Akhoni Pourhosseini, F. & Ebrahimi, K. (2020). Shannon’s Entropy Evaluation on Determination of Surfaceس Water Quality, Case Studies: Karun and Babolrood Rivers. Water and Irrigation Management, 9(2), 171-183.
Ammari, A. & Remini, B. )2010(. Estimation of Algerian Rivers dischargesbased on chiu’s equation. Arab Journal of Geosci, 3, 59–65.
Barbe, D., Cruise, J. & Singh, V. )1991(. Solution of three-constraint entropy-based velocity distribution. J. Hydraul. Eng., 117(10), 1389–1396.
Brunsell, N.A. (2010). A multiscale information theory approach to assess spatial-temporal variability of Precipitation. J. Hydrol., 385, 165-172.
Chiu, C.L. (1987). Entropy and probability concepts in hydraulics. J. Hydr Hydraulic Engineering, 113(5), 583-600.
Chiu, C.L. (1988). Entropy and 2-D velocity distribution in open channels. J. Hydraulic Engineering, 114(7), 738-756.
Chiu C.L., (1989). Velocity distribution in open-channel flow. Journal of Hydraulic Engineering, ASCE, 115(5), 576-594.
Chiu, C.L. (1991). Application of entropy concept in open-channel flow. J. Hydraul. Eng., 117(5), 615-628.
Chiu, C.L. & Said, C.A. (1995). Maximum and mean velocities and entropy in open- channel flow. J. Hydraul. Engineering, 121(1), 26-35.
Chiu, C.L. & Murray, D.W. (1992). Variation of velocity distribution along non-uniform open-channel flow. J. Hydraul. Eng., 118, 989–1001.
Chiu, C.L. & Tung, N.C. (2002). Maximum velocity and regularities in open-channel flow. J. Hydraul. Engineering, 128(8), 803-803.
Choo, Y.-M., Jeon, H.-S. & Seo, J.-C. )2021(. Entropy-Based Shear Stress Distribution in Open Channel for All Types of Flow Using Experimental Data. Entropy, 23, 1540, https://doi.org/10.3390/ e23111540.
Daneshfaraz, R., Moazamnia, M. & Sadeghfam S. (2018). Estimating the Velocity Distribution in Narrow Combined. Sewers using Entropy Theory Irrigation and Drainage Structures Engineering Research, 19(71), 1-18.
Esmaeili Varaki, M., Ghorbani Nasralah Abadi, S. & Navabian, M. (2013). Evaluation of entropy based chiu’s method for prediction of the velocity distribution and discharge in rivers.
Journal of Water and Soil Conservation, 6(6), 147-164.
Farina, G., Alvisi, S., Franchini, M. & Moramarco, T. )2014(. Three methods for estimating the entropy parameter M based on a decreasing number of velocity measurements in a river cross-section. Entropy, 16, 2512–2529.
Farsadizadeh, D., Hosseinzadeh Dalir, A., Ghorbani, MA. & Samadian Fard, S. (2011). Estimation of Flow Velocity Distribution in Smooth-Bed Open Channels with a Smooth Bed Using Entropy Theory and Genetic Programming, Journal of Water and Soil Science, 21(3), 61-74.
Gell-Mann, M. & Tsallis, C. (2004). Nonextensive Entropy—Interdisciplinary Applications., Oxford University Press, New York, 1–52.
Gholami, A., Bonakdari, H. & Mohammadian, A. (2019). A method based on the Tsallis entropy for characterizing threshold channel bank profiles. Physica A: Statistical Mechanics and Its Applications, 121089. doi:10.1016/j.physa.2019. 121089.
Guo, J. & Julien, P.Y. )2008(. Application of the Modified Log-Wake Law in Open-Channels. Journal of Applied Mechanics, 1(2), 17-23.
Jaynes, E.T. (1957). Information theory and statistical mechanics. Phys. Rev., 106(4), 620–630.
Jaynes, E.T. (1982). On the rationale of maximum entropy methods. Proc. IEEE, 70(9), 939–952
Jha, R. & Singh. V.P. )2008(. Evaluation of river water quality by entropy. KSCE J. Civil Eng., 12(1), 61-69.
Karamouz, M., Nokhandan, A.K., Kerachian, R. & Maksimovic, C. (2009). Design of on-line river water quality monitoring systems using the entropy theory: a case study. Environ. Monit. Assess., 155(1-4), 63-81.
Kazemian-Kale-Kale, A., Bonakdari, H., Gholami, A., Sheikh Khozani, Z., Akhtari, A.A. & Gharabaghi, B. (2018), Uncertainty analysis of shear stress estimation in circular channels by Tsallis entropy, Physica A, 510, 558-576.
Kumbhakar, M., Rajendra K.R., Ghoshal, K., Singh, V.P. (2020), On the role of Tsallis entropy index for velocity modelling in open channels, Physica A: Statistical Mechanics and its Applications, 557, https://doi.org/10.1016/j.physa. 2020.124901.
Leopold, L.B., Wolman, M.G. & Miller, J.P. (1964). Fluvial Processes in Geomorphology. San Francisco, Calif.: W.H. Freeman, 522p.
Luo, H. (2009). Tsallis entropy-based velocity distributions in open channel flows. M. Sc. Thesis, Texas A&M University. College Station, TX.
