40 research outputs found
Resonance induced by repulsive interactions in a model of globally-coupled bistable systems
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
Climate bifurcation during the last deglaciation?
There were two abrupt warming events during the last deglaciation, at the start of the Bølling-Allerød and at the end of the Younger Dryas, but their underlying dynamics are unclear. Some abrupt climate changes may involve gradual forcing past a bifurcation point, in which a prevailing climate state loses its stability and the climate tips into an alternative state, providing an early warning signal in the form of slowing responses to perturbations, which may be accompanied by increasing variability. Alternatively, short-term stochastic variability in the climate system can trigger abrupt climate changes, without early warning. Previous work has found signals consistent with slowing down during the last deglaciation as a whole, and during the Younger Dryas, but with conflicting results in the run-up to the Bølling-Allerød. Based on this, we hypothesise that a bifurcation point was approached at the end of the Younger Dryas, in which the cold climate state, with weak Atlantic overturning circulation, lost its stability, and the climate tipped irreversibly into a warm interglacial state. To test the bifurcation hypothesis, we analysed two different climate proxies in three Greenland ice cores, from the Last Glacial Maximum to the end of the Younger Dryas. Prior to the Bølling warming, there was a robust increase in climate variability but no consistent slowing down signal, suggesting this abrupt change was probably triggered by a stochastic fluctuation. The transition to the warm Bølling-Allerød state was accompanied by a slowing down in climate dynamics and an increase in climate variability. We suggest that the Bølling warming excited an internal mode of variability in Atlantic meridional overturning circulation strength, causing multi-centennial climate fluctuations. However, the return to the Younger Dryas cold state increased climate stability. We find no consistent evidence for slowing down during the Younger Dryas, or in a longer spliced record of the cold climate state before and after the Bølling-Allerød. Therefore, the end of the Younger Dryas may also have been triggered by a stochastic perturbation
Early warning of climate tipping points from critical slowing down: comparing methods to improve robustness
We address whether robust early warning signals can, in principle, be provided before a climate tipping point is reached, focusing on methods that seek to detect critical slowing down as a precursor of bifurcation. As a test bed, six previously analysed datasets are reconsidered, three palaeoclimate records approaching abrupt transitions at the end of the last ice age and three models of varying complexity forced through a collapse of the Atlantic thermohaline circulation. Approaches based on examining the lag-1 autocorrelation function or on detrended fluctuation analysis are applied together and compared. The effects of aggregating the data, detrending method, sliding window length and filtering bandwidth are examined. Robust indicators of critical slowing down are found prior to the abrupt warming event at the end of the Younger Dryas, but the indicators are less clear prior to the Bølling-Allerød warming, or glacial termination in Antarctica. Early warnings of thermohaline circulation collapse can be masked by inter-annual variability driven by atmospheric dynamics. However, rapidly decaying modes can be successfully filtered out by using a long bandwidth or by aggregating data. The two methods have complementary strengths and weaknesses and we recommend applying them together to improve the robustness of early warnings
Detrended fluctuation analysis as a statistical tool to monitor the climate
Detrended fluctuation analysis is used to investigate power law relationship
between the monthly averages of the maximum daily temperatures for different
locations in the western US. On the map created by the power law exponents, we
can distinguish different geographical regions with different power law
exponents. When the power law exponents obtained from the detrended fluctuation
analysis are plotted versus the standard deviation of the temperature
fluctuations, we observe different data points belonging to the different
climates, hence indicating that by observing the long-time trends in the
fluctuations of temperature we can distinguish between different climates.Comment: 8 pages, 4 figures, submitted to JSTA
Multifactor Analysis of Multiscaling in Volatility Return Intervals
We study the volatility time series of 1137 most traded stocks in the US
stock markets for the two-year period 2001-02 and analyze their return
intervals , which are time intervals between volatilities above a given
threshold . We explore the probability density function of ,
, assuming a stretched exponential function, . We find that the exponent depends on the threshold
in the range between and 6 standard deviations of the volatility. This
finding supports the multiscaling nature of the return interval distribution.
To better understand the multiscaling origin, we study how depends on
four essential factors, capitalization, risk, number of trades and return. We
show that depends on the capitalization, risk and return but almost
does not depend on the number of trades. This suggests that relates to
the portfolio selection but not on the market activity. To further characterize
the multiscaling of individual stocks, we fit the moments of , , in the range of by a
power-law, . The exponent is found also to
depend on the capitalization, risk and return but not on the number of trades,
and its tendency is opposite to that of . Moreover, we show that
decreases with approximately by a linear relation. The return
intervals demonstrate the temporal structure of volatilities and our findings
suggest that their multiscaling features may be helpful for portfolio
optimization.Comment: 16 pages, 6 figure
Early warning signals of simulated Amazon rainforest dieback
Copyright Š The Author(s) 2013. This article is published with open access at Springerlink.comWe test proposed generic tipping point early warning signals in a complex climate model (HadCM3) which simulates future dieback of the Amazon rainforest. The equation governing tree cover in the model suggests that zero and non-zero stable states of tree cover co-exist, and a transcritical bifurcation is approached as productivity declines. Forest dieback is a non-linear change in the non-zero tree cover state, as productivity declines, which should exhibit critical slowing down. We use an ensemble of versions of HadCM3 to test for the corresponding early warning signals. However, on approaching simulated Amazon dieback, expected early warning signals of critical slowing down are not seen in tree cover, vegetation carbon or net primary productivity. The lack of a convincing trend in autocorrelation appears to be a result of the system being forced rapidly and non-linearly. There is a robust rise in variance with time, but this can be explained by increases in inter-annual temperature and precipitation variability that force the forest. This failure of generic early warning indicators led us to seek more system-specific, observable indicators of changing forest stability in the model. The sensitivity of net ecosystem productivity to temperature anomalies (a negative correlation) generally increases as dieback approaches, which is attributable to a non-linear sensitivity of ecosystem respiration to temperature. As a result, the sensitivity of atmospheric CO2 anomalies to temperature anomalies (a positive correlation) increases as dieback approaches. This stability indicator has the benefit of being readily observable in the real world.NERCJoint DECC/Defra Met Office Hadley Centre Climate ProgrammeUniversity of
Exete
A recent tipping point in the Arctic sea-ice cover: abrupt and persistent increase in the seasonal cycle since 2007
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 summerâautumn 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 winterâspring 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 summerâautumn 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
Tipping Point Analysis of Electrical Resistance Data with Early Warning Signals of Failure for Predictive Maintenance
Potential analysis reveals changing number of climate states during the last 60 kyr
We develop and apply a new statistical method of potential analysis for detecting the number of states of a geophysical system, from its recorded time series. Estimation of the degree of a polynomial potential allows us to derive the number of potential wells in a system. The method correctly detects changes in the number of wells in artificial data. In ice-core proxy records of Greenland paleotemperature, a reduction in the number of climate states from two to one is detected sometime prior to the last glacial maximum (LGM), 23â19 kyr BP. This result is also found in analysis of Greenland Ca data. The bifurcation can be interpreted as loss of stability of the warm interstadial state of the Dansgaard-Oeschger (DO) events. The proposed method can be applied to a wide range of geophysical time series exhibiting bifurcations