Accuracy and Uncertainty Analysis of Intelligent Techniques for Predicting the Longitudinal Dispersion Coefficient in Rivers

Document Type : Research Paper


1 Assist. Prof., Water Research Institute, Ministry of Energy, Tehran

2 Member of Water Research Institute, Ministry of Energy, Ph.D. Student of Environmental Eng., Dept. of Environmental Eng., Tehran University

3 Member of Water Research Institute, Ministry of Energy, Ph.D. Student of Hydraulic Structures Eng., Tarbiat Modarres University, Tehran.

4 Management Director of CELCO., Ph.D. Student of Environmental Eng., Dept. of Environmental, Tehran University

5 Ph.D. Student of Environmental Eng., Dept. of Environmental, Tehran University


Accurate prediction of longitudinal dispersion coefficient (LDC) can be useful for the determination of pollutants concentration distribution in natural rivers. However, the uncertainty associated with the results obtained from forecasting models has a negative effect on pollutant management in water resources. In this research, appropriate models are first developed using ANN and ANFIS techniques to predict the LDC in natural streams. Then, an uncertainty analysis is performed for ANN and ANFIS models based on Monte-Carlo simulation. The input parameters of the models are related to hydraulic variables and stream geometry. Results indicate that ANN is a suitable model for predicting the LDC, but it is also associated with a high level of uncertainty. However, results of uncertainty analysis show that ANFIS model has less uncertainty; i.e. it is the best model for forecasting satisfactorily the LDC in natural streams.


