Modeling of stage-discharge relationship in compound channels using multi-stage gene expression programming

Document Type : Research Article


North Khorasan Water Regional Co.


In flood conditions at the alluvial rivers with compound sections, due to momentum exchange between main channel and floodplains, flow discharge prediction by traditional methods is very erroneous. In this paper, a new method known as multi-stage gene expression programming has been used for computation of flow discharge in straight compound channels. For modeling, three dimensionless parameters of relative depth, coherence and relative calculated flow discharge, and one parameter of relative measured flow discharge were selected as inputs and output, respectively. Using 402 stage-discharge dataset from 31 laboratory and field compound channels, explicit relationships were developed for flow discharge prediction. The mean absolute errors of this method were obtained as 10.2% and 11.6%, respectively for training and testing phases. Hence compared with the Manning's formula (with mean absolute error of 19.3%), the proposed method is quit outperform. Hence, application of this method is recommended for flood flow discharge in rivers having compound channel forms. Also, by incorporating this new idea with the computation procedures of the river water surface profiles and flood routing, the design of flood alleviation schemes will be improved.


Main Subjects

 Ackers, P. Hydraulic design of two-stage channels. Journal of Water and Maritime Engineering. 1992 Dec ; 96: 247-257.
[2]. Jiang, B,, Yang, K,, and Cao, S. An analytical model for the distributions of velocity and discharge in compound channels with submerged vegetation. PLoS ONE. 2015 Jul 10; 10(7): 1-17.
[3]. Yang, Z., Gao, W. and Huai, W. Estimation of discharge in compound channels based on energy concept. Journal of Hydraulic Research. 2102 Aug 31; 50(1): 105-113.
[4]. Conway, Ph., O’Sullivan, J.J., and Lambert, M.F. Stage–discharge prediction in straight compound channels using 3D numerical models. Proceedings of the Institution of Civil Engineers, Water Management. 2013 Jun; 166(1): 3-15.
[5]. Wark, J.B., Samuels, P.G., and Ervine, D.A. A practical method of estimating velocity and discharge in compound channels. International Conference on River Flood Hydraulics. London, 1990 Sep; 163-172.
[6]. Shiono, K. and Knight, D.W. Turbulent open-channel flows with variable depth across the channel. Journal of Fluid Mechanics. 1991 Jun; 222: 617-646.
[7]. Hu, C., Ju, Z., and Guo, Q. Flow movement and sediment transport in compound channels. Journal of Hydraulic Research. 2010 Mar 18; 48(1): 23-32.
[8]. Wormleaton, P.R. and Merrett, D.J. 1990. An improved method of calculation for steady uniform flow in prismatic main channel/floodplain sections. Journal of Hydraulic Research. 1990 Apr; 28(2): 157-174.
[9]. Bousmar, D., and Zech, Y. Momentum transfer for practical flow computation in compound channels. Journal of Hydraulic Engineering. 1999 Jul 1; 125(7): 696-70.
[10]. Naik, B. and Khatua, K.K. Water surface profile computation in nonprismatic compound channels. Aquatic Procedia. 2015 Jun 25; 4: 1500-1507.
[11]. Zahiri, A., Azamathulla, H.Md. Comparison between linear genetic programming and M5 tree models to predict flow discharge in compound channels. Neural Computing & Applications. 2014 Feb; 24(2):413-420.
[12]. Zahiri, A., Dehghani, A.A. and Azamathulla, H.Md. "Chapter 4. Application of gene-expression programming in hydraulics engineering". Handbook of Genetic Programming Applications, A.H. Gandomi, A.H. Alavi and C. Ryan (eds). Springer. 2015; 71-98.
[13]. Huthoff, F., Roose, P.C., Augustijn, D.C.M., and Hulscher, S.J.M.H. Interacting divided channel method for compound channel flow. Journal of Hydraulic Engineering. 2008 Aug; 134(8):1158-1165.
[14]. Liu, W., and James, C. S. Estimating of discharge capacity in meandering compound channels using artificial neural networks. Canadian Journal of Civil Engineering. 2000 Nov 2; 27(2): 297-308.
