot. We then demonstrate how physiological states can be assessed by making repeated recurrence plot calculations within a window sliding down any physiological dynamic. Unlike other predominant time series techniques, recurrence plot analyses are not limited by data stationarity and size constraints. Pertinent physiological examples from respiratory and skeletal motor systems illustrate the utility of recurrence plots in the diagnosis of nonlinear systems. The methodology is fully applicable to any rhythmical system, whether it be mechanical, electrical, neural, hormonal, chemical, or even spacial.
14803032
Recurrence-plot-based measures of complexity and their application to heart-rate-variability data.
The knowledge of transitions between regular, laminar or chaotic behaviors is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods that, however, require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart-rate-variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e., chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our measures to the heart-rate-variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias.
17697017
Confidence bounds of recurrence-based complexity measures
In the recent past, recurrence quantification analysis (RQA) has gained an increasing interest in various research areas. The complexity measures the RQA provides have been useful in describing and analysing a broad range of data. It is known to be rather robust to noise and nonstationarities. Yet, one key question in empirical research concerns the confidence bounds of measured data. In the present Letter we suggest a method for estimating the confidence bounds of recurrence-based complexity measures. We study the applicability of the suggested method with model and real-life data.
16292266
Complex network from pseudoperiodic time series: topology versus dynamics.
We construct complex networks from pseudoperiodic time series, with each cycle represented by a single node in the network. We investigate the statistical properties of these networks for various time series and find that time series with different dynamics exhibit distinct topological structures. Specifically, noisy periodic signals correspond to random networks, and chaotic time series generate networks that exhibit small world and scale free features. We show that this distinction in topological structure results from the hierarchy of unstable periodic orbits embedded in the chaotic attractor. Standard measures of structure in complex networks can therefore be applied to distinguish different dynamic regimes in time series. Application to human electrocardiograms shows that such statistical properties are able to differentiate between the sinus rhythm cardiograms of healthy volunteers and those of coronary care patients.
25436777
Superfamily phenomena and motifs of networks induced from time series
We introduce a transformation from time series to complex networks and then study the relative frequency of different subgraphs within that network. The distribution of subgraphs can be used to distinguish between and to characterize different types of continuous dynamics: periodic, chaotic, and periodic with noise. Moreover, although the general types of dynamics generate networks belonging to the same superfamily of networks, specific dynamical systems generate characteristic dynamics. When applied to discrete (map-like) data this technique distinguishes chaotic maps, hyperchaotic maps, and noise data.
7761398
Complex network approach for recurrence analysis of time series
We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. By using the logistic map, we illustrate the potential of these complex network measures for the detection of dynamical transitions. Finally, we apply the proposed approach to a marine palaeo-climate record and identify the subtle changes to the climate regime.
10331346
Recurrence networks—a novel paradigm for nonlinear time series analysis
This paper presents a new approach for analysing the structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network, which links different points in time if the considered states are closely neighboured in phase space. In comparison with similar network-based techniques the new approach has important conceptual advantages, and can be considered as a unifying framework for transforming time series into complex networks that also includes other existing methods as special cases. It has been demonstrated here that there are fundamental relationships between many topological properties of recurrence networks and different nontrivial statistical properties of the phase space density of the underlying dynamical system. Hence, this novel interpretation of the recurrence matrix yields new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the recurrence network) related to the dynamical complexity of a time series, most of which are not yet provided by other existing methods of nonlinear time series analysis.
9805280
Testing time series irreversibility using complex network methods
The absence of time-reversal symmetry is a fundamental property of many nonlinear time series. Here, we propose a new set of statistical tests for time series irreversibility based on standard and horizontal visibility graphs. Specifically, we statistically compare the distributions of time-directed variants of the common complex network measures degree and local clustering coefficient. Our approach does not involve surrogate data and is applicable to relatively short time series. We demonstrate its performance for paradigmatic model systems with known time-reversal properties as well as for picking up signatures of nonlinearity in neuro-physiological data.
