Mathematical model of solute transport in rivers with storage zones using nonlinear dispersion flux approach

References

• Altunkaynak, A., 2016. Prediction of longitudinal dispersion coefficient in natural streams by prediction map. Journal of Hydro-Environment Research, 12, 105–116. doi:10.1016/j.jher.2016.05.001
   Web of Science ®Google Scholar
• Atkinson, T.C. and Davis, P.M., 2000. Longitudinal dispersion in natural channels: 1. Experimental results from the River Severn, UK. Hydrology and Earth System Sciences, 4 (3), 345–353. doi:10.5194/hess-4-345-2000
   Web of Science ®Google Scholar
• Avanzino, R.J., et al., 1984. Results of a solute transport experiment at Uvas Creek, September 1972. Vol. California, Reston, Virginia: US Geological Survey Report Number 84-236. doi:10.3133/ofr84236
   Google Scholar
• Bencala, K.E. and Walters, R.A., 1983. Simulation of solute transport in a mountain pool-and-riffle stream: a transient storage zone model. Water Resources Research, 19 (3), 718–724. doi:10.1029/WR019i003p00718
   Web of Science ®Google Scholar
• Chapra, S.C., 2008. Surface water-quality modeling. Long Grove, USA: Waveland press.
   Google Scholar
• Chapra, S.C. and Canale, R.P., 2011. Numerical methods for engineers. Vol. 1221, New York: Mcgraw-hill.
   Google Scholar
• Davis, P.M. and Atkinson, T.C., 2000. Longitudinal dispersion in natural channels: 3. An aggregated dead zone model applied to the River Severn, U.K. Hydrology and Earth System Sciences, 4 (3), 373–381. doi:10.5194/hess-4-373-2000
   Web of Science ®Google Scholar
• Davis, P.M., Atkinson, T.C., and Wigley, T.M.L., 2000. Longitudinal dispersion in natural channels: 2. The roles of shear flow dispersion and dead zones in the River Severn, UK. Hydrology and Earth System Sciences, 4 (3), 355–371. doi:10.5194/hess-4-355-2000
   Web of Science ®Google Scholar
• Day, T.J., 1975. Longitudinal dispersion in natural channels. Water Resources Research, 11 (6), 909–918. doi:10.1029/WR011i006p00909
   Web of Science ®Google Scholar
• Deng, Z.Q. and Jung, H.S., 2009. Variable residence time–based model for solute transport in streams. Water Resources Research, 45 (3), W03415. doi:10.1029/2008WR007000
   Web of Science ®Google Scholar
• Deng, Z.Q., Jung, H.S., and Ghimire, B., 2010. Effect of channel size on solute residence time distributions in rivers. Advances in Water Resources, 33 (9), 1118–1127. doi:10.1016/j.advwatres.2010.06.016
   Web of Science ®Google Scholar
• Deng, Z.Q., Singh, V.P., and Bengtsson, L., 2004. Numerical solution of fractional advection-dispersion equation. Journal of Hydraulic Engineering, 130 (5), 422–431. doi:10.1061/(ASCE)0733-9429(2004)130:5(422)
   Web of Science ®Google Scholar
• Fischer, H.B., et al., 1979. Mixing in inland and coastal waters. Cambridge, Massachusetts, USA: Academic press.
   Google Scholar
• Fletcher, C.A., 1991. Computational techniques for fluid dynamics. Vol. I, Berlin, Germany: Springer Verlag.
   Google Scholar
• Kazezyılmaz-Alhan, C.M. and Medina, M.A., Jr, 2006. Stream solute transport incorporating hyporheic zone processes. Journal of Hydrology, 329 (1–2), 26–38. doi:10.1016/j.jhydrol.2006.02.003
   Web of Science ®Google Scholar
• Kelleher, C., et al., 2013. Identifiability of transient storage model parameters along a mountain stream. Water Resources Research, 49 (9), 5290–5306. doi:10.1002/wrcr.20413
   Web of Science ®Google Scholar
• Kelleher, C., et al., 2019. Exploring tracer information and model framework trade‐offs to improve estimation of stream transient storage processes. Water Resources Research, 55 (4), 3481–3501. doi:10.1029/2018WR023585
   Web of Science ®Google Scholar
• Kim, S. and Kavvas, M.L., 2006. Generalized Fick’s law and fractional ADE for pollution transport in a river: detailed derivation. Journal of Hydrologic Engineering, 11 (1), 80–83. doi:10.1061/(ASCE)1084-0699(2006)11:1(80)
   Web of Science ®Google Scholar
• Knapp, J.L. and Kelleher, C., 2020. A perspective on the future of transient storage modeling: let’s stop chasing our tails. Water Resources Research, 56 (3), e2019WR026257. doi:10.1029/2019WR026257
   Web of Science ®Google Scholar
• Noh, H., et al., 2021. Multi-gene genetic programming regression model for prediction of transient storage model parameters in natural rivers. Water, 13 (1), 76. doi:10.3390/w13010076
   Web of Science ®Google Scholar
• Nordin, C.F. and Sabol, G.V., 1974. Empirical data on longitudinal dispersion in rivers. Report Number 20–74. Reston, Virginia: US Geological Survey. doi:10.3133/wri7420
   Google Scholar
• Nordin, C.F. and Troutman, B.M., 1980. Longitudinal dispersion in rivers: the persistence of skewness in observed data. Water Resources Research, 16 (1), 123–128. doi:10.1029/WR016i001p00123
   Web of Science ®Google Scholar
• Riahi-Madvar, H., et al., 2009. An expert system for predicting longitudinal dispersion coefficient in natural streams by using ANFIS. Expert Systems with Applications, 36 (4), 8589–8596. doi:10.1016/j.eswa.2008.10.043
   Web of Science ®Google Scholar
• Runkel, R.L. and Bencala, K.E., 1995. Transport of reacting solutes in rivers and streams. In: V.P. Singh, ed. Water science and technology library. Dordrecht: Springer, 137–164. doi:10.1007/978-94-017-1439-6_5
   Google Scholar
• Sattar, A.M. and Gharabaghi, B., 2015. Gene expression models for prediction of longitudinal dispersion coefficient in streams. Journal of Hydrology, 524, 587–596. doi:10.1016/j.jhydrol.2015.03.016
   Web of Science ®Google Scholar
• Singh, S.K., 2003. Treatment of stagnant zones in riverine advection-dispersion. Journal of Hydraulic Engineering, 129 (6), 470–473. doi:10.1061/(ASCE)0733-9429(2003)129:6(470)
   Web of Science ®Google Scholar
• Thackston, E.L. and Schnelle, K.B., 1970. Predicting effects of dead zones on stream mixing. Journal of the Sanitary Engineering Division, 96 (2), 319–331. doi:10.1061/JSEDAI.0001078
   Google Scholar
• Valentine, E.M. and Wood, I.R., 1977. Longitudinal dispersion with dead zones. Journal of the Hydraulics Division, 103 (9), 975–990. doi:10.1061/JYCEAJ.0004845
   Web of Science ®Google Scholar
• Versteeg, H.K. and Malalasekera, W., 2007. An introduction to computational fluid dynamics: the finite volume method. London: Pearson education.
   Google Scholar
• Wallis, S.G., Young, P.C., and Beven, K.J., 1989. Experimental investigation of the aggregated dead zone model. Proceedings of the Institution of Civil Engineers, 87 (1), 1–22. doi:10.1680/iicep.1989.1450
   Web of Science ®Google Scholar
• Zwillinger, D., 1998. Handbook of differential equations. Vol. 1, Houston, Texas: Gulf Professional Publishing.
   Google Scholar