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

Recurrence intervals between earthquakes strongly depend on history

We study the statistics of the recurrence times between earthquakes above a certain magnitude M$in California. We find that the distribution of the recurrence times strongly depends on the previous recurrence time$\tau_0$. As a consequence, the conditional mean recurrence time$\hat \tau(\tau_0)$between two events increases monotonically with$\tau_0$. For$\tau_0$well below the average recurrence time$\ov{\tau}, \hat\tau(\tau_0)$is smaller than$\ov{\tau}$, while for$\tau_0>\ov{\tau}$,$\hat\tau(\tau_0)$is greater than$\ov{\tau}$. Also the mean residual time until the next earthquake does not depend only on the elapsed time, but also strongly on$\tau_0$. The larger$\tau_0$ is, the larger is the mean residual time. The above features should be taken into account in any earthquake prognosis.Comment: 5 pages, 3 figures, submitted to Physica

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

The human physiological impact of global deoxygenation

There has been a clear decline in the volume of oxygen in Earth’s atmosphere over the past 20 years. Although the magnitude of this decrease appears small compared to the amount of oxygen in the atmosphere, it is difficult to predict how this process may evolve, due to the brevity of the collected records. A recently proposed model predicts a non-linear decay, which would result in an increasingly rapid fall-off in atmospheric oxygen concentration, with potentially devastating consequences for human health. We discuss the impact that global deoxygenation, over hundreds of generations, might have on human physiology. Exploring the changes between different native high-altitude populations provides a paradigm of how humans might tolerate worsening hypoxia over time. Using this model of atmospheric change, we predict that humans may continue to survive in an unprotected atmosphere for ~3600 years. Accordingly, without dramatic changes to the way in which we interact with our planet, humans may lose their dominance on Earth during the next few millennia

Detectability of an AMOC decline in current and projected climate changes

Determining whether the Atlantic Meridional Overturning Circulation (AMOC)'s transport is in decline is challenging due to the short duration of continuous observations. To estimate how many years are needed to detect a decline, we conduct a simulation study using synthetic data that mimics an AMOC time series. The time series' characteristics are reproduced using the trend, variance, and autocorrelation coefficient of the AMOC strength at 26.5°N from 20 Coupled Model Intercomparison Project Phase 5 (CMIP5) models under the RCP8.5 future scenario, and from RAPID observations (2004–2018). Our results suggest that the 14‐year RAPID length has just entered the lower limits of the trend's “detection window” based on synthetic data generated using CMIP5 trends and variability (14–42 years; median urn:x-wiley:grl:media:grl61393:grl61393-math-0001 24 years), but twice the length is required for detectability based on RAPID variability (29–67 years; median urn:x-wiley:grl:media:grl61393:grl61393-math-0002 43 years). The annual RAPID trend is currently not statistically significant (−0.11 Sv yr−1, p > 0.05)

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

Generalized early warning signals in multivariate and gridded data with an application to tropical cyclones

Tipping events in dynamical systems have been studied across many applications, often by measuring changes in variance or autocorrelation in a one-dimensional time series. In this paper, methods for detecting early warning signals of tipping events in multidimensional systems are reviewed and expanded. An analytical justification of the use of dimension-reduction by empirical orthogonal functions, in the context of early warning signals, is provided and the one-dimensional techniques are also extended to spatially separated time series over a 2D field. The challenge of predicting an approaching tropical cyclone by a tipping-point analysis of the sea-level pressure series is used as the primary example, and an analytical model of a moving cyclone is also developed in order to test predictions. We show that the one-dimensional power spectrum indicator may be used following dimension-reduction or over a 2D field. We also show the validity of our moving cyclone model with respect to tipping-point indicators. Many dynamical systems experience sudden shifts in behavior, often referred to as tipping points or critical transitions. A volume of work is dedicated to detecting and predicting these critical transitions, often making use of generic early warning signal (EWS) indicators based on autocorrelation1,2 and increasing variance.3,4 Similar indicators based on other scaling properties of the time series, namely, detrended fluctuation analysis (DFA)5,6 and power spectrum scaling,7 have also been used. Other methods have estimated parameters to fit a model to the data, both for detecting critical transitions8–10 and for predicting future transitions dynamics

Early Warning Signals of Ecological Transitions: Methods for Spatial Patterns

A number of ecosystems can exhibit abrupt shifts between alternative stable states. Because of their important ecological and economic consequences, recent research has focused on devising early warning signals for anticipating such abrupt ecological transitions. In particular, theoretical studies show that changes in spatial characteristics of the system could provide early warnings of approaching transitions. However, the empirical validation of these indicators lag behind their theoretical developments. Here, we summarize a range of currently available spatial early warning signals, suggest potential null models to interpret their trends, and apply them to three simulated spatial data sets of systems undergoing an abrupt transition. In addition to providing a step-by-step methodology for applying these signals to spatial data sets, we propose a statistical toolbox that may be used to help detect approaching transitions in a wide range of spatial data. We hope that our methodology together with the computer codes will stimulate the application and testing of spatial early warning signals on real spatial data

Early warning signals of simulated Amazon rainforest dieback

Copyright © 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