55711560
Multifractal analysis of solar flare indices and their horizontal visibility graphs
Abstract. The multifractal properties of the daily solar X-ray brightness, X l and X s , during the period from 1 January 1986 to 31 December 2007 which includes two solar cycles are examined using the universal multifractal approach and multifractal detrended fluctuation analysis. Then we convert these time series into networks using the horizontal visibility graph technique. Multifractal analysis of the resulting networks is performed using an algorithm proposed by us. The results from the multifractal analysis show that multifractality exists in both raw daily time series of X-ray brightness and their horizontal visibility graphs. It is also found that the empirical K ( q ) curves of raw time series can be fitted by the universal multifractal model. The numerical results on the raw data show that the Solar Cycle 23 is weaker than the Solar Cycle 22 in multifractality. The values of h (2) from multifractal detrended fluctuation analysis for these time series indicate that they are stationary and persistent, and the correlations in the time series of Solar Cycle 23 are stronger than those for Solar Cycle 22. Furthermore, the multifractal scaling for the networks of the time series can reflect some properties which cannot be picked up by using the same analysis on the original time series. This suggests a potentially useful method to explore geophysical data.
2256176
Long-term changes in the north-south asymmetry of solar activity: a nonlinear dynamics characterization using visibility graphs
Abstract. Solar activity is characterized by complex dynamics superimposed onto an almost periodic, approximately 11-year cycle. One of its main features is the presence of a marked, time-varying hemispheric asymmetry, the deeper reasons for which have not yet been completely uncovered. Traditionally, this asymmetry has been studied by considering amplitude and phase differences. Here, we use visibility graphs, a novel tool of nonlinear time series analysis, to obtain complementary information on hemispheric asymmetries in dynamical properties. Our analysis provides deep insights into the potential and limitations of this method, revealing a complex interplay between factors relating to statistical and dynamical properties, i.e., effects due to the probability distribution and the regularity of observed fluctuations. We demonstrate that temporal changes in the hemispheric predominance of the graph properties lag those directly associated with the total hemispheric sunspot areas. Our findings open a new dynamical perspective on studying the north–south sunspot asymmetry, which is to be further explored in future work.
18979395
The geometry of chaotic dynamics — a complex network perspective
Abstract
Recently, several complex network approaches to time series analysis have been developed
and applied to study a wide range of model systems as well as real-world data, e.g.,
geophysical or financial time series. Among these techniques, recurrence-based concepts
and prominently ε-recurrence networks, most faithfully represent the
geometrical fine structure of the attractors underlying chaotic (and less interestingly
non-chaotic) time series. In this paper we demonstrate that the well known graph
theoretical properties local clustering coefficient and global (network) transitivity can
meaningfully be exploited to define two new local and two new global measures of dimension
in phase space: local upper and lower clustering dimension as well as global upper and
lower transitivity dimension. Rigorous analytical as well as numerical results for
self-similar sets and simple chaotic model systems suggest that these measures are
well-behaved in most non-pathological situations and that they can be estimated reasonably
well using ε-recurrence networks constructed from relatively short time
series. Moreover, we study the relationship between clustering and transitivity dimensions
on the one hand, and traditional measures like pointwise dimension or local Lyapunov
dimension on the other hand. We also provide further evidence that the local clustering
coefficients, or equivalently the local clustering dimensions, are useful for identifying
unstable periodic orbits and other dynamically invariant objects from time series. Our
results demonstrate that ε-recurrence networks exhibit an important link
between dynamical systems and graph theory.

16158901
Analytical framework for recurrence network analysis of time series.
Recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems. While there are already many successful applications ranging from medicine to paleoclimatology, a solid theoretical foundation of the method has still been missing so far. Here, we interpret an ɛ-recurrence network as a discrete subnetwork of a "continuous" graph with uncountably many vertices and edges corresponding to the system's attractor. This step allows us to show that various statistical measures commonly used in complex network analysis can be seen as discrete estimators of newly defined continuous measures of certain complex geometric properties of the attractor on the scale given by ɛ. In particular, we introduce local measures such as the ɛ-clustering coefficient, mesoscopic measures such as ɛ-motif density, path-based measures such as ɛ-betweennesses, and global measures such as ɛ-efficiency. This new analytical basis for the so far heuristically motivated network measures also provides an objective criterion for the choice of ɛ via a percolation threshold, and it shows that estimation can be improved by so-called node splitting invariant versions of the measures. We finally illustrate the framework for a number of archetypical chaotic attractors such as those of the Bernoulli and logistic maps, periodic and two-dimensional quasiperiodic motions, and for hyperballs and hypercubes by deriving analytical expressions for the novel measures and comparing them with data from numerical experiments. More generally, the theoretical framework put forward in this work describes random geometric graphs and other networks with spatial constraints, which appear frequently in disciplines ranging from biology to climate science.
