Climate Dynamics: A Network-Based Approach for the Analysis of Global Precipitation

Precipitation is one of the most important meteorological variables for defining the climate dynamics, but the spatial patterns of precipitation have not been fully investigated yet. The complex network theory, which provides a robust tool to investigate the statistical interdependence of many interacting elements, is used here to analyze the spatial dynamics of annual precipitation over seventy years (1941-2010). The precipitation network is built associating a node to a geographical region, which has a temporal distribution of precipitation, and identifying possible links among nodes through the correlation function. The precipitation network reveals significant spatial variability with barely connected regions, as Eastern China and Japan, and highly connected regions, such as the African Sahel, Eastern Australia and, to a lesser extent, Northern Europe. Sahel and Eastern Australia are remarkably dry regions, where low amounts of rainfall are uniformly distributed on continental scales and small-scale extreme events are rare. As a consequence, the precipitation gradient is low, making these regions well connected on a large spatial scale. On the contrary, the Asiatic South-East is often reached by extreme events such as monsoons, tropical cyclones and heat waves, which can all contribute to reduce the correlation to the short-range scale only. Some patterns emerging between mid-latitude and tropical regions suggest a possible impact of the propagation of planetary waves on precipitation at a global scale. Other links can be qualitatively associated to the atmospheric and oceanic circulation. To analyze the sensitivity of the network to the physical closeness of the nodes, short-term connections are broken. The African Sahel, Eastern Australia and Northern Europe regions again appear as the supernodes of the network, confirming furthermore their long-range connection structure. Almost all North-American and Asian nodes vanish, revealing that extreme events can enhance high precipitation gradients, leading to a systematic absence of long-range patterns

Local Difference Measures between Complex Networks for Dynamical System Model Evaluation

Acknowledgments We thank Reik V. Donner for inspiring suggestions that initialized the work presented herein. Jan H. Feldhoff is credited for providing us with the STARS simulation data and for his contributions to fruitful discussions. Comments by the anonymous reviewers are gratefully acknowledged as they led to substantial improvements of the manuscript.Peer reviewedPublisher PD

Mutual information rate and bounds for it

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two data sets (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators

Complex networks for climate model evaluation with application to statistical versus dynamical modeling of South American climate

Acknowledgments: This paper was developed within the scope of the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP. Furthermore, this work has been financially supported by the Leibniz Society (project ECONS), and the Stordalen Foundation (JFD). For certain calculations, the software packages pyunicorn (Donges et al. 2013a) and igraph (Csa´rdi and Nepusz 2006) were used. The authors would like to thank Manoel F. Cardoso, Niklas Boers, and the reviewers for helpful comments on the manuscript. Open Access: This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.Peer reviewedPostprin

Dynamic Evolution of Microscopic Wet Cracking Noises

Characterizing the interaction between water and microscopic defects is one of the long-standing challenges in understanding a broad range of cracking processes. Different physical aspects of microscopic events, driven or influenced by water, have been extensively discussed in atomistic calculations but have not been accessible in microscale experiments. Through the analysis of the emitted noises during the evolution of individual, dynamic microcracking events, we show that the onset of a secondary instability known as hybrid events occurs during the fast healing phase of microcracking, which leads to (local) sudden increase of pore water pressure in the process zone, inducing a secondary instability, which is followed by a fast-locking phase on the microscopic faults (pulse-like rupture)

A combinatorial framework to quantify peak/pit asymmetries in complex dynamics

LL’s acknowledges funding from an EPSRC Early Career Fellowship EP/P01660X/1

Is the astronomical forcing a reliable and unique pacemaker for climate? A conceptual model study

There is evidence that ice age cycles are paced by astronomical forcing, suggesting some kind of synchronisation phenomenon. Here, we identify the type of such synchronisation and explore systematically its uniqueness and robustness using a simple paleoclimate model akin to the van der Pol relaxation oscillator and dynamical system theory. As the insolation is quite a complex quasiperiodic signal involving different frequencies, the traditional concepts used to define synchronisation to periodic forcing are no longer applicable. Instead, we explore a different concept of generalised synchronisation in terms of (coexisting) synchronised solutions for the forced system, their basins of attraction and instabilities. We propose a clustering technique to compute the number of synchronised solutions, each of which corresponds to a different paleoclimate history. In this way, we uncover multistable synchronisation (reminiscent of phase- or frequency-locking to individual periodic components of astronomical forcing) at low forcing strength, and monostable or unique synchronisation at stronger forcing. In the multistable regime, different initial conditions may lead to different paleoclimate histories. To study their robustness, we analyse Lyapunov exponents that quantify the rate of convergence towards each synchronised solution (local stability), and basins of attraction that indicate critical levels of external perturbations (global stability). We find that even though synchronised solutions are stable on a long term, there exist short episodes of desynchronisation where nearby climate trajectories diverge temporarily (for about 50 kyr). (...)Comment: 22 pages, 18 figure

Temporal organization of magnetospheric fluctuations unveiled by recurrence patterns in the Dst index

Magnetic storms constitute the most remarkable large-scale phenomena of nonlinear magnetospheric dynamics. Studying the dynamical organization of macroscopic variability in terms of geomagnetic activity index data by means of complexity measures provides a promising approach for identifying the underlying processes and associated time scales. Here, we apply a suite of characteristics from recurrence quantification analysis (RQA) and recurrence network analysis (RNA) in order to unveil some key nonlinear features of the hourly Disturbance storm-time (Dst) index during periods with magnetic storms and such of normal variability. Our results demonstrate that recurrence-based measures can serve as excellent tracers for changes in the dynamical complexity along non-stationary records of geomagnetic activity. In particular, trapping time (characterizing the typical length of “laminar phases” in the observed dynamics) and recurrence network transitivity (associated with the number of the system’s effective dynamical degrees of freedom) allow for a very good discrimination between magnetic storm and quiescence phases. In general, some RQA and RNA characteristics distinguish between storm and non-storm times equally well or even better than other previously considered nonlinear characteristics like Hurst exponent or symbolic dynamics based entropy concepts. Our results point to future potentials of recurrence characteristics for unveiling temporal changes in the dynamical complexity of the magnetosphere. Geomagnetic activity indices trace the temporal variability of the Earth’s magnetic field across different spatial domains of the near-Earth environment. Among others, the Disturbance storm-time (Dst) index has been used in many previous studies as a diagnostic of the overall state of the magnetosphere. Here, we employ different techniques based upon the concept of recurrence plots to improve our understanding of the complex variability patterns exhibited by this index when the geomagnetic field undergoes a sequence of magnetic storm and quiescence periods triggered by non-stationary solar wind forcing. We demonstrate that recurrence characteristics provide unique tools for discriminating between the dynamical complexity properties of Dst during times with strong geomagnetic activity and quiescence phases. Thus, future applications of these measures to other geomagnetic activity indices with higher temporal resolution may potentially allow us to identify characteristic signatures of complexity variations preceding intense magnetic storms, which could open new perspectives for space weather short-term forecasting