Technical Papers
May 15, 2012

Predicting Longitudinal Dispersion Coefficient in Natural Streams Using M5′ Model Tree

Publication: Journal of Hydraulic Engineering
Volume 138, Issue 6

Abstract

The longitudinal dispersion coefficient is a key parameter in determining the distribution of pollution concentration, especially in temporally time-varying source cases after full cross-sectional mixing has occurred. Several studies have been performed to present simple formulas to predict it. However, they may not always result in an accurate prediction because of the complexity of the phenomenon. In this study, a M5′ model tree was used to develop a new model for predicting the longitudinal dispersion coefficient. The main advantages of the model trees are that (1) they provide transparent formulas and offer more insight into the obtained formulas and (2) they are more convenient to develop and employ compared with other soft computing methods. To develop the model tree, extensive field data sets consisting of hydraulic and geometrical characteristics of different rivers were used. By using error measures, the performance of the model was also compared with the performance of other existing equations. Overall, the results showed that the developed model outperforms the existing formulas and can serve as a valuable tool for predicting of the longitudinal dispersion coefficient.

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Acknowledgments

The authors acknowledge the comments of professor Jorg Imberger on the previous version of the manuscript. The authors also thank Meysam Bali, Ebrahim Jafari, Ali Behnood and Amin Asgarian for their help in improving the manuscript.

