Modeling One-Dimensional Nonreactive Solute Transport in Open Channel Flows Under Uncertain Flow and Solute Loading Conditions
Publication: Journal of Hydrologic Engineering
Volume 25, Issue 8
Abstract
The study of solute transport processes in open channel flows is important for water quality management and environment protection. Solute transported in open channel flows is usually uncertain because of the underlying stochastic flow and uncertain solute source/sink conditions. Here a stochastic one-dimensional nonreactive transport model based on the Fokker-Planck equation (FPE) approach is developed. The governing equation for the developed stochastic model is a two-dimensional FPE that can explain the effect of both uncertain flow fields and solute source/sink conditions on the stochastic solute transport behavior. The proposed model can provide the spatiotemporal probability density function (PDF) of the solute concentration. Ensemble mean and standard deviation behavior in space and time can then be easily obtained through the corresponding PDF. A numerical experiment is conducted to demonstrate the capabilities of the two-dimensional stochastic transport model. The two-dimensional ULTIMATE QUICKEST finite difference scheme is applied to solve the FPE. Monte Carlo simulation is performed to validate the results obtained from the proposed approach. The validation results indicate that the proposed FPE approach can capture the complete probabilistic dynamics of a one-dimensional solute transport system under uncertain flow fields and solute source/sink conditions by providing the evolutionary PDF of solute concentration in both time and space in a computationally efficient way.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
References
Barati Moghaddam, M., M. Mazaheri, and J. MohammadVali Samani. 2017. “A comprehensive one-dimensional numerical model for solute transport in rivers.” Hydrol. Earth Syst. Sci. 21 (1): 99–116. https://doi.org/10.5194/hess-21-99-2017.
Ceyhan, M. S., and M. L. Kavvas. 2018. “Ensemble modeling of the theis equation under uncertain parameter conditions.” J. Hydrol. Eng. 23 (5): 1–12. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001632.
Dib, A., and M. Kavvas. 2018. “Ensemble modeling of stochastic unsteady open-channel flow in terms of its time–space evolutionary probability distribution. Part 2: Numerical application.” Hydrol. Earth Syst. Sci. 22 (3): 2007–2021. https://doi.org/10.5194/hess-22-2007-2018.
Ercan, A., and M. Kavvas. 2011. “Ensemble modeling of hydrologic and hydraulic processes at one shot: Application to kinematic open-channel flow under uncertain channel properties by the stochastic method of characteristics.” J. Hydrol. Eng. 17 (1): 168–181. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000425.
Ferrarin, C., et al. 2008. “Development and validation of a finite element morphological model for shallow water basins.” Coastal Eng. 55 (9): 716–731. https://doi.org/10.1016/j.coastaleng.2008.02.016.
Gates, T. K., and M. A. Al-Zahrani. 1996. “Spatiotemporal stochastic open-channel flow. I: Model and its parameter data.” J. Hydraul. Eng. 122 (11): 641–651. https://doi.org/10.1061/(ASCE)0733-9429(1996)122:11(641).
He, S., and N. Ohara. 2019. “Modeling sub-grid variability of snow depth using the Fokker-Planck equation approach.” Water Resour. Res. 55 (4): 3137–3155. https://doi.org/10.1029/2017WR022017.
Higashino, M., and H. G. Stefan. 2017. “Oxygen uptake prediction in rivers and streams: A stochastic approach.” J. Environ. Manage. 203 (Dec): 200–207. https://doi.org/10.1016/j.jenvman.2017.07.059.
Hu, J., L. Sun, C. H. Li, X. Wang, X. L. Jia, and Y. P. Cai. 2018. “Water quality risk assessment for the Laoguanhe River of China using a stochastic simulation method.” J. Environ. Inf. 6 (2): 123–136. https://doi.org/10.3808/jei.200500059.
Ji, Z. G. 2017. Hydrodynamics and water quality: Modeling rivers, lakes, and estuaries. Hoboken, NJ: Wiley.
Kavvas, M. L. 2003. “Nonlinear hydrologic processes: Conservation equations for determining their means and probability distributions.” J. Hydrol. Eng. 8 (2): 44–53. https://doi.org/10.1061/(ASCE)1084-0699(2003)8:2(44).
Kerr, J. G., M. C. Eimers, and H. Yao. 2016. “Estimating stream solute loads from fixed frequency sampling regimes: The importance of considering multiple solutes and seasonal fluxes in the design of long-term stream monitoring networks.” Hydrol. Processes 30 (10): 1521–1535. https://doi.org/10.1002/hyp.10733.
Kim, S., M. L. Kavvas, and J. Yoon. 2005. “Upscaling of vertical unsaturated flow model under infiltration condition.” J. Hydrol. Eng. 10 (2): 151–159. https://doi.org/10.1061/(ASCE)1084-0699(2005)10:2(151).
Lee, I., et al. 2017. “Modeling approach to evaluation of environmental impacts on river water quality: A case study with Galing River, Kuantan, Pahang, Malaysia.” Ecol. Modell. 353 (Jun): 167–173. https://doi.org/10.1016/j.ecolmodel.2017.01.021.
