Pseudo resonance induced quasi-periodic behavior in stochastic threshold dynamics

Here we present a simple stochastic threshold model consisting of a deterministic slowly decaying term and a fast stochastic noise term. The process shows a pseudo-resonance, in the sense that for small and large intensities of the noise the signal is irregular and the distribution of threshold crossings is broad, while for a tuned intermediate value of noise intensity the signal becomes quasi-periodic and the distribution of threshold crossings is narrow. The mechanism captured by the model might be relevant for explaining apparent quasi-periodicity of observed climatic variations where no internal or external periodicities can be identified.Comment: 8 pages, 4 figures, to appear in Stochastics and Dynamic

Warning of a forthcoming collapse of the Atlantic meridional overturning circulation

Tipping to an undesired state in the climate when a control parameter slowly approaches a critical value is a growing concern with increasing greenhouse gas concentrations. Predictions rely on detecting early warning signals (EWSs) in observations of the system. The primary EWSs are increase in variance, (loss of resilience), and increased autocorrelation (critical slow down). These measures are statistical in nature, which implies that the reliability and statistical significance of the detection depends on the sample size in observations and the magnitude of the change away from the base value prior to the approach to the tipping point. Thus, the possibility of providing useful early warning depends on the relative magnitude of several interdependent time scales in the system. These are (a) the time before the critical value is reached, (b) the (inverse) rate of approach to the tipping point, (c) the size of the time window required to detect a significant change in the EWS and finally, (d) the escape time for noise-induced transition (prior to the tipping). Conditions for early warning of tipping of the Atlantic meridional overturning circulation (AMOC) are marginally fulfilled for the existing past $\sim$150 years of proxy observations where indicators of tipping have recently been reported. Here we provide statistical significance and data driven estimators for the time of tipping. We estimate a collapse of the AMOC to occur around the year 2057 under the assumption of a "business as usual" scenario of future emissions.Comment: 18 pages, 7 figure

A climatic thermostat making Earth habitable

The mean surface temperature on Earth and other planets with atmospheres is determined by the radiative balance between the non-reflected incoming solar radiation and the outgoing long-wave black-body radiation from the atmosphere. The surface temperature is higher than the black-body temperature due to the greenhouse warming. Balancing the ice-albedo cooling and the greenhouse warming gives rise to two stable climate states. A cold climate state with a completelyice-covered planet, called Snowball Earth, and a warm state similar to our present climate where greenhouse warming prevents the total glacition. The warm state has dominated Earth in most of its geological history despite a 30 % fainter young Sun. The warming could have been controlled by a greenhouse thermostat operating by temperature control of the weathering process depleting the atmosphere from $CO_2$. This temperature control has permitted life to evolve as early as the end of the heavy bombartment 4 billion years ago.Comment: 4 figures, Proceedings, NORDITA conf. Astrobiology 200

The recurrence time of Dansgaard-Oeschger events and limits on the possible periodic component

By comparing the high-resolution isotopic records from the GRIP and NGRIP icecores, we approximately separate the climate signal from local noise to obtain an objective criterion for defining Dansgaard-Oeschger events. Our analysis identifies several additional short lasting events, increasing the total number of DO events to 27 in the period 12-90 kyr BP. The quasi-regular occurrence of the DO events could indicate a stochastic or coherent resonance mechanism governing their origin. From the distribution of waiting times we obtain a statistical upper bound on the strength of a possible periodic forcing. This finding indicates that the climate shifts are purely noise driven with no underlying periodicity.Comment: 9 figure

Random and externally controlled occurrences of Dansgaard-Oeschger events

Dansgaard–Oeschger (DO) events constitute the most pronounced mode of centennial to millennial climate variability of the last glacial period. Since their discovery, many decades of research have been devoted to understand the origin and nature of these rapid climate shifts. In recent years, a number of studies have appeared that report emergence of DO-type variability in fully coupled general circulation models via different mechanisms. These mechanisms result in the occurrence of DO events at varying degrees of regularity, ranging from periodic to random. When examining the full sequence of DO events as captured in the North Greenland Ice Core Project (NGRIP) ice core record, one can observe high irregularity in the timing of individual events at any stage within the last glacial period. In addition to the prevailing irregularity, certain properties of the DO event sequence, such as the average event frequency or the relative distribution of cold versus warm periods, appear to be changing throughout the glacial. By using statistical hypothesis tests on simple event models, we investigate whether the observed event sequence may have been generated by stationary random processes or rather was strongly modulated by external factors. We find that the sequence of DO warming events is consistent with a stationary random process, whereas dividing the event sequence into warming and cooling events leads to inconsistency with two independent event processes. As we include external forcing, we find a particularly good fit to the observed DO sequence in a model where the average residence time in warm periods are controlled by global ice volume and cold periods by boreal summer insolation

A stochastic model of cascades in 2D turbulence

The dual cascade of energy and enstrophy in 2D turbulence cannot easily be understood in terms of an analog to the Richardson-Kolmogorov scenario describing the energy cascade in 3D turbulence. The coherent up- and downscale fluxes points to non-locality of interactions in spectral space, and thus the specific spatial structure of the flow could be important. Shell models, which lack spacial structure and have only local interactions in spectral space, indeed fail in reproducing the correct scaling for the inverse cascade of energy. In order to exclude the possibility that non-locality of interactions in spectral space is crucial for the dual cascade, we introduce a stochastic spectral model of the cascades which is local in spectral space and which shows the correct scaling for both the direct enstrophy - and the inverse energy cascade.Comment: 4 pages, 3 figure

The middle Pleistocene transition by frequency locking and slow ramping of internal period

The increase in glacial cycle length from approximately $41$ to on average $100$ thousand years around $1$ million years ago, called the Middle Pleistocene Transition (MPT), lacks a conclusive explanation. We describe a dynamical mechanism which we call Ramping with Frequency Locking (RFL), that explains the transition by an interaction between the internal period of a self-sustained oscillator and forcing that contains periodic components. This mechanism naturally explains the abrupt increase in cycle length from approximately $40$ to $80$ thousand years observed in proxy data, unlike some previously proposed mechanisms for the MPT. A rapid increase in durations can be produced by a rapid change in an external parameter, but this assumes rather than explains the abruptness. In contrast, models relying on frequency locking can produce a rapid change in durations assuming only a slow change in an external parameter. We propose a scheme for detecting RFL in complex, computationally expensive models, and motivate the search for climate variables that can gradually increase the internal period of the glacial cycles.Comment: 14 pages, 12 figure