VII. Pedia Sapiens: A Genesis Future on Earth and in the Heavens
2. Global Climate as a Complex Dynamical System
A new subsection added in 2011 to gather and report how the vast intricacy of world weather today, and in the paleological past, is coming to be appreciated, distinguished, and quantified by the same nonlinear critically self-organizing dynamics as everywhere else in cosmos, nature, and society. In regard "warming" could not be more of a misnomer, for by these measures abrupt, catastrophic change is more likely. As I again edit in September 2013, a 1000 year flood is presently washing away central Colorado. It would serve climate scientists, under siege by the deniers, to cite themselves say as “physicians of the planet” simply trying to check its relative health, temperature, pressures, electrolytes, and so on. See also Geosphere and Atmosphere for further entries.
American Physical Society Topical Group on the Physics of Climate. www.aps.org/units/gpc/index.cfm. As reported in the New York Times by Andrew Revkin on February 2, 2012, in “Two Nobelists Offer Views of Human-Driven Global Warming” about scientists now standing against deniers and smearers, this national organization has initiated this effort to apply physical and mathematical insights to our real planetary peril. The APS journal Physics Today, in its February 2012 issue, carries a similar report by Tom Feder “Climate Scientists not Cowed by Relentless Climate Change Deniers.”
The objective of the GPC shall be to promote the advancement and diffusion of knowledge concerning the physics, measurement, and modeling of climate processes, within the domain of natural science and outside the domains of societal impact and policy, legislation and broader societal issues. The objective includes the integration of scientific knowledge and analysis methods across disciplines to address the dynamical complexities and uncertainties of climate physics. Broad areas of initial scientific inquiry are described in the Areas of Interest below. These are expected to evolve with scientific progress, while remaining entirely within the domain of natural science.
Shaun Lovejoy Website. www.physics.mcgill.ca/~gang/Lovejoy.htm. The home site for the McGill University geophysicist at the forefront of understanding of earth’s atmosphere by way of nonlinear multifractal computations such as Mathematicia software and satellite imaging. The “gang” above is the “Group for the Analysis of Nonlinear variability in Geophysics,” whose interests run from soils and hydrology to cloud convections and aerosol emissions, each by way of multifractal dynamics. From this site many PDF papers can be accessed, with multiple authors, such as “Towards a New Synthesis for Atmospheric Dynamics” in press for the journal Atmospheric Research (96/01004, 2010). A New Scientist report “And Now the Forecast: Cloudy with a Chance of Fractals” extols these novel advances (November 7, 2009, search).
My research has been directly linked to a series of new geophysical paradigms. A particularly exciting one is the idea that atmospheric dynamics repeat scale after scale from large to small scales in a cascade-like way. The key is recognizing that as the scales get smaller, the horizontal gets “squashed” much more than the vertical so that the stratification which starts out being extreme (structures very flat at planetary scales) become rounder and rounder at small scales.
Barnosky, Anthony, et al. Approaching a State Shift in Earth’s Biosphere. Nature. 486/52, 2012. Some 22 researchers from the University of California, Berkeley, Stanford University, Integrative Ecology Group, Estacion Biologica de Donana, Spain, University of New Mexico, University of Helsinki, Pontificia Universidad Catolica de Chile, Simon Fraser University, California Academy of Sciences, University of Wisconsin, and Missouri Botanical Garden, including Jordi Boscompte, James Brown, John Harte, Pablo Marquet, Geerat Vermeij, and Rosemary Gillespie, seriously worry by way of realistic nonlinear “planetary-scale critical transitions” about an increasingly imminent, forced, epochal climate change.
Localized ecological systems are known to shift abruptly and irreversibly from one state to another when they are forced across critical thresholds. Here we review evidence that the global ecosystem as a whole can react in the same way and is approaching a planetary-scale critical transition as a result of human influence. The plausibility of a planetary-scale ‘tipping point’ highlights the need to improve biological forecasting by detecting early warning signs of critical transitions on global as well as local scales, and by detecting feedbacks that promote such transitions. It is also necessary to address root causes of how humans are forcing biological changes. (Abstract)
Bathiany, Sebastion, et al. Abrupt Climate Change in an Oscillating World. Nature Scientific Reports. 8/5040, 2018. Wageningen University and University of Exeter researchers including Marten Scheffer and Tim Lenton push the concept of global weather as a dynamic complex nonlinear phenomenon to an inevitable consequence. As it becomes more energetically perturbed in small and large ways, a “tipping point” of maximum instability will be reached, untoward, whence the whole system will suddenly oscillate to a radical new set condition on its own.
