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window.loswp.work = {"work":{"id":95138958,"created_at":"2023-01-16T23:16:58.137-08:00","from_world_paper_id":225495764,"updated_at":"2024-11-23T08:24:56.390-08:00","_data":{"publisher":"American Geophysical Union (AGU)","grobid_abstract":"Optimal channel networks (OCNs) are dendritic structures obtained by minimizing the local and global rates of energy dissipation in a continuously fed (in space and time) plane aggregation system reminiscent, and based on the properties, of the planform of three-dimensional natural drainage networks. Geomorphological and fractal properties of OCNs are known from earlier studies by the authors. This paper explores further the structures derived by optimization of energy dissipation rates. Optimality of subnetworks and of basin shapes is investigated as a by-product of competition for drainage. A new perspective on the possible prediction of the width function of a basin network, and hence of its hydrologic response, is obtained by exploiting OCN techniques, requiting only the definition of the outer boundaries of the basin. The interplay between hillslope processes and the development of drainage networks is addressed, aiming at the relative role and the mutual interrelations of geology and optimal organization in the structure of mature fiver basins. Also addressed is the issue of multiscaling and multifractality in the spatial organization of the network. It is concluded that OCN approaches provide a comprehensive framework for the study of the morphology of geophysical structures. !. INTRODUCTION Important processes affect the planimetric structure of drainage basins. Chief among these are the development of channel links by headward growth and branching, migration of valleys and divides, capture processes, and adjustments of junction angles of confluent streams. It has been suggested that after an initial rudimentary drainage network is rapidly created upon strong influence of local topography and structural controls, a more regular, process-controlled, network is slowly formed [e.g., Howard, 1990]. The theoretical treatment of drainage network morphology has been dominated in the last 50 years by two approaches of different nature. One was based on deterministic rules, chiefly opti","publication_date":"1993,,","publication_name":"Water Resources Research","grobid_abstract_attachment_id":"97403658"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Optimal channel networks: A framework for the study of river basin morphology","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [1998070]; 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.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; window.userInChina = "false";</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 class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":97403658,"attachmentType":"pdf"}"><img alt="First page of “Optimal channel networks: A framework for the study of river basin morphology”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/97403658/mini_magick20230117-1-1yhbnqx.png?1673939921" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Optimal channel networks: A framework for the study of river basin morphology</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="1998070" href="https://unive.academia.edu/AchilleGiacometti"><img alt="Profile image of Achille Giacometti" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/1998070/660870/820486/s65_achille.giacometti.jpg" />Achille Giacometti</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">1993, 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" translate="no">description</span><p class="ds2-5-body-sm">12 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 95138958; const worksViewsPath = "/v0/works/views?subdomain_param=api&work_ids%5B%5D=95138958"; const getWorkViews = async (workId) => { const response = await fetch(worksViewsPath); if (!response.ok) { throw new Error('Failed to load work views'); } const data = await response.json(); return data.views[workId]; }; // Get the view count for the work - we send this immediately rather than waiting for // the DOM to load, so it can be available as soon as possible (but without holding up // the backend or other resource requests, because it's a bit expensive and not critical). const viewCount = await getWorkViews(workId); const updateViewCount = (viewCount) => { try { const viewCountNumber = parseInt(viewCount, 10); if (viewCountNumber === 0) { // Remove the whole views element if there are zero views. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); return; } const commaizedViewCount = viewCountNumber.toLocaleString(); const viewCountBody = document.getElementById('work-metadata-view-count'); if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">Optimal channel networks (OCNs) are dendritic structures obtained by minimizing the local and global rates of energy dissipation in a continuously fed (in space and time) plane aggregation system reminiscent, and based on the properties, of the planform of three-dimensional natural drainage networks. Geomorphological and fractal properties of OCNs are known from earlier studies by the authors. This paper explores further the structures derived by optimization of energy dissipation rates. Optimality of subnetworks and of basin shapes is investigated as a by-product of competition for drainage. A new perspective on the possible prediction of the width function of a basin network, and hence of its hydrologic response, is obtained by exploiting OCN techniques, requiting only the definition of the outer boundaries of the basin. The interplay between hillslope processes and the development of drainage networks is addressed, aiming at the relative role and the mutual interrelations of geology and optimal organization in the structure of mature fiver basins. Also