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VIII. Earth Earns: An Open Participatory Earthropocene to Astropocene CoCreativity

2. Global Climate Change as a Complex Dynamical System

Kuna, Tobias and Sandro Valenti. Special Issue on Mathematics for the Fluid Earth. Journal of Physics A. 50/170301, 2015. An introduction by Reading University and Aix-Marseille University physicists. Some papers are Extreme Value Laws for Fractal Intensity Functions in Dynamical Systems, The Role of Nonlinear Self-Interaction in the Dynamics of Planetary-Scale Atmospheric Fluctuations, and Extreme Event Statistics of Daily Rainfall.

The fluid Earth is an excellent example of a forced, dissipative non-equilibrium system dominated by nonlinear processes and featuring multi-scale interactions. This collection consists of reviews and original research articles which span the full spectrum from mathematical papers addressing general questions, articles considering these questions for more realistic problems in theoretical physics and articles that apply new mathematical tools to concrete physical situations with application to the Fluid Earth system. The complexity of this system and its phenomena are presented in relation to the statistical manifestation of large scale systems in the asymptotic regimes far from equilibrium; where loss of memory and recurrence prevail.

Lana, Xavier, et al. Multifractal Structure of the Monthly Rainfall Regime in Catalonia: Evaluation of the Non-linear Complexity. Chaos. July, 2020. The rain in Spain stays mainly in the plain was famously sung in My Fair Lady (1956). In 2020 Polytechnic University of Catalonia physicists proceed to quantify predictable patterns by way of advanced topological and computational methods.

The complex non-linear regime of the monthly rainfall in Catalonia is analyzed by means of the reconstruction fractal theorem and the multifractal detrended fluctuation analysis algorithm. Areas with a notable degree of complex physical mechanisms are detected by using the concepts of persistence (Hurst exponent), complexity (embedding dimension), predictive uncertainty (Lyapunov exponents), loss of memory of the mechanism (Kolmogorov), and the set of multifractal parameters (spectral asymmetry, width, and complexity). Besides these analyses permitting a detailed description of monthly rainfall pattern characteristics, the obtained results should also be relevant for new research studies concerning monthly amounts forecasting at a monthly scale. (Abstract excerpt)

Lenton, Timothy, et al. Climate Tipping Points are Too Risky to Bet Against. Nature. 575/592, 2019. Seven senior climate scientists including Will Steffen and Hans Schellnhuber seek to inform and warn that near and far world weather, as a hyper-complex, quite over-stressed dynamical system, is capable of a sudden, abrupt change of (attractor) state. But then Hollywood has long picked up on this peril with biosphere busters such as The Day After Tomorrow, Geostorm, Category Seven, Twister, and more.

Lenton, Timothy, et al. Tipping Elements in the Earth’s Climate System. Proceedings of the National Academy of Sciences. 105/1786, 2008. A summary of a meeting at the British Embassy, Berlin, facilitated by Hans Joachim Schellnhuber, a German environmentalist and advisor to Chancellor Andrea Merkel, which contends that many biospheric realms such as West African monsoons, Arctic ozone, permafrost depth and expanse, are critically poised and any one could suddenly set off a dramatic shift in global weather conditions.

Human activities may have the potential to push components of the Earth system past critical states into qualitatively different modes of operation, implying large-scale impacts on human and ecological systems. Examples that have received recent attention include the potential collapse of the Atlantic thermohaline circulation, dieback of the Amazon rainforest, and decay of the Greenland ice sheet. Such phenomena have been described as "tipping points" following the popular notion that, at a particular moment in time, a small change can have large, long-term consequences for a system, i.e., "little things can make a big difference.” (1786)

Lovejoy, Shaun and Daniel Schertzer. The Weather and Climate: Emergent Laws and Multifractal Cascades. Cambridge: Cambridge University Press, 2013. A McGill University physicist and University of Paris hydrologist contribute a major text to the crucial project of gaining theoretical insights to this most dynamically complex realm. Select chapters and sections could be: A New Synthesis, An Introduction to Multiplicative Cascades, Universal Multifractal Processes, Generalized Scale Invariance and Cloud Morphology, and The Emergent Laws of the Weather. By these lights “a quiet revolution in atmospheric modeling,” aided by global computer capacities, is now underway. A key finding is a stochastic self-organized criticality that repeats on every global to local regime. Search Lovejoy for his McGill website and more papers.

