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Multifractality of river runoff and precipitation: comparison of fluctuation analysis and wavelet methods

2003-09-22
Jan W. Kantelhardt , Diego Rybski , Stephan Zschiegner +5 more
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Nonlinear volatility of river flux fluctuations

2003-04-07
Valerie Livina , Yosef Ashkenazy , Peter Braun +3 more
We study the spectral properties of the magnitudes of daily river flux increments, the volatility. The volatility series exhibits (i) strong seasonal periodicity and (ii) power-law correlations for time scales … We study the spectral properties of the magnitudes of daily river flux increments, the volatility. The volatility series exhibits (i) strong seasonal periodicity and (ii) power-law correlations for time scales less than 1 yr. We test the nonlinear properties of the river flux increment series by randomizing its Fourier phases and find that the surrogate volatility series (i) has almost no seasonal periodicity and (ii) is weakly correlated for time scales less than 1 yr. We quantify the degree of nonlinearity by measuring (i) the amplitude of the power spectrum at the seasonal peak and (ii) the correlation power-law exponent of the volatility series.
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A recent tipping point in the Arctic sea-ice cover: abrupt and persistent increase in the seasonal cycle since 2007

2013-02-12
Valerie Livina , Timothy M. Lenton
Abstract. There is ongoing debate over whether Arctic sea ice has already passed a "tipping point", or whether it will do so in the future. Several recent studies argue that … Abstract. There is ongoing debate over whether Arctic sea ice has already passed a "tipping point", or whether it will do so in the future. Several recent studies argue that the loss of summer sea ice does not involve an irreversible bifurcation, because it is highly reversible in models. However, a broader definition of a "tipping point" also includes other abrupt, non-linear changes that are neither bifurcations nor necessarily irreversible. Examination of satellite data for Arctic sea-ice area reveals an abrupt increase in the amplitude of seasonal variability in 2007 that has persisted since then. We identified this abrupt transition using recently developed methods that can detect multi-modality in time-series data and sometimes forewarn of bifurcations. When removing the mean seasonal cycle (up to 2008) from the satellite data, the residual sea-ice fluctuations switch from uni-modal to multi-modal behaviour around 2007. We originally interpreted this as a bifurcation in which a new lower ice cover attractor appears in deseasonalised fluctuations and is sampled in every summer–autumn from 2007 onwards. However, this interpretation is clearly sensitive to how the seasonal cycle is removed from the raw data, and to the presence of continental land masses restricting winter–spring ice fluctuations. Furthermore, there was no robust early warning signal of critical slowing down prior to the hypothesized bifurcation. Early warning indicators do however show destabilization of the summer–autumn sea-ice cover since 2007. Thus, the bifurcation hypothesis lacks consistent support, but there was an abrupt and persistent increase in the amplitude of the seasonal cycle of Arctic sea-ice cover in 2007, which we describe as a (non-bifurcation) "tipping point". Our statistical methods detect this "tipping point" and its time of onset. We discuss potential geophysical mechanisms behind it, which should be the subject of further work with process-based models.
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Dansgaard–Oeschger events: bifurcation points in the climate system

2013-02-06
Andrea Cimatoribus , Sybren Drijfhout , Valerie Livina +1 more
Dansgaard-Oeschger events are a prominent mode of variability in the records of the last glacial cycle. Various prototype models have been proposed to explain these rapid climate fluctuations, and no … Dansgaard-Oeschger events are a prominent mode of variability in the records of the last glacial cycle. Various prototype models have been proposed to explain these rapid climate fluctuations, and no agreement has emerged on which may be the more correct for describing the paleoclimatic signal. In this work, we assess the bimodality of the system reconstructing the topology of the multi--dimensional attractor over which the climate system evolves. We use high-resolution ice core isotope data to investigate the statistical properties of the climate fluctuations in the period before the onset of the abrupt change. We show that Dansgaard-Oeschger events have weak early warning signals if the ensemble of events is considered. We find that the statistics are consistent with the switches between two different climate equilibrium states in response to a changing external forcing (e.g. solar, ice sheets...), either forcing directly the transition or pacing it through stochastic resonance. These findings are most consistent with a model that associates Dansgaard-Oeschger with changing boundary conditions, and with the presence of a bifurcation point.
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Resonance induced by repulsive interactions in a model of globally coupled bistable systems