addressed is the issue of multiscaling and multifractality in the spatial organization of the network. It is concluded that OCN approaches provide a comprehensive framework for the study of the morphology of geophysical structures. !. INTRODUCTION Important processes affect the planimetric structure of drainage basins. Chief among these are the development of channel links by headward growth and branching, migration of valleys and divides, capture processes, and adjustments of junction angles of confluent streams. It has been suggested that after an initial rudimentary drainage network is rapidly created upon strong influence of local topography and structural controls, a more regular, process-controlled, network is slowly formed [e.g., Howard, 1990]. The theoretical treatment of drainage network morphology has been dominated in the last 50 years by two approaches of different nature. One was based on deterministic rules, chiefly opti</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":97403658,"attachmentType":"pdf","workUrl":"https://www.academia.edu/95138958/Optimal_channel_networks_A_framework_for_the_study_of_river_basin_morphology"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":97403658,"attachmentType":"pdf","workUrl":"https://www.academia.edu/95138958/Optimal_channel_networks_A_framework_for_the_study_of_river_basin_morphology"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div><div class="ds-signup-banner-trigger-container"><div class="ds-signup-banner-trigger ds-signup-banner-trigger-control"></div></div><div class="ds-signup-banner ds-signup-banner-control"><div id="ds-signup-banner-close-button"><button class="ds2-5-button ds2-5-button--secondary ds2-5-button--inverse"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">close</span></button></div><div class="ds-signup-banner-ctas"><img src="//a.academia-assets.com/images/academia-logo-capital-white.svg" /><h4 class="ds2-5-heading-serif-sm">Sign up for access to the world's latest research</h4><button class="ds2-5-button ds2-5-button--inverse ds2-5-button--full-width js-swp-download-button" data-signup-modal="{"location":"signup-banner"}">Sign up for free<span class="material-symbols-outlined" style="font-size: 20px" translate="no">arrow_forward</span></button></div><div class="ds-signup-banner-divider"></div><div class="ds-signup-banner-reasons"><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Get notified about relevant papers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Save papers to use in your research</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Join the discussion with peers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Track your impact</span></div></div></div><script>(() => { // Set up signup banner show/hide behavior: // 1. 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A concentration of flow is induced at the outlet with resulting erosion which propagates upslope. The model permits study of the patterns of growth of the drainage network. When the hillslope contains a random topographic field of elevations or a random field of critical shear stresses in soil properties (or both) the resulting growth upslope quickly develops into a branching structure which fulfils Horton&#x27;s laws.</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":"On the development of drainage networks","attachmentId":73073814,"attachmentType":"pdf","work_url":"https://www.academia.edu/58873833/On_the_development_of_drainage_networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/58873833/On_the_development_of_drainage_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="5557036" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/5557036/Minimum_Energy_and_Fractal_Structures_of_Drainage_Networks">Minimum Energy and Fractal Structures of Drainage Networks</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="7892475" href="https://blogspot.academia.edu/RiccardoRigon">Riccardo Rigon</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Water Resources Research, 1992</p><p class="ds-related-work--abstract ds2-5-body-sm">This paper explores the similarities of digital elevation maps (DEMs) of natural river basins and optimal channel network (OCN) configurations obtained minimizing the total rate of energy expenditure in the system as a whole and in its parts. Striking similarities are observed for natui'al and optimal networks in their fractal aggregation structure and in certain multifractal structures found to be characteristic of river basins. Our results suggest, upon critical assessment of the reliability of the identification of the attractor of the underlying dynamics implied by our optimality concepts, that fractal structures are indeed possibly a product of least energy dissipation. Power laws emerging in the description of the distribution of aggregated quantities from both DEMs anal OCNs suggest a link with the framework of self-organized criticality in the dynamics of natural channel network formation. Also, the geomorphological description of OCNs i-eveals surprising analogies with well-known empirical or experimental results. A comparison of Peano's basins with OCNs suggests that nature seems to reject the type of strict self-similarity exhibited by Peano's construct in favor of different shapes implying statistical self-similarity not only because of chance acting through random conditions but also because of necessity as reflected by least energy expenditure considerations. Trento, Trent, Italy. 2Instituto International de Estudios Avanzados, Caracas, Venezuela. 3Ralph M. Parsons Laboratory, Massachusetts Institute of Technology Cambridge ß D•partxmento Scienze Ambientali, Universit/t di Venezia, Ventee, Italyß Paper number 92WR00801. 