Sensitivity Analysis of Transient Storage Parameters in Mathematical Modeling of Pollution Transport in Rivers Containing Storage Zone

Document Type : Research Paper

Authors

1 M.Sc. Student of Water Structures, Tarbiat Modares University.

2 Associate Professor, Department of Water Engineering and Management, Tarbiat Modares University.

Abstract

Hydrologists studying rivers must determine the relative importance of in-river processes to understand the fate of pollutants. Storage processes are one of the most of this. Currently, the most reliable method for determining the importance of storage processes in the solute transfer is to estimate the stream-storage exchange coefficient (α) and the cross-sectional area ratio (AS/A) in the transient storage model (TSM) with tracer experiment data (Wallis and Manson, 2019). Calibrating the parameters depends on the reciprocal coverage between parameter effects on BTCs and the model's sensitivity to each parameter (Zaramella et al., 2016). Previous studies have quantified the sensitivity of the TSM in inverse modeling (Kelleher et al., 2013; Wlostowski et al., 2013). Due to tracer test data for these studies, their results cannot provide a comprehensive picture of the model behavior. In this study, using Monte Carlo-based methods, an attempt has been made to investigate the effect of different pollutant transfer circumstances in the river by defining a framework with Peclet and Damkohler numbers and pollutant injection time series on storage parameters sensitivity.

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Main Subjects

References

  • Aster, R.C., Borchers, B. and Thurber, C.H., 2018. Parameter estimation and inverse problems. Elsevier.

 

  • Barati Moghaddam, M., Mazaheri, M., and MohammadVali Samani, J. 2017. A comprehensive one-dimensional numerical model for solute transport in rivers. Hydrology and Earth System Sciences, 21(1), pp.99–116.

 

  • Boano, F., Harvey, J. W., Marion, A., Packman, A. I., Revelli, R., Ridolfi, L., and Wörman, A. 2014. Hyporheic flow and transport processes: Mechanisms, models, and biogeochemical implications, Reviews of Geophysics. 52(4), pp.603–679.

 

  • Chapra, S. C. 1997. Surface Water-Quality Modeling. McGraw-Hill Series.

 

  • Cheme, E. K., and Mazaheri, M. 2021. The effect of neglecting spatial variations of the parameters in pollutant transport modeling in rivers. Environmental Fluid Mechanics, 21(3), pp.587–603.

 

6- Choi, S.Y., Seo, I.W. and Kim, Y.O., 2020. Parameter uncertainty estimation of transient storage model using Bayesian inference with formal likelihood based on breakthrough curve segmentation. Environmental Modelling & Software, 123, p.104558.

 

  • Femeena, P. V, Chaubey, I., Aubeneau, A., McMillan, S., Wagner, P. D., and Fohrer, N. 2019. Simple regression models can act as calibration-substitute to approximate transient storage parameters in streams. Advances in Water Resources, 123, pp.201–209.

 

  • Fernald, A. G., Wigington Jr, P. J., and Landers, D. H. 2001. Transient storage and hyporheic flow along the Willamette River, Oregon: Field measurements and model estimates. Water Resources Research, 37(6), pp.1681–1694.

 

  • Gooseff, M. N., Bencala, K. E., Scott, D. T., Runkel, R. L., and McKnight, D. M. 2005. Sensitivity analysis of conservative and reactive stream transient storage models applied to field data from multiple-reach experiments. Advances in Water Resources, 28(5), pp.479–492.

 

  • Gooseff, M. N., Briggs, M. A., Bencala, K. E., McGlynn, B. L., and Scott, D. T. 2013. Do transient storage parameters directly scale in longer, combined stream reaches? Reach length dependence of transient storage interpretations. Journal of Hydrology, 483, pp.16–25.

 

  • Gooseff, M. N., Wondzell, S. M., Haggerty, R., and Anderson, J. 2003. Comparing transient storage modeling and residence time distribution (RTD) analysis in geomorphically varied reaches in the Lookout Creek basin, Oregon, USA. Advances in Water Resources, 26(9), pp.925–937.

 

  • Guozhen, W., Zhang, C., Li, Y., Haixing, L., & Zhou, H. 2016. Source identification of sudden contamination based on the parameter uncertainty analysis. Journal of Hydroinformatics, 18(6), pp.919–927.

 

  • Hammersley, J. 2013. Monte carlo methods. Springer Science and Business Media.

 

  • Hirsch, C. 2007. Numerical computation of internal and external flows: The fundamentals of computational fluid dynamics. Elsevier.

 

  • Kelleher, C., Wagener, T., McGlynn, B., Ward, A. S., Gooseff, M. N., & Payn, R. A. 2013. Identifiability of transient storage model parameters along a mountain stream. Water Resources Research, 49(9), pp.5290–5306.