2010-04-09
T. Vaz Martins , Valerie Livina , A. P. Majtey +1 more
We show the existence of a competition-induced resonance effect for a generic globally coupled bistable system. In particular, we demonstrate that the response of the macroscopic variable to an external … We show the existence of a competition-induced resonance effect for a generic globally coupled bistable system. In particular, we demonstrate that the response of the macroscopic variable to an external signal is optimal for a particular proportion of repulsive links. Furthermore, we show that a resonance also occurs for other system parameters, like the coupling strength and the number of elements. We relate this resonance to the appearance of a multistable region, and we predict the location of the resonance peaks, by a simple spectral analysis of the Laplacian matrix.
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Recurrence intervals between earthquakes strongly depend on history

2004-09-16
Valerie Livina , S. I. Tuzov , Shlomo Havlin +1 more
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Forecasting the underlying potential governing the time series of a dynamical system

2013-05-02
Valerie Livina , Gerrit Lohmann , Manfred Mudelsee +1 more
We introduce a technique of time series analysis, potential forecasting, which is based on dynamical propagation of the probability density of time series. We employ polynomial coefficients of the orthogonal … We introduce a technique of time series analysis, potential forecasting, which is based on dynamical propagation of the probability density of time series. We employ polynomial coefficients of the orthogonal approximation of the empirical probability distribution and extrapolate them in order to forecast the future probability distribution of data. The method is tested on artificial data, used for hindcasting observed climate data, and then applied to forecast Arctic sea-ice time series. The proposed methodology completes a framework for `potential analysis' of tipping points which altogether serves anticipating, detecting and forecasting non-linear changes including bifurcations using several independent techniques of time series analysis. Although being applied to climatological series in the present paper, the method is very general and can be used to forecast dynamics in time series of any origin.
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Tipping Point Analysis of Electrical Resistance Data with Early Warning Signals of Failure for Predictive Maintenance

2020-08-22
Valerie Livina , Adam Lewis , M Wickham
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Tipping point analysis of electrical resistance data with early warning signals of failure for predictive maintenance

2019-04-08
Valerie Livina , Adam Lewis , M Wickham
We apply tipping point analysis to measurements of electronic components commonly used in applications in the automotive or aviation industries and demonstrate early warning signals based on scaling properties of … We apply tipping point analysis to measurements of electronic components commonly used in applications in the automotive or aviation industries and demonstrate early warning signals based on scaling properties of resistance time series. The analysis utilises the statistical physics framework with stochastic modelling by representing the measured time series as a composition of deterministic and stochastic components estimated from measurements. The early warning signals are observed much earlier than those estimated from conventional techniques, such as threshold-based failure detection, or bulk estimates used in Weibull failure analysis. The introduced techniques may be useful for predictive maintenance of power electronics, with industrial applications. We suggest that this approach can be applied to various electromagnetic measurements in power systems and energy applications.

A recent bifurcation in Arctic sea-ice cover

2012-04-24
Valerie Livina , Timothy M. Lenton

A recent tipping point in the Arctic sea-ice cover: abrupt and persistent increase in the seasonal cycle since 2007

2012-04-24
Valerie Livina , Timothy M. Lenton
There is ongoing debate over whether Arctic sea-ice has already passed a `tipping point', or whether it will do so in the future. Several recent studies argue that the loss … There is ongoing debate over whether Arctic sea-ice has already passed a `tipping point', or whether it will do so in the future. Several recent studies argue that the loss of summer sea ice does not involve an irreversible bifurcation, because it is highly reversible in models. However, a broader definition of a `tipping point' also includes other abrupt, non-linear changes that are neither bifurcations nor necessarily irreversible. Examination of satellite data for Arctic sea-ice area reveals an abrupt increase in the amplitude of seasonal variability in 2007 that has persisted since then. We identified this abrupt transition using recently developed methods that can detect multi-modality in time-series data and sometimes forewarn of bifurcations. When removing the mean seasonal cycle (up to 2008) from the satellite data, the residual sea-ice fluctuations switch from uni-modal to multi-modal behaviour around 2007. We originally interpreted this as a bifurcation in which a new lower ice cover attractor appears in deseasonalised fluctuations and is sampled in every summer-autumn from 2007 onwards. However, this interpretation is clearly sensitive to how the seasonal cycle is removed from the raw data, and to the presence of continental land masses restricting winter-spring ice fluctuations. Furthermore, there was no robust early warning signal of critical slowing down prior to the hypothesized bifurcation. Early warning indicators do however show destabilization of the summer-autumn sea-ice cover since 2007. Thus, the bifurcation hypothesis lacks consistent support, but there was an abrupt and persistent increase in the amplitude of the seasonal cycle of Arctic sea-ice cover in 2007, which we describe as a (non-bifurcation) `tipping point'. Our statistical methods detect this `tipping point' and its time of onset.

