Neural Computing and Applications

, Volume 31, Issue 3, pp 909–921 | Cite as

Incorporating a machine learning technique to improve open-channel flow computations

  • Hamed Farhadi
  • Abdolreza Zahiri
  • M. Reza HashemiEmail author
  • Kazem Esmaili
Original Article


The objective of this study is to employ support vector machine as a machine learning technique to improve flow discharge predictions in compound open channels. Accurate estimation of channel conveyance is a major step in prediction of the flow discharge in open-channel flow computations (e.g., river flood simulations, design of canals, and water surface profile computation). Common methods to estimate the conveyance are highly simplified and are a main source of uncertainty in compound channels, since popular river/canal models still incorporate 1-D hydrodynamic formulations. Further, the reliability of using a specific method (e.g., vertical divided channel method, the coherence method) over other methods for different applications involving various geometric and hydraulic conditions is questionable. Using available experimental and field data, a novel method was developed, based on SVM, to compute channel conveyance. The data included 394 flow rating curves from 30 different laboratory and natural compound channel sections which were used for the training, and verification of the SVM method. The data were limited to straight compound channels. The performance of SVM was compared with those from other commonly used methods, such as the vertical divided channel method, the coherence method and the Shiono and Knight model. Additionally, SVM estimations were compared with available data for River Main and River Severn, UK. Results indicated that SVM outperforms traditional methods for both laboratory and field data. It is concluded that the proposed SVM approach could be applied as a reliable technique for the prediction of flow discharge in straight compound channels. The proposed SVM can be potentially incorporated into 1-D river hydrodynamic models in future studies.


Compound channels Support vector machine Stage–discharge relationship Machine learning 

List of symbols


Cross-sectional area


Bias term


Penalty parameter


Coherence parameter


Dual function


Relative depth (ratio of floodplain depth to main channel depth)


Discharge adjustment factor


Discharge deficit


SVM function


Bank-full depth


Flow depth


Conveyance parameter

K(xi, xj)

Kernel function


Lagrange function


Loss function


Mean absolute percentage error


Manning coefficient


Wetted perimeter


Bank-full discharge


Measured flow discharge


Predicted flow discharge


Total flow discharge


Discharge calculated by VDCM


Lagrangian multiplier


Risk function


Coefficient of determination


Difference between predicted and observed results


Root mean square error


Support vector machine


Channel side slope


Longitudinal slope


Friction slope


Depth-averaged velocity


Weight parameter


Difference of observed data and mean observed data


Observed data

\( \bar{X} \)

Mean observed data


Data used to build the SVM model


Maximum of data values


Minimum of data values


Normalized data


Difference of predicted data and mean predicted data


Predicted data

\( \bar{Y} \)

Mean predicted data


Target values


Lagrangian multiplier

\( \varGamma \)