0043-1397/92/92 WR-00801 $05.00 the development of drainage basins [e.g., Leopold and Langbein, 1962; Stevens, 1974; Howard, 1990]. Similarities of previous contributions with the present approach and the use of previous contributions as points of departure have been discussed at length by Rodriguez-Iturbe et al. [1992a].</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":"Minimum Energy and Fractal Structures of Drainage Networks","attachmentId":49243974,"attachmentType":"pdf","work_url":"https://www.academia.edu/5557036/Minimum_Energy_and_Fractal_Structures_of_Drainage_Networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/5557036/Minimum_Energy_and_Fractal_Structures_of_Drainage_Networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="63171582" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/63171582/Junction_angles_in_drainage_networks">Junction angles in drainage networks</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="7681425" href="https://jpl-nasa.academia.edu/DavidPieri">David Pieri</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Geophysical Research, 1984</p><p class="ds-related-work--abstract ds2-5-body-sm">The systematics of tributary junction angles are an important link between the topology of a drainage network and its topography because the angle of junction depends on the relative slopes of the intersecting tributaries. I present here a model for stream junction angle as a function of position (link magnitude) within the network which quantitatively predicts the observed down-network increase of junction angle for tributaries joining progressively larger recipient links. Good agreement between model and data exists for mature drainage networks mapped at varying scales. Additionally, the dependency of junction angle on relative tributary slopes suggests that as individual links within the network modify their slopes to evolve toward graded longitudinal profiles, there exists a central tendency within the network, modulated by structural and lithologic controls, for evolution to an equilibrium or "graded" planimetric pattern. Extraction of process-related (as opposed to purely topological) information from network planimetric pattern is important in terrestrial and planetary remote sensing applications.</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":"Junction angles in drainage networks","attachmentId":75683674,"attachmentType":"pdf","work_url":"https://www.academia.edu/63171582/Junction_angles_in_drainage_networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/63171582/Junction_angles_in_drainage_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="20976667" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/20976667/Are_river_basins_optimal_channel_networks">Are river basins optimal channel networks?</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="7892475" href="https://blogspot.academia.edu/RiccardoRigon">Riccardo Rigon</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Advances in Water Resources, 1993</p><p class="ds-related-work--abstract ds2-5-body-sm">Drainage networks generated with a simulation model based on the scaling relationship between slopes and areas were found to have total energy expenditure values very near the minimum value of optimal channel networks. Using this model to grow networks inside the boundaries of real basins, it is shown that the drainage networks identified with the aid of digital elevation maps in such basins tend to organize themselves in configurations that minimize total energy expenditure. The role of perturbations in the search for configurations with lower energy and the existence of unstable equilibrium landscapes are also examined.</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":"Are river basins optimal channel networks?","attachmentId":41654378,"attachmentType":"pdf","work_url":"https://www.academia.edu/20976667/Are_river_basins_optimal_channel_networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/20976667/Are_river_basins_optimal_channel_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="55804678" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/55804678/On_the_description_of_the_basin_effective_drainage_structure">On the description of the basin effective drainage structure</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="3309715" href="https://unibas-it.academia.edu/michelegreco">michele greco</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Hydrology, 1996</p><p class="ds-related-work--abstract ds2-5-body-sm">The relationships between the local properties of the morphological elements of a drainage basin and its drainage structure are analysed. Two theoretical approaches are used for which hydrodynamics and basin morphology are respectively assumed to represent the lowest and the highest starting scale level. The results show a convergence toward the idea of slope scaling with contributing area in fiver networks. This concept is then used as an indicator of channel initiation and maintenance for the identification of the effective drainage structure of the basin on the basis of existing digital elevation models (DEMs). Integral properties of the single DEM pixel are finally introduced to reduce the noise owing to a possible DEM low accuracy, e.g. in the estimation of the local slope value from the elevation data set. The resulting network is characterized by a nonuniform drainage density, as expected for natural fiver networks.