Skip to main content
SpringerLink
Log in

River flow forecasting through nonlinear local approximation in a fuzzy model

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This study investigates the potential of nonlinear local function approximation in a Takagi–Sugeno (TS) fuzzy model for river flow forecasting. Generally, in a TS framework, the local approximation is performed by a linear model, while in this approach, linear function approximation is substituted using a nonlinear function approximation. The primary hypothesis herein is that the process being modeled (rainfall–runoff in this study) is highly nonlinear, and a linear approximation at the local domain might still leave a lot of unexplained variance by the model. In this study, subtractive clustering technique is used for domain partition, and neural network is used for function approximation. The modeling approach has been tested on two case studies: Kolar basin in India and Kentucky basin in USA. The results of fuzzy nonlinear local approximation (FNLLA) model are highly promising. The performance of the FNLLA is compared with that of a pure fuzzy inference system (FIS), and it is observed that both the models perform similar at 1-step-ahead forecasts. However, the FNLLA performs much better than FIS at higher lead times. It is also observed that FNLLA forecasts the river flow with lesser error compared to FIS. In the case of Kolar River, more than 40 % of the total data are forecasted with <2 % error by FNLLA at 1 h ahead, while the corresponding value for FIS is only 20 %. In the case of 3-h-ahead forecasts, these values are 25 % for FNLLA and 15 % for FIS. Performance of FNLLA in the case of Kentucky River basin was also better compared to FIS. It is also found that FNLLA simulates the peak flow better than FIS, which is certainly an improvement over the existing models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Abrahart RJ, Anctil F, Coulibaly P, Dawson CW, Mount NJ, See LM, Shamseldin AY, Solomatine DP, Toth E, Wilby RL (2012) Two decades of anarchy? Emerging themes and outstanding challenges for neural network modelling of surface hydrology. Prog Phys Geogr 36:480–513

    Article  Google Scholar 

  2. Amorocho J, Brandstetter A (1971) A critique of current methods of hydrologic systems investigations. EOS Trans AGU 45:307–321

    Article  Google Scholar 

  3. Anders U, Korn O (1999) Model selection in neural networks. Neural Netw 12:309–323

  4. Beven KJ (2001) Rainfall–runoff modelling—the primer. Wiley, Chichester

    Google Scholar 

  5. Chang F-J, Hu H-F, Chen Y-C (2001) Counterpropagation fuzzy-neural network for streamflow reconstruction. Hydrol Process 15:219–232

    Article  Google Scholar 

  6. Chang L-C, Chang F-J, Tsai Y-H (2005) Fuzzy exemplar-based inference system for flood forecasting. Water Resour Res 41:W02005. doi:10.1029/2004WR003037

    Google Scholar 

  7. Chen YH, Chang FJ (2009) Evolutionary artificial neural networks for hydrological systems forecasting. J Hydrol 367:125–137

    Article  Google Scholar 

  8. Chiang YM, Hsu KL, Chang FJ, Hong Y, Sorooshian S (2007) Merging multiple precipitation sources for flash flood forecasting. J Hydrol 340:183–196

    Article  Google Scholar 

  9. Chiu S (1994) Fuzzy model identification based on cluster estimation. J Intell Fuzzy Syst 2(3):267–278

    Google Scholar 

  10. Cigizoglu HK, Kisi O (2006) Methods to improve the neural network performance in suspended sediment estimation. J Hydrol 317:221–238

    Article  Google Scholar 

  11. Daniel TM (1991) Neural networks—applications in hydrology and water resources engineering. In: Proceedings on international hydrology and water resources symposium. Institution of Engineers, Perth, Australia

  12. Farmer JD, Sidorowich JJ (1987) Predicting chaotic time series. Phys Rev Lett 5(59):845–848

    Article  MathSciNet  Google Scholar 

  13. Hsu K, Gupta VH, Sorooshian S (1995) Artificial neural network modeling of the rainfall–runoff process. Water Resour Res 31(10):2517–2530

    Article  Google Scholar 

  14. Ikeda S, Ochiai M, Sawaragi Y (1976) Sequential GMDH algorithm and its applications to river flow prediction. IEEE Trans Syst Manag Cybern 6(7):473–479

    Article  Google Scholar 

  15. Imrie CE, Durucan S, Korre A (2000) River flow prediction using artificial neural networks: generalization beyond the calibration range. J Hydrol 233:138–153

    Article  Google Scholar 

  16. Jain A, Srinivasulu S (2004) Development of effective and efficient rainfall–runoff models using integration of deterministic, real-coded genetic algorithms and artificial neural network techniques. Water Resour Res 40(4):W04302. doi:10.1029/2003WR002355

    Article  Google Scholar 

  17. Jain A, Sudheer KP, Srinivasulu S (2004) Identification of physical processes inherent in artificial neural rainfall–runoff models. Hydrol Process 18(3):571–581

    Article  Google Scholar 

  18. Jain SK (2008) Development of integrated discharge and sediment rating relation using a compound neural network. J Hydrol Eng ASCE 13(3):124–131

    Article  Google Scholar 

  19. Jones LK (2000) Local greedy approximation for nonlinear regression and neural network training. Ann Stat 28(5):1379–1389

    Article  MATH  Google Scholar 

  20. Maier HR, Jain A, Dandy GC, Sudheer KP (2010) Methods used for the development of neural networks for the prediction of water resources variables in river systems: current status and future directions. Env Mod Softw 25:891–909. doi:10.1016/j.envsoft.2010.02.003

