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

2. Global Climate Change as a Complex Dynamical System

Steinhaeuser, Karsten, et al. Multivariate and Multiscale Dependence in the Global Climate System Revealed through Complex Networks. Climate Dynamics. 39/3-4, 2012. Steinhaeuser, and Auroop Ganguly, Geographic Information Science Group, ORNL, with Nitesh Chawla, University of Notre Dame, Interdisciplinary Center for Network Science, offer theory and examples of how weather patterns can be modeled by way of nonlinear network topologies and dynamics.

Thompson, J. Michael and Jan Sieber. Introduction: Climate Predictions: The Influence of Nonlinearity and Randomness. Philosophical Transactions of the Royal Society A. 370/1007, 2012. University of Aberdeen and University of Portsmouth mathematicians engage daunting climate complexities which yet are seen to lend themselves to nonlinear discernment. A core concern is then a better warning system for abrupt weather “tipping points.” A typical paper could be Tipping Points in Open Systems by Peter Ashwin, et al. Also search herein for a companion article by Axel Kleidon on non-equilibrium thermodynamics.

The current threat of global warming and the public demand for confident projections of climate change pose the ultimate challenge to science: predicting the future behaviour of a system of such overwhelming complexity as the Earth's climate. This Theme Issue addresses two practical problems that make even prediction of the statistical properties of the climate, when treated as the attractor of a chaotic system (the weather), so challenging. The first is that even for the most detailed models, these statistical properties of the attractor show systematic biases. The second is that the attractor may undergo sudden large-scale changes on a time scale that is fast compared with the gradual change of the forcing (the so-called climate tipping). (Abstract)

Toppaladoddi, Srikanth and John Wettlaufer. Statistical Mechanics and the Climatology of the Arctic Sea Ice Thickness Distribution. Journal of Statistical Physics. Online January, 2017. We note this work by Yale University mathematical geophysicists for its achievement, and also to record how nature’s dynamic materiality is subject to, and can be seen to exhibit, an exemplary presence everywhere.

We study the seasonal changes in the thickness distribution of Arctic sea ice, g(h), under climate forcing. Our analytical and numerical approach is based on a Fokker–Planck equation for g(h) in which the thermodynamic growth rates are determined using observed climatology. We find that due to the combined effects of thermodynamics and mechanics, g(h) spreads during winter and contracts during summer. This behavior is in agreement with recent satellite observations from CryoSat-2. Because g(h) is a probability density function, we quantify all of the key moments (e.g., mean thickness, fraction of thin/thick ice, mean albedo, relaxation time scales) as greenhouse-gas radiative forcing, ΔF0, increases. This exhibits the crucial role that ice mechanics plays in maintaining the ice cover, by redistributing thin ice to thick ice-far more rapidly than can thermal growth alone. (Abstract excerpts)

Tsonis, Anastasios and James Elsner, eds. Nonlinear Dynamics in Geosciences. Berlin: Springer, 2012. Noted more in Geosphere and Atmosphere, its lead chapter, Introducing Networks in Climate Studies by Tsonis, a University of Wisconsin meteorologist, is a review of early attempts to understand weather phenomena as complex systems. See also Tsonis herein for a 2012 update.

Tsonis, Anastasios and K. L. Swanson. On the Origins of Decadal Climate Variability: A Network Perspective. Nonlinear Processes in Geophysics. 19/5, 2012. University of Wisconsin mathematical meteorologists seek novel ways to conceive weather dynamics in a generic complex system format. Logging on a few days after the Sandy Superstorm, whence commentators from scientists to politicians agree is due to forced global “warming,” we need to move apace to a “systems climatology” able to conceive such increasingly erratic oscillations as critically poised nonlinear phenomena.