References

Asai, K., and Fujisaki, K. (1991). “Effect of aspect ratio on longitudinal dispersion coefficient.” Proc., Int. Symp. on Envir. Hydr., A. A. Balkema, Rotterdam, Netherlands, 493–498.
Azamathulla, H. M., and Ghani, A. A. (2011). “Genetic programming for predicting longitudinal dispersion coefficients in streams.” Water Resour. Manage.WRMAEJ, 25(6), 1537–1544.
Azamathulla, H. M., and Wu, F.-C. (2011). “Support vector machine approach for longitudinal dispersion coefficients in natural streams.” Appl. Soft Comput., 11(2), 2902–2905.
Bashitialshaaer, R., Bengtsson, L., Larson, M., Persson, K. M., Aljaradin, M., and Hossam, A.-I. (2011). “Sinuosity effects on longitudinal dispersion coefficient.” Int. J. Sust. Water Environ. Sys., 2(2), 77–84.
Bhattacharya, B., Price, R. K., and Solomatine, D. P. (2007). “Machine learning approach to modeling sediment transport.” J. Hydraul. Eng.JHEND8, 133(4), 440–450.
Bhattacharya, B., and Solomatine, D. P. (2005). “Neural networks and M5 model trees in modelling water level-discharge relationship.” Neurocomp., 63, 381–396.
Bonakdar, L., and Etemad-Shahidi, A. (2011). “Predicting wave run-up on rubble-mound structures using M5′ machine learning method.” Ocean Eng.OCENBQ, 38(1), 111–118.
Boxall, J. B., and Guymer, I. (2007). “Longitudinal mixing in meandering channels: New experimental data set and verification of a predictive technique.” Water Res.WATRAG, 41(2), 341–354.
Boxall, J. B., Guymer, I., and Marion, A. (2003). “Transverse mixing in sinuous natural open channel flows.” J. Hydraul Res.JHYRAF, 41(2), 153–165.
Caplow, T., Schlosser, P., and Ho, D. T. (2004). “Tracer study of mixing and transport in the upper Hudson River with multiple dams.” J. Environ. Eng.JOEEDU, 130(12), 1498–1506.
Chapra, S. C. (1977). Surface water-quality modeling, McGraw-Hill, New York.
Cheong, T. S., Younis, B. A., and Seo, I. W. (2007). “Estimation of key parameters in model for solute transport in rivers and streams.” Water Resour. Manage.WRMAEJ, 21(7), 1165–1186.
Deng, Z. Q., Bengtsson, L., Singh, V. P., and Adrian, D. D. (2002). “Longitudinal dispersion coefficient in single-channel streams.” J. Hydraul. Eng.JHEND8, 128(10), 901–916.
Deng, Z. Q., Singh, V. P., and Bengtsson, L. (2001). “Longitudinal dispersion coefficient in straight rivers.” J. Hydraul. Eng.JHEND8, 127(11), 919–927.
Elder, J. W. (1959). “The dispersion of a marked fluid in turbulent shear flow.” J. Fluid Mech.JFLSA7, 5(4), 544–560.
Etemad-Shahidi, A., and Bonakdar, L. (2009). “Design of rubble-mound breakwaters using M5′ machine learning method.” Appl. Ocean Res.AOCRDS, 31(3), 197–201.
Etemad-shahidi, A., and Mahjoobi, J. (2009). “Comparison between M5′ model tree and neural networks for prediction of significant wave height in Lake Superior.” Ocean Eng.OCENBQ, 36(15–16), 1175–1181.
Fischer, H. B. (1967). “The mechanics of dispersion in natural streams.” J. Hydraul. Div.JYCEAJ, 93(HY6), 187–216.
Fischer, H. B. (1968). “Dispersion predictions in natural streams.” J. Sanit. Eng. Div.JSEDAI, 94(5), 927–943.
Fischer, H. B. (1975). “Discussion of ‘simple method for predicting dispersion in streams.’ by R. S. McQuivey and T. N. Keefer.” J. Environ. Eng. Div.JEEGAV, 101(3), 453–455.
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J., and Brooks, N. H. (1979). Mixing in land and costal waters, Academic, New York, 104–138.
Fukuoka, S., and Sayre, W. W. (1973). “Longitudinal dispersion in sinuous channels.” J. Hydraul. Div.JYCEAJ, 99(1), 195–217.
Graf, B. (1995). “Observed and predicted velocity and longitudinal dispersion at steady and unsteady flow, Colorado River, Glen Canyon Dam to Lake Mead.” J. Am. Water Resour. Assoc.WARBAQ, 31(2), 265–281.
Guymer, I. (1998). “Longitudinal dispersion in sinuous channel with changes in shape.” J. Hydraul. Eng.JHEND8, 124(1), 33–40.
Iwasa, Y., and Aya, S. (1991). “Predicting longitudinal dispersion coefficient in open-channel flows.” Proc., Int. Symp on Envir. Hydr., Hong Kong University Press, Hong Kong, 505–510.
Jafari, E., and Etemad-Shahidi, A. (2012). “Derivation of a new model for prediction of wave overtopping at rubble-mound structures.” J. Waterw., Port, Coastal Eng. Div.AWHCAR, 138(1), 42–52.
Jung, N.-C., Popescu, I., Kelderman, P., Solomatine, D. P., and Price, R. K. (2010). “Application of model trees and other machine learning techniques for algal growth prediction in Yongdam reservoir, Republic of Korea.” J. Hydroinf., 12(3), 262–274.
Kashefipour, S. M., and Falconer, R. A. (2002). “Longitudinal dispersion coefficients in natural channels.” Water Res.WATRAG, 36(6), 1596–1608.
Koussis, A. D., and Rodríguez-Mirasol, J. (1998). “Hydraulic estimation of dispersion coefficient for streams.” J. Hydraul. Eng.JHEND8, 124(3), 317–320.
Liu, H. (1977). “Predicting dispersion coefficient of streams.” J. Environ. Eng. Div.JEEGAV, 103(1), 59–69.
Mahjoobi, J., Etemad-Shahidi, A., and Kazeminezhad, M. H. (2008). “Hindcasting of wave parameters using different soft computing methods.” Appl. Ocean Res.AOCRDS, 30(1), 28–36.
Marion, A., Zaramella, M., and Bottacin-Busolin, A. (2008). “Solute transport in rivers with multiple storage zones: The STIR model.” Water Resour. Res.WRERAQ, 44(10), W10406.
McQuivey, R. S., and Keffer, T. N. (1974). “Simple method for predicting dispersion in streams.” J. Environ. Eng. Div.JEEGAV, 100(4), 997–1011.
Murphy, E., Ghisalberti, M., and Nepf, H. (2007). “Model and laboratory study of dispersion in flows with submerged vegetation.” Water Resour. Res.WRERAQ, 43(5), W05438.
Nepf, H. M., Mugnier, C. G., and Zavistoski, R. A. (1997). “The effects of vegetation on longitudinal dispersion.” Estuary Coast Shelf Sci.ECSSD3, 44(6), 675–684.
