scholarly journals Comparison of chaotic aspects of magnetosphere under various physical conditions using AE index time series

2008 ◽  
Vol 26 (4) ◽  
pp. 941-953 ◽  
Author(s):  
K. Unnikrishnan
Keyword(s):  
Time Series ◽  
Solar Activity ◽  
Lyapunov Exponent ◽  
Degrees Of Freedom ◽  
High Solar Activity ◽  
Nonlinear Prediction ◽  
Physical Conditions ◽  
Ae Index ◽  
Significant Difference ◽  
Index Time Series

Abstract. The deterministic chaotic behaviour of magnetosphere was analyzed, using AE index time series. The significant chaotic quantifiers like, Lyapunov exponent, spatio-temporal entropy and nonlinear prediction error for AE index time series under various physical conditions were estimated and compared. During high solar activity (1991), the values of Lyapunov exponent for AE index time series representing quiet conditions (yearly mean = 0.5±0.1 min−1) have no significant difference from those values for corresponding storm conditions (yearly mean = 0.5±0.17 min−1). This implies that, for the cases considered here, geomagnetic storms may not be an additional source to increase or decrease the deterministic chaotic aspects of magnetosphere, especially during high solar activity. During solar minimum period (1994), the seasonal mean value of Lyapunov exponent for AE index time series belong to quiet periods in winter (0.7±0.11 min−1) is higher compared to corresponding value of storm periods in winter (0.36±0.09 min−1). This may be due to the fact that, stochastic part, which is Dst dependent could be more prominent during storms, thereby increasing fluctuations/stochasticity and reducing determinism in AE index time series during storms. It is observed that, during low solar active period (1994), the seasonal mean value of entropy for time series representing storm periods of equinox is greater than that for quiet periods. However, significant difference is not observed between storm and quiet time values of entropy during high solar activity (1991), which is also true for nonlinear prediction error for both low and high solar activities. In the case of both high and low solar activities, the higher standard deviations of yearly mean Lyapunov exponent values for AE index time series for storm periods compared to those for quiet periods might be due to the strong interplay between stochasticity and determinism during storms. It is inferred that, the external driving forces, mainly due to solar wind, make the solar-magnetosphere-ionosphere coupling more complex, which generates many active degrees of freedom with various levels of coupling among them, under various physical conditions. Hence, the superposition of a large number of active degrees of freedom can modify the stability/instability conditions of magnetosphere.

scholarly journals Nonlinear analysis of magnetospheric data Part I. Geometric characteristics of the AE index time series and comparison with nonlinear surrogate data

1999 ◽  
Vol 6 (1) ◽  
pp. 51-65 ◽  
Author(s):  
G. P. Pavlos ◽  
M. A. Athanasiu ◽  
D. Kugiumtzis ◽  
N. Hatzigeorgiu ◽  
A. G. Rigas ◽  
...  
Keyword(s):  
Time Series ◽  
State Space ◽  
Null Hypothesis ◽  
Surrogate Data ◽  
Statistical Testing ◽  
Geometrical Parameters ◽  
Geometric Characteristics ◽  
Geometrical Characteristics ◽  
Ae Index ◽  
Index Time Series

Abstract. A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper) and dynamical characteristics (Part II, which is the work a separate paper), and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index) signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.

scholarly journals New possibilities of the PCA-Seq method in the analysis of time series (on the example of solar activity)

2021 ◽  
Vol 2099 (1) ◽  
pp. 012034
Author(s):  
V M Efimov ◽  
K V Efimov ◽  
D A Polunin ◽  
V Y Kovaleva
Keyword(s):  
Time Series ◽  
Solar Activity ◽  
Maunder Minimum ◽  
High Solar Activity ◽  
External Influence ◽  
Average Period ◽  
Time Axis ◽  
Constant Amplitude ◽  
The Impact ◽  
Analysis Of Time Series

Abstract When analyzing a 1D time series, it is traditional to represent it as the sum of the trend, cyclical components and noise. The trend is seen as an external influence. However, the impact can be not only additive, but also multiplicative. In this case, not only the level changes, but also the amplitude of the cyclic components. In the PCA-Seq method, a generalization of SSA, it is possible to pre-standardize fragments of a time series to solve this problem. The algorithm is applied to the Anderson series – a sign alternating version of the well-known Wolf series, reflecting the 22-year Hale cycle. The existence of this cycle is not disputed at high solar activity, but there are doubts about the constancy of its period at this time, as well as its existence during the epoch of low solar activity. The processing of the series by the PCA-Seq method revealed clear oscillations fluctuations of almost constant amplitude with an average period of 21.9 years, and it was found that the correlation of these oscillations with the time axis for 300 years does not differ significantly from zero. This confirms the hypothesis of the existence of 22-year oscillations in solar activity even at its minima, like the Maunder minimum.

