Stream Flow Forecasting Using Least Square Support Vector Regression

Document Type : Regular Article

Authors

1 Professor, Vishwakarma Institute of Information Technology, Pune, India

2 PG Student, Vishwakarma Institute of Information Technology, Pune, India

Abstract

Accurate forecasting of streamflow for different lead-times is useful in the design of almost all hydraulic structures. The Support Vector Machines (SVMs) use a hypothetical space of linear functions in a kernel-induced higher dimensional feature space and are trained with a learning algorithm from optimization theory. The support vector regression attempts to fit a curve on data points such that the points lie between two marginal hyperplanes which will minimize the error. The current paper presents least square support vector regression (LS-SVR) to predict one day ahead stream flow using past values of the rainfall and river flow at three stations in India, namely Nighoje and Budhwad in Krishna river basin and Mandaleshwar in Narmada river basin. The relevant inputs are finalized on the basis of three techniques namely autocorrelation, Cross-correlation and trial and error. The forecasting model results are reasonable as can be seen from a low value of Root Mean Square Error (RMSE), Mean Absolute Relative Error (MARE) and high values of Coefficient of Efficiency (CE) accompanied by balanced scatter plots and hydrographs.

Highlights

Google Scholar

Keywords

Main Subjects


[1]       Shalamu A. Monthly and seasonal streamflow forecasting in the Rio Grande Basin. Ph.D. thesis, New Mixico State University, 2009.
[2]       Bhatnagar A. Hydrologic Time Series Analysis using Support Vector Regression, M. Tech Thesis-2009, Indian Inst Technol Bombay 2009.
[3]       Solomatine DP, Wagener T. Hydrological modeling 2011.
[4]       Shrestha RR, Nestmann F. Physically Based and Data-Driven Models and Propagation of Input Uncertainties in River Flood Prediction. J Hydrol Eng 2009;14:1309–19. doi:10.1061/(ASCE)HE.1943-5584.0000123.
[5]       http://www.cwc.gov.in/main/HP n.d.
[6]       www.mahap.org n.d.
[7]       Mahjoobi J, Adeli Mosabbeb E. Prediction of significant wave height using regressive support vector machines. Ocean Eng 2009;36:339–47. doi:10.1016/j.oceaneng.2009.01.001.
[8]       Vapnik VN. An overview of statistical learning theory. IEEE Trans Neural Networks 1999;10:988–99. doi:10.1109/72.788640.
[9]       Dibike YB, Velickov S, Solomatine D, Abbott MB. Model Induction with Support Vector Machines: Introduction and Applications. J Comput Civ Eng 2001;15:208–16. doi:10.1061/(ASCE)0887-3801(2001)15:3(208).
[10]     Wu CL, Chau KW, Li YS. River stage prediction based on a distributed support vector regression. J Hydrol 2008;358:96–111. doi:10.1016/j.jhydrol.2008.05.028.
[11]     Suykens JAK, Vandewalle J. Least Squares Support Vector Machine Classifiers. Neural Process Lett 1999;9:293–300. doi:10.1023/A:1018628609742.
[12]     Rajasekaran S, Gayathri S, Lee T-L. Support vector regression methodology for storm surge predictions. Ocean Eng 2008;35:1578–87. doi:10.1016/j.oceaneng.2008.08.004.
[13]     Dibike YB, Velickov S, Solomatine D. Support vector machines: Review and applications in civil engineering. Proc. 2nd Jt. Work. Appl. AI Civ. Eng., Citeseer; 2000, p. 215–8.
[14]     Bray M, Han D. Identification of support vector machines for runoff modelling. J Hydroinformatics 2004;6:265 LP-280.
[15]     Asefa T, Kemblowski M, McKee M, Khalil A. Multi-time scale stream flow predictions: The support vector machines approach. J Hydrol 2006;318:7–16. doi:10.1016/j.jhydrol.2005.06.001.
[16]     LIN J-Y, CHENG C-T, CHAU K-W. Using support vector machines for long-term discharge prediction. Hydrol Sci J 2006;51:599–612. doi:10.1623/hysj.51.4.599.
[17]     Yu P-S, Chen S-T, Chang I-F. Support vector regression for real-time flood stage forecasting. J Hydrol 2006;328:704–16. doi:10.1016/j.jhydrol.2006.01.021.
[18]     Behzad M, Asghari K, Eazi M, Palhang M. Generalization performance of support vector machines and neural networks in runoff modeling. Expert Syst Appl 2009;36:7624–9. doi:10.1016/j.eswa.2008.09.053.
[19]     Noori R, Karbassi AR, Moghaddamnia A, Han D, Zokaei-Ashtiani MH, Farokhnia A, et al. Assessment of input variables determination on the SVM model performance using PCA, Gamma test, and forward selection techniques for monthly stream flow prediction. J Hydrol 2011;401:177–89. doi:10.1016/j.jhydrol.2011.02.021.
[20]     Kisi O. Modeling discharge-suspended sediment relationship using least square support vector machine. J Hydrol 2012;456–457:110–20. doi:10.1016/j.jhydrol.2012.06.019.
[21]     Bhagwat PP, Maity R. Hydroclimatic streamflow prediction using Least Square-Support Vector Regression. ISH J Hydraul Eng 2013;19:320–8. doi:10.1080/09715010.2013.819705.
[22]     Sahraei S, Andalani SZ, Zakermoshfegh M, Sisakht BN, Talebbeydokhti N, Moradkhani H. Daily discharge forecasting using least square support vector regression and regression tree. Sci Iran Trans A, Civ Eng 2015;22:410.
[23]     Kalteh AM. Wavelet Genetic Algorithm-Support Vector Regression (Wavelet GA-SVR) for Monthly Flow Forecasting. Water Resour Manag 2015;29:1283–93. doi:10.1007/s11269-014-0873-y.
[24]     Kalteh AM. Monthly river flow forecasting using artificial neural network and support vector regression models coupled with wavelet transform. Comput Geosci 2013;54:1–8. doi:10.1016/j.cageo.2012.11.015.
[25]     Kalteh AM. Improving Forecasting Accuracy of Streamflow Time Series Using Least Squares Support Vector Machine Coupled with Data-Preprocessing Techniques. Water Resour Manag 2016;30:747–66. doi:10.1007/s11269-015-1188-3.
[26]     Kisi O. Streamflow Forecasting and Estimation Using Least Square Support Vector Regression and Adaptive Neuro-Fuzzy Embedded Fuzzy c-means Clustering. Water Resour Manag 2015;29:5109–27. doi:10.1007/s11269-015-1107-7.
[27]     Zamani A, Solomatine D, Azimian A, Heemink A. Learning from data for wind–wave forecasting. Ocean Eng 2008;35:953–62. doi:10.1016/j.oceaneng.2008.03.007.
[28]     Londhe S., N., Dixit P.,R. CSB. Forecasting Ocean Waves using Support Vector Regression. Proc. of 18thIAHR-APD2012- 2012, Jeju, South Korea, n.d., p. 38–41.
[29]     Legates DR, McCabe GJ. Evaluating the use of “goodness-of-fit” Measures in hydrologic and hydroclimatic model validation. Water Resour Res 1999;35:233–41. doi:10.1029/1998WR900018.
[30]     Dawson CW, Wilby RL. Hydrological modelling using artificial neural networks. Prog Phys Geogr 2001;25:80–108. doi:10.1177/030913330102500104.
[31]     Londhe SN, Panchang V. One-Day Wave Forecasts Based on Artificial Neural Networks. J Atmos Ocean Technol 2006;23:1593–603. doi:10.1175/JTECH1932.1.