Secondary flow parameter


Parameter of insensitive loss function


Dimensionless eddy viscosity


Slack variable


Higher-dimensional space map function


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Knight DW, Hamed ME (1984) Boundary shear in symmetrical compound channels. J Hydraul Eng 110(10):1412–1430Google Scholar
  2. 2.
    Wormleaton PR, Hadjipanos P (1985) Flow distribution in compound channels. J Hydraul Eng 111(2):357–361Google Scholar
  3. 3.
    Myers R, Lyness J (1997) Discharge ratios in smooth and rough compound channels. J Hydraul Eng 123(3):182–188Google Scholar
  4. 4.
    Martin L, Myers W (1991) Measurement of overbank flow in a compound river channel. ICE Proc 91(4):645–657Google Scholar
  5. 5.
    Lai S, Bessaih N (2004) Flow in compound channels. In: 1st International conference on managing rivers in the 21st century, Malaysia, pp 275–280Google Scholar
  6. 6.
    Ackers P (1992) Hydraulic design of two-stage channels. Proc ICE-Water Marit Energy 96(4):247–257Google Scholar
  7. 7.
    Ackers P (1993) Flow formulae for straight two-stage channels. J Hydraul Res 31(4):509–531Google Scholar
  8. 8.
    Shiono K, Knight D (1988) Two-dimensional analytical solution for a compound channel. In: Proceedings of 3rd international symposium on refined flow modelling and turbulence measurements, pp 503–510Google Scholar
  9. 9.
    Shiono K, Knight DW (1991) Turbulent open-channel flows with variable depth across the channel. J Fluid Mech 222:617–646Google Scholar
  10. 10.
    Sharifi S, Sterling M, Knight DW (2009) A novel application of a multi-objective evolutionary algorithm in open channel flow modelling. J Hydroinform 11(1):31. doi: 10.2166/hydro.2009.033 Google Scholar
  11. 11.
    Unal B, Mamak M, Seckin G, Cobaner M (2010) Comparison of an ANN approach with 1-D and 2-D methods for estimating discharge capacity of straight compound channels. Adv Eng Softw 41(2):120–129. doi: 10.1016/j.advengsoft.2009.10.002 zbMATHGoogle Scholar
  12. 12.
    Zahiri A, Azamathulla HM (2012) Comparison between linear genetic programming and M5 tree models to predict flow discharge in compound channels. Neural Comput Appl 24(2):413–420. doi: 10.1007/s00521-012-1247-0 Google Scholar
  13. 13.
    MacLeod AB (1997) Development of methods to predict the discharge capacity in model and prototype meandering compound channels. University of GlasgowGoogle Scholar
  14. 14.
    Liu W, James C (2000) Estimation of discharge capacity in meandering compound channels using artificial neural networks. Can J Civ Eng 27(2):297–308Google Scholar
  15. 15.
    Zahiri A, Dehghani A (2009) Flow discharge determination in straight compound channels using ANN. World Acad Sci Eng Technol 58:1–8Google Scholar
  16. 16.
    Sharifi S (2009) Application of evolutionary computation to open channel flow modelling. University of Birmingham, Birmingham, UKGoogle Scholar
  17. 17.
    Azamathulla HM, Zahiri A (2012) Flow discharge prediction in compound channels using linear genetic programming. J Hydrol 454–455:203–207Google Scholar
  18. 18.
    Dibike YB, Velickov S, Solomatine D, Abbott MB (2001) Model induction with support vector machines: introduction and applications. J Comput Civ EngGoogle Scholar
  19. 19.
    Bray M, Han D (2004) Identification of support vector machines for runoff modelling. J Hydroinform 6:265–280Google Scholar
  20. 20.
    Eslamian S, Gohari S, Biabanaki M, Malekian R (2008) Estimation of monthly pan evaporation using artificial neural networks and support vector machines. J Appl Sci 8(19):3497–3502Google Scholar
  21. 21.
    Samui P (2011) Application of least square support vector machine (LSSVM) for determination of evaporation losses in reservoirs. Engineering 3(04):431Google Scholar
  22. 22.
    Tabari H, Kisi O, Ezani A, Talaee PH (2012) SVM, ANFIS, regression and climate based models for reference evapotranspiration modeling using limited climatic data in a semi-arid highland environment. J Hydrol 444:78–89Google Scholar
  23. 23.
    Han D, Chan L, Zhu N (2007) Flood forecasting using support vector machines. J Hydroinform 9(4):267–276Google Scholar
  24. 24.
    Chen S-T, Yu P-S (2007) Pruning of support vector networks on flood forecasting. J Hydrol 347(1):67–78Google Scholar
  25. 25.
    Yu P-S, Chen S-T, Chang I-F (2006) Support vector regression for real-time flood stage forecasting. J Hydrol 328(3):704–716Google Scholar
  26. 26.
    Hashemi MR, Spaulding ML, Shaw A, Farhadi H, Lewis M (2016) An efficient artificial intelligence model for prediction of tropical storm surge. Nat Hazards 82(1):471–491Google Scholar
  27. 27.
    Behzad M, Asghari K, Coppola EA Jr (2009) Comparative study of SVMs and ANNs in aquifer water level prediction. J Comput Civ Eng 24(5):408–413Google Scholar