scholarly journals Statistical issues about solar–climate relations

2010 ◽  
Vol 6 (5) ◽  
pp. 565-573 ◽  
Author(s):  
P. Yiou ◽  
E. Bard ◽  
P. Dandin ◽  
B. Legras ◽  
P. Naveau ◽  
...  
Keyword(s):  
Time Series ◽  
Solar Activity ◽  
Geomagnetic Field ◽  
Degrees Of Freedom ◽  
Statistical Significance ◽  
Data Sets ◽  
Statistical Issues ◽  
The Relationship ◽  
Temperature Time ◽  
Field Variability

Abstract. The relationship between solar activity and temperature variation is a frequently discussed issue in climatology. This relationships is usually hypothesized on the basis of statistical analyses of temperature time series and time series related to solar activity. Recent studies (Le Mouël et al., 2008, 2009; Courtillot et al., 2010) focus on the variabilities of temperature and solar activity records to identify their relationships. We discuss the meaning of such analyses and propose a general framework to test the statistical significance for these variability-based analyses. This approach is illustrated using European temperature data sets and geomagnetic field variations. We show that tests for significant correlation between observed temperature variability and geomagnetic field variability is hindered by a low number of degrees of freedom introduced by excessively smoothing the variability-based statistics.

scholarly journals Assessing the Performance of EUHFORIA Modeling the Background Solar Wind

Solar Physics ◽  
2019 ◽  
Vol 294 (12) ◽  
Author(s):  
Jürgen Hinterreiter ◽  
Jasmina Magdalenic ◽  
Manuela Temmer ◽  
Christine Verbeke ◽  
Immanuel Christopher Jebaraj ◽  
...  
Keyword(s):  
Time Series ◽  
Solar Wind ◽  
Solar Activity ◽  
Coronal Holes ◽  
High Solar Activity ◽  
Time Interval ◽  
Input Parameters ◽  
First Results ◽  
Combined Time Series

AbstractIn order to address the growing need for more accurate space-weather predictions, a new model named (EUropean Heliospheric FORecasting Information Asset) was recently developed. We present the first results of the performance assessment for the solar-wind modeling with and identify possible limitations of its present setup. Using the basic 1.0.4 model setup with the default input parameters, we modeled background solar wind (no coronal mass ejections) and compared the obtained results with Advanced Composition Explorer (ACE) in-situ measurements. For the purposes of statistical study we developed a technique of combining daily runs into continuous time series. The combined time series were derived for the years 2008 (low solar activity) and 2012 (high solar activity), from which in-situ speed and density profiles were extracted. We find for the low-activity phase a better match between model results and observations compared to the high-activity time interval considered. The quality of the modeled solar-wind parameters is found to be rather variable. Therefore, to better understand the results obtained we also qualitatively inspected characteristics of coronal holes, i.e. the sources of the studied fast streams. We discuss how different characteristics of the coronal holes and input parameters to influence the modeled fast solar wind, and suggest possibilities for the improvement of the model.

scholarly journals SVD analysis of the magnetospheric AE index time series and comparison with low-dimensional chaotic dynamics

2001 ◽  
Vol 8 (1/2) ◽  
pp. 95-125 ◽  
Author(s):  
M. A. Athanasiu ◽  
G. P. Pavlos
Keyword(s):  
Time Series ◽  
Colored Noise ◽  
External Noise ◽  
Original Time Series ◽  
Svd Analysis ◽  
Ae Index ◽  
Low Dimensional ◽  
Original Time ◽  
Value Decomposition ◽  
Index Time Series

Abstract. The singular value decomposition (SVD) analysis is used at different stages in this paper in order to extract useful information concerning the underlying dynamics of the magnetospheric AE index. As a frame of reference we use the dynamics of the Lorenz system perturbed by external noise, white or colored. One of the critical results is that the colored noise can be differentiated from the white noise when we study their perturbation upon the eigenvalue spectrum of the trajectory matrix, the SVD reconstructed components of the original time series and other characteristics. This result is used in order to conclude the existence of strong component of colored noise included in the magnetospheric AE index time series. Moreover, the study of the SVD reconstructed components of the original time series can confirm the low-dimensionality of a dynamical system strongly perturbed by external colored noise. Finally, the results of this study strengthen the hypothesis of the magnetospheric chaos.

scholarly journals Chaos and magnetospheric dynamics

1994 ◽  
Vol 1 (2/3) ◽  
pp. 124-135 ◽  
Author(s):  
G. P. Pavlos ◽  
D. Diamandidis ◽  
A. Adamopoulos ◽  
A. G. Rigas ◽  
I. A. Daglis ◽  
...  
Keyword(s):  
Time Series ◽  
Chaotic Dynamics ◽  
Electric Circuit ◽  
Dynamical Chaos ◽  
Ae Index ◽  
Reconstructed Phase Space ◽  
Magnetospheric Dynamics ◽  
Low Dimensional ◽  
Value Decomposition ◽  
Index Time Series

Abstract. Our intention in this work is to show, by using two different methods, that magnetospheric dynamics reveal low dimensional chaos. In the first method we extend the chaotic analysis for the AE index time series by including singular value decomposition (SVD) analysis in combination with Theiler's test in order to discriminate dynamical chaos from self-affinity or "crinkliness". The estimated fractality of the AE index time series which is obtained belongs to a strange attractor structure with close returns in the reconstructed phase space. In the second method we extend the linear equivalent magnetospheric electric circuit to a nonlinear one, the arithmetic solution of which reveals low dimensional chaotic dynamics. Both methods strongly support the existence of low dimensional magnetospheric chaos.