 

  • Loucks, D. P., and Van Beek, E. 2017. Water resource systems planning and management: An introduction to methods, models, and applications. Springer.

 

  • McCuen, R. H. 2016. Modeling hydrologic change: statistical methods. CRC press.

 

  • Noh, H., Kwon, S., Seo, I. W., Baek, D., and Jung, S. H. 2020. Multi-gene genetic programming regression model for prediction of transient storage model parameters in natural rivers. Water, 13(1), 76.

 

  • Rana, S. M. M., Boccelli, D. L., Scott, D. T., and Hester, E. T. 2019. Parameter uncertainty with flow variation of the one-dimensional solute transport model for small streams using Markov chain Monte Carlo. Journal of Hydrology,  575, pp.1145-1154.

 

  • Rana, S. M. M., Scott, D. T., and Hester, E. T. 2017. Effects of in-stream structures and channel flow rate variation on transient storage. Journal of Hydrology, 548, pp.157–169.

 

  • Runkel, R. L. 1998. One-dimensional transport with inflow and storage (OTIS): A solute transport model for streams and rivers. US Department of the Interior, US Geological Survey.

 

  • Scott, D. T., Gooseff, M. N., Bencala, K. E., and Runkel, R. L. 2003. Automated calibration of a stream solute transport model: implications for interpretation of biogeochemical parameters. Journal of the North American Benthological Society, 22(4), pp.492–510.

 

  • Seo, I. W., and Cheong, T. S. 2001. Moment-Based Calculation of Parameters for the Storage Zone Model for River Dispersion. Journal of Hydraulic Engineering, 127(6), No: 453.

 

  • Singh, S. K. 2008. Comparing Three Models for Treatment of Stagnant Zones in Riverine Transport. Journal of Irrigation and Drainage Engineering, 134(6), No: 853.

 

  • Vrugt, J. A. 2016. Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation. Environmental Modelling and Software, 75, pp.273–316.

 

  • Vrugt, J. A., Ter Braak, C. J. F., Gupta, H. V, and Robinson, B. A. 2009. Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling. Stochastic Environmental Research and Risk Assessment, 23(7), pp.1011–1026.

 

  • Wagener, T., McIntyre, N., Lees, M. J., Wheater, H. S., and Gupta, H. V. 2003. Towards reduced uncertainty in conceptual rainfall‐runoff modelling: Dynamic identifiability analysis. Hydrological Processes, 17(2), pp.455–476.

 

  • Wagener, T., Wheater, H. S., and Camacho, L. A. 2002. Dynamic identifiability analysis of the transient storage model for solute transport in rivers. Journal of Hydroinformatics, 4(3), pp.199–211

 

  • Wagner, B. J., and Harvey, J. W. 1997. Experimental design for estimating parameters of rate‐limited mass transfer: Analysis of stream tracer studies. Water Resources Research, 33(7), pp.1731–1741.

 

  • Wallis, S., and Manson, R. 2019. Sensitivity of optimized transient storage model parameters to spatial and temporal resolution. Acta Geophysica, 67(3), pp.951–960.

 

  • Ward, A. S., Kelleher, C. A., Mason, S. J. K., Wagener, T., McIntyre, N., McGlynn, B., Runkel, R. L., and Payn, R. A. 2017. A software tool to assess uncertainty in transient-storage model parameters using Monte Carlo simulations. Freshwater Science, 36(1), 195–217.

 

  • Wlostowski, A. N., Gooseff, M. N., and Wagener, T. 2013. Influence of constant rate versus slug injection experiment type on parameter identifiability in a 1-D transient storage model for stream solute transport. Water Resources Research, 49(2), 1184–1188

 

  • Zaghiyan, M. R., and Ketabchi, H. 2022. Investigating the relationship between the river flow and dissolved solids concentration. Proceedings of the Institution of Civil Engineers-Water Management, 175(2),89–97.

 

  • Zaramella, M., Marion, A., Lewandowski, J., and Nützmann, G. 2016. Assessment of transient storage exchange and advection–dispersion mechanisms from concentration signatures along breakthrough curves. Journal of Hydrology, 538,794–801.

 

  • Zhao, X., Chang, Y., Wu, J., Li, Q., and Cao, Z. 2021. Investigating the relationships between parameters in the transient storage model and the pool volume in karst conduits through tracer experiments. Journal of Hydrology, 593, No: 125825.
Irrigation Sciences and Engineering
Volume 45, Issue 4
February 2023
Pages 101-116

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History

  • Receive Date: 04 December 2021
  • Revise Date: 02 July 2022
  • Accept Date: 06 July 2022
  • Publish Date: 20 February 2023

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