Entropy and 2‐D Velocity Distribution in Open Channels

Chiu, Chao‐Lin

doi:10.1061/(asce)0733-9429(1988)114:7(738)

Cited by 202 publications

(121 citation statements)

References 8 publications

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“…In the area of water resources (SINGH, 1997;HUSAIN, 1989), in the application in hydrology (WANG;ZHU, 2001;SINGH, 1998), in historical series of precipitation and flow, mainly. In the prediction of hydrological variables (CONTE, 2005;WEIJS et al, 2010), in the evaluation of the prediction and stability of river flows (MUKHOPADHYAY; KHAN, 2015), in the estimation of the sediment concentration (SINGH; CUI, 2015;CUI;SINGH, 2014;GAN et al, 2014;LIEN;TSAI, 2003;CHIU et al, 2000;LUO;SINGH, 2011;GOMEZ;PHILLIPS, 1999;SING et al, 1988;CHIU, 1988;CHAO-LIN CHIU, 1987;KRSTANOVIC, 1987), in the estimation of the precipitation ratio X flow (SINGH, 2012;CONTE, 2005;SONUGA, 1976), in river processes (XU; ZHAO, 2013;DESHPANDE;KUMAR, 2013), among other applications.…”

Section: Application Of Entropy In Hydrology and Hydraulicsmentioning

confidence: 99%

Principle of maximum entropy in the estimation of suspended sediment concentration

Martins

Poleto

2017

RBRH

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The concern with water quality has been promoting development of better monitoring and control techniques every day. As sediments transport most of water contaminants, their study is fundamental. Given the large number of variables for estimating sediment concentration and high costs of monitoring campaigns, it becomes necessary to develop more accessible methods which bring satisfactory practical results. Therefore, this work deals with application of the principle of maximum entropy, a probabilistic method to determine concentration of sediments in river channels with various concentrations and particle sizes. For this purpose, it was proposed a relationship between the theory of entropy parameters in order to reduce the computational effort. The results were satisfactory at concentrations above 10 g/L with R 2 greater than 0.88. The calculated squared errors in this study were lower than those found when using the theory of entropy by Tsallis and the equation of Rouse, classic models for determining the sediment concentration profile. The applicability of the proposed model and the ease of using the probabilistic method, since it reduces the amount of data needed to perform the estimate, makes it feasible on a global scale.Keywords: Sedimentology; Water resources; Modeling. RESUMOA preocupação com a qualidade das águas vem promovendo o desenvolvimento de técnicas cada dia melhores de monitoramento e controle. Como os sedimentos transportam a maior parte dos contaminantes da água, seu estudo é fundamental. Diante do elevado número de variáveis existentes para a estimativa da concentração de sedimentos e elevados custos de campanhas de monitoramento, torna-se necessário o desenvolvimento de métodos mais acessíveis e que tragam resultados práticos satisfatórios. Para tanto, este trabalho trata da aplicação do princípio da entropia máxima, um método probabilístico, para determinar a concentração de sedimentos em calhas com diversas concentrações e granulometrias. Para isso, foi proposta uma relação entre os parâmetros do princípio da entropia máxima para determinar o índice entrópico e facilitar o cálculo. Os resultados mostraram-se satisfatórios para concentrações acima de 10 g/L com R 2 superiores a 0,88. Os erros quadráticos calculados neste trabalho foram inferiores aos encontrados quando utilizada a teoria da entropia por Tsallis e pela Equação de Rouse, modelos clássicos de estimativa do perfil de concentração de sedimentos. A aplicabilidade do modelo proposto e a facilidade da utilização do método probabilístico, já que reduz a quantidade de dados necessários para realizar a estimativa, torna-o viável em escala global.Palavras-chave: Sedimentologia; Recursos hídricos; Modelagem.RBRH, Porto Alegre, v. 22, e23, 2017Principle of maximum entropy in the estimation of suspended sediment concentration

