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Distribution of sediment concentration in debris flow using Rényi entropy

Author

Listed:
  • Ghoshal, Koeli
  • Kumbhakar, Manotosh
  • Singh, Vijay P.

Abstract

Debris flow is a destructive natural phenomenon that normally occurs in mountainous regions or steeply sloping areas. Its destructive force is so high that whatever comes in its way is obliterated. It is therefore difficult to collect field observations of debris flow. This study developed a model of the vertical distribution of sediment concentration in debris flow by maximizing Rényi entropy. The model contains a parameter, called entropy parameter, which is a combination of Lagrange multipliers and has a physical justification. An expression for the equilibrium sediment concentration is also developed, and is found to be a function of the entropy parameter and an entropy index. The proposed model is validated with experimental data and is compared with other entropy-based models reported in the literature. It is observed that the prediction accuracy of the proposed models is superior to that of the other models. Errors, namely relative error and relative root-mean-squared error, are computed and are reported in the paper in support of the derived model.

Suggested Citation

  • Ghoshal, Koeli & Kumbhakar, Manotosh & Singh, Vijay P., 2019. "Distribution of sediment concentration in debris flow using Rényi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 267-281.
    • Handle: RePEc:eee:phsmap:v:521:y:2019:i:c:p:267-281
    DOI: 10.1016/j.physa.2019.01.081
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    References listed on IDEAS

    as
    1. Kundu, Snehasis, 2017. "Derivation of Hunt equation for suspension distribution using Shannon entropy theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 488(C), pages 96-111.
    2. Khozani, Zohreh Sheikh & Bonakdari, Hossein, 2018. "Formulating the shear stress distribution in circular open channels based on the Renyi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 114-126.
    3. Kumbhakar, Manotosh & Ghoshal, Koeli & Singh, Vijay P., 2017. "Derivation of Rouse equation for sediment concentration using Shannon entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 494-499.
    4. Singh, Vijay P. & Cui, Huijuan, 2015. "Modeling sediment concentration in debris flow by Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 420(C), pages 49-58.
    5. Kumbhakar, Manotosh & Ghoshal, Koeli, 2016. "Two dimensional velocity distribution in open channels using Renyi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 546-559.
    6. Kazemian-Kale-Kale, Amin & Bonakdari, Hossein & Gholami, Azadeh & Khozani, Zohreh Sheikh & Akhtari, Ali Akbar & Gharabaghi, Bahram, 2018. "Uncertainty analysis of shear stress estimation in circular channels by Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 558-576.
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    Cited by:

    1. Secrest, J.A. & Conroy, J.M. & Miller, H.G., 2020. "A unified view of transport equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).

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