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A Sourcebook for the Worldwide Discovery of a Creative Organic Universe
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III. Ecosmos: A Revolutionary Fertile, Habitable, Solar-Bioplanet Incubator Lifescape

4. Geosphere, Hydrosphere, Atmosphere as Complex, Network Systems

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.

Terui, Akira, et al. Metapopulation Stability in Branching River Networks. Proceedings of the National Academy of Sciences. 115/E5963, 2018. University of Minnesota and Hokkaido University system environmentalists provide a sophisticated analysis of the pervasive presence of self-similar network topologies even in these ever variable fluid flow geoscape regimes.

Intraspecific population diversity is an essential component of metapopulation stability and persistence in nature. However, current theories developed in simplified landscapes may be inadequate to predict emergent properties of branching ecosystems, a prime feature of habitat geometry. Here, we analyze a long-term dataset to show that a scale-invariant characteristic of fractal river networks, branching complexity stabilizes watershed metapopulations. In riverine systems, each branch (tributary) exhibits distinctive ecological dynamics, and confluences serve as “merging” points of those branches. We theoretically revealed that the stabilizing effect of branching complexity is due to probabilistic processes in natural conditions, where within-branch synchrony exceeds among-branch synchrony. (Abstract excerpt)

Tsonis, Anastasios and James Elsner, eds. Nonlinear Dynamics in Geosciences. Berlin: Springer, 2007. As the abstract notes, a collation to date of incipient research seeking to model earth system phenomena in this realistic actuality. Sample papers could be Two Paradigms in Landscape Dynamics: Self-Similar Processes and Emergence by Brad Murray, Abstract below, and The Role of El Niño—Southern Oscillation in Regulating its Background State by DE-Zheng Sun.

This volume is comprised of the proceedings of "20 Years of Nonlinear Dynamics in Geosciences", held June 11-16, 2006 in Rhodes, Greece as part of the Aegean Conferences. The volume brings together research from the atmospheric sciences, hydrology, geology, and other areas of Geosciences, and discusses the advances made and the future directions of nonlinear dynamics. Topics covered include predictability, ensemble prediction, nonlinear prediction, nonlinear time series analysis, low-dimensional chaos, nonlinear modeling, fractals and multifractals, bifurcation, and other aspects of nonlinear science. (Publisher)

Landscapes often exhibit self-similar (fractal, self-affine, multifractal) patterns, expressed in terms of power-law scalings. These scaling signatures are commonly interpreted as indicating that the same physical processes operate across a wide range of scales. Landscape researchers have also employed another productive perspective, that of emergent phenomena. To address relatively large-scale patterns and behaviors, rather than basing models directly on the vast number of small-scale processes occurring within the landscape, many models treat variables and interactions that arise from (and in turn influence) the collective behavior of smaller-scale degrees of freedom. Models that treat the coupled evolution of hillslopes and channels—synthesizing the effects of the many processes within these units—can explain the emergence of self-similarity (or self-affinity) of large-scale topography and river networks. A model of the evolution of sandy-coastline shapes highlights how interactions between emergent structures can offer clear, direct explanations for scaling properties. In this case, the processes and patterns are scale-independent in the sense that the length scale changes over time, while a temporally self-similar shape persists, although at any time during the evolution a single wavelength dominates. However, models treating interactions between emergent landscape features show that complex, self-similar patterns and behaviors can be understood in terms of relatively simple, essentially deterministic processes. (Abstract, Brad Murray)

Turcotte, Donald. Self-Organized Complexity in Geomorphology. Geomorphology. 91/302, 2007. The University of California, Davis, geologist has been a pioneer advocate for the view that all forms of earth’s crustal geo and hydro spheres – coastlines, landscape contours, lakes, branching rivers, and so on – express a self-similar fractal topography.

Turcotte, Donald. The Relationship of Fractals in Geophysics to “The New Science”. Chaos, Solitons and Fractals. 19/255, 2004. The earth’s strata is distinguished by many self-similar patterns. In addition, cellular automata models such as advanced by Stephan Wolfram are also found to apply. The entire journal issue is devoted to “Fractals in Geophysics.”

Valentini, Luca, et al. The “Small World” Topology of Rock Fracture Networks. Physica A. 377/323, 2007. In every diverse nook and cranny the same geometry and grace is apparently at work.

The fractal nature of fracture networks suggests that they might be regarded as complex systems, i.e., systems formed by a series of non-linearly interacting elements whose behavior cannot be fully characterized by studying the system at the scale of single components. (323-324)

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