</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":"On the description of the basin effective drainage structure","attachmentId":71501953,"attachmentType":"pdf","work_url":"https://www.academia.edu/55804678/On_the_description_of_the_basin_effective_drainage_structure","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/55804678/On_the_description_of_the_basin_effective_drainage_structure"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="86542048" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/86542048/Determination_of_Drainage_Networks_From_Plot_Size_and_Basin_Size_Areas">Determination of Drainage Networks From Plot-Size and Basin-Size Areas</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="36041627" href="https://independent.academia.edu/Couger">Gordon C Couger</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Applied Engineering in Agriculture, 1992</p><p class="ds-related-work--abstract ds2-5-body-sm">An algorithm to identify drainage networks from point elevation data is described. The algorithm is specifically designed to handle very fine grid spacings used to study erosion processes. The algorithm has been expanded to include basin-size areas. Flow paths are determined by recursively linking data and drainage networks are characterized using ordered flow paths. The algorithm is evaluated using data gathered from a physical model made from plaster, an erosion plot, and a basin-size area. It is shown to be an effective way to identify flow paths. KEYWORDS.</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":"Determination of Drainage Networks From Plot-Size and Basin-Size Areas","attachmentId":90970220,"attachmentType":"pdf","work_url":"https://www.academia.edu/86542048/Determination_of_Drainage_Networks_From_Plot_Size_and_Basin_Size_Areas","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/86542048/Determination_of_Drainage_Networks_From_Plot_Size_and_Basin_Size_Areas"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="18628009" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/18628009/Structural_patterns_in_river_network_organization_at_both_infra_and_supra_basin_levels_the_case_of_a_granitic_relief">Structural patterns in river network organization at both infra- and supra-basin levels: the case of a granitic relief</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="38683290" href="https://agrocampus-ouest.academia.edu/ChristopheCudennec">Christophe Cudennec</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Earth Surface Processes and Landforms, 2006</p><p class="ds-related-work--abstract ds2-5-body-sm">Within a landform, the channelized water path from any point to the corresponding outlet is split into successive components within the Strahler ordering scheme. The probability density functions ( pdf ) of the length L of the whole channelized path and of the lengths of the components are studied as multi-level structural functions. We have considered a granitic area and studied both its main basin and the set of its 48 constituent basins. With respect to the main basin, the pdf of the component lengths exhibit a strong scaling property, except for the highest orders, due to a hierarchical constraint; hence, the pdf of sum L has no particular shape. We have nevertheless identified an underlying structural pattern at particular infra-and suprabasin levels, where the hierarchical constraint is weaker. This identification process entails noting structurally emerging patterns based on multi-level variables and distributions, which satisfy the general self-similarity of networks. The fairly good fit of an analytical gamma law with most of these emerging patterns can prove to be a positive step towards both a general modelling approach to the geomorphometric functions and a stronger geomorphological basement of hydrological transfer functions.</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":"Structural patterns in river network organization at both infra- and supra-basin levels: the case of a granitic relief","attachmentId":40167253,"attachmentType":"pdf","work_url":"https://www.academia.edu/18628009/Structural_patterns_in_river_network_organization_at_both_infra_and_supra_basin_levels_the_case_of_a_granitic_relief","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/18628009/Structural_patterns_in_river_network_organization_at_both_infra_and_supra_basin_levels_the_case_of_a_granitic_relief"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="5557033" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/5557033/Energy_Dissipation_Runoff_Production_and_the_Three_Dimensional_Structure_of_River_Basins">Energy Dissipation, Runoff Production, and the Three-Dimensional Structure of River Basins</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="7892475" href="https://blogspot.academia.edu/RiccardoRigon">Riccardo Rigon</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Water Resources Research, 1992</p><p class="ds-related-work--abstract ds2-5-body-sm">Three principles of optimal energy expenditure are used to derive the most important structural characteristics observed in drainage networks: (I) the principle of minimum energy expenditure in any link of the network, (2) the principle of equal energy expenditure per unit area of channel anywhere in the network, and (3) the principle of minimum total energy expenditure in the network as a whole. Their joint applica,tion results in a unified picture of the most important empirical facts which have been observed in the dynamics of the network and its three-dimensional structure. They also link the process of runoff production in the basin with the characteris.tics of the network.