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basin is its mean elevation, the connection between entropy and potential energy is explored to analyze drainage basins morphological characteristics. The mean basin elevation is found to be linearly related to the entropy of the drainage basin. This relation leads to a linear relation between the mean elevation of a subnetwork and the logarithm of its topological diameter. Furthermore, the relation between the fall in elevation from the source to the outlet of the main channel and the entropy of its drainage basin is found to be linear and so is also the case between the elevation of a node and the logarithm of its distance from the source. When a drainage basin is ordered according to the Horton-Strahler ordering scheme, a linear relation is found between the drainage basin entropy and the basin order. This relation can be characterized as a measure of the basin network complexity. The basin entropy is found to be linearly related to the logarithm of the magnitude of the basin network. This relation leads to a nonlinear relation between the network diameter and magnitude, where the exponent is found to be related to the fractal dimension of the drainage network. Also, the exponent of the power law relating the channel slope to the network magnitude is found to be related to the fractal dimension of the network. These relationships are verified on three drainage basins in southern Italy, and the results are found to be promising. 1. INTRODUCTION A multitude of definitions of entropy, corresponding to different uses, have been reported in the scientific literature [Wilson, 1970]. All of these definitions can, however, be traced to one of the three types of entropies: (1) thermodynamic entropy [e.g., Prigogine, 1967] that forms the basis of the second law of thermodynamics, (2) statistical mechanical entropy [Boltzmann, 1872], and (3) informational entropy [Shannon, 1948]. The thermodynamic entropy and statistical mechanical entropy are related and can simply be clubbed as physical entropy. One can also designate physical entropy as Boltzmann entropy and informational entropy as Shannon entropy. The link between physical entropy and informational entropy has thus far been elusive. A distinction can, however, be made between physical entropy as an objective measure of some property of a system, and informational entropy as a subjective concept for use as a model-building tool to maximize the use of available information [Wilson, 1970]. This distinction is important in that developments in hydrology and water resources employing the entropy concepts have occurred along the separated lines of physical and informational entropies, without exploiting the relationship between them. Nearly 30 years ago, Leopold and Langbein [1962] applied for the first time the concepts of physical entropy to study the behavior of streams. Their application was based on the analogy between heat energy and temperature in a thermodynamic system and potential energy and elevation, respectively, in a stream system. Two thermodynamic principles were applied. The first principle is that the most probable state of a system is the one of maximum entropy. The second","publication_date":"1993,,","publication_name":"Water Resources Research","grobid_abstract_attachment_id":"73441280"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"An entropy-based morphological analysis of river basin networks","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [132247625]; 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 class="ds-work-card--cover"><div 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class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">An entropy-based morphological analysis of river basin 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="132247625" href="https://unibas-it.academia.edu/MFiorentino"><img alt="Profile image of Mauro Fiorentino" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Mauro Fiorentino</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">1993, Water Resources Research</p></div><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":73441280,"attachmentType":"pdf","workUrl":"https://www.academia.edu/59601705/An_entropy_based_morphological_analysis_of_river_basin_networks"}">See full PDF</button><button 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The results showed that the methods analyzed, which use the concept of entropy, are adequate and efficient for evaluation of existing fluviometric networks, since ...</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":"Analysis of the fluviometric network of Rio das Velhas using Entropy","attachmentId":75972048,"attachmentType":"pdf","work_url":"https://www.academia.edu/63593818/Analysis_of_the_fluviometric_network_of_Rio_das_Velhas_using_Entropy","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/63593818/Analysis_of_the_fluviometric_network_of_Rio_das_Velhas_using_Entropy"><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="49812974" 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/49812974/Investigation_of_flow_properties_in_natural_streams_using_the_entropy_concept">Investigation of flow properties in natural streams using the entropy concept</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="110444020" href="https://independent.academia.edu/MArdiclioglu">Mehmet Ardiclioglu</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="54382164" href="https://independent.academia.edu/NecatiAgiralioglu">Necati Agiralioglu</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Water and Environment Journal, 2012</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":"Investigation of flow properties in natural streams using the entropy