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A Sourcebook for the Worldwide Discovery of a Creative Organic Universe
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VI. Earth Life Emergence: Development of Body, Brain, Selves and Societies

1. Geosphere and Atmosphere

Quattrochi, Dale and Michael Goodchild, eds. Scale in Remote Sensing and GIS. Boca Raton, FL: Lewis Publishers, 1997. Many papers find Geographic Information Systems GIS in both environmental and social domains to be based on a fractal, scale-invariant nature.

Rinaldo, Andrea, et al. Evolution and Selection of River Networks: Statics, Dynamics, and Complexity. Proceedings of the National Academy of Sciences. 111/2417, 2014. Environmental scientists Rinaldo, University of Padova, with Riccardo Rigon, University of Trento, Jayanth Banavar, University of Maryland, Amos Maritan, National Institute of Nuclear Physics, Padova, and Ignacio Rodriguez-Iturbe, Princeton University, quantify how riverine courses and currents can be seen to exemplify nature’s universal self-organizing propensities. So to wax, the one same river seems to roll and run on through cosmos, earth, and evolution as it flows to and carries us.

Significance: Our focus is on a rich interdisciplinary problem touching on earth science, hydrology, and statistical mechanics — an understanding of the statics and dynamics of the network structures that we observe in the fluvial landscape, and their relation to evolution and selection of recurrent patterns of self-organization. It is an exemplar of how diverse ideas, numerical simulation, and elementary mathematics can come together to help solve the mystery of understanding a ubiquitous pattern of nature.

Moving from the exact result that drainage network configurations minimizing total energy dissipation are stationary solutions of the general equation describing landscape evolution, we review the static properties and the dynamic origins of the scale-invariant structure of optimal river patterns. Optimal channel networks (OCNs) are feasible optimal configurations of a spanning network mimicking landscape evolution and network selection through imperfect searches for dynamically accessible states. OCNs are spanning loopless configurations, however, only under precise physical requirements that arise under the constraints imposed by river dynamics—every spanning tree is exactly a local minimum of total energy dissipation. It is remarkable that dynamically accessible configurations, the local optima, stabilize into diverse metastable forms that are nevertheless characterized by universal statistical features. Such universal features explain very well the statistics of, and the linkages among, the scaling features measured for fluvial landforms across a broad range of scales regardless of geology, exposed lithology, vegetation, or climate, and differ significantly from those of the ground state, known exactly. (Abstract)

Rinaldo, Andrea, et al. Trees, Networks, and Hydrology. Water Resources Research. 42/W06D07, 2006. For some background, Andrea Rinaldo of the University of Padova wrote in his 1994 paper On Landscape Self-Organization in this journal: A new quantitative characterization of landscape-forming processes in the general framework of self-organized criticality and of fractal analyses is proposed. A decade or so later, now with Amos Maritan of Padova, and Jayanth Banavar of Penn State University, the accepted presence of such mathematical dynamics can be articulated and understood.

This paper reviews theoretical and observational material on form and function of natural networks appeared in somewhat disparate contexts from physics to biology, whose study is related to hydrologic research. Moving from the exact result that drainage network configurations minimizing total energy dissipation are stationary solutions of the general equation describing landscape evolution, we discuss the properties and the dynamic origin of the scale-invariant structure of river patterns and its relation to optimal selection. (Abstract) We thus conclude that one recurrent self-organized mechanism for the dynamic origin of fractal forms is the robust strive for imperfect optimality that we see embedded in many natural patterns, chief and foremost hydrologic ones. (Abstract)

Ripl, Wilhelm. Water: The Bloodstream of the Biosphere. Philosophical Transactions of the Royal Society of London B. 358/1921, 2003. In this analogy, human society is adversely interfering with its indispensable flow. By proper ecological and complex system understandings, we need to intentionally restore this global aqueous resource and its cycles.

Rodriguez-Iturbe, Ignacio and Andrea Rinaldo. Fractal River Basins. Cambridge: Cambridge University Press, 1997. Fractals are an ubiquitous property of branching systems such as rivers, streams and estuaries. The book also provides a good introduction to self-organization and criticality concepts.