Here we show how abrupt and sometimes even irreversible change may be evoked by even small shifts in the amplitude or time scale of such environmental oscillations. By using model simulations and reconciling evidence from previous studies we illustrate how these phenomena can be relevant for ecosystems and elements of the climate system including terrestrial ecosystems, Arctic sea ice and monsoons. Although the systems we address are very different and span a broad range of time scales, the phenomena can be understood in a common framework that can help clarify and unify the interpretation of abrupt shifts in the Earth system. (Abstract excerpt)
Berezin, Yehiel, et al. Stability of Climate Networks with Time. Nature Scientific Reports. 2/666, 2012. The online journal places this in a “Statistical Physics, Thermodynamics and Nonlinear Dynamics” section. With coauthors Avi Gozolchiani, Oded Guez, and Shlomo Havlin, Bar Ilan University physicists contribute to the imperative challenge of defining a “Systems Climatology,” whence nature’s universal intricacies can be equally availed in this ultra-complex local and global weather realm to better quantify, and surely mediate.
The pattern of local daily fluctuations of climate fields such as temperatures and geopotential heights is not stable and hard to predict. Surprisingly, we find that the observed relations between such fluctuations in different geographical regions yields a very robust network pattern that remains highly stable during time. Using a new systematic methodology we track the origins of the network stability. It is found that about half of this network stability is due to the spatial 2D embedding of the network, and half is due to physical coupling between climate in different locations. We also find that around the equator, the contribution of the physical coupling is significantly less pronounced compared to off–equatorial regimes. Finally, we show that there is a gradual monotonic modification of the network pattern as a function of altitude difference. (Abstract)
Bodai, Tamas and Tamas Tel. Annual Variability in a Conceptual Climate Model: Snapshot Attractors, Hysteresis in Extreme Events, and Climate Sensitivity. Chaos. 22/023110, 2012. Max Planck Institute, Physics of Complex Systems, researchers investigate such wild weather, which is seen to exhibit the classic features of dynamical phenomena.
We have investigated the effect of periodic driving on a conceptual climate model. In spite of the temporal simplicity of the driving, 2D snapshot attractors proved to be useful representations of the dynamics and show fractal features throughout the annual cycle, which owes to the fact that transient chaos and chaotic saddles are ubiquitous in the considered parameter regimes. (023110-9)
Boers, Niklas, et al. Prediction of Extreme Floods in the Eastern Central Andes based on a Complex Networks Approach. Nature Communications. 5/5199, 2014. Humboldt University, UC Santa Barbara, and University of Sao Paulo researchers including Jurgen Kurths achieve a working mathematical representation of such weather phenomena by way of dynamic nonlinear theories. See also Complex Network Analysis Helps to Identify Impacts of the El Nino Southern Oscillation on Moisture Divergence in South America in Climate Dynamics (45/3-4, 2015) and Complex Networks for Climate Model Evaluation with Application to Statistical versus Dynamical Modeling of South American Climate (44/5-6, 2015), by this team, and the full journal, for further progress.
Changing climatic conditions have led to a significant increase in the magnitude and frequency of extreme rainfall events in the Central Andes of South America. These events are spatially extensive and often result in substantial natural hazards for population, economy and ecology. Here we develop a general framework to predict extreme events by introducing the concept of network divergence on directed networks derived from a non-linear synchronization measure. We apply our method to real-time satellite-derived rainfall data and predict more than 60% (90% during El Niño conditions) of rainfall events above the 99th percentile in the Central Andes. In addition to the societal benefits of predicting natural hazards, our study reveals a linkage between polar and tropical regimes as the responsible mechanism: the interplay of northward migrating frontal systems and a low-level wind channel from the western Amazon to the subtropics. (Abstract)
Dijkstra, Henk. Nonlinear Climate Dynamics. Cambridge: Cambridge University Press, 2013. A Professor of Dynamical Oceanography at the Institute for Marine and Atmospheric Research, Utrecht University, offers an overdue re-assessment of our ultra-intricate and variable local and global weather in terms of mathematical systems science. Chapters range from Climate Variability, Stochastic Dynamical Systems, and Climate Modelling Hierarchy, to the North Atlantic Oscillation, El Nino, Pleistocene Ice Ages, and onto Predictability. While still weighted more toward physical mechanism than self-organizing networks, a turn in a better direction if we are ever to understand and resolve.
This book introduces stochastic dynamical systems theory in order to synthesize our current knowledge of climate variability. Nonlinear processes, such as advection, radiation and turbulent mixing, play a central role in climate variability. These processes can give rise to transition phenomena, associated with tipping or bifurcation points, once external conditions are changed. The theory of dynamical systems provides a systematic way to study these transition phenomena. Its stochastic extension also forms the basis of modern (nonlinear) data analysis techniques, predictability studies and data assimilation methods. Early chapters apply the stochastic dynamical systems framework to a hierarchy of climate models to synthesize current knowledge of climate variability. Later chapters analyse phenomena such as the North Atlantic Oscillation, El Niño/Southern Oscillation, Atlantic Multidecadal Variability, Dansgaard-Oeschger Events, Pleistocene Ice Ages, and climate predictability. This book will prove invaluable for graduate students and researchers in climate dynamics, physical oceanography, meteorology and paleoclimatology. (Publisher)
Donges, Jonathan, et al. Identification of Dynamical Transitions in Marine Palaeoclimate Records by Recurrence Network Analysis. Nonlinear Processes in Geophysics. 18/5, 2011. A companion article in this effort by systems physicists and climatologists from the Universities of Potsdam, Humboldt, and Dresden to attain novel insights, as every other scientific field has done, to the hyper-complex in scale and intricacy of such ancient climes and biotas.
