Water Resources Management

, Volume 31, Issue 1, pp 1–23 | Cite as

A New Approach for Modeling Sediment-Discharge Relationship: Local Weighted Linear Regression

  • Ozgur Kisi
  • Coskun Ozkan


Accurate estimation of suspended sediment is important for water resources projects. The accuracy of local weighted linear regression (LWLR) technique is investigated in this study for modeling streamflow-suspended sediment relationship. Daily data from two stations on the Eel River in California were used in the applications. In the first part of the study, the LWLR results were compared with those of the least square support vector machine (LSSVM), artificial neural networks (ANNs) and sediment rating curve (SRC) for modeling sediment data of upstream and downstream stations, separately. Root mean square errors (RMSE), mean absolute errors (MAE) and determination coefficient (R2) statistics were used for comparison of the applied models Comparison results indicated that the LWLR model performed better than the LSSVM, ANN and SRC models. Accuracies of the sediment modeling increased by the LWLR model compared with the LSSVM model: 14 % (60 %) and 33 % (42 %) decrease in the RMSE (MAE) values for the upstream and downstream stations, respectively. The second part of the study focused on the comparison of the models in estimating downstream suspended sediment data by using data from both stations. LWLR was found to be better than the LSSVM, ANN and SRC models. The RMSE accuracy of the LSSVM model was increased by 39 % using the LWLR model.


Suspended sediment modeling Local weighted linear regression Least square support vector machine Neural networks Rating curve 



The data used in this study were downloaded from the web server of the USGS. The author would like to thank the personnels of the USGS who are associated with data observation, processing, and management of USGS Web sites.