  28. 28.
    Yoon H, Jun S-C, Hyun Y, Bae G-O, Lee K-K (2011) A comparative study of artificial neural networks and support vector machines for predicting groundwater levels in a coastal aquifer. J Hydrol 396(1):128–138Google Scholar
  29. 29.
    Liu J, Chang J-X, Zhang W-G (2009) Groundwater level dynamic prediction based on chaos optimization and support vector machine. In: Genetic and evolutionary computing, 2009. WGEC’09. 3rd International Conference on. IEEE, pp 39–43Google Scholar
  30. 30.
    Liu J, Chang M, Ma X (2009) Groundwater quality assessment based on support vector machine. In: HAIHE river basin research and planning approach-proceedings of 2009 international symposium of HAIHE basin integrated water and environment management, pp 173–178Google Scholar
  31. 31.
    Auria L, Moro RA (2008) Support vector machines (SVM) as a technique for solvency analysis. German Institute for Economic Research, Berlin, GermanyGoogle Scholar
  32. 32.
    Chow VT (1959) Open-channel hydraulic. McGraw-Hill, New YorkGoogle Scholar
  33. 33.
    McGahey C, Samuels P (2003) Methodology for conveyance estimation in two-stage straight, skewed and meandering channels. In: Proceedings of the XXX congress of the international association for hydraulic research, pp 33–40Google Scholar
  34. 34.
    Abril J, Knight D (2004) Stage-discharge prediction for rivers in flood applying a depth-averaged model. J Hydraul Res 42(6):616–629Google Scholar
  35. 35.
    Vapnik V (1995) The nature of statistical learning theory. Springer, BerlinzbMATHGoogle Scholar
  36. 36.
    Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273–297zbMATHGoogle Scholar
  37. 37.
    Schölkopf B, Burges C, Vapnik V (1995) Extracting support data for a given task. In: KDDGoogle Scholar
  38. 38.
    Mattera D, Haykin S (1999) Support vector machines for dynamic reconstruction of a chaotic system. In: Advances in kernel methods. MIT Press, Cambridge, pp 211–241Google Scholar
  39. 39.
    Smola AJ, Schölkopf B (2004) A tutorial on support vector regression. Stat Comput 14(3):199–222MathSciNetGoogle Scholar
  40. 40.
    Chang C-C, Lin C-J (2011) LIBSVM: a library for support vector machines. ACM Trans Intell Syst Technol 2(3):27Google Scholar
  41. 41.
    Knight D, Sellin R (1987) The SERC flood channel facility. Water Environ J 1(2):198–204Google Scholar
  42. 42.
    Blalock ME, Sturm TW (1981) Minimum specific energy in compound open channel. J Hydraul Div 107(6):699–717Google Scholar
  43. 43.
    Knight DW, Demetriou JD (1983) Flood plain and main channel flow interaction. J Hydraul Eng 109(8):1073–1092Google Scholar
  44. 44.
    Lambert M, Sellin R (1996) Discharge prediction in straight compound channels using the mixing length concept. J Hydraul Res 34(3):381–394Google Scholar
  45. 45.
    Lambert MF, Myers W (1998) Estimating the discharge capacity in straight compound channels. Proc ICE-Water Marit Energy 130(2):84–94Google Scholar
  46. 46.
    Bousmar D, Zech Y (1999) Momentum transfer for practical flow computation in compound channels. J Hydraul Eng 125(7):696–706Google Scholar
  47. 47.
    Haidera M, Valentine E (2002) A practical method for predicting the total discharge in mobile and rigid boundary compound channels. In: International conference on fluvial hydraulics, Belgium. pp 153–160Google Scholar
  48. 48.
    Bousmar D, Wilkin N, Jacquemart J-H, Zech Y (2004) Overbank flow in symmetrically narrowing floodplains. J Hydraul Eng 130(4):305–312Google Scholar
  49. 49.
    Knight D, Shiono K, Pirt J (1989) Prediction of depth mean velocity and discharge in natural rivers with overbank flow. In: Proceedings of the international conference on hydraulic and environmental modelling of Coastal, Estuarine and River Waters, pp 419–428Google Scholar
  50. 50.
    Tarrab L, Weber J (2004) Predicción del coeficiente de mezcla transversal en cauces aturales. Mecánica Computacional, XXIII, Asociación Argentina de Mecanica Computacional, San Carlos de Bariloche, pp 1343–1355Google Scholar
  51. 51.
    Brunner GW CEIWR-HEC (2010) HEC-RAS river analysis system user’s manual version 4.1. In: Tech. Rep., US Army Corps of Engineers Institute for Water Resources Hydrologic Engineering Center (HEC), CA, USAGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  • Hamed Farhadi
    • 1
  • Abdolreza Zahiri
    • 2
  • M. Reza Hashemi
    • 3
    Email author
  • Kazem Esmaili
    • 1
  1. 1.Department of Water Science and EngineeringFerdowsi University of MashhadMashhadIran
  2. 2.Department of Water EngineeringGorgan University of Agricultural Sciences and Natural ResourcesGorganIran
  3. 3.Department of Ocean Engineering; Graduate School of OceanographyUniversity of Rhode IslandNarragansettUSA

Personalised recommendations