</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":"Energy Dissipation, Runoff Production, and the Three-Dimensional Structure of River Basins","attachmentId":49243966,"attachmentType":"pdf","work_url":"https://www.academia.edu/5557033/Energy_Dissipation_Runoff_Production_and_the_Three_Dimensional_Structure_of_River_Basins","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/5557033/Energy_Dissipation_Runoff_Production_and_the_Three_Dimensional_Structure_of_River_Basins"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="52818188" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/52818188/A_comparison_of_experimental_and_natural_drainage_basin_morphology_across_a_range_of_scales">A comparison of experimental and natural drainage basin morphology across a range of scales</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="37786467" href="https://independent.academia.edu/LeslieHasbargen">Leslie Hasbargen</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Geophysical Research, 2005</p><p class="ds-related-work--abstract ds2-5-body-sm">Numerous quantitative models have been developed to simulate the long-term evolution of river basin topography. Most of these models reach an equilibrium state when the base level is lowered at a constant rate and the substrate and climate are constant in time. At equilibrium the erosion balances the base level lowering, so the topography remains frozen in time. However, some recent laboratory experiments contradict this behavior. In these experiments the space-time mean erosion rate balances the base level lowering rate, but the actual erosion rates are highly variable in space and time. Consequently, the channel networks are substantially mobile. The experimental flow conditions are approximately similar but not dynamically equivalent to those in nature, so it is unclear whether the observed dynamics are representative. This paper examines whether the processes occurring in the experiments produce basins that are geometrically similar to typical natural basins. To make this comparison, the conceptual framework of scaling invariance is used. Many similarities are observed, but we find that the experimental basins are slightly more elongated across a range of scales than the natural basins we consider and the relationship between channel slope and drainage area exhibits a break that is not found in the natural basins we analyze. In the experiments the slopes of small channels also depend on the proximity of large channels. This dependency is more pronounced for experiments with more mobile channel networks, and it is not observed in most of the natural basins we analyze.</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 comparison of experimental and natural drainage basin morphology across a range of scales","attachmentId":69899311,"attachmentType":"pdf","work_url":"https://www.academia.edu/52818188/A_comparison_of_experimental_and_natural_drainage_basin_morphology_across_a_range_of_scales","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/52818188/A_comparison_of_experimental_and_natural_drainage_basin_morphology_across_a_range_of_scales"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="4061854" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/4061854/Constructal_view_of_scaling_laws_of_river_basins">Constructal view of scaling laws of river basins</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="3351588" href="https://hot-trends.academia.edu/AntonioHeitorReis">Antonio Heitor Reis</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Geomorphology, 2006</p><p class="ds-related-work--abstract ds2-5-body-sm">River basins are examples of naturally organized flow architectures whose scaling properties have been noticed long ago. Based on data of geometric characteristics, Horton [Horton, R.E., 1932. Drainage basin characteristics. EOS Trans. AGU 13, 350–361.], Hack [Hack, J.T., 1957. Studies of longitudinal profiles in Virginia and Maryland. USGS Professional Papers 294-B, Washington DC, pp. 46–97.], and Melton [Melton, M.A, 1958. Correlation structure of morphometric properties of drainage systems and their controlling agents. J. of Geology 66, 35–56.] proposed scaling laws that are considered to describe rather accurately the actual river basins. What we show here is that these scaling laws can be anticipated based on Constructal Theory, which views the pathways by which drainage networks develop in a basin not as the result of chance but as flow architectures that originate naturally as the result of minimization of the overall resistance to flow (Constructal Law).</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":"Constructal view of scaling laws of river basins","attachmentId":36937028,"attachmentType":"pdf","work_url":"https://www.academia.edu/4061854/Constructal_view_of_scaling_laws_of_river_basins","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/4061854/Constructal_view_of_scaling_laws_of_river_basins"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":97403658,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":97403658,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_97403658" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/55816767/A_procedure_for_drainage_network_identification_from_geomorphology_and_its_application_to_the_prediction_of_the_hydrologic_response">A procedure for drainage network identification from geomorphology and its application to the prediction of the hydrologic response</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="22214904" href="https://independent.academia.edu/RobertoRudari">Roberto Rudari</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Advances in Water Resources, 2005</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 procedure for drainage network identification from geomorphology and its application to the prediction of the hydrologic response","attachmentId":71507797,"attachmentType":"pdf","work_url":"https://www.academia.edu/55816767/A_procedure_for_drainage_network_identification_from_geomorphology_and_its_application_to_the_prediction_of_the_hydrologic_response","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/55816767/A_procedure_for_drainage_network_identification_from_geomorphology_and_its_application_to_the_prediction_of_the_hydrologic_response"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="4" data-entity-id="59601705" 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/59601705/An_entropy_based_morphological_analysis_of_river_basin_networks">An entropy-based morphological analysis of river basin networks</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="132247625" href="https://unibas-it.academia.edu/MFiorentino">Mauro