scholarly journals Repeat-station surveys: implications from chaos and ergodicity of the recent geomagnetic field

2013 ◽  
Vol 56 (1) ◽  
Author(s):  
Angelo De Santis ◽  
Enkelejda Qamili ◽  
Gianfranco Cianchini
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Time Domain ◽  
Secular Variation ◽  
Geomagnetic Field ◽  
Repeat Station ◽  
Reconstructed Phase Space ◽  
Time Averages ◽  
The Time Domain ◽  
Strong Necessity

<p>The present geomagnetic field is chaotic and ergodic: chaotic because it can no longer be predicted beyond around 6 years; and ergodic in the sense that time averages correspond to phase-space averages. These properties have already been deduced from complex analyses of observatory time series in a reconstructed phase space and from global predicted and definitive models of differences in the time domain. These results imply that there is a strong necessity to make repeat-station magnetic surveys more frequently than every 5 years. This, in turn, will also improve the geomagnetic field secular variation models. This report provides practical examples and case studies.</p><p> </p>

scholarly journals Geomagnetic Virtual Observatories: monitoring geomagnetic secular variation with the Swarm satellites

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Magnus D. Hammer ◽  
Grace A. Cox ◽  
William J. Brown ◽  
Ciarán D. Beggan ◽  
Christopher C. Finlay
Keyword(s):  
Time Series ◽  
Secular Variation ◽  
Geomagnetic Field ◽  
Time Windows ◽  
Low Earth Orbit ◽  
Data Selection ◽  
Spherical Harmonic Analysis ◽  
Core Field ◽  
The Core ◽  
Swarm Satellites

AbstractWe present geomagnetic main field and secular variation time series, at 300 equal-area distributed locations and at 490 km altitude, derived from magnetic field measurements collected by the three Swarm satellites. These Geomagnetic Virtual Observatory (GVO) series provide a convenient means to globally monitor and analyze long-term variations of the geomagnetic field from low-Earth orbit. The series are obtained by robust fits of local Cartesian potential field models to along-track and East–West sums and differences of Swarm satellite data collected within a radius of 700 km of the GVO locations during either 1-monthly or 4-monthly time windows. We describe two GVO data products: (1) ‘Observed Field’ GVO time series, where all observed sources contribute to the estimated values, without any data selection or correction, and (2) ‘Core Field’ GVO time series, where additional data selection is carried out, then de-noising schemes and epoch-by-epoch spherical harmonic analysis are applied to reduce contamination by magnetospheric and ionospheric signals. Secular variation series are provided as annual differences of the Core Field GVOs. We present examples of the resulting Swarm GVO series, assessing their quality through comparisons with ground observatories and geomagnetic field models. In benchmark comparisons with six high-quality mid-to-low latitude ground observatories we find the secular variation of the Core Field GVO field intensities, calculated using annual differences, agrees to an rms of 1.8 nT/yr and 1.2 nT/yr for the 1-monthly and 4-monthly versions, respectively. Regular sampling in space and time, and the availability of data error estimates, makes the GVO series well suited for users wishing to perform data assimilation studies of core dynamics, or to study long-period magnetospheric and ionospheric signals and their induced counterparts. The Swarm GVO time series will be regularly updated, approximately every four months, allowing ready access to the latest secular variation data from the Swarm satellites.

scholarly journals A New Method for Time Series Filtering near Endpoints

2008 ◽  
Vol 25 (4) ◽  
pp. 534-546 ◽  
Author(s):  
Anthony Arguez ◽  
Peng Yu ◽  
James J. O’Brien
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Time Domain ◽  
Southern Oscillation ◽  
Fundamental Property ◽  
Great Promise ◽  
Constraint Forces ◽  
Variance Method ◽  
Equal Variance ◽  
The Time Domain

Abstract Time series filtering (e.g., smoothing) can be done in the spectral domain without loss of endpoints. However, filtering is commonly performed in the time domain using convolutions, resulting in lost points near the series endpoints. Multiple incarnations of a least squares minimization approach are developed that retain the endpoint intervals that are normally discarded due to filtering with convolutions in the time domain. The techniques minimize the errors between the predetermined frequency response function (FRF)—a fundamental property of all filters—of interior points with FRFs that are to be determined for each position in the endpoint zone. The least squares techniques are differentiated by their constraints: 1) unconstrained, 2) equal-mean constraint, and 3) an equal-variance constraint. The equal-mean constraint forces the new weights to sum up to the same value as the predetermined weights. The equal-variance constraint forces the new weights to be such that, after convolved with the input values, the expected time series variance is preserved. The three least squares methods are each tested under three separate filtering scenarios [involving Arctic Oscillation (AO), Madden–Julian oscillation (MJO), and El Niño–Southern Oscillation (ENSO) time series] and compared to each other as well as to the spectral filtering method—the standard of comparison. The results indicate that all four methods (including the spectral method) possess skill at determining suitable endpoints estimates. However, both the unconstrained and equal-mean schemes exhibit bias toward zero near the terminal ends due to problems with appropriating variance. The equal-variance method does not show evidence of this attribute and was never the worst performer. The equal-variance method showed great promise in the ENSO project involving a 5-month running mean filter, and performed at least on par with the other realistic methods for almost all time series positions in all three filtering scenarios.