  1. Adamowski J, Karapataki C (2010) Comparison of multivariate regression and artificial neural networks for peak urban water-demand forecasting: evaluation of different ANN learning algorithms. J Hydrol Eng 15(10):729–743CrossRefGoogle Scholar
  2. Agarwal A, Mishra SK, Ram S, Singh JK (2006) Simulation of runoff and sediment yield using artificial neural networks. Biosyst Eng 94(4):597–613CrossRefGoogle Scholar
  3. Alikhani A (2009) Combination of neuro fuzzy and wavelet model usage in river engineering. Int J Energy Environ 3(3):122–134Google Scholar
  4. Allison PD (1998) Multiple regression: a primer. Pine forge PressGoogle Scholar
  5. Alp M, Cigizoglu H (2007) Suspended sediment load simulation by two artificial neural network methods using hydrometeorological data. Environ Model Softw 22(1):2–13CrossRefGoogle Scholar
  6. Aydogdu M, Firat M (2015) Estimation of failure rate in water distribution network using fuzzy clustering and LS-SVM methods. Water Resour Manag 29(5):1575–1590CrossRefGoogle Scholar
  7. Barnett WA, Powell J, Tauchen GE (1991) Nonparametric and semiparametric methods in econometrics and statistics. Cambridge University Press, New YorkGoogle Scholar
  8. Baylar A, Hanbay D, Batan M (2009) Application of least square support vector machines in the prediction of aeration performance of plunging overfall jets from weirs. Expert Syst Appl 36(4):8368–8374CrossRefGoogle Scholar
  9. Bhattacharya B, Price RK, Solomatine DP (2005) Data-driven modelling in the context of sediment transport. Phys Chem Earth 30(4–5):297–302CrossRefGoogle Scholar
  10. Casetti E (1997) The expansion method, mathematical modeling, and spatial econometrics. Int Reg Sci Rev 20:9–32CrossRefGoogle Scholar
  11. Cigizoglu HK (2004) Estimation and forecasting of daily suspended sediment data by multi-layer perceptrons. Adv Water Resour 27(2):185–195CrossRefGoogle Scholar
  12. Cigizoglu HK, Kisi O (2006) Methods to improve the neural network performance in suspended sediment estimation. J Hydrol 317(3–4):221–238CrossRefGoogle Scholar
  13. Clark MP, Slater AG (2006) Probabilistic quantitative precipitation estimation in complex terrain. J Hydrometeorol 7:3–22CrossRefGoogle Scholar
  14. Cleveland WS (1979) Robust locally weighted regression and smoothing scatterplots. J Am Stat Assoc 74:829–36CrossRefGoogle Scholar
  15. Cleveland WS, Devlin SJ (1988) Locally weighted regression: an approach to regression analysis by local fitting. J Am Stat Assoc 83:596–610CrossRefGoogle Scholar
  16. Cutore, PI Mauro GD, Cancelliere A (2009) Forecasting palmer index using neural networks and climatic indexes. J Hydrol Eng 10.1061/(ASCE)HE.1943-5584.0000028, 588–595Google Scholar
  17. Daly C, Neilson RP, Phillips DL (1994) A statistical-topographic model for mapping climatological precipitation over mountainous terrain. J Appl Meteorol 33:140–158CrossRefGoogle Scholar
  18. Fahimi F, El-Shafie AH (2014) Comment on “a hybrid model of self organizing maps and least square support vector machine for river flow forecasting” by Ismail et al. (2012). Hydrol Earth Syst Sci 18(7):2711–2714CrossRefGoogle Scholar
  19. Fan J, Gijbels I (1996) Local polynomial modelling and its applications. Chapman & Hall, LondonGoogle Scholar
  20. Fotheringham AS, Brunsdon C, Charlton M (2000) Quantitative geography: perspectives on spatial analysis. Sage, LondonGoogle Scholar
  21. Fotheringham AS, Charlton ME, Brunsdon C (2001) Spatial variations in school performance: a local analysis using geographically weighted regression. Geogr Environ Model 5:43–66CrossRefGoogle Scholar
  22. Fotheringham AS, Brunsdon C and Charlton M (2002) Geographically weighted regression: the analysis of spatially varying relationships. WileyGoogle Scholar
  23. Fox J (2000a) Nonparametric simple regression. Thousand Oaks, CA, SageCrossRefGoogle Scholar
  24. Fox J (2000b) Multiple and generalized nonparametric regression. Thousand Oaks, CA, SageCrossRefGoogle Scholar
  25. Friedman JH (1991) Multivariate adaptive regression splines (with discussion). Ann Stat 19:1–141CrossRefGoogle Scholar
  26. Green PJ, Silverman BW (1994) Nonparametric regression and generalized linear models: a roughness penalty approach. Chapman & Hall, LondonCrossRefGoogle Scholar
  27. Hanbay D, Baylar A, Batan M (2009) Prediction of aeration efficiency on stepped cascades by using least square support vector machines. Expert Syst Appl 36(3):4248–4252CrossRefGoogle Scholar
  28. Hardle W (1990) Applied nonparametric regression. Cambridge University Press, New YorkCrossRefGoogle Scholar