Advances in nonlinear dynamics, especially modern multifractal cascade models, allow us to investigate the weather and climate at unprecedented levels of accuracy. Using new stochastic modelling and data analysis techniques, this book provides an overview of the nonclassical, multifractal statistics. By generalizing the classical turbulence laws, emergent higher-level laws of atmospheric dynamics are obtained and are empirically validated over time-scales of seconds to decades and length-scales of millimetres to the size of the planet. In generalizing the notion of scale, atmospheric complexity is reduced to a manageable scale-invariant hierarchy of processes, thus providing a new perspective for modelling and understanding the atmosphere. This new synthesis of state-of-the-art data and nonlinear dynamics is systematically compared with other analyses and global circulation model outputs.

1.2.1 The basic form of the emergent laws and spectral analysis Without further mathematical or physical restrictions, the high number of degrees of freedom paradigm of stochastic chaos is too general to be practical. But with the help of a scale-invariant symmetry such that in some generalized sense the dynamics repeat scale after scale, it becomes tractable and even seductive. It turns out that the equations of the atmosphere are indeed formally scale-invariant (Chapter 2), and even fields for which no theoretically “clean” equations exist (such as for precipitation) still apparently respect such scale symmetries.

Lucarini, Valerio. Introduction to the Special Issue on the Statistical Mechanics of Climate. Journal of Statistical Physics. 179/5-6, 2020. As another instance of the 2020 confirmation of complex dynamic systems in effect at every phenomenal phase, the University of Reading mathematician (search) introduces 24 papers such as Nonequilibrium Oscillations, Probability Angular Momentum and the Climate System, Extreme Sensitivity and Climate Tipping Points, and Phase Transitions and Extreme Events which contribute highly technical studies of local and global weather. And I log this in as hurricane Isaias with embedded tornados passes over my western Massachusetts, a very rare climate change result.

We introduce the special issue on the Statistical Mechanics of Climate by presenting an informal discussion of some theoretical aspects of climate dynamics that make it a topic of great interest for mathematicians and theoretical physicists. In particular, we briefly discuss its nonequilibrium and multiscale properties, the relationship between natural climate variability and climate change, the different regimes of climate response to perturbations, and critical transitions. (Abstract)

Lucarini, Valerio, et al. Habitability and Multistability in Earth-like Planets. Astronomische Nachrichten. 334/6, 2013. Reviewed more in ExoEarths, this University of Hamburg group, with colleagues worldwide, are at the same while beginning to characterize their relative (bio)chemical atmospheres and weather dynamics. See also Bistability of the Climate around the Habitable Zone: A Thermodynamic Investigation by VL, et al, in Icarus (226/1724, 2013).

Lucarini, Valerio, et al. Mathematical and Physical Ideas for Climate Science. arXiv:1311.1190. Online December 2013, University of Hamburg, Germany, and National Center for Atmospheric Research, USA, researchers find the world’s weather to epitomize an ultra-complex, non-equilibrium dynamical system. For this reason science has been slow to proceed with studies, but of such importance it is vital to move ahead with this project. One might observe that coming from statistical physics and mathematics experience, this approach gets very technical, as in prior efforts. An international consortium, which this section reports is incipiently forming, ought to coordinate inputs from all aspects of systems science.

The climate is an excellent example of a forced, dissipative system dominated by nonlinear processes and featuring non-trivial dynamics of a vast range of spatial and temporal scales. The understanding of the climate's structural and multiscale properties is crucial for the provision of a unifying picture of its dynamics and for the implementation of accurate and efficient numerical models. In this interdisciplinary review, we are guided by our interest in exploring the nexus between climate and concepts such as energy, entropy, symmetry, response, multiscale interactions, and its potential relevance in terms of numerical modeling. We focus on the very promising results on the statistical mechanics of quasi-equilibrium geophysical flows, which are extremely useful in the direction of constructing a robust theory of geophysical macro turbulence.