Noori, R., Karbassi, A. R., Farokhnia, A., and Dehghani, M. (2009). “Predicting the longitudinal dispersion coefficient using support vector machine and adaptive neuro-fuzzy inference system techniques.” Environ. Eng. Sci.EESCF5, 26(10), 1503–1510.
Nordin, C. F., and Sabol, G. V. (1974). “Empirical data on longitudinal dispersion in rivers.” Water-Resources Investigations 20-74, U.S. Geological Survey, Reston, VA.
Papadimitrakis, I., and Orphanos, I. (2004). “Longitudinal dispersion characteristics of rivers and natural streams in Greece.” Water, Air, Soil Pol.: Focus., 4(4–5), 289–305.
Pyle, D. (1992). Data preparation for data mining, Morgan Kaufmann, San Francisco.
Quinlan, J. R. (1992). “Learning with continuous classes.” Proc., 5th Australian Joint Conf. on Artificial Intelligence, World Scientific, Singapore, 343–348.
Riahi-Madvar, H., Ayyoubzadeh, S. A., Khadangi, E., and Ebadzadeh, M. M. (2009). “An expert system for predicting longitudinal dispersion coefficient in natural streams by using ANFIS.” Expert Syst. Appl.ESAPEH, 36(4), 8589–8596.
Rowiński, P. M., Piotrowski, A., and Napiórkowski, J. J. (2005). “Are artificial neural network techniques relevant for the estimation of longitudinal dispersion coefficient in rivers?Hydrol. Sci. J.HSJODN, 50(1), 175–187.
Rutherford, J. C. (1994). River mixing, Wiley, Chichester, UK.
Sahay, R. R. (2011). “Prediction of longitudinal dispersion coefficients in natural rivers using artificial neural network.” J. Fluid Mech.JFLSA7, 11(3), 247–261.
Sahay, R. R., and Dutta, S. (2009). “Prediction of longitudinal dispersion coefficients in natural rivers using genetic algorithm.” Hydrol. Res.HRYEAO, 40(6), 544–552.
Seo, I. W., and Baek, K. O. (2004). “Estimation of the longitudinal dispersion coefficient using the velocity profile in natural streams.” J. Hydraul. Eng.JHEND8, 130(3), 227–236.
Seo, I. W., and Cheong, T. S. (1998). “Predicting longitudinal dispersion coefficient in natural streams.” J. Hydraul. Eng.JHEND8, 124(1), 25–32.
Seo, I. W., and Cheong, T. S. (2001). “Moment-based calculation of parameters for the storage zone model for river dispersion.” J. Hydraul. Eng.JHEND8, 127(6), 453–465.
Shucksmith, J. D., Boxall, J. B., and Guymer, I. (2010). “Effects of emergent and submerged natural vegetation on longitudinal mixing in open channel flow.” Water Resour. Res.WRERAQ, 46(4), W04504.
Singh, S. K. (2003). “Treatment of stagnant zones in riverine advection-dispersion.” J. Hydraul. Eng.JHEND8, 129(6), 470–473.
Solomatine, D. P., Dulal K. N. (2003). “Model trees as an alternative to neural networks in rainfall-runoff modelling.” Hydrol. Sci. J.HSJODN, 48(3), 399–411.
Solomatine, D. P., and Xue, Y. P. (2004). “M5 model trees and neural networks: Application to flood forecasting in the upper reach of the Huai River in China.” J. Hydrol. Eng.JHYEFF, 9(6), 491–501.
Smith, P., Beven, K., Tawn, J., Blazkova, S., and Merta, L. (2006). “Discharge-dependent pollutant dispersion in rivers: Estimation of aggregated dead zone parameters with surrogate data.” Water Resour. Res.WRERAQ, 42(4), W04412.
Tayfur, G. (2006). “Fuzzy, ANN, and regression models to predict longitudinal dispersion coefficient in natural streams.” Nord. Hydrol.NOHYBB, 37(2), 143–164.
Tayfur, G. (2009). “GA-optimized model predicts dispersion coefficient in natural channels.” Hydrol. Res.HRYEAO, 40(1), 65–78.
Tayfur, G., and Singh, V. P. (2005). “Predicting longitudinal dispersion coefficient in natural streams by artificial neural network.” J. Hydraul. Eng.JHEND8, 131(11), 991–1000.
Taylor, G. I. (1954). “The dispersion of matter in turbulent flow through a pipe.” Proc. R. Soc. Lond. A, The Royal Society, London, 223(1155), 446–468.
Toprak, Z. F., and Cigizoglu, H. K. (2008). “Predicting longitudinal dispersion coefficient in natural streams by artificial intelligence methods.” Hydrol. ProcessesHYPRE3, 22(20), 4106–4129.
Toprak, Z. F., and Savci, M. E. (2007). “Longitudinal dispersion coefficient modeling in natural channels using fuzzy logic.” Clean-Soil Air WaterCSAWAC, 35(6), 626–637.
Valentine, E. M., and Wood, I. R. (1977). “Longitudinal dispersion with dead zones.” J. Hydraul. Div.JYCEAJ, 103(9), 975–990.
Wang, Y., and Witten, I. H. (1997). “Induction of model trees for predicting continuous classes.” Proc. of the Poster Papers of the European Conf. on Machine Learning, 1997, Univ. of Economics, Faculty of Informatics and Statistics, Prague, Czech Republic.
White, W. R., Milli, H., and Crabbe, A. D. (1973). “Sediment transport an appraisal methods, Vol 2: Performance of theoretical methods when applied to flume and field data.” Hydraulic Research Station Rep., No. 1T119, Wallingford, UK.
Witten, I. H., and Frank, E. (2005). Data mining: Practical machine learning tools and techniques, Morgan Kaufmann, San Francisco.
Yotsukura, N., Fischer, H. B., and Sayre, W. W. (1970). “Measurement of mixing characteristics of the Missouri River between Sioux City, Iowa and Plattsmouth, Nebraska.” U.S. Geological Survey Water-Supply Paper 1899-G, U.S. Government Printing Office, Washington, DC.

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Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 138Issue 6June 2012
Pages: 542 - 554

History

Received: Feb 16, 2011
Accepted: Dec 14, 2011
Published online: May 15, 2012
Published in print: Jun 1, 2012

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Amir Etemad-Shahidi, Ph.D. [email protected]
Griffith School of Engineering, Gold Coast Campus, Griffith Univ., QLD 4222, Australia; and School of Civil Engineering, Iran Univ. of Science and Technology, Narmak, Tehran, Iran (corresponding author). E-mail: [email protected]; [email protected]
Milad Taghipour [email protected]
M.Sc., School of Civil Engineering, Iran Univ. of Science and Technology, Narmak, Tehran, Iran. E-mail: [email protected]

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