115949562
Identifying shrimps in continuous dynamical systems using recurrence-based methods
In this work, we demonstrate that nonlinear measures based on recurrence plots obtained from individual trajectories provide a practicable alternative for automatically distinguishing periodic and chaotic dynamics and, hence, numerically detecting shrimps. Traditional diagonal line-based measures of recurrence quantification analysis as well as measures from complex network theory are shown to allow an excellent classification of periodic and chaotic behavior in parameter space. Average path length and clustering coefficient of the resulting recurrence networks are found to be particularly powerful discriminatory statistics for the identification of shrimps. Our results are illustrated in detail for the Roessler system. Implications for detecting bifurcations between regular and chaotic dynamics in other models of geophysical phenomena (such as the Lorenz-84 system) are discussed.
13881500
Non-linear regime shifts in Holocene Asian monsoon variability: potential impacts on cultural change and migratory patterns
Abstract. The Asian monsoon system is an important tipping element in Earth's climate with a large impact on human societies in the past and present. In light of the potentially severe impacts of present and future anthropogenic climate change on Asian hydrology, it is vital to understand the forcing mechanisms of past climatic regime shifts in the Asian monsoon domain. Here we use novel recurrence network analysis techniques for detecting episodes with pronounced non-linear changes in Holocene Asian monsoon dynamics recorded in speleothems from caves distributed throughout the major branches of the Asian monsoon system. A newly developed multi-proxy methodology explicitly considers dating uncertainties with the COPRA (COnstructing Proxy Records from Age models) approach and allows for detection of continental-scale regime shifts in the complexity of monsoon dynamics. Several epochs are characterised by non-linear regime shifts in Asian monsoon variability, including the periods around 8.5–7.9, 5.7–5.0, 4.1–3.7, and 3.0–2.4 ka BP. The timing of these regime shifts is consistent with known episodes of Holocene rapid climate change (RCC) and high-latitude Bond events. Additionally, we observe a previously rarely reported non-linear regime shift around 7.3 ka BP, a timing that matches the typical 1.0–1.5 ky return intervals of Bond events. A detailed review of previously suggested links between Holocene climatic changes in the Asian monsoon domain and the archaeological record indicates that, in addition to previously considered longer-term changes in mean monsoon intensity and other climatic parameters, regime shifts in monsoon complexity might have played an important role as drivers of migration, pronounced cultural changes, and the collapse of ancient human societies.
119520707
Spurious Structures in Recurrence Plots Induced by Embedding
In this paper we show that delay embedding produces spurious structures in a recurrence plot (RP) that are not present in the real attractor. We analyze typical sets of simulated data, such as white noise and data from the chaotic Rössler system to show the relevance of this effect.In the second part of the paper we show that the second order Rényi entropy and the correlation dimension are dynamical invariants that can be estimated from Recurrence Plots with arbitrary embedding dimension and delay.
57270764
Statistics A Guide To The Use Of Statistical Methods In The Physical Sciences
Thank you very much for downloading statistics a guide to the use of statistical methods in the physical sciences. Maybe you have knowledge that, people have search numerous times for their favorite readings like this statistics a guide to the use of statistical methods in the physical sciences, but end up in infectious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they are facing with some harmful bugs inside their desktop computer.
53662922
Individual Comparisons by Ranking Methods
The comparison of two treatments generally falls into one of the following two categories: (a) we may have a number of replications for each of the two treatments, which are unpaired, or (b) we may have a number of paired comparisons leading to a series of differences, some of which may be positive and some negative. The appropriate methods for testing the significance of the differences of the means in these two cases are described in most of the textbooks on statistical methods.
124992873
Detection of Dynamical Complexity Changes in Dst Time Series Using Entropy Concepts and Rescaled Range Analysis
Using an array of diagnostic tools including entropy concepts and rescaled range analysis, we establish that the Dst index time series exhibits long-range correlations, and that the underlying stochastic process can be modeled as fractional Brownian motion. We show the emergence of two distinct patterns in the geomagnetic variability of the terrestrial magnetosphere: (1) a pattern associated with intense magnetic storms, which is characterized by a higher degree of organization (i.e., lower complexity or higher predictability for the system) and persistent behavior, and (2) a pattern associated with normal periods, which is characterized by a lower degree of organization (i.e., higher complexity or lower predictability for the system) and anti-persistent behavior.