Forecasting the underlying potential governing climatic time series

2012-12-17
Valerie Livina , Gabriele Lohmann , Manfred Mudelsee +1 more
We introduce a technique of time series analysis, potential forecasting, which is based on dynamical propagation of the probability density of time series. We employ polynomial coefficients of the orthogonal … We introduce a technique of time series analysis, potential forecasting, which is based on dynamical propagation of the probability density of time series. We employ polynomial coefficients of the orthogonal approximation of the empirical probability distribution and extrapolate them in order to forecast the future probability distribution of data. The method is tested on artificial data, used for hindcasting observed climate data, and then applied to forecast Arctic sea-ice time series. The proposed methodology completes a framework for `potential analysis' of climatic tipping points which altogether serves anticipating, detecting and forecasting climate transitions and bifurcations using several independent techniques of time series analysis.

Tipping point analysis of electrical resistance data with early warning signals of failure for predictive maintenance

2019-01-01
Valerie Livina , Adam Lewis , Martin S. J. Wickham
We apply tipping point analysis to measurements of electronic components commonly used in applications in the automotive or aviation industries and demonstrate early warning signals based on scaling properties of … We apply tipping point analysis to measurements of electronic components commonly used in applications in the automotive or aviation industries and demonstrate early warning signals based on scaling properties of resistance time series. The analysis utilises the statistical physics framework with stochastic modelling by representing the measured time series as a composition of deterministic and stochastic components estimated from measurements. The early warning signals are observed much earlier than those estimated from conventional techniques, such as threshold-based failure detection, or bulk estimates used in Weibull failure analysis. The introduced techniques may be useful for predictive maintenance of power electronics, with industrial applications. We suggest that this approach can be applied to various electromagnetic measurements in power systems and energy applications.
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A recent tipping point in the Arctic sea-ice cover: abrupt and persistent increase in the seasonal cycle since 2007

2012-01-01
Valerie Livina , Timothy M. Lenton
There is ongoing debate over whether Arctic sea-ice has already passed a `tipping point', or whether it will do so in the future. Several recent studies argue that the loss … There is ongoing debate over whether Arctic sea-ice has already passed a `tipping point', or whether it will do so in the future. Several recent studies argue that the loss of summer sea ice does not involve an irreversible bifurcation, because it is highly reversible in models. However, a broader definition of a `tipping point' also includes other abrupt, non-linear changes that are neither bifurcations nor necessarily irreversible. Examination of satellite data for Arctic sea-ice area reveals an abrupt increase in the amplitude of seasonal variability in 2007 that has persisted since then. We identified this abrupt transition using recently developed methods that can detect multi-modality in time-series data and sometimes forewarn of bifurcations. When removing the mean seasonal cycle (up to 2008) from the satellite data, the residual sea-ice fluctuations switch from uni-modal to multi-modal behaviour around 2007. We originally interpreted this as a bifurcation in which a new lower ice cover attractor appears in deseasonalised fluctuations and is sampled in every summer-autumn from 2007 onwards. However, this interpretation is clearly sensitive to how the seasonal cycle is removed from the raw data, and to the presence of continental land masses restricting winter-spring ice fluctuations. Furthermore, there was no robust early warning signal of critical slowing down prior to the hypothesized bifurcation. Early warning indicators do however show destabilization of the summer-autumn sea-ice cover since 2007. Thus, the bifurcation hypothesis lacks consistent support, but there was an abrupt and persistent increase in the amplitude of the seasonal cycle of Arctic sea-ice cover in 2007, which we describe as a (non-bifurcation) `tipping point'. Our statistical methods detect this `tipping point' and its time of onset.