    Article  Google Scholar 

  21. Maiorov VE (1999) On best approximation by ridge functions. J Approx Theory 99:68–94

    Article  MATH  MathSciNet  Google Scholar 

  22. Nayak PC (2010) Explaining internal behavior in a fuzzy if–then rule-based flood-forecasting model. J Hydrol Eng 15(1):20–28. doi:10.1061/(ASCE)HE.1943-5584.0000146

    Article  Google Scholar 

  23. Nayak PC, Sudheer KP (2008) Fuzzy model identification based on cluster estimation for reservoir inflow forecasting. Hydrol Process 22:827–841. doi:10.1002/hyp.6644

    Article  Google Scholar 

  24. Nayak PC, Sudheer KP, Ramasastri KS (2005) Fuzzy computing based rainfall–runoff model for real time flood forecasting. Hydrol Process 19:955–968. doi:10.1002/hyp.5553

    Article  Google Scholar 

  25. Nayak PC, Sudheer KP, Rangan DM, Ramasastri KS (2004) A neuro-fuzzy computing technique for modeling hydrological time series. J Hydrol 291(1–2):52–66

    Article  Google Scholar 

  26. Parasuraman K, Elshorbagy A, Carey SK (2006) Spiking modular neural networks: a neural network modeling approach for hydrological processes. Water Resour Res 42:W05412. doi:10.1029/2005WR004317

    Article  Google Scholar 

  27. Sajikumar N, Thandaveswara BS (1999) A non-linear rainfall–runoff model using an artificial neural network. J Hydrol 216:32–35

    Article  Google Scholar 

  28. See L, Openshaw S (1999) Applying soft computing approaches to river level forecasting. Hydrol Sci J 44(5):763–779

    Article  Google Scholar 

  29. Shamseldin AY, Nasr AE, O’Connor KM (2002) Comparison of different forms of the multi-layer feed-forward neural network method used for river flow forecasting. Hydrol Earth Syst Sci 6:671–684

    Article  Google Scholar 

  30. Singer AC, Wornell G, Oppenheim A (1992) Codebook prediction: a nonlinear signal modeling paradigm. In: Proceedings of the international conference on acoustics, speech and signal processing, San Francisco, vol 5. IEEE, pp 325–328

  31. Sudheer KP (2005) Knowledge extraction from trained neural network river flow models. J Hydrol Eng ASCE 10(4):264–269

    Article  Google Scholar 

  32. Sudheer KP, Gosain AK, Ramasastri KS (2002) A data-driven algorithm for constructing artificial neural network rainfall–runoff models. Hydrol Process 16:1325–1330

    Article  Google Scholar 

  33. Sudheer KP, Nayak PC, Ramasastri KS (2003) Improving peak flow estimates in artificial neural network river flow models. Hydrol Process 17(1):671–686

    Google Scholar 

  34. Takagi T, Sugeno M (1985) Fuzzy identification of systems and its application to modeling and control. IEEE Trans Syst Man Cybern 15(1):116–132

    Article  MATH  Google Scholar 

  35. Tayfur G (2006) Fuzzy, ANN, and regression models to predict longitudinal dispersion coefficient in natural streams. Nord Hydrol 37(2):143–164

    Google Scholar 

  36. Tayfur G, Singh VP (2006) ANN and fuzzy logic models for simulating event-based rainfall–runoff. J Hydraul Eng 132(12):1321–1330

    Article  Google Scholar 

  37. Tayfur G, Singh VP (2011) Predicting mean and bankfull discharge from channel cross-sectional area by expert and regression methods. Water Resour Manag 25(5):1253–1267

    Article  Google Scholar 

  38. Tokar AS, Markus M (2000) Precipitation-runoff modeling using artificial neural network and conceptual models. J Hydrol Eng Am Soc Civil Eng 5(2):156–161

    Google Scholar 

  39. Vernieuwe H, Georgieva O, De Baets B, Pauwels VRN, Verhoest NEC, De Troch FP (2005) Comparison of data-driven Takagi–Sugeno models of rainfall–discharge dynamics. J Hydrol 302(1–4):173–186

    Article  Google Scholar 

  40. Wilby RL, Abrahart RJ, Dawson CW (2003) Detection of conceptual model rainfall–runoff processes inside an artificial neural network. Hydrol Sci J 48(2):163–181

    Article  Google Scholar 

  41. Xiong LH, Shamseldin AY, O’Connor KM (2001) A nonlinear combination of the forecasts of rainfall–runoff models by the first order Takagi–Sugeno fuzzy system. J Hydrol 245(1–4):196–217

    Article  Google Scholar 

  42. Yager R, Filev D (1994) Generation of fuzzy rules by Mountain clustering. J Intell Fuzzy Syst 2(3):209–219

    Google Scholar 

  43. Zhang B, Govindaraju RS (2000) Prediction of watershed runoff using Bayesian concepts and modular neural networks. Water Resour Res 36(3):753–762

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Deltaic Regional Centre, National Institute of Hydrology, Siddartha Nagar, Kakinada, 533 003, AP, India

    P. C. Nayak

  2. Department of Civil Engineering, Indian Institute of Technology Madras, Chennai, 600 036, India

    K. P. Sudheer

  3. Water Resources System Division, National Institute of Hydrology, Roorkee, 247 667, India

    S. K. Jain

Authors
  1. P. C. Nayak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. P. Sudheer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. K. Jain
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. C. Nayak.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nayak, P.C., Sudheer, K.P. & Jain, S.K. River flow forecasting through nonlinear local approximation in a fuzzy model. Neural Comput & Applic 25, 1951–1965 (2014). https://doi.org/10.1007/s00521-014-1684-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-014-1684-z

Keywords

Search

Navigation