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false window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":5557037,"created_at":"2013-12-29T21:31:21.017-08:00","from_world_paper_id":121675030,"updated_at":"2024-11-17T02:13:23.190-08:00","_data":{"grobid_abstract":"This paper studies the relation between the structure of river networks and the features of their geomorphologic hydrologic response. A mathematical formulation of connectivity of a drainage network is proposed to relate contributing areas and the network geometry. In view of the connectivity conjecture, Horton's bifurcation ratio RB tends, for high values of Strahler's order ft of the basin, to the area ratio RA, and Horton\"s length ratio R oe equals, in the limit, the single-order contributing area ratio R a . The relevance of'•these argu•ments is examined by reference to data from real basins.","publication_date":"1991,,","publication_name":"Water Resources Research","grobid_abstract_attachment_id":"49243972"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"A Note on Fractal Channel Networks","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [7892475]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div 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class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">A Note on Fractal Channel Networks</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="7892475" href="https://blogspot.academia.edu/RiccardoRigon"><img alt="Profile image of Riccardo Rigon" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/7892475/2783811/3245424/s65_riccardo.rigon.jpg" />Riccardo Rigon</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">1991, Water Resources Research</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" 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Five fractal dimensions are recognized for stream networks, namely, topological dimension (dt), minimum path dimension (dm), fractal dimension of stream networks as a whole (df), diffusion dimension (dw), and spectral dimension (ds). Mathematical definitions and derivations of the fractal dimensions are proposed, which provide a theoretical basis for some recognized empirical relationships in drainage basin geomorphology. Relationships among the fractal dimensions are examined, and the average values of the fractal dimensions for natural stream networks are estimated. 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I. Scaling, fluctuations, and deviations</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32398886" href="https://vermont.academia.edu/PeterDodds">Peter Sheridan Dodds</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical review. E, Statistical, nonlinear, and soft matter physics, 2001</p><p class="ds-related-work--abstract ds2-5-body-sm">This paper is the first in a series of three papers investigating the detailed geometry of river networks. Branching networks are a universal structure employed in the distribution and collection of material. Large-scale river networks mark an important class of two-dimensional branching networks, being not only of intrinsic interest but also a pervasive natural phenomenon. In the description of river network structure, scaling laws are uniformly observed. Reported values of scaling exponents vary, suggesting that no unique set of scaling exponents exists. To improve this current understanding of scaling in river networks and to provide a fuller description of branching network structure, here we report a theoretical and empirical study of fluctuations about and deviations from scaling. We examine data for continent-scale river networks such as the Mississippi and the Amazon and draw inspiration from a simple model of directed, random networks. We center our investigations on the sc...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Geometry of river networks. I. 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data-collection-position="13" data-entity-id="117023307" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/117023307/A_reformulation_of_Hortons_Laws_for_large_river_networks_in_terms_of_statistical_self_similarity">A reformulation of Horton's Laws for large river networks in terms of statistical self‐similarity</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="301198365" href="https://independent.academia.edu/PeckhamScott">Scott Peckham</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Water Resources Research, 1999</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A reformulation of Horton's Laws for large river networks in terms of statistical 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translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="17" data-entity-id="4329956" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/4329956/Fractal_analyses_of_tree_like_channel_networks_from_digital_elevation_model_data">Fractal analyses of tree-like channel networks from digital elevation model data</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="5278741" href="https://nationalagriculturalresearchinra.academia.edu/RogerMoussa">Roger Moussa</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Hydrology, 1996</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" 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