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Multi-Scale Analyses of Landscape: New Tools for Studying the Effect of Erosion and Deposition on Landscape Morphology and Complexity
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  • Christopher Keylock,
  • Arvind Singh,
  • Paola Passalacqua,
  • Efi Foufoula-Georgiou
Christopher Keylock
University of Loughborough

Corresponding Author:c.j.keylock@lboro.ac.uk

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Arvind Singh
University of Central Florida
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Paola Passalacqua
University of Texas at Austin
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Efi Foufoula-Georgiou
University of California Irvine
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Understanding the complex interplay between erosional and depositional processes, and their relative roles in shaping landscape morphology is a question at the heart of geomorphology. A unified framework for examining this question can be developed by simultaneously considering terrain elevation statistics over multiple scales. We show how a long-standing tool for landscape analysis, the elevation-area or hypsometry, can be complemented by an analysis of the elevation scalings to produce a more sensitive tool for studying the interplay between processes, and their impact on morphology. We then use this method, as well as well-known geomorphic techniques (slope-area scaling relations, the number of basins and basin size as a function of channel order) to demonstrate how the complexity of an experimental landscape evolves through time. Our primary result is that the complexity increases once a flux equilibrium is established as a consequence of the role of diffusive processes acting at intermediate elevations. We gauge landscape complexity by comparing results between the experimental landscape surfaces and those produced from a new algorithm that fixes in place the elevation scaling statistics, but randomizes the elevations with respect to these scalings. We constrain the degree of randomization systematically and use the amount of constraint as a measure of complexity. The starting point for the method is illustrated in the figure, which shows the original landscape (top-left) and three synthetic variants generated with no constraints to the randomization. The value quoted in these panels is the root-mean-squared difference in the elevation values for the synthetic cases relative to the original terrain. This value is greatest where the original ridge becomes a valley. All these landscapes contain the same elevation values (i.e. the same probability distribution functions), and the same elevation scalings at a point. The differences emerge because the elevations themselves are distributed randomly across the surface.