This review is a synthesis of work spanning the last 25 yr. It is largely based on the use of climate networks to identify climate subsystems/major modes and to subsequently study how their collective behavior explains decadal variability. The central point is that a network of coupled nonlinear subsystems may at times begin to synchronize. If during synchronization the coupling between the subsystems increases, the synchronous state may, at some coupling strength threshold, be destroyed shifting climate to a new regime. This climate shift manifests itself as a change in global temperature trend. This mechanism, which is consistent with the theory of synchronized chaos, appears to be a very robust mechanism of the climate system. It is found in the instrumental records, in forced and unforced climate simulations, as well as in proxy records spanning several centuries. (Abstract)

Tuck, Adrian. From Molecules to Meteorology via Turbulent Scale Invariance. Quarterly Journal of the Royal Meteorological Society. 136/1125, 2010. An Imperial College, London physicist details the self-similar, “statistical multifractal” nature of dynamical climate phenomena from jet streams and ring currents to temperature, humidity and ozone levels.

This review attempts to interpret the generalized scale invariance observed in common atmospheric variables—wind, temperature, humidity, ozone and some trace species—in terms of the computed emergence of ring currents (vortices) in simulations of populations of Maxwellian molecules subject to an anisotropy in the form of a flux. The data are taken from ‘horizontal’ tracks of research aircraft and from ‘vertical’ trajectories of research dropsondes. It is argued that any attempt to represent the energy distribution in the atmosphere quantitatively must have a proper basis in molecular physics, a prerequisite to accommodate the observed long-tailed velocity probability distributions and the implied effects on radiative transfer, atmospheric chemistry, turbulent structure and the definition of temperature itself. The relationship between fluctuations and dissipation is discussed in a framework of non-equilibrium statistical mechanics, and a link between maximization of entropy production and scale invariance is hypothesized. (Abstract)

Voosen, Paul. The Earth Machine. Science. 361/344, 2018. In a Frontiers of Computation section, a staff writer reports on a well-funded project to apply the latest deep learning AI methods to better cope with and analyze the vast amounts of dynamic weather data from around the world. The title above is its working name, of course quite inappropriate and part of the problem, which need be revised to a Gaian organismic anatomy and physiology personsphere if we are ever to adequately understand, and to respectfully care for.

This summer, an academic consortium led by Tapio Schneider, a German-born climate dynamicist at the California Institute of Technology in Pasadena, and backed by prominent technology philanthropists, including Microsoft co-founder Paul Allen, will launch an ambitious project to create a new climate model. Their upstart project seeks to leverage breakthroughs in artificial intelligence, satellite imaging, and high-resolution simulation to change how climate models render small-scale phenomena, such as sea ice and cloud formation, that have long bedeviled efforts to forecast climate. A focus will be on the major source of uncertainty in current models: the decks of stratocumulus clouds that form off coastlines and populate the trade winds. A shift in their extent by just a few percentage points could turn the global thermostat up or down by a couple of degrees or more within this century—and current models can't predict which way they will go. (Summary)

Yalcin, G. Cigdem, et al. Extreme Event Statistics of Daily Rainfall: Dynamical Systems Approach. Journal of Physics A. 49/154001, 2016. Istanbul University and Queen Mary University of London system scientists apply the latest complexity theories to discern that even rainy days can be found to exhibit universal nonlinear patterns. One then wonders what manner of natural genesis ecosmos are we altogether finding which is due to and so exemplifies this mathematical domain.

We analyse the probability densities of daily rainfall amounts at a variety of locations on Earth. The observed distributions of the amount of rainfall fit well to a q-exponential distribution. We discuss possible reasons for the emergence of this power law. In contrast, the waiting time distribution between rainy days is observed to follow a near-exponential distribution. We discuss the extreme value statistics for extreme daily rainfall, which can potentially lead to flooding. Looking at extreme event statistics of waiting times between rainy days (leading to droughts for very long dry periods) we discuss superstatistical dynamical systems as simple models in this context. (Abstract edits)

Yang, Wang, et al. Dominant Imprint of Rossby Waves in the Climate Network. Physical Review Letters. 111/13, 2013. Israeli physicists including Shlomo Havlin are able to discern and quantify complex systems that characterize even these global weather phenomena. The paper was considered by the journal to merit a special review, which is appended after the abstract.