Early warnings are too late when parameters change rapidly

2024-07-30
Rohit Radhakrishnan , Induja Pavithran , Valerie Livina +2 more
Early warning signals (EWSs) forewarn a sudden transition (or tipping) from a desirable state to an undesirable state. However, we observe that EWSs detect an impending tipping past bifurcation points … Early warning signals (EWSs) forewarn a sudden transition (or tipping) from a desirable state to an undesirable state. However, we observe that EWSs detect an impending tipping past bifurcation points when control parameters are varied fast; this questions the applicability of EWSs in real-world systems. When a control parameter is changed at a finite rate, the tipping is also delayed, providing a borrowed stability (in the parameter space) before the system tips. In this study, we use the Hurst exponent as EWS in a thermoacoustic system - a horizontal Rijke tube. We find that upon receiving an EWS alert, a quick reversal of the control parameter within the region of borrowed stability cannot always prevent tipping in real-world systems. We show this failure is due to the (i) delay in receiving the EWS alert and (ii) dispersion observed in the warning points received. For fast variation of parameters, where preventive measures fall short, we demonstrate EWS-based control actions to rescue the system after tipping. Our results in a real-world system for a fast variation of parameter highlight the limits of applicability of EWSs in preventing tipping.
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Early warnings are too late when parameters change rapidly

2024-07-30
Rohit Radhakrishnan , Induja Pavithran , Valerie Livina +2 more
Early warning signals (EWSs) forewarn a sudden transition (or tipping) from a desirable state to an undesirable state. However, we observe that EWSs detect an impending tipping past bifurcation points … Early warning signals (EWSs) forewarn a sudden transition (or tipping) from a desirable state to an undesirable state. However, we observe that EWSs detect an impending tipping past bifurcation points when control parameters are varied fast; this questions the applicability of EWSs in real-world systems. When a control parameter is changed at a finite rate, the tipping is also delayed, providing a borrowed stability (in the parameter space) before the system tips. In this study, we use the Hurst exponent as EWS in a thermoacoustic system - a horizontal Rijke tube. We find that upon receiving an EWS alert, a quick reversal of the control parameter within the region of borrowed stability cannot always prevent tipping in real-world systems. We show this failure is due to the (i) delay in receiving the EWS alert and (ii) dispersion observed in the warning points received. For fast variation of parameters, where preventive measures fall short, we demonstrate EWS-based control actions to rescue the system after tipping. Our results in a real-world system for a fast variation of parameter highlight the limits of applicability of EWSs in preventing tipping.
View PDF Chat

Tipping Point Analysis of Electrical Resistance Data with Early Warning Signals of Failure for Predictive Maintenance

2020-08-22
Valerie Livina , Adam Lewis , M Wickham
View PDF Chat

Tipping point analysis of electrical resistance data with early warning signals of failure for predictive maintenance

2019-04-08
Valerie Livina , Adam Lewis , M Wickham
We apply tipping point analysis to measurements of electronic components commonly used in applications in the automotive or aviation industries and demonstrate early warning signals based on scaling properties of … We apply tipping point analysis to measurements of electronic components commonly used in applications in the automotive or aviation industries and demonstrate early warning signals based on scaling properties of resistance time series. The analysis utilises the statistical physics framework with stochastic modelling by representing the measured time series as a composition of deterministic and stochastic components estimated from measurements. The early warning signals are observed much earlier than those estimated from conventional techniques, such as threshold-based failure detection, or bulk estimates used in Weibull failure analysis. The introduced techniques may be useful for predictive maintenance of power electronics, with industrial applications. We suggest that this approach can be applied to various electromagnetic measurements in power systems and energy applications.

