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

Anomalous jumping in a double-well potential

Noise induced jumping between meta-stable states in a potential depends on the structure of the noise. For an $\alpha$-stable noise, jumping triggered by single extreme events contributes to the transition probability. This is also called Levy flights and might be of importance in triggering sudden changes in geophysical flow and perhaps even climatic changes. The steady state statistics is also influenced by the noise structure leading to a non-Gibbs distribution for an $\alpha$-stable noise.Comment: 11 pages, 7 figure

Accuracy of the Aspartic Acid Racemization Technique in Age Estimation of Mammals and the Influence of Body Temperature

The aspartic acid racemization (AAR) technique has been applied for age estimation of humans and other mammals for more than four decades. In this study, eye lenses from 124 animals representing 25 mammalian species were collected and D/L ratios obtained using the AAR technique. The animals were either of known age or had the age estimated by other methods. The purpose of the study was to: a) estimate the accuracy of the AAR technique, and b) examine the effect of body temperature on racemization rates. Samples from four of the 25 species covered the range of ages that is needed to estimate species-specific racemization rates. The sample size from a single species of known age, the pygmy goat (Capra hircus, n = 35), was also large enough to investigate the accuracy of ages obtained using the AAR technique. The 35 goats were divided into three datasets: all goats (n = 35), goats >0.5 yrs old (n = 26) and goats >2 yrs old (n = 19). Leave-one-out analyses were performed on the three sets of data. Normalized root mean squared errors for the group of goats >0.5 yrs old were found to be the smallest. The higher variation in D/L measurements found for young goats 0.5 yrs old was for three age groups of the goats: 0.934 yrs for young goats 8 yrs (n = 4). Thus, the age of an adult or an old animal can be predicted with approximately 10% accuracy, whereas the age of a young animal is difficult to predict. A goat specific racemization rate, as a 2kAsp value, was estimated to 0.0107 ± 3.8 x 10-4 SE (n = 26). The 2kAsp values from 12 species, four estimated in this study and another eight published, were used to examine the effect of core body temperature on the rate of racemization. A positive relationship between AAR and temperature was found (r2 = 0.321) but results also suggest that other factors besides temperature are involved in the racemization process in living animals. Based on our results we emphasize that non-species-specific racemization rates should be used with care in AAR age estimation studies and that the period of postnatal growth of the eye lens be considered when estimating species-specific D/L0 values and ages of young individuals

On the state dependency of fast feedback processes in (palaeo) climate sensitivity

Palaeo data have been frequently used to determine the equilibrium (Charney) climate sensitivity $S^a$, and - if slow feedback processes (e.g. land ice-albedo) are adequately taken into account - they indicate a similar range as estimates based on instrumental data and climate model results. Most studies implicitly assume the (fast) feedback processes to be independent of the background climate state, e.g., equally strong during warm and cold periods. Here we assess the dependency of the fast feedback processes on the background climate state using data of the last 800 kyr and a conceptual climate model for interpretation. Applying a new method to account for background state dependency, we find $S^a=0.61\pm0.06$ K(Wm$^{-2}$)$^{-1}$ using the latest LGM temperature reconstruction and significantly lower climate sensitivity during glacial climates. Due to uncertainties in reconstructing the LGM temperature anomaly, $S^a$ is estimated in the range $S^a=0.55-0.95$ K(Wm$^{-2}$)$^{-1}$.Comment: submitted to Geophysical Research Letter

Levy flights and Levy -Schroedinger semigroups

We analyze two different confining mechanisms for L\'{e}vy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Levy-Schroedinger semigroups which induce so-called topological Levy processes (Levy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological L\'{e}vy process with the very same invariant pdf and in the reverse.Comment: To appear in Cent. Eur. J. Phys. (2010

Two techniques of age estimation in cetaceans: GLGs in teeth and earplugs, and measuring the AAR rate in eye lens nucleus

The ages of three species of cetaceans were estimated by counting the growth layer groups (GLG) and measuring the aspartic acid racemization rate (kAsp) by what is referred to as the Aspartic Acid Racemization (AAR) technique. Data on kAsp and the D/L ratio of aspartic acid at birth [(D/L)0] in North Atlantic common minke whales (Balaenoptera acutorostrata) are presented along with data on fin whales (B. physalus) and harbour porpoises (Phocoena phocoena) already published by Nielsen et al. (2012). The kAsp specific for minke whales was 1.40 x 10-3 yr-1 (SE ± 0.00005) and the (D/L)0 was 0.0194 (SE ± 0.0012). The correlation of GLG age and D/L ratio for all three species was highly significant; however, the correlation coefficient varied greatly (fin whales: R2 = 0.59, p <0.0001; minke whales: ­R2=0.96, P <0.0001; harbour porpoises: ­R2=0.36, P <0.0001). Asymptotic body length for all three species was estimated by a von Bertalanffy growth model on both the GLG and AAR techniques, and showed no difference

Feller Processes: The Next Generation in Modeling. Brownian Motion, L\'evy Processes and Beyond

We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of L\'evy processes. Brownian Motion is one of the most frequently used continuous time Markov processes in applications. In recent years also L\'evy processes, of which Brownian Motion is a special case, have become increasingly popular. L\'evy processes are spatially homogeneous, but empirical data often suggest the use of spatially inhomogeneous processes. Thus it seems necessary to go to the next level of generalization: Feller processes. These include L\'evy processes and in particular Brownian motion as special cases but allow spatial inhomogeneities. Many properties of Feller processes are known, but proving the very existence is, in general, very technical. Moreover, an applicable framework for the generation of sample paths of a Feller process was missing. We explain, with practitioners in mind, how to overcome both of these obstacles. In particular our simulation technique allows to apply Monte Carlo methods to Feller processes.Comment: 22 pages, including 4 figures and 8 pages of source code for the generation of sample paths of Feller processe