Abstract. The analysis of palaeoclimate time series is usually affected by severe methodological problems, resulting primarily from non-equidistant sampling and uncertain age models. As an alternative to existing methods of time series analysis, in this paper we argue that the statistical properties of recurrence networks are promising candidates for characterising the system’s nonlinear dynamics and quantifying structural changes in its reconstructed phase space as time evolves. Specifically, we investigate the behaviour of recurrence network measures for both paradigmatic model systems with non-stationary parameters and four marine records of long-term palaeoclimate variations. We show that the obtained results are qualitatively robust under changes of the relevant parameters of our method, including detrending, size of the running window used for analysis, and embedding delay. We demonstrate that recurrence network analysis is able to detect relevant regime shifts in synthetic data as well as in problematic geoscientific time series. (545)
Donges, Jonathan, et al. Investigating the Topology of Interacting Networks: Theory and Application to Coupled Climate Subnetworks. European Physical Journal B. 84/4, 2011. n a Focus Section on Frontiers in Network Science, Potsdam Institute for Climate Impact Research, Humboldt University, and Free University Berlin systems physicists provide further application of nature’s universal inherency to animate and abide via robust systems to global and local weather patterns and processes. Again, a novel, imperative phase of climate research is commencing, as most other fields of study have done, moving beyond masses of measurements to engage the equally present dynamical network interactions. An important feature, it is emphasized, is a “vertical” topological structure of atmospheric microclimes.
Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems of interest should be treated, more appropriately, as interacting networks or networks of networks. Here we introduce a novel graph-theoretical framework for studying the interaction structure between subnetworks embedded within a complex network of networks. This framework allows us to quantify the structural role of single vertices or whole subnetworks with respect to the interaction of a pair of subnetworks on local, mesoscopic and global topological scales. Climate networks have recently been shown to be a powerful tool for the analysis of climatological data. Applying the general framework for studying interacting networks, we introduce coupled climate subnetworks to represent and investigate the topology of statistical relationships between the fields of distinct climatological variables. Using coupled climate subnetworks to investigate the terrestrial atmosphere’s three-dimensional geopotential height field uncovers known as well as interesting novel features of the atmosphere’s vertical stratification and general circulation. The promising results obtained by following the coupled climate subnetwork approach present a first step towards an improved understanding of the Earth system and its complex interacting components from a network perspective. (635)
Donges, Jonathan, et al. Nonlinear Detection of Paleoclimate Variability Transitions Possibly Related to Human Evolution. Proceedings of the National Academy of Sciences. 108/20422, 2011. Donges, with the European team of Reik Donner, Martin Trauth, Norbert Marwan, Hans Schellnhuber, Jurgen Kurths, and colleagues, continue their extensive, daunting project of rightly interpreting prehistoric and current atmospheres by way of nature’s universally present complex systems phenomena.
Potential paleoclimatic driving mechanisms acting on human evolution present an open problem of cross-disciplinary scientific interest. The analysis of paleoclimate archives encoding the environmental variability in East Africa during the past 5 Ma has triggered an ongoing debate about possible candidate processes and evolutionary mechanisms. In this work, we apply a nonlinear statistical technique, recurrence network analysis, to three distinct marine records of terrigenous dust flux. Our method enables us to identify three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Middle Pliocene (3.35–3.15 Ma B.P.), (ii) Early Pleistocene (2.25–1.6 Ma B.P.), and (iii) Middle Pleistocene (1.1–0.7 Ma B.P.). A reexamination of the available fossil record demonstrates statistically significant coincidences between the detected transition periods and major steps in hominin evolution. This result suggests that the observed shifts between more regular and more erratic environmental variability may have acted as a trigger for rapid change in the development of humankind in Africa. (20422)
Donner, Reik, et al. Recurrence Networks – A Novel Paradigm for Nonlinear Time Series Analysis. New Journal of Physics. 12/3, 2010. With Yong Zou, J. Donges, N. Marwan, and J. Kurths, a technical paper about this method being found of much utility for understanding climate and weather as a complex dynamical system, as other articles in this section put to good avail.
Since the early stages of quantitative nonlinear sciences, numerous conceptual approaches have been introduced for studying the characteristic features of dynamical systems based on observational time series. Popular methods that are increasingly used in a variety of applications include, among others, Lyapunov exponents, fractal dimensions, symbolic discretization and measures of complexity such as entropies and quantities derived from them. All these techniques have in common that they quantify certain discretized realizations of individual trajectories. (2) As an appealing solution, we have suggested recurrence networks as a unifying framework for studying time series as complex networks, which is based on a novel approach for the quantitative assessment of recurrence plots in terms of complex network measures. (30)