35670355
Approximate entropy as a measure of system complexity.
Techniques to determine changing system complexity from data are evaluated. Convergence of a frequently used correlation dimension algorithm to a finite value does not necessarily imply an underlying deterministic model or chaos. Analysis of a recently developed family of formulas and statistics, approximate entropy (ApEn), suggests that ApEn can classify complex systems, given at least 1000 data values in diverse settings that include both deterministic chaotic and stochastic processes. The capability to discern changing complexity from such a relatively small amount of data holds promise for applications of ApEn in a variety of contexts.
2389971
Physiological time-series analysis using approximate entropy and sample entropy.
Entropy, as it relates to dynamical systems, is the rate of information production. Methods for estimation of the entropy of a system represented by a time series are not, however, well suited to analysis of the short and noisy data sets encountered in cardiovascular and other biological studies. Pincus introduced approximate entropy (ApEn), a set of measures of system complexity closely related to entropy, which is easily applied to clinical cardiovascular and other time series. ApEn statistics, however, lead to inconsistent results. We have developed a new and related complexity measure, sample entropy (SampEn), and have compared ApEn and SampEn by using them to analyze sets of random numbers with known probabilistic character. We have also evaluated cross-ApEn and cross-SampEn, which use cardiovascular data sets to measure the similarity of two distinct time series. SampEn agreed with theory much more closely than ApEn over a broad range of conditions. The improved accuracy of SampEn statistics should make them useful in the study of experimental clinical cardiovascular and other biological time series.
7073701
Characterization of Surface EMG Signal Based on Fuzzy Entropy
Fuzzy entropy (FuzzyEn), a new measure of time series regularity, was proposed and applied to the characterization of surface electromyography (EMG) signals. Similar to the two existing related measures ApEn and SampEn, FuzzyEn is the negative natural logarithm of the conditional probability that two vectors similar for m points remain similar for the next m+1 points. Importing the concept of fuzzy sets, vectors' similarity is fuzzily defined in FuzzyEn on the basis of exponential function and their shapes. Besides possessing the good properties of SampEn superior to ApEn, FuzzyEn also succeeds in giving the entropy definition in the case of small parameters. Its performance on characterizing surface EMG signals, as well as independent, identically distributed (i.i.d.) random numbers and periodical sinusoidal signals, shows that FuzzyEn can more efficiently measure the regularity of time series. The method introduced here can also be applied to other noisy physiological signals with relatively short datasets.
55965026
Universality in solar flare, magnetic storm and earthquake dynamics using Tsallis statistical mechanics
The universal character of the dynamics of various extreme phenomena is an outstanding scientific challenge. We show that X-ray flux and Dst time series during powerful solar flares and intense magnetic storms, respectively, obey a nonextensive energy distribution function for earthquake dynamics with similar values for the Tsallis entropic index q. Thus, evidence for universality in solar flares, magnetic storms and earthquakes arise naturally in the framework of Tsallis statistical mechanics. The observed similarity suggests a common approach to the interpretation of these diverse phenomena in terms of driving physical mechanisms that have the same character.
14499846
Distinguishing dynamics using recurrence-time statistics.
The probability densities of the mean recurrence time, which is the average time needed for a system to recur to a previously visited neighborhood, are investigated in various dynamical regimes and are found to be in agreement with those of the finite-time Lyapunov exponents. The important advantages of the former ones are that they are easy to estimate and that comparable short time series are sufficient. Asymmetric distributions with exponential tails are observed for intermittency and crisis-induced intermittency, while for typical chaos, the distribution has a Gaussian shape. Further, the shape of the distribution distinguishes intermittent strange nonchaotic attractors from those appearing through fractalization and tori collision mechanisms. Furthermore, statistics performed on the peaks in the frequency distribution of recurrence times unveil scaling behavior in agreement with that obtained from the spectral distribution function defined as the number of peaks in the Fourier spectrum greater than a predefined value. The results of the present recurrence statistics are of relevance in classifying different dynamics and providing important insights into the dynamics of a system when only one realization of this system is available. The practical use of this approach for experimental data is shown on experimental electrochemical time series.