Fiorentino</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Water Resources Research, 1993</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":"An entropy-based morphological analysis of river basin 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href="https://www.academia.edu/77317134/Path_selection_in_the_growth_of_rivers">Path selection in the growth of rivers</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="61971067" href="https://independent.academia.edu/YossiCohen8">Yossi Cohen</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Proceedings of the National Academy of Sciences, 2015</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":"Path selection in the growth of rivers","attachmentId":84725931,"attachmentType":"pdf","work_url":"https://www.academia.edu/77317134/Path_selection_in_the_growth_of_rivers","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free 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Waymire</a></div><p class="ds-related-work--metadata ds2-5-body-xs">1992</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":"Fundamental Studies on Hydrology, Hydraulics and Geometry of River Networks","attachmentId":98223025,"attachmentType":"pdf","work_url":"https://www.academia.edu/96280183/Fundamental_Studies_on_Hydrology_Hydraulics_and_Geometry_of_River_Networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/96280183/Fundamental_Studies_on_Hydrology_Hydraulics_and_Geometry_of_River_Networks"><span class="ds2-5-text-link__content">View PDF</span><span 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Phillip Guertin</a></div><p class="ds-related-work--metadata ds2-5-body-xs">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":"Influences of Map Scale on Drainage Network Representation","attachmentId":98552551,"attachmentType":"pdf","work_url":"https://www.academia.edu/96737016/Influences_of_Map_Scale_on_Drainage_Network_Representation","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/96737016/Influences_of_Map_Scale_on_Drainage_Network_Representation"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="8" data-entity-id="62264955" 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/62264955/Trees_networks_and_hydrology">Trees, networks, and hydrology</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="34280990" href="https://independent.academia.edu/AmosMaritan">Amos Maritan</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Water Resources Research, 2006</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":"Trees, networks, and hydrology","attachmentId":75087676,"attachmentType":"pdf","work_url":"https://www.academia.edu/62264955/Trees_networks_and_hydrology","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/62264955/Trees_networks_and_hydrology"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="9" data-entity-id="35265430" 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/35265430/Functional_Topology_of_Evolving_Urban_Drainage_Networks">Functional Topology of Evolving Urban Drainage Networks</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="71914174" href="https://independent.academia.edu/SureshRao21">Suresh Rao</a></div><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":"Functional Topology of Evolving Urban Drainage Networks","attachmentId":55125679,"attachmentType":"pdf","work_url":"https://www.academia.edu/35265430/Functional_Topology_of_Evolving_Urban_Drainage_Networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/35265430/Functional_Topology_of_Evolving_Urban_Drainage_Networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="10" data-entity-id="47603464" 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/47603464/Principles_of_drainage_basin_analysis_from_multisource_data_Application_to_the_structural_analysis_of_the_Zaire_Basin">Principles of drainage basin analysis from multisource data: Application to the structural analysis of the Zaire Basin</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="34613700" href="https://u-pem.academia.edu/BDeffontaines">B. Deffontaines</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Tectonophysics, 1991</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":"Principles of drainage basin analysis from multisource data: Application to the structural analysis of the Zaire Basin","attachmentId":66611737,"attachmentType":"pdf","work_url":"https://www.academia.edu/47603464/Principles_of_drainage_basin_analysis_from_multisource_data_Application_to_the_structural_analysis_of_the_Zaire_Basin","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" 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href="https://www.academia.edu/3000170/A_study_of_drainage_basin_linearity_and_non_linearity">A study of drainage basin linearity and non-linearity</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="417374" href="https://ntua.academia.edu/MariaMimikou">Maria Mimikou</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Hydrology, 1983</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 study of drainage basin linearity and non-linearity","attachmentId":50513223,"attachmentType":"pdf","work_url":"https://www.academia.edu/3000170/A_study_of_drainage_basin_linearity_and_non_linearity","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span 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ds2-5-body-xs">Geomorphology, 1992</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 physical basis for drainage density","attachmentId":66738611,"attachmentType":"pdf","work_url":"https://www.academia.edu/47805828/A_physical_basis_for_drainage_density","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/47805828/A_physical_basis_for_drainage_density"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div><div class="ds-related-content--container"><h2 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