[15]. Zahiri, A., and Dehghani, A.A. Flow discharge determination in straight compound channels using ANN. World Academy of Science, Engineering and Technology. Italy, 2009 Oct 28-30; 58: 12-15.
[16]. Unal, B., Mamak, M., Seckin, G., and Cobaner, M. Comparison of an ANN approach with 1-D and 2-D methods for estimating discharge capacity of straight compound channels. Advances in Engineering Software. 2010 Feb 1; 41: 120-129.
[17]. Parsaeei, A., Yonesi, H. and Najafian, S. Predictive modeling of discharge in compound open channel by support vector machine technique. Earth System Environment. 2015 May 9; 1:1-6.
[18]. Azamathulla, H.Md., and Zahiri, A. Flow discharge prediction in compound channels using linear genetic programming. Journal of Hydrology. 2012 Aug 6; 454-455C: 203-207.
[19]. Chow, V.T. Open channel hydraulics. McGraw-Hill. London. 1959.
[20]. Chadwick, A., and Morfett, J., and Borthwick, M. Hydraulics in civil and environmental engineering. CRC Press, Fourth Edition. 2004.
[21]. Martin, L.A. and Myers, R.C. Measurement of overbank flow in a compound river channel. Journal of Institution of Water and Environment Management. 1991 Dec; 91(2): 645-657.
[22]. Ferreira, C. Gene expression programming: a new adaptive algorithm for solving problems. Complex Systems. 2001 Feb 25; 13(2): 87-129.
[23]. Sattar, M.A. Gene expression models for the prediction of longitudinal dispersion coefficients in transitional and turbulent pipe flow. Journal of Pipeline Systems Engineering and Practice. 2014 Feb; 5(1): 04013011.
[24]. Gandomi A.H., and Alavi, A.H. Multi-stage genetic programming: A new strategy to nonlinear system modeling. Information Sciences. 2011 Jul 23; 181(23): 5227-5239.
[25]. Blalock, M.E. and Sturm, T.W. Minimum specific energy in compound channel. Journal of Hydraulic Division. 1981 Nov; 107: 699–717.
[26]. Knight, D.W. and Demetriou. J.D. Flood plain and main channel flow interaction. Journal of Hydraulic Division. 1983 Aug 1; 109(8):1073-1092.
[27]. Knight, D.W. and Sellin, R.H. J. The SERC flood channel facility. Journal of Institution of Water and Environment Management. 1987 Jan 23; 1(2): 198-204.
[28]. Lambert, M.F. and Sellin, R.H.J. Discharge prediction in straight compound channels using the mixing length concept. Journal of Hydraulic Research. 1996 Mar 18; 34: 381-394.
[29]. Myers, R.C. and Lyness. J.F. Discharge ratios in smooth and rough compound channels. Journal of Hydraulic Engineering. 1997 Mar 1; 123(3): 182-188.
[30]. Lambert, M.F., and Myers, R.C. Estimating the discharge capacity in straight compound channels. Water, Maritime and Energy. 1998 Jan; 130:84-94.
[31]. Haidera, M.A., and Valentine, E.M. A practical method for predicting the total discharge in mobile and rigid boundary compound channels. International Conference on Fluvial Hydraulics. Belgium. 2002 Sep 4-6; 153-160.
[32]. Lai, S.H. and Bessaih, N. Flow in compound channels. 1st International Conference on Managing Rivers in the 21st Century. Malaysia. 2004 Sep 21-23; 275-280.
[33]. Atabay, S., and Knight, D.W. 1-D modelling of conveyance, boundary shear and sediment transport in overbank flow. Journal of Hydraulic Research. 2006 Nov; 44(6): 739-754.
[34]. Bousmar, D., Wilkin, N., Jacquemart, H. and Zech, Y. Overbank flow in symmetrically narrowing floodplains. Journal of Hydraulic Engineering. 2004 Apr; 130(4): 305-312.
[35]. Fernandes, J.N., Leal, J.B. and Cardoso, A.H. Analysis of flow characteristics in a compound channel: comparison between experimental data and 1-D numerical simulations. Proceedings of the 10th Urban Environment Symposium. Sweden 2010 Jun 9-11; 249–262.
[36]. Knight, D.W., Shiono, K., and Pirt, J. Predictions of depth mean velocity and discharge in natural rivers with overbank flow. International Conference on Hydraulics and Environmental Modeling of Coastal, Estuarine and River Waters. UK. 1989 Sep 19-21; 419-428.
[37]. Tarrab, L., and Weber, J.F. Transverse mixing coefficient prediction in natural channels. Computational Mechanics. 2004 Jun; 13: 1343-1355.
Volume 5, Issue 1
April 2018
Pages 37-48
  • Receive Date: 02 March 2017
  • Revise Date: 17 June 2017
  • Accept Date: 20 June 2017
  • First Publish Date: 21 March 2018