Nonlinear prediction of condition parameter degradation trend for hydropower unit based on radial basis function interpolation and wavelet transform

2015 ◽  
Vol 229 (18) ◽  
pp. 3515-3525 ◽  
Author(s):  
Xueli An ◽  
Li Yang ◽  
Luoping Pan
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Lyapunov Exponent ◽  
Basis Function ◽  
High Frequency ◽  
Low Frequency ◽  
Prediction Method ◽  
Largest Lyapunov Exponent ◽  
Nonlinear Prediction ◽  
Radial Basis Function Interpolation

A nonlinear prediction model of condition parameter degradation trend of hydropower unit is proposed. This model is based on radial basis function interpolation, wavelet transform, largest Lyapunov exponent prediction method, and grey prediction model (GM(1, 1) method). The condition parameter degradation trend model of hydropower unit is built by using RBF interpolation regression method. In this model, the effect of active power and working head is taken into consideration. The degradation trend time series is decomposed into several high-frequency parts and one low-frequency part. For high-frequency parts, their chaotic characteristics are identified. The largest Lyapunov exponent prediction method or GM(1, 1) method is selected to predict each frequency part according to their different properties. For low-frequency part, the GM(1, 1) method is used to predict it. Finally, the predicted results of high-frequency parts and low-frequency part are reconstructed by wavelet theory. The predicted results of the original condition parameter degradation trend time series are obtained. The results show that the proposed method has a high prediction precision.

scholarly journals Long-term solar irradiance variability

1997 ◽  
Vol 181 ◽  
pp. 235-250 ◽  
Author(s):  
Judit M. Pap
Keyword(s):  
Solar Activity ◽  
Solar Atmosphere ◽  
Solar Irradiance ◽  
Structural Changes ◽  
Solar Spectrum ◽  
Magnetic Activity ◽  
Solar Interior ◽  
High Solar Activity ◽  
Physical Conditions

Measurements of the solar energy throughout the solar spectrum and understanding its variability provide important information about the physical processes and structural changes in the solar interior and in the solar atmosphere. Solar irradiance measurements (both bolometric and at various wavelengths) over the last two decades have demonstrated that the solar radiative output changes with time as an effect of the waxing and waning solar activity. Although the overall pattern of the long-term variations is similar in the entire spectrum and at various wavelengths, being higher during high solar activity conditions, remarkable differences exist between the magnitude and shape of the observed changes. These differences arise from the different physical conditions in the solar atmosphere where the irradiances are emitted. The aim of this paper is to discuss the solar-cycle-related long-term changes in solar total and UV irradiances. The space-borne irradiance observations are compared to ground-based indices of solar magnetic activity, such as the Photometric Sunspot Index, full disk magnetic flux, and the Mt. Wilson Magnetic Plage Strength Index. Considerable part of the research described in this paper was stimulated by the discussions with the late Philippe Delache, who will always remain in the heart and memory of the author of this paper.

scholarly journals Nonlinear analysis of magnetospheric data Part II. Dynamical characteristics of the AE index time series and comparison with nonlinear surrogate data

1999 ◽  
Vol 6 (2) ◽  
pp. 79-98 ◽  
Author(s):  
G. P. Pavlos ◽  
D. Kugiumtzis ◽  
M. A. Athanasiu ◽  
N. Hatzigeorgiu ◽  
D. Diamantidis ◽  
...  
Keyword(s):  
Time Series ◽  
Nonlinear Analysis ◽  
Dynamic Models ◽  
Surrogate Data ◽  
Dynamical Characteristics ◽  
Ae Index ◽  
The Family ◽  
Nonlinear Dynamic Models ◽  
Original Time ◽  
Index Time Series

Abstract. In this study we have used dynamical characteristies such as Lyapunov exponents, nonlinear dynamic models and mutual information for the nonlinear analysis of the magnetospheric AE index time series. Similarly with the geometrical characteristic studied in Pavlos et al. (1999b), we have found significant differences between the original time series and its surrogate data. These results also suggest the rejection of the null hypothesis that the AE index belongs to the family of stochastic linear signals undergoing a static nonlinear distortion. Finally, we believe that these results support the hypothesis of nonlinearity and chaos for the magnetospheric dynamics.

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