The connectivity pattern of networks based on ground level temperature records shows a dense stripe of links in the extra tropics of the southern hemisphere. We show that statistical categorization of these links yields a clear association with the pattern of an atmospheric Rossby wave, one of the major mechanisms associated with the weather system and with planetary scale energy transport. It is shown that alternating densities of negative and positive links are arranged in half Rossby wave distances around 3500, 7000, and 10 000 km and are aligned with the expected direction of energy flow, distribution of time delays, and the seasonality of these waves. In addition, long distance links that are associated with Rossby waves are the most dominant in the climate network.

Rossby waves are planetary-scale meanders in the high-altitude winds that flow about 10km above ground (between the troposphere and the stratosphere). They arise because of the temperature difference between polar air and tropical air, together with variation of the Coriolis force with latitude. Meteorologists know them well, as they determine low-pressure systems that have a major influence on the weather. But according to a study published in Physical Review Letters, such waves may determine more than whether it will rain or shine in the short term. By transporting energy around the planet, they may act as important interconnecting links between remote regions, thereby affecting the longer-term dynamics of the climate system. (Abstract)

Yang Wang, at the Bar-Ilan University in Israel, and colleagues describe the climate system using a recently developed approach based on network theory: different regions of the world are considered as nodes of a network, interconnected by links representing the channels through which heat and materials (air and water) are exchanged. The authors apply the method to extract the statistical properties of these links from a database of climate parameters (such as temperature, pressure, and wind velocities) measured during the years 1948–2010. These links exhibit the patterns of an atmospheric Rossby wave: they have undulations that match Rossby wavelengths (3500, 7000, and 10000km), are aligned along the same directions, and have the same seasonality. (PRL Synopsis)

Yao, Qing, et al. Emergence of Universal Scaling in Weather Extreme Events. arXiv:2209.02292. From a disparate realm, seven complexity theorists based in China, Germany, the UK, and Japan including Valerio Lucarini (University of Reading, Center for the Mathematics of Planet Earth) and Henrik Jensen (Imperial College London, Center for Complexity Science) contribute another late 2022 result which again avers and proves a recurrent affinity across many domains.

The frequency and magnitude of weather extreme events have increased significantly during the past few years in response to anthropogenic climate change. However, global characteristics and physical mechanisms are not fully understood. Here, we adopt a statistical probability theory method to study extreme weather events with especial regard to daily temperature differences. We find universal scaling laws which are very stable. Which provides a fresh perspective on natural regularities and climate systems. Our work thus sheds light on the nature of the weather variabilities and could guide us to better forecast extreme events. (Abstract excerpt)

Natural or social systems far from equilibrium often show complex dynamic behaviours. In addition an increasing empirical evidence reveals that fields as diverse as physic, biology, ecology, human mobility, economics, and financial markets may all sufficiently follow the principles of scale invariance and universality. Scaling functions are then seen to characterize the critical phenomena of phase transitions. These many results can serve as models and methods for understanding the behaviours of various complex phenomena, such as the climate system and earthquakes. (3)

Zu-Guo, Yu, et al. Multifractal Analyses of Daily Rainfall Time Series in Pearl River Basin of China. Physica A. 405/1, 2014. As all manner of climate, weather, and atmospheric phenomena now found to reflect a common nonlinear dynamics, Chinese mathematicians and environmentalists here show that rainy days likewise reflect a self-similar pattern.

The multifractal properties of daily rainfall time series at the stations in Pearl River basin of China over periods of up to 45 years are examined using the universal multifractal approach based on the multiplicative cascade model and the multifractal detrended fluctuation analysis (MF-DFA). The results from these two kinds of multifractal analyses show that the daily rainfall time series in this basin have multifractal behavior in two different time scale ranges. It is found that the empirical multifractal moment function K(q)K(q) of the daily rainfall time series can be fitted very well by the universal multifractal model (UMM). (Abstract)

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