Tipping point analysis of electrical resistance data with early warning signals of failure for predictive maintenance

2019-01-01
Valerie Livina , Adam Lewis , Martin S. J. Wickham
We apply tipping point analysis to measurements of electronic components commonly used in applications in the automotive or aviation industries and demonstrate early warning signals based on scaling properties of … We apply tipping point analysis to measurements of electronic components commonly used in applications in the automotive or aviation industries and demonstrate early warning signals based on scaling properties of resistance time series. The analysis utilises the statistical physics framework with stochastic modelling by representing the measured time series as a composition of deterministic and stochastic components estimated from measurements. The early warning signals are observed much earlier than those estimated from conventional techniques, such as threshold-based failure detection, or bulk estimates used in Weibull failure analysis. The introduced techniques may be useful for predictive maintenance of power electronics, with industrial applications. We suggest that this approach can be applied to various electromagnetic measurements in power systems and energy applications.
View PDF Chat

Forecasting the underlying potential governing the time series of a dynamical system

2013-05-02
Valerie Livina , Gerrit Lohmann , Manfred Mudelsee +1 more
We introduce a technique of time series analysis, potential forecasting, which is based on dynamical propagation of the probability density of time series. We employ polynomial coefficients of the orthogonal … We introduce a technique of time series analysis, potential forecasting, which is based on dynamical propagation of the probability density of time series. We employ polynomial coefficients of the orthogonal approximation of the empirical probability distribution and extrapolate them in order to forecast the future probability distribution of data. The method is tested on artificial data, used for hindcasting observed climate data, and then applied to forecast Arctic sea-ice time series. The proposed methodology completes a framework for `potential analysis' of tipping points which altogether serves anticipating, detecting and forecasting non-linear changes including bifurcations using several independent techniques of time series analysis. Although being applied to climatological series in the present paper, the method is very general and can be used to forecast dynamics in time series of any origin.
View PDF Chat

A recent tipping point in the Arctic sea-ice cover: abrupt and persistent increase in the seasonal cycle since 2007

2013-02-12
Valerie Livina , Timothy M. Lenton
Abstract. There is ongoing debate over whether Arctic sea ice has already passed a "tipping point", or whether it will do so in the future. Several recent studies argue that … Abstract. There is ongoing debate over whether Arctic sea ice has already passed a "tipping point", or whether it will do so in the future. Several recent studies argue that the loss of summer sea ice does not involve an irreversible bifurcation, because it is highly reversible in models. However, a broader definition of a "tipping point" also includes other abrupt, non-linear changes that are neither bifurcations nor necessarily irreversible. Examination of satellite data for Arctic sea-ice area reveals an abrupt increase in the amplitude of seasonal variability in 2007 that has persisted since then. We identified this abrupt transition using recently developed methods that can detect multi-modality in time-series data and sometimes forewarn of bifurcations. When removing the mean seasonal cycle (up to 2008) from the satellite data, the residual sea-ice fluctuations switch from uni-modal to multi-modal behaviour around 2007. We originally interpreted this as a bifurcation in which a new lower ice cover attractor appears in deseasonalised fluctuations and is sampled in every summer–autumn from 2007 onwards. However, this interpretation is clearly sensitive to how the seasonal cycle is removed from the raw data, and to the presence of continental land masses restricting winter–spring ice fluctuations. Furthermore, there was no robust early warning signal of critical slowing down prior to the hypothesized bifurcation. Early warning indicators do however show destabilization of the summer–autumn sea-ice cover since 2007. Thus, the bifurcation hypothesis lacks consistent support, but there was an abrupt and persistent increase in the amplitude of the seasonal cycle of Arctic sea-ice cover in 2007, which we describe as a (non-bifurcation) "tipping point". Our statistical methods detect this "tipping point" and its time of onset. We discuss potential geophysical mechanisms behind it, which should be the subject of further work with process-based models.
View PDF Chat