The second half of the review is dedicated to the non-equilibrium properties of the climate system. First, we describe some recent findings showing how to use basic concepts of macroscopic non-equilibrium thermodynamics for characterizing the energy and entropy budgets of the climate systems, with the ensuing protocols for intercomparing climate models and developing methods aimed at studying tipping points. These ideas can also create a link between climate science and the growing sector of astrophysics devoted to the investigation of exoplanetary atmospheres. We conclude by focusing on non-equilibrium statistical mechanics, which allows for framing in a unified way problems as different as climate response to forcings of general nature, the effect of altering the boundary conditions or the coupling between geophysical flows, and the derivation of parametrizations for numerical models. (Abstract excerpts)

Ludescher, Josef, et al. Network-based Forecasting of Climate Phenomena. PNAS. 118/47, 2021. With a base at the Potsdam Institute for Climate Impact Research, thirteen complexity theorists and climate researchers in Germany, the UK, China, Israel, Russia and Switzerland including Jurgen Kurths, Shlomo Havlin and Hans Shellenhuber, contribute a major confirmation of this 21st century project to analyze even hyper-intricate world and bioregion weather phenomena by way of the same nonlinear complexities now found in formative kind everywhere else. By extension, nature’s actual organic essence, form and process are in apparent “genetic” effect as they must be. In every respect, a node/link, DNA/AND, bigender universality and familial triality is present as metabolic networks. Into later 2021 (November), if these many robust, disparate verifications of a natural source code program are seen altogether, they bode well for such an imminent ecosmic discovery event.

Network theory, as emerging from complex systems science, can provide critical predictive power for mitigating the global warming crisis and other societal challenges. Here we discuss the main differences of this approach to classical numerical modeling and highlight several cases where the network approach substantially improved the prediction of high-impact phenomena: 1) El Niño events, 2) droughts in the central Amazon, 3) extreme rainfall in the eastern Central Andes, 4) the Indian summer monsoon, and 5) extreme stratospheric polar vortex states that influence the occurrence of wintertime cold spells in northern Eurasia. (Abstract)

Ma, Tian and Shouhong Wang. Phase Transition Dynamics. Berlin: Springer, 2014. Sichuan University and Indiana University mathematicians draw upon statistical physics to formulate an innovative thermodynamic theory for equilibrium and nonequilibrium phenomena. With a view that natural systems are situated and poised as an active fluidity, these principles are effectively applied to Geophysical and Climate Dynamics such as oceanic and atmospheric circulation, e.g. El Nino. Dynamic Transition in Chemistry and Biology follows as bacterial chemotaxis and speciations.

Margazoglou, Georgios, et al. Dynamical Landscape and Multistability of a Climate Model. Proceedings of the Royal Society A. June, 2021. Centre for the Mathematics of the Planet Earth, University of Reading, University of Warwick and International School for Advanced Studies, Trieste systems physicists including Valerio Lucarini continue to quantify the Global Stability Properties of the Climate System by way of nonlinear complex network dynamics across four dimensions. In 2021 regard, a quality aspect ought to be entered as a worldwide realization that such a generative source-code does independently exist on its universal own. However we wonder can this actual 2020s philosophic mindset and revolutionary discovery come into our aware, agreed recognition.

We apply two independent data analysis methods to locate stable climate states in an intermediate complexity climate model. First, by way of the theory of quasipotentials we view the state space as an energy landscape so to infer the likelihood of the multistable climate states,. Second, we avail data science techniques to characterize to find climate states and basin boundaries. Both approaches show remarkable agreement, and reveal, apart from the well known warm and snowball earth states, an intermediate stable state. These approaches can altogether identify how the negative feedback of ocean heat transport and entropy production via the hydrological cycle drastically changes the topography of Earth's dynamic climate. (Abstract excerpt)

Molkenthin, Nora, et al. Network from Flows: From Dynamics to Topology. Nature Scientific Reports. 4/4119, 2014. A team from the Potsdam Institute for Climate Impact Research including Jurgen Kurths make a significant contribution to the study and understanding of ultra-intricate global weather patterns and processes by way of universal network principles.

Complex network approaches have recently been applied to continuous spatial dynamical systems, like climate, successfully uncovering the system's interaction structure. However the relationship between the underlying atmospheric or oceanic flow's dynamics and the estimated network measures have remained largely unclear. We bridge this crucial gap in a bottom-up approach and define a continuous analytical analogue of Pearson correlation networks for advection-diffusion dynamics on a background flow. Analysing complex networks of prototypical flows and from time series data of the equatorial Pacific, we find that our analytical model reproduces the most salient features of these networks and thus provides a general foundation of climate networks. The relationships we obtain between velocity field and network measures show that line-like structures of high betweenness mark transition zones in the flow rather than, as previously thought, the propagation of dynamical information. (Abstract)

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