Dynamics of Thermoacoustic Oscillations Leading to Lean Flame Blowout

2012 ◽  
Author(s):  
Lipika Kabiraj ◽  
R. I. Sujith
Keyword(s):  
Time Series ◽  
Steady State ◽  
Phase Space ◽  
Dynamical Systems ◽  
Nonlinear Oscillation ◽  
Bifurcation Analysis ◽  
Nonlinear Time Series Analysis ◽  
Pressure Oscillations ◽  
Reconstructed Phase Space ◽  
Thermoacoustic Oscillations

Lean flame blowout induced by thermoacoustic oscillations is a serious problem faced by the power and propulsion industry. We analyze a prototypical thermoacoustic system through systematic bifurcation analysis and find that starting from a steady state, this system exhibits successive bifurcations resulting in complex nonlinear oscillation states, eventually leading to flame blowout. To understand the observed bifurcations, we analyze the oscillation states using nonlinear time series analysis, particularly through the representation of pressure oscillations on a reconstructed phase space. Prior to flame blowout, a bursting phenomenon is observed in pressure oscillations. These burst oscillations are found to exhibit similarities with the phenomenon known as intermittency in the dynamical systems theory. This investigation based on nonlinear analysis of experimentally acquired data from a thermoacoustic system sheds light on how thermoacoustic oscillations lead to flame blowout.

DETECTION AND MODELING OF REGRESSION PARAMETER VARIATION ACROSS FREQUENCIES

1999 ◽  
Vol 3 (1) ◽  
pp. 69-83 ◽  
Author(s):  
Hui Boon Tan ◽  
Richard Ashley
Keyword(s):  
Time Series ◽  
Regression Model ◽  
Time Domain ◽  
Simple Technique ◽  
Parameter Variation ◽  
Missing Observations ◽  
Regression Parameter ◽  
Time Series Regression ◽  
Parameter Instability ◽  
The Time Domain

A simple technique for directly testing the parameters of a time-series regression model for instability across frequencies is presented. The method can be implemented easily in the time domain, so that parameter instability across frequency bands can be conveniently detected and modeled in conjunction with other econometric features of the problem at hand, such as simultaneity, cointegration, missing observations, and cross-equation restrictions. The usefulness of the new technique is illustrated with an application to a cointegrated consumption-income regression model, yielding a straightforward test of the permanent income hypothesis.

scholarly journals Random time series in astronomy

2013 ◽  
Vol 371 (1984) ◽  
pp. 20110549 ◽  
Author(s):  
Simon Vaughan
Keyword(s):  
Time Series ◽  
Black Holes ◽  
Time Domain ◽  
Gamma Ray ◽  
Power Spectra ◽  
Polarization Angle ◽  
Noise Power ◽  
Future Challenges ◽  
Nearby Galaxies ◽  
The Time Domain

Progress in astronomy comes from interpreting the signals encoded in the light received from distant objects: the distribution of light over the sky (images), over photon wavelength (spectrum), over polarization angle and over time (usually called light curves by astronomers). In the time domain, we see transient events such as supernovae, gamma-ray bursts and other powerful explosions; we see periodic phenomena such as the orbits of planets around nearby stars, radio pulsars and pulsations of stars in nearby galaxies; and we see persistent aperiodic variations (‘noise’) from powerful systems such as accreting black holes. I review just a few of the recent and future challenges in the burgeoning area of time domain astrophysics, with particular attention to persistently variable sources, the recovery of reliable noise power spectra from sparsely sampled time series, higher order properties of accreting black holes, and time delays and correlations in multi-variate time series.

scholarly journals A skewed perspective of the Indian rainfall–El Niño–Southern Oscillation (ENSO) relationship

2020 ◽  
Vol 24 (11) ◽  
pp. 5473-5489 ◽  
Author(s):  
Justin Schulte ◽  
Frederick Policielli ◽  
Benjamin Zaitchik
Keyword(s):  
Time Series ◽  
Time Domain ◽  
El Niño ◽  
El Nino ◽  
Southern Oscillation ◽  
Wavelet Coherence ◽  
El Niño Southern Oscillation ◽  
El Nino Southern Oscillation ◽  
The Time Domain ◽  
Time Domain Correlation