Dansgaard–Oeschger events: bifurcation points in the climate system

2013-02-06
Andrea Cimatoribus , Sybren Drijfhout , Valerie Livina +1 more
Dansgaard-Oeschger events are a prominent mode of variability in the records of the last glacial cycle. Various prototype models have been proposed to explain these rapid climate fluctuations, and no … Dansgaard-Oeschger events are a prominent mode of variability in the records of the last glacial cycle. Various prototype models have been proposed to explain these rapid climate fluctuations, and no agreement has emerged on which may be the more correct for describing the paleoclimatic signal. In this work, we assess the bimodality of the system reconstructing the topology of the multi--dimensional attractor over which the climate system evolves. We use high-resolution ice core isotope data to investigate the statistical properties of the climate fluctuations in the period before the onset of the abrupt change. We show that Dansgaard-Oeschger events have weak early warning signals if the ensemble of events is considered. We find that the statistics are consistent with the switches between two different climate equilibrium states in response to a changing external forcing (e.g. solar, ice sheets...), either forcing directly the transition or pacing it through stochastic resonance. These findings are most consistent with a model that associates Dansgaard-Oeschger with changing boundary conditions, and with the presence of a bifurcation point.
View PDF Chat

Forecasting the underlying potential governing climatic time series

2012-12-17
Valerie Livina , Gabriele Lohmann , Manfred Mudelsee +1 more
We introduce a technique of time series analysis, potential forecasting, which is based on dynamical propagation of the probability density of time series. We employ polynomial coefficients of the orthogonal … We introduce a technique of time series analysis, potential forecasting, which is based on dynamical propagation of the probability density of time series. We employ polynomial coefficients of the orthogonal approximation of the empirical probability distribution and extrapolate them in order to forecast the future probability distribution of data. The method is tested on artificial data, used for hindcasting observed climate data, and then applied to forecast Arctic sea-ice time series. The proposed methodology completes a framework for `potential analysis' of climatic tipping points which altogether serves anticipating, detecting and forecasting climate transitions and bifurcations using several independent techniques of time series analysis.

A recent tipping point in the Arctic sea-ice cover: abrupt and persistent increase in the seasonal cycle since 2007

2012-04-24
Valerie Livina , Timothy M. Lenton
There is ongoing debate over whether Arctic sea-ice has already passed a `tipping point', or whether it will do so in the future. Several recent studies argue that the loss … There is ongoing debate over whether Arctic sea-ice has already passed a `tipping point', or whether it will do so in the future. Several recent studies argue that the loss of summer sea ice does not involve an irreversible bifurcation, because it is highly reversible in models. However, a broader definition of a `tipping point' also includes other abrupt, non-linear changes that are neither bifurcations nor necessarily irreversible. Examination of satellite data for Arctic sea-ice area reveals an abrupt increase in the amplitude of seasonal variability in 2007 that has persisted since then. We identified this abrupt transition using recently developed methods that can detect multi-modality in time-series data and sometimes forewarn of bifurcations. When removing the mean seasonal cycle (up to 2008) from the satellite data, the residual sea-ice fluctuations switch from uni-modal to multi-modal behaviour around 2007. We originally interpreted this as a bifurcation in which a new lower ice cover attractor appears in deseasonalised fluctuations and is sampled in every summer-autumn from 2007 onwards. However, this interpretation is clearly sensitive to how the seasonal cycle is removed from the raw data, and to the presence of continental land masses restricting winter-spring ice fluctuations. Furthermore, there was no robust early warning signal of critical slowing down prior to the hypothesized bifurcation. Early warning indicators do however show destabilization of the summer-autumn sea-ice cover since 2007. Thus, the bifurcation hypothesis lacks consistent support, but there was an abrupt and persistent increase in the amplitude of the seasonal cycle of Arctic sea-ice cover in 2007, which we describe as a (non-bifurcation) `tipping point'. Our statistical methods detect this `tipping point' and its time of onset.

A recent bifurcation in Arctic sea-ice cover

2012-04-24
Valerie Livina , Timothy M. Lenton

A recent tipping point in the Arctic sea-ice cover: abrupt and persistent increase in the seasonal cycle since 2007