Rodriquez-Iturbe, Ignacio, et al. Metabolic Principles of River Basin Organization. Proceedings of the National Academy of Sciences. 108/11751, 2011. Over the past decade, as this section reports, researchers have found dynamical earth systems to exemplify self-organizing processes and geometries. Here Princeton University and Ecole Polytechnique Fédérale de Lausanne hydrologists attest to a natural self-similarity for riverine phenomena, which the authors liken to an organic physiology, indeed much akin to a circulatory system.

The metabolism of a river basin is defined as the set of processes through which the basin maintains its structure and responds to its environment. Green (or biotic) metabolism is measured via transpiration and blue (or abiotic) metabolism through runoff. A principle of equal metabolic rate per unit area throughout the basin structure is developed and tested in a river basin characterized by large heterogeneities in precipitation, vegetation, soil, and geomorphology. This principle is suggested to have profound implications for the spatial organization of river basin hydrologic dynamics, including the minimization of energy expenditure known to control the scale-invariant characteristics of river networks over several orders of magnitude. (11751)

The empirical evidence suggests that river basin metabolic activity is linked with the spatial organization that takes place around the drainage network and therefore with the mechanisms responsible for the fractal geometry of the network, suggesting a new coevolutionary framework for biological, geomorphological, and hydrologic dynamics. (11751)

Rowan, Linda and Jessie Smith. The Terrestrial Web. Science. 288/1983, 2000. A summary of findings about Earth’s atmosphere, broadly conceived, from outer space to its crustal mantle and liquid core.

sarker, Shiblu, et al. Critical Nodes in River Networks. Nature Scientific Reports. 9/11178, 2019. By way of a novel application of network theory even to this geological realm, University of Central Florida civil engineers are able to perceive their inherent presence. Once again nature’s universal mathematical program can be seen in formative effect.

River drainage networks are important landscape features that have been studied from a range of geomorphological and hydrological perspectives. However, identifying the most vital (critical) nodes on river networks and their relationships with geomorphic and climatic properties has not yet been addressed. In this study, we use an algorithm that determines the set of critical nodes whose removal results in network fragmentation and apply it to simulated and natural river networks. Our results indicate a power-law relationship between the number of connected node pairs in the remaining network and the number of removed critical nodes. (Abstract excerpt)

Sinha, A. Krishna, ed. Geoinformatics. Boulder, CO: Geological Society of America, 2006. Via the worldwide Internet, earth sciences have rightly attained an interactive resource of data and knowledge. Upon reflection, in this way our home planet achieves its own quantified description so as to further enhance its viability in a developmental cosmos.

Sun, HongGuang, et al. Fractal Nature of Groundwater Level Fluctuations Affected by Riparian Zone Vegetation Water Use. Nature Scientific Reports. 9/15383, 2019. State Key Laboratory of Hydrology-Water Resources and University of Wyoming engineers provide a latest mathematical and geometric analysis by way of these intrinsic common, nested complexities. Whenever could it finally dawn upon us that all this facile phenomena actually has an independent existence of its own as it engenders everywhere this anatomy and physiology of Earth’s animate bio/noosphere.

Groundwater systems affected by various factors can exhibit complex fractal behaviors, whose characterization is not straightforward. This study explores their fractal scaling affected by plant water use and river stage fluctuations in the riparian zone, using multifractal detrended fluctuation analysis. The results show that the water level variations of the Colorado River, USA, exhibit multifractals caused by the memory of time series of the water level fluctuations. For the site with high-density plants the groundwater level fluctuation becomes persistent in spring and summer, since the plants have the most sustained influence in these seasons. (Abstract excerpts)

Tate, Nicholas and Peter Atkinson, eds. Modelling Scale in Geographical Information Science. Chichester: Wiley, 2001. Further explorations of the fractal, self-similarity of natural patterns

Teisseyre, Roman and Eugeniusz Majewski, eds. Earthquake Thermodynamics and Phase Transformations in the Earth’s Interior. San Diego: Academic Press, 2001. The application of the nonlinear sciences to a dynamic planet still in formation perceives a “fractal universality” of self-organizing systems.

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