Luo, H. & Singh, V.P. (2011). Entropy theory for two-dimensional velocity distribution. J. Hydrol. Eng., 18(2), 331-339.
Luo, H., Singh, V. & Schmidt, A. (2018). Comparative study of 1D entropy-based and conventional deterministic velocity distribution equations for open channel flows. J. Hydrol., 563, 679–693.
Mirabbasi Najafabadi, R., Dinpazhoh, Y. & Fakheri-Fard., A. )2012(. Rainfall Runoff Modelling Using the Principle of Maximum Entropy (Case Study: Kasilian Watershed). JWSS, 15 (58), 39-52.
Mirauda, D. & Russo, M.G. (2020). Modeling Bed Shear Stress Distribution in Rectangular Channels Using the Entropic Parameter. Entropy, 22, 87, https://doi.org/10.3390/e22010087.
Moazamnia, M. & Sadeghfam, S. (2018). Estimating the Velocity Distribution in Narrow Combined Sewers using Entropy Theory, Irrigation and Drainage Structures Engineering Research, 19(71), 1-18. (In Persian)
Moramarco, T., Barbetta, S. & Tarpanelli, A. (2017). From surface flow velocity measurements to discharge assessment by the entropy theory. Water, 9(2), 120, https://doi.org/10.3390/w9020120.
Moramarco, T., Saltalippi & Singh, V.P. (2004). Estimation of mean velocity in natural channels based on Chiu's velocity distribution equation. J. Hydrologic Engrg., 9(1), 42-50.
Moramarco, T. & Termini, D. (2015). Entropic approach to estimate the mean flow velocity: experimental investigation in laboratory flumes. Environ. Fluid Mech., 15(6), 1163–1179.
Pan, Y., Li, Z., Yanga, K. & Jia, D. (2019). Velocity distribution characteristics in meandering compound channels with one-sided vegetated floodplains, Journal of Hydrology, 578, 124068. http://dx.doi.org/10.1016/j.jhydrol.2019.124068.
Pathak, K., Pandey, K.K. & Singh, V.P., (2020). Entropy-based velocity and shear stress distributions for trapezoidal channel. Journal of Hydrologic Engineering, 25(11), 04020047, https://doi.org/ 10.1061/(ASCE)HE.1943-5584.0002001
Shannon, C.E. (1948). A mathematical theory of communication. J. Bell Systems Technical, 27(3), 379-423.
Shiono, K. & Muto, Y. (1998). Complex flow mechanisms in compound meandering channels with overbank flow. Journal of Fluid Mechanics, 376, 221–261.
Singh, G., Khosa, R., Jain, M.K., Moramarco, T. & Singh, V.P. (2023), Influence of the channel bed slope on Shannon, Tsallis, and Renyi entropy parameters, Journal of Hydroinformatics, 25(6), 2195–2209.
Singh, V.P. & Cui, H. (2014). Suspended sediment concentration distribution using Tsallis entropy. Physica A: Statistical Mechanics and Its Applications, 414, 31–42.
Singh, V.P. & Luo, H. (2011), Entropy Theory for Distribution of One-Dimensional
Velocity in Open Channels, Journal of Hydraulic Engineering, 16(9), 725-735.
Singh, V P., Marini, G. & Fontana, N. (2013). Derivation of 2D Power-Law Velocity Distribution Using Entropy Theory. Entropy, 15(4), 1221-1231.
Singh, V.P. (2016). Introduction to Tsallis entropy theory in water engineering. CRC Press.
Sontek (2001). Acoustic Doppler Velocimeter (Field) Technical Documentation. Sontek/YSI, Inc., San Diego, CA.
Termini, D. & Moramarco, M. (2020), Entropic model application to identify cross-sectional flow effect on velocity distribution in a large amplitude meandering channel, Advances in Water Resources, 143,103678, https://doi.org/10.1016/j.advwatres. 2020.103678.
Tsallis, C. (1988). Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys., 52(1–2), 479–487.
Tsallis, C. (2002). Entropic nonextensivity: A possible measure of complexity. Chaos Solitons Fractals, 13, 371–391.
Tsallis, C., & Bukman, D. J. (1996). Anomalous diffusion in the presence of external forces: Exact time-dependent solutions and their thermostatistical basis. Phys. Rev. E, 54(3), R2197–R2200.
Tsallis, C., Mendes, R.S. & Plastino, A.R. (1998). The role of constraints within generalized nonextensive statistics. Physica A: Statistical Mechanics and its Applications, 261(3), 534–554.
Vyas, J.K., Perumal, M. & Moramarco, T., 2020. Discharge estimation using Tsallis and Shannon entropy theory in natural channels. Water, 12(6), 1786, https://doi.org/10.3390/w12061786.
Xia, R. (1997). Relation between mean and maximum velocities in a natural river, Journal of Hydraulic Engineering, 123(8), 720-723.
Ya, P., Lib, Z., Yanga, K. & Jia, D. (2019). Velocity distribution characteristics in meandering compound channels with one-sided vegetated floodplains, Journal of Hydrology, 578, 124068, https://doi.org/ 10.1016/j.jhydrol.2019.124068.
Zahiri, A., Hashemi, F. & Yousefabadi, I. (2017). Simulation of two-dimensional velocity distributions in rivers based on Chiu's theory (Case Study: Gorganrood River). Iranian Journal of Ecohydrology, 4(3), 791-802. (In Persian)