Abstract. Wavelet coherence is a method that is commonly used in hydrology to extract scale-dependent, nonstationary relationships between time series. However, we show that the method cannot always determine why the time-domain correlation between two time series changes in time. We show that, even for stationary coherence, the time-domain correlation between two time series weakens if at least one of the time series has changing skewness. To overcome this drawback, a nonlinear coherence method is proposed to quantify the cross-correlation between nonlinear modes embedded in the time series. It is shown that nonlinear coherence and auto-bicoherence spectra can provide additional insight into changing time-domain correlations. The new method is applied to the El Niño–Southern Oscillation (ENSO) and all-India rainfall (AIR), which is intricately linked to hydrological processes across the Indian subcontinent. The nonlinear coherence analysis showed that the skewness of AIR is weakly correlated with that of two ENSO time series after the 1970s, indicating that increases in ENSO skewness after the 1970s at least partially contributed to the weakening ENSO–AIR relationship in recent decades. The implication of this result is that the intensity of skewed El Niño events is likely to overestimate India's drought severity, which was the case in the 1997 monsoon season, a time point when the nonlinear wavelet coherence between AIR and ENSO reached its lowest value in the 1871–2016 period. We determined that the association between the weakening ENSO–AIR relationship and ENSO nonlinearity could reflect the contribution of different nonlinear ENSO modes to ENSO diversity.

scholarly journals Hydrological model performance and parameter estimation in the wavelet-domain

2009 ◽  
Vol 6 (2) ◽  
pp. 2451-2498 ◽  
Author(s):  
B. Schaefli ◽  
E. Zehe
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Time Domain ◽  
Model Performance ◽  
Time Varying ◽  
Wavelet Domain ◽  
Frequency Content ◽  
Time Varying Frequency ◽  
The Time Domain

Abstract. This paper proposes a method for rainfall-runoff model calibration and performance analysis in the wavelet-domain by fitting the estimated wavelet-power spectrum (a representation of the time-varying frequency content of a time series) of a simulated discharge series to the one of the corresponding observed time series. As discussed in this paper, calibrating hydrological models so as to reproduce the time-varying frequency content of the observed signal can lead to different results than parameter estimation in the time-domain. Therefore, wavelet-domain parameter estimation has the potential to give new insights into model performance and to reveal model structural deficiencies. We apply the proposed method to synthetic case studies and a real-world discharge modeling case study and discuss how model diagnosis can benefit from an analysis in the wavelet-domain. The results show that for the real-world case study of precipitation – runoff modeling for a high alpine catchment, the calibrated discharge simulation captures the dynamics of the observed time series better than the results obtained through calibration in the time-domain. In addition, the wavelet-domain performance assessment of this case study highlights which frequencies are not well reproduced by the model, which gives specific indications about how to improve the model structure.

scholarly journals Application of L1 Trend Filtering Technology on the Current Time Domain Spectroscopy of Dielectrics

Electronics ◽  
2019 ◽  
Vol 8 (9) ◽  
pp. 1046
Author(s):  
Changyou Suo ◽  
Zhonghua Li ◽  
Yunlong Sun ◽  
Yongsen Han
Keyword(s):  
Time Series ◽  
Time Domain ◽  
Time Complexity ◽  
Time Range ◽  
Test Results ◽  
Current Time ◽  
Time Domain Spectroscopy ◽  
Filtering Algorithms ◽  
Wide Range ◽  
The Time Domain

The current time domain spectroscopy of dielectrics provides important information for the analysis of dielectric properties and mechanisms. However, there is always interference during the testing process, which seriously affects the analysis of the test results. Therefore, the effective filtering of current time domain spectroscopy is particularly necessary. L1 trend filtering can estimate the trend items exactly in a set of time series. It has been widely used in the fields of economics and sociology. Therefore, this paper attempts to apply L1 trend filtering to the current time domain spectroscopy. Firstly, polarization and depolarization currents are measured in the laboratory. Then the test results are filtered by L1 trend filtering and the filtering effects are compared with several common filtering algorithms, such as a sliding mean filter and Savitzky–Golay smoothing filter. Finally, the robustness and time complexity of L1 trend filtering are analyzed. The filtering results show that because the polarization currents vary in a wide range of the time domain (about 2–3 orders of magnitude), smooth and undistorted curves in the whole test time range can hardly be obtained through common filtering algorithms, while they can be obtained by L1 trend filtering. The results of robustness analysis and time complexity analysis show that L1 trend filtering can extract the trend items accurately in the time series under given different noise levels, and the execution time is also lower than 176.67 s when the number of tested points is no more than 20,000. Those results show that L1 trend filtering can be applied to the time domain current spectroscopy of dielectrics.

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