  29. Ismail S, Shabri A, Samsudin R (2012) A hybrid model of self organizing maps and least square support vector machine for river flow forecasting. Hydrol Earth Syst Sci 16(11):4417–4433CrossRefGoogle Scholar
  30. Kalteh AM (2016) Improving forecasting accuracy of streamflow time series using least squares support vector machine coupled with data-preprocessing techniques 30(2): 747–766Google Scholar
  31. Klausner A, Tengg A, Rinner B (2007) Vehicle classification on multi-sensor smart cameras using feature- and decision-fusion. In: Proceedings of the First ACM/IEEE International Conference on Distributed Smart Cameras (ICDSC-07), p 67–74Google Scholar
  32. Kisi Ö (2008) Constructing neural network sediment estimation models using a data-driven algorithm. Math Comput Simul 79(1):94–103CrossRefGoogle Scholar
  33. Kisi O (2012) Modeling discharge-suspended sediment relationship using least square support vector machine. J Hydrol 456:110–120CrossRefGoogle Scholar
  34. Kisi O, Yuksel I, Dogan E (2008) Modelling daily suspended sediment of rivers in Turkey using several data-driven techniques. Hydrol Sci J 53(6):1270–1285CrossRefGoogle Scholar
  35. Kitsikoudis V, Sidiropoulos E, Hrissanthou V (2014) Machine learning utilization for bed load transport in gravel-bed rivers. Water Resour Manag 28(11):3727–3743CrossRefGoogle Scholar
  36. Kuh A (2004) “Least squares kernel methods and applications.” Chapter 17, Soft computing in communications. Springer, Berlin, pp 365–387Google Scholar
  37. Kumar M, Kar IN (2002) Non-linear HVAC computations using least square support vector machines. Energy Convers Manag 50:1411–1418CrossRefGoogle Scholar
  38. Kutner MH, Nachtsheim CJ, Neter J, Li W (2005) Applied linear statistical models, 5th edn. McGraw-Hill/Irwin, New YorkGoogle Scholar
  39. Loader C (1999) Local regression and likelihood. Springer, New YorkGoogle Scholar
  40. Md Ghani IM, Ahmad S (2010) Stepwise multiple regression method to forecast fish landing. Procedia Soc Behav Sci 8:549–554CrossRefGoogle Scholar
  41. Mustafa MR, Rezaur RB, Saiedi S, Isa MH (2012) River suspended sediment prediction using various multilayer perceptron neural network training algorithms—a case study in Malaysia. Water Resour Manag 26(7):1879–1897CrossRefGoogle Scholar
  42. Rajagopalan B, Lall U (1998) Locally weighted polynomial estimation of spatial precipitation. J Geogr Inf Decis Anal 2:44–50Google Scholar
  43. Rencher AC and Schaalje GB (2008) Linear models in statistics. 2nd edn. WileyGoogle Scholar
  44. Sachindra DA, Huang F, Barton A, Perera BJC (2013) Least square support vector and multi-linear regression for statistically downscaling general circulation model outputs to catchment streamflows. Int J Climatol 33(5):1087–1106CrossRefGoogle Scholar
  45. Shabri A, Suhartono (2012) Streamflow forecasting using least-squares support vector machines. Hydrol Sci J 57(7):1275–1293CrossRefGoogle Scholar
  46. Sivakumar B, Wallender WW (2005) Predictability of river flow and suspended sediment transport in the Mississippi River basin: a non-linear deterministic approach. Earth Surf Process Landf 30(6):665–677CrossRefGoogle Scholar
  47. Suykens JAK, Vandewalle J (1999) Least square support vector machine classifiers. Neural Process Lett 9(3):293–300CrossRefGoogle Scholar
  48. Tabari H, Kisi O, Ezani A, Hosseinzadeh Talaee P (2012) SVM, ANFIS, regression and climate based models for reference evapotranspiration modeling using limited climatic data in a semi-arid highland environment. J Hydrol 444:78–89CrossRefGoogle Scholar
  49. Thorsnes P, McMillen D (1998) Land value and parcel size: a semiparametric analysis. J Real Estate Financ Econ 17:233–44CrossRefGoogle Scholar
  50. Tu JV (1996) Advantages and disadvantages of using artificial neural networks versus logistic regression for predicting medical outcomes. J Clin Epidemiol 49(11):1225–1231CrossRefGoogle Scholar
  51. van Maanen B, Coco G, Bryan KR, Ruessink BG (2010) The use of artificial neural networks to analyze and predict alongshore sediment transport. Nonlinear Process Geophys 17(5):395–404CrossRefGoogle Scholar
  52. Wand MP, Jones MC (1995) Kernel smoothing. Chapman & Hall, LondonCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Center for Interdisciplinary ResearchInternational Black Sea UniversityTbilisiGeorgia
  2. 2.Engineering Faculty, Geomatics Engineering DepartmentErciyes UniversityKayseriTurkey

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