1- Tayfur, G., and Singh, V.P. (2005). “Predicting longitudinal dispersion coefficient in natural streams by artificial neural network.” J. of Hydraulic Engineering, 131 (11) , 991-1000.
2- Kashefipour, M.S., and Falconer, R. A. (2002). “Longitudinal dispersion coefficients in natural channels.” Water Res., 36 (6), 1596-1608.
3- Fischer, B.H. (1975). “Discussion of ‘Simple method for predicting dispersion in streams,’ by R. S. McQuivey and T. N. Keefer.” J. of Environmental Engineering Div., 101 (3), 453-455.
4- Seo I. W., and Cheong, T.S. (1998). “Predicting longitudinal dispersion coefficient in natural Streams.” J. of Hydraulics Engineering, 124 (1), 25-32.
5- Deng, Z.Q., Singh, V.P., and Bengtsson, L. (2001). “Longitudinal dispersion coefficient in straight rivers.”
J. of Hydraulic Engineering, 127 (1), 919-927.
6- Toprak, Z. F., and Cigizoglu, H.K. (2008). “Predicting longitudinal dispersion coefficient in natural streams by artificial intelligence methods.” Hydrol. Process, 22 (20), 4106-4129.
7- Noori, R., Karbassi, A., Farokhnia, A., and Dehghani, M. (2009). “Predicting the longitudinal dispersion coefficient using support vector machine and adaptive neuro-fuzzy inference system techniques.” Environmental Engineering Science, 26 (10), 1503-1510.
8- 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 Systems with Applications, 36 (4), 8589-8596.
9- Kashefipour, M. (2007). “Prediction of longitudinal dispersion coefficient in natural rivers using artificial neural networks.” Iranian J. of Hydraulic, 3, 15-25. (In Persian)
10- Riahi madvar, H., and Ayyaoubzadeh, S. A. (2008). “Estimating longitudinal dispersion coefficient of pollutants using adaptive neuro-fuzzy inference system.” J. of Water and Wastewater, 67, 34-46. (In Persian)
11- Tibshirani, R. (1994). A comparison of some error estimates for neural network models, No. 94-10, Technical Working Report, Department of Statistics, University of Toronto.
12- Dybowski, R. (1997). Assigning confidence intervals to neural network predictions, Technical report, Division of Infection (St Thomas’ Hospital), King’s College, London.
13- Marce, R., Comerma, M., García, J.C., and Armengol, J. (2004). “A neuro-fuzzy modeling tool to estimate fluvial nutrient loads in watersheds under time-varying human impact.” Limnology and Oceanography Methods, 2, 342-355.
14- Aqil, M., Kita, I., Yano, A., and Nishiyama, S. (2007). “Analysis and prediction of flow from local source in a river basin using a Neuro-fuzzy modeling tool.” J. of Environmental Management, 85 (1), 215-223.
15- Noori, R., Abdoli, M.A., Farokhnia, A., and Abbasi, M. (2009). “Results uncertainty of solid waste generation forecasting by hybrid of wavelet transform-ANFIS and wavelet transform-neural network.” Expert Systems with Applications, 36 (6), 9991-9999.
16- Fischer, H.B. (1968). “Dispersion predictions in natural streams.” J. of Hydraulic Division, 94(5), 927-943.
17- Godfrey, R.G., and Frederick, B.J. (1970). “Stream dispersion at selected sites.” U.S. Geological Survey, Prof. Paper 433-K, WashingtonD.C.
18- 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.” US Geological Survey Water-Supply, Paper 1899-G, Washington, D.C.
19- McQuivey, R.S., and Keefer, T.N. (1974). “Simple method for prediction dispersion in streams.” J. of Environment Engineering, 100 (4), 997-1011.
20- Nordin, C.F., and Sabol, G.V. (1974). “Empirical data on longitudinal dispersion in rivers.” U.S. Geological Survey Water Resources Investigation, Washington D.C., 20-74.
21- Haykin, S. (1999). Neural networks: A comprehensive foundation, 2nd Ed., Prentice Hall, New Jersey.
22- Noori, R., Abdoli, M.A., Jalili-Ghazizade, M., and Samifard, R. (2009). “Comparison of ANN and PCA based multivariate linear regression applied to predict the weekly municipal solid waste generation in Tehran.” Iranian J. of Public Health, 38 (1), 74-84.
23- Jalili-Ghazizade, M., and Noori, R. (2008). “Prediction of municipal solid waste generation by use of artificial neural network: A case study of Mashhad.” International J. of Environmental Research, 2 (1), 22-33.
24- Noori, R., Farokhnia, A., Morid, S., and Riahi Madvar, H. (2009). “Effect of input variables preprocessing in artificial neural network on monthly flow prediction by PCA and wavelet transformation.” J. of Water and Wastewater, 69, 13-22. (In Persian)
25- Jang, J.S.R., and Gulley, N. (1995). The fuzzy logic toolbox for use with MATLAB, Mathworks Inc., Massachusetts.
26- Jang, J.S.R., Sun, C.T, and Mizutani, E. (1997). Neuro-fuzzy and soft computing: A computational approach to learning and machine intelligence, Prentice-Hall, New Jersey.
27- Jang, J.S.R. (1991). “Rule extraction using generalized neural networks.” Proc. of the 4th IFSA World Congress, 82-86.
28- Eckhardt, K., Breuer, L., and Frede, H.G. (2003). “Parameter uncertainty and the significance of simulated land use change effects.” J. of Hydrology, 273 (1-4), 164-176.
29- Efron, B., and Tibshirani, R.J. (1993). An introduction to the bootstrap, Chapman and Hall, New York.
30- Abbaspour, K.C., Yang, J., Maximov, I., Siber, R., Bogner, K., Mieleitner, J., Zobrist, J., and Srinivasan, R. (2007). “Modelling hydrology and water quality in the pre-alpine/alpine thur watershed using SWAT.” J. of Hydrology, 333 (2-4), 413-430.
31- Jang, J. S. R., and Sun, C. T. (1995). “Neuro-fuzzy modeling and control.” Proc. of the IEEE, 83, 378-406.
32- Chiu, S.L. (1994). “Fuzzy model identification based on cluster estimation.” J. of Intelligent and Fuzzy Systems, 2 (3), 267-278.