Leonard, B. 1991. “The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection.” Comput. Method Appl. Mech. Eng. 88 (1): 17–74. https://doi.org/10.1016/0045-7825(91)90232-U.
Li, D., L. Shi, Z. Dong, J. Liu, and W. Xu. 2019. “Risk analysis of sudden water pollution in a plain river network system based on fuzzy-stochastic methods.” Stochastic Environ. Res. Risk Assess. 33 (2): 359–374. https://doi.org/10.1007/s00477-018-01645-z.
Liang, L., 2003. “One-dimensional numerical modeling of the conservation equation for non-reactive stochastic solute transport by unsteady flow field in stream channels.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Univ. of California.
Liang, L., and M. L. Kavvas. 2008. “Modeling of solute transport and macrodispersion by unsteady stream flow under uncertain conditions.” J. Hydrol. Eng. 13 (6): 510–520. https://doi.org/10.1061/(ASCE)1084-0699(2008)13:6(510).
Lin, B., and R. A. Falconer. 1997. “Tidal flow and transport modeling using ULTIMATE QUICKEST scheme.” J. Hydraul. Eng. 123 (4): 303–314. https://doi.org/10.1061/(ASCE)0733-9429(1997)123:4(303).
Liu, Y., P. Yang, C. Hu, and H. Guo. 2008. “Water quality modeling for load reduction under uncertainty: A Bayesian approach.” Water Res. 42 (13): 3305–3314. https://doi.org/10.1016/j.watres.2008.04.007.
Martin, J. L., and S. C. McCutcheon. 2018. Hydrodynamics and transport for water quality modeling. Boca Raton, FL: CRC Press.
Neumann, L. E., J. Šimůnek, and F. J. Cook. 2011. “Implementation of quadratic upstream interpolation schemes for solute transport into HYDRUS-1D.” Environ. Software 26 (11): 1298–1308. https://doi.org/10.1016/j.envsoft.2011.05.010.
Ohara, N., M. Kavvas, and Z. Chen. 2008. “Stochastic upscaling for snow accumulation and melt processes with PDF approach.” J. Hydrol. Eng. 13 (12): 1103–1118. https://doi.org/10.1061/(ASCE)1084-0699(2008)13:12(1103).
Parsaie, A., and A. H. Haghiabi. 2017. “Computational modeling of pollution transmission in rivers.” Appl. Water Sci. 7 (3): 1213–1222. https://doi.org/10.1007/s13201-015-0319-6.
Sahoo, M. M., and K. C. Patra. 2018. “Stochastic risk assessment of water quality using advection dispersion equation and Bayesian approximation: A case study.” Human Ecol. Risk Assess. Int. J. 24 (3): 567–589. https://doi.org/10.1080/10807039.2017.1394174.
Sharma, S., and M. Kavvas. 2005. “Modeling noncohesive suspended sediment transport in stream channels using an ensemble-averaged conservation equation.” J. Hydraul. Eng. 131 (5): 380–389. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:5(380).
Tu, T., K. Carr, A. Ercan, T. Trinh, M. Kavvas, and J. Nosacka. 2017. “Assessment of the effects of multiple extreme floods on flow and transport processes under competing flood protection and environmental management strategies.” Sci. Total Environ. 607 (Dec): 613–622. https://doi.org/10.1016/j.scitotenv.2017.06.271.
Tu, T., A. Ercan, and M. Kavvas. 2019. “One-dimensional solute transport in open channel flow from a stochastic systematic perspective.” Stoch. Environ. Res. Risk Assess. 33 (7): 1403. https://doi.org/10.1007/s00477-019-01699-7.
Tu, T., A. Ercan, and M. Kavvas. 2020. “Probabilistic solution to two-dimensional stochastic solute transport model by the Fokker-Planck equation approach.” J. Hydrol. 580 (Jan): 124250. https://doi.org/10.1016/j.jhydrol.2019.124250.
Wang, Y., W. Zhang, Y. Zhao, H. Peng, and Y. Shi. 2016. “Modelling water quality and quantity with the influence of inter-basin water diversion projects and cascade reservoirs in the Middle-lower Hanjiang River.” J. Hydrol. 541 (Oct): 1348–1362. https://doi.org/10.1016/j.jhydrol.2016.08.039.
Wu, X. F., and D. Liang. 2019. “Study of pollutant transport in depth-averaged flows using random walk method.” J. Hydrodyn. 31 (2): 303–316. https://doi.org/10.1007/s42241-018-0105-7.
Yoshioka, H., K. Unami, and T. Kawachi. 2012. “Stochastic process model for solute transport and the associated transport equation.” Appl. Math. Modell. 36 (4): 1796–1805. https://doi.org/10.1016/j.apm.2011.09.011.
Zhang, D. X., and S. P. Neuman. 1996. “Effect of local dispersion on solute transport in randomly heterogeneous media.” Water Resour. Res. 32 (9): 2715–2723. https://doi.org/10.1029/96WR01335.
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Published In
Journal of Hydrologic Engineering
Volume 25 • Issue 8 • August 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Nov 1, 2019
Accepted: Mar 4, 2020
Published online: May 27, 2020
Published in print: Aug 1, 2020
Discussion open until: Oct 27, 2020
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