concept","attachmentId":68034254,"attachmentType":"pdf","work_url":"https://www.academia.edu/49812974/Investigation_of_flow_properties_in_natural_streams_using_the_entropy_concept","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/49812974/Investigation_of_flow_properties_in_natural_streams_using_the_entropy_concept"><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="9850261" 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/9850261/Entropy_application_to_evaluate_the_stability_of_landscape_in_Kunur_River_Basin_West_Bengal_India">Entropy application to evaluate the stability of landscape in Kunur River Basin, West Bengal, India</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="3118889" href="https://knu-in.academia.edu/SujayBandyopadhyay">Sujay Bandyopadhyay</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="3583499" href="https://buruni.academia.edu/NarayanJana">Narayan Jana</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2014</p><p class="ds-related-work--abstract ds2-5-body-sm">The river network analysis using thermodynamic entropy approach has been studied over the past several decades to decipher the behaviour of streams and landscape stability. The entropy-based study has been taken up in Kunur River Basin of eastern India to verify the level of adjustment for its present longitudinal profile to the calculated and equilibrium longitudinal profiles adopting Yang’s (1971) theory of average river fall. The verification reveals that the fall ratio is less than 1, which indicates the basin has not yet reached the dynamic equilibrium phase and the whole process–response system sustains tremendous human pressure. It is inferred from the thermodynamic river profiles that there is poor agreement between observed data and the law of average stream fall, and the concave river profile emerging from several scales of process-form interaction is characterized by human interference. The present analyses also demonstrate that the lithological control, grain size and channel morphology influence the gradient in short term and climate-induced hydrological changes control the long-term stability of the total landscape.</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":"Entropy application to evaluate the stability of landscape in Kunur River Basin, West Bengal, India","attachmentId":36015443,"attachmentType":"pdf","work_url":"https://www.academia.edu/9850261/Entropy_application_to_evaluate_the_stability_of_landscape_in_Kunur_River_Basin_West_Bengal_India","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/9850261/Entropy_application_to_evaluate_the_stability_of_landscape_in_Kunur_River_Basin_West_Bengal_India"><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="23548318" 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/23548318/The_long_range_dependence_of_hydrological_processes_as_a_result_of_the_maximum_entropy_principle">The long-range dependence of hydrological processes as a result of the maximum entropy principle</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="26417811" href="https://ntua.academia.edu/DemetrisKoutsoyiannis">Demetris Koutsoyiannis</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":"The long-range dependence of hydrological processes as a result of the maximum entropy principle","attachmentId":43977568,"attachmentType":"pdf","work_url":"https://www.academia.edu/23548318/The_long_range_dependence_of_hydrological_processes_as_a_result_of_the_maximum_entropy_principle","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/23548318/The_long_range_dependence_of_hydrological_processes_as_a_result_of_the_maximum_entropy_principle"><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="28958689" 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/28958689/Use_of_Entropy_in_the_Assessment_of_Uncertainty_of_River_Runoff_Regime_in_Poland">Use of Entropy in the Assessment of Uncertainty of River Runoff Regime in Poland</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="64413" href="https://amu.academia.edu/DariuszWrzesi%C5%84ski">Dariusz Wrzesiński</a></div><p class="ds-related-work--abstract ds2-5-body-sm">A b s t r a c t The objective of this paper is to describe spatial differences in the uncertainty of features of the runoff regimes of Polish rivers based on en-tropy in Shannon's information theory. They included: the entropy of monthly river runoff and the entropy of river runoff distribution over time. An analysis of monthly flow series for the years 1951-2010 from 395 gauging stations located on 248 rivers in Poland was performed. This allowed a quantitative determination of the degree of uncertainty of two regime characteristics indirectly establishing the predictability, regularity , and stability of their appearance and their spatial variability. An analysis of relations between the calculated entropy, as well as between the entropy and the classical parameters commonly used was performed in describing the hydrological regime. The obtained grouping of rivers into four categories in terms of entropy of volume and distribution of runoff in the annual cycle clearly coincides with the types of river regime distinguished in Poland.</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":"Use of Entropy in the Assessment of Uncertainty of River Runoff Regime in Poland","attachmentId":49399350,"attachmentType":"pdf","work_url":"https://www.academia.edu/28958689/Use_of_Entropy_in_the_Assessment_of_Uncertainty_of_River_Runoff_Regime_in_Poland","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/28958689/Use_of_Entropy_in_the_Assessment_of_Uncertainty_of_River_Runoff_Regime_in_Poland"><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":73441280,"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":73441280,"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_73441280" 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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