2012-01-01
Valerie Livina , Timothy M. Lenton
There is ongoing debate over whether Arctic sea-ice has already passed a `tipping point', or whether it will do so in the future. Several recent studies argue that the loss … There is ongoing debate over whether Arctic sea-ice has already passed a `tipping point', or whether it will do so in the future. Several recent studies argue that the loss of summer sea ice does not involve an irreversible bifurcation, because it is highly reversible in models. However, a broader definition of a `tipping point' also includes other abrupt, non-linear changes that are neither bifurcations nor necessarily irreversible. Examination of satellite data for Arctic sea-ice area reveals an abrupt increase in the amplitude of seasonal variability in 2007 that has persisted since then. We identified this abrupt transition using recently developed methods that can detect multi-modality in time-series data and sometimes forewarn of bifurcations. When removing the mean seasonal cycle (up to 2008) from the satellite data, the residual sea-ice fluctuations switch from uni-modal to multi-modal behaviour around 2007. We originally interpreted this as a bifurcation in which a new lower ice cover attractor appears in deseasonalised fluctuations and is sampled in every summer-autumn from 2007 onwards. However, this interpretation is clearly sensitive to how the seasonal cycle is removed from the raw data, and to the presence of continental land masses restricting winter-spring ice fluctuations. Furthermore, there was no robust early warning signal of critical slowing down prior to the hypothesized bifurcation. Early warning indicators do however show destabilization of the summer-autumn sea-ice cover since 2007. Thus, the bifurcation hypothesis lacks consistent support, but there was an abrupt and persistent increase in the amplitude of the seasonal cycle of Arctic sea-ice cover in 2007, which we describe as a (non-bifurcation) `tipping point'. Our statistical methods detect this `tipping point' and its time of onset.

Resonance induced by repulsive interactions in a model of globally coupled bistable systems

2010-04-09
T. Vaz Martins , Valerie Livina , A. P. Majtey +1 more
We show the existence of a competition-induced resonance effect for a generic globally coupled bistable system. In particular, we demonstrate that the response of the macroscopic variable to an external … We show the existence of a competition-induced resonance effect for a generic globally coupled bistable system. In particular, we demonstrate that the response of the macroscopic variable to an external signal is optimal for a particular proportion of repulsive links. Furthermore, we show that a resonance also occurs for other system parameters, like the coupling strength and the number of elements. We relate this resonance to the appearance of a multistable region, and we predict the location of the resonance peaks, by a simple spectral analysis of the Laplacian matrix.
View PDF Chat

Recurrence intervals between earthquakes strongly depend on history

2004-09-16
Valerie Livina , S. I. Tuzov , Shlomo Havlin +1 more
View PDF Chat

Multifractality of river runoff and precipitation: comparison of fluctuation analysis and wavelet methods

2003-09-22
Jan W. Kantelhardt , Diego Rybski , Stephan Zschiegner +5 more
View PDF Chat

Nonlinear volatility of river flux fluctuations

2003-04-07
Valerie Livina , Yosef Ashkenazy , Peter Braun +3 more
We study the spectral properties of the magnitudes of daily river flux increments, the volatility. The volatility series exhibits (i) strong seasonal periodicity and (ii) power-law correlations for time scales … We study the spectral properties of the magnitudes of daily river flux increments, the volatility. The volatility series exhibits (i) strong seasonal periodicity and (ii) power-law correlations for time scales less than 1 yr. We test the nonlinear properties of the river flux increment series by randomizing its Fourier phases and find that the surrogate volatility series (i) has almost no seasonal periodicity and (ii) is weakly correlated for time scales less than 1 yr. We quantify the degree of nonlinearity by measuring (i) the amplitude of the power spectrum at the seasonal peak and (ii) the correlation power-law exponent of the volatility series.
View PDF Chat
Coauthor Papers Together
Timothy M. Lenton 6
Armin Bunde 3
Manfred Mudelsee 2
Adam Lewis 2
Peter Braun 2
Shlomo Havlin 2
M Wickham 2
Stephan Zschiegner 1
Jan W. Kantelhardt 1
Gabriele Lohmann 1
Gerrit Lohmann 1
R. I. Sujith 1
Raúl Toral 1
Gerard van der Schrier 1
Andrea Cimatoribus 1
Jürgen Kurths 1
T. Vaz Martins 1
Shlomo Havlin 1
Eva Koscielny–Bunde 1
Roberto Monetti 1
Rohit Radhakrishnan 1
Martin S. J. Wickham 1
Adam Lewis 1
S. I. Tuzov 1
Diego Rybski 1
Induja Pavithran 1
A. P. Majtey 1
Yosef Ashkenazy 1
Sybren Drijfhout 1