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Section: Application Of Entropy In Hydrology and Hydraulicsmentioning

confidence: 99%

Principle of maximum entropy in the estimation of suspended sediment concentration

Martins

Poleto

2017

RBRH

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“…Therefore, the present study proposed a formula that can calculate a mean sediment concentration by simplifying parameters as much as possible. The detailed elicitation process in the calculation formula of velocity distribution and mean velocity, which are required to understand the calculation formula of mean sediment concentration using the probabilistic entropy concept, are found in the previous studies done by Chiu and Choo so they were omitted in this paper [4], [6], [11]- [14].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…In other nations, [2] developed a formula of distribution of suspended sediments concentration and [3] proposed the effect of sediments on velocity distribution. Furthermore, [4] proposed a distribution formula of suspended sediments concentration by modifying the Rouse formula utilizing the entropy concept. Reference [5] proposed a distribution formula of suspended sediments concentration utilizing the Tsallis entropy concept but no significant error was found at a relatively low concentration distribution but a large range of error was found at high concentration distribution.…”

Section: Introductionmentioning

confidence: 99%

Derivation of Equation for Mean Suspended Sediment Based on Probabilistic Concept

Yoon¹,

Lee²,

Park³

2017

IJESD

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Abstract-An accurate estimation of sediment discharge in rivers and streams should be solved for the appropriate river management and monitoring. In this study, a new formula which has minimum parameters considering existing ones with a concept of entropy by a probabilistic approach, was developed and mean suspended sediment concentration were estimated. Results of this new formula were verified with the experimental results which were conducted with a steady state and gradually injecting sediment (D= 105 ㎛) in a rectangular cross-sectional flume previously. The relationship between the measured sediment distribution and the estimated sediment distribution has a good agreement.Index Terms-Entropy, entropy suspended sediment parameter, mean suspended sediment concentration, Probabilistic approach.

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“…A valid alternative to the velocity-area method is the entropy method [1]: it is founded on the principle of entropy maximization [2] and has been used in different fields of research, including geomorphology [3,4] and hydrology [5][6][7][8], to derive the probability density function of a specific random variable. In the particular case of flow through a river cross-section, this approach has been applied by Chiu [1,9] to identify the corresponding (probability) distribution of flow velocity and from which a linear relationship between the mean velocity and the maximum velocity u max in a river cross-section is derived [1,[10][11][12], i.e.,…”

Section: Introductionmentioning

confidence: 99%

Three Methods for Estimating the Entropy Parameter M Based on a Decreasing Number of Velocity Measurements in a River Cross-Section

Farina

Alvisi

Franchini

et al. 2014

Entropy

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Abstract:The theoretical development and practical application of three new methods for estimating the entropy parameter M used within the framework of the entropy method proposed by Chiu in the 1980s as a valid alternative to the velocity-area method for measuring the discharge in a river is here illustrated. The first method is based on reproducing the cumulative velocity distribution function associated with a flood event and requires measurements regarding the entire cross-section, whereas, in the second and third method, the estimate of M is based on reproducing the cross-sectional mean velocity U by following two different procedures. Both of them rely on the entropy parameter M alone and look for that value of M that brings two different estimates of U , obtained by using two different M-dependent-approaches, as close as possible. From an operational viewpoint, the acquisition of velocity data becomes increasingly simplified going from the first to the third approach, which uses only one surface velocity measurement. The procedures proposed are applied in a case study based on the Ponte Nuovo hydrometric station on the Tiber River in central Italy.

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Entropy and 2‐D Velocity Distribution in Open Channels

Cited by 202 publications

References 8 publications

Principle of maximum entropy in the estimation of suspended sediment concentration

Principle of maximum entropy in the estimation of suspended sediment concentration

Derivation of Equation for Mean Suspended Sediment Based on Probabilistic Concept

Three Methods for Estimating the Entropy Parameter M Based on a Decreasing Number of Velocity Measurements in a River Cross-Section

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