Abstract
Hydrologic time series modeling using historical records plays a crucial role in forecasting different hydrological processes. The objective of this study is to analyze the suitability of Support Vector Regression (SVR) for modeling monthly low flows time series for three stations in Mahanadi river basin, India. The ‘low flow’ threshold was taken as the Q75 discharge, i.e., the flow is equal to or surpassed for the duration of 75% of the observation period which was obtained from the daily discharge data. The potential applicability of SVR model is assessed with two different framework models (ANN-ELM, GPR) based on various statistical measures (r2, RMSE, MAE, Nash-Sutcliffe coefficient, objective function (OBJ), Scatter Index (SI) and BIAS). The model selection was based on lowest OBJ value for each station amongst three models (SVR, ANN-ELM, GPR). The SVR model was trained using the Radial Basis Function (RBF). Using the same inputs, the other two models (ANN-ELM and GPR) was also tested. From results, among all the stations, the SVR outperformed GPR and ANN-ELM with lowest OBJ value for the three stations a (1.378, 1.202, 1.570). In addition, the accuracy of the three models were checked using mean forecasting error which were (0.474, 0.421, 0.509) for SVR, (0.507, 0.489 0.500) for GPR and (0.564, 0.603, 0.772) ANN-ELM for the three stations. The results confirm that SVR can be used satisfactorily for modeling monthly low flows in the Mahanadi river basin, India. Hence, the SVR model could be employed as a new reliable and accurate data intelligent approach for predicting the ‘low flow’ (Q75 discharge) based on precedent data in water resources and its allied field.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Abbot, J. and Marohasy, J. (2012). “Application of artificial neural networks to rainfall forecasting in Queensland, Australia.” Advances in Atmospheric Sciences, Vol. 29, No. 4, pp. 717–730, DOI: 10.1007/s00376-012-1259-9.
Acharya, N., Shrivastava, N. A., Panigrahi, B., and Mohanty, U. (2014). “Development of an artificial neural network based multi-model ensemble to estimate the northeast monsoon rainfall over south peninsular India: An application of extreme learning machine.” Climate dynamics, Vol. 43, Nos. 5–6, pp. 1303–1310, DOI: 10.1007/s00382-013-1942-2.
Ahn, K. H. and Palmer, R. N. (2016). “Use of a nonstationary copula to predict future bivariate low flow frequency in the connecticut river basin.” Hydrological Processes, Vol. 30, No. 19, pp. 3518–3532, DOI: 10.1002/hyp.10876.
Alavi, A. H. and Gandomi, A. H. (2011). “Prediction of principal groundmotion parameters using a hybrid method coupling artificial neural networks and simulated annealing.” Computers & Structures, Vol. 89, Nos. 23–24, pp. 2176–2194, DOI: 10.1016/j.compstruc.2011.08.019.
Alvisi, S., Mascellani, G., Franchini, M., and Bardossy, A. (2006). “Water level forecasting through fuzzy logic and artificial neural network approaches.” Hydrology and Earth System Sciences Discussions, Vol. 10, No. 1, pp. 1–17, DOI: 10.5194/hess-10-1-2006.
Arena, C., Cannarozzo, M., and Mazzola, M. R. (2006). “Multi-year drought frequency analysis at multiple sites by operational hydrology–A comparison of methods.” Physics and Chemistry of the Earth, Parts A/B/C, Vol. 31, No. 18, pp. 1146–1163, DOI: 10.1016/j.pce.2006.03.021.
Atiquzzaman, M. and Kandasamy, J. (2016). “Prediction of hydrological time-series using extreme learning machine.” Journal of Hydroinformatics, Vol. 18, No. 2, pp. 345–353, DOI: 10.2166/hydro.2015.020.
Azamathulla, H. M., Haghiabi, A. H., and Parsaie, A. (2016). “Prediction of side weir discharge coefficient by support vector machine technique.” Water Science and Technology: Water Supply, Vol. 16, No. 4, pp. 1002–1016, DOI: 10.2166/ws.2016.014.
Belayneh, A. and Adamowski, J. (2012). “Standard precipitation index drought forecasting using neural networks, wavelet neural networks, and support vector regression.” Applied Computational Intelligence and Soft Computing, Vol. 2012, No. 6, DOI: 10.1155/2012/794061.
Box, G. and Jenkins, G. (1970). Time series analysis; Forecasting and control, Holden-Day, San Francisco(CA).
Burges, C. J. (1998). “A tutorial on support vector machines for pattern recognition.” Data mining and Knowledge Discovery, Vol. 2, No. 2, pp. 121–167, DOI: 10.1023/A:1009715923555.
Campolo, M., Soldati, A., and Andreussi, P. (2003). “Artificial neural network approach to flood forecasting in the River Arno.” Hydrological Sciences Journal, Vol. 48, No. 3, pp. 381–398, DOI: 10.1623/hysj.48.3.381.45286.
Chen, H.-L. and Rao, A. R. (2003). “Linearity analysis on stationary segments of hydrologic time series.” Journal of Hydrology, Vol. 277, Nos. 1–2, pp. 89–99, DOI: 10.1016/S0022-1694(03)00086-6.
Cheng, C.-T., Lin, J.-Y., Sun, Y.-G., and Chau, K. (2005). “Long-term prediction of discharges in Manwan Hydropower using adaptivenetwork-based fuzzy inference systems models.” Advances in Natural Computation, Vol. 3612, pp. 1152–1161, DOI: 10.1007/11539902_145.
Deka, P. C. (2014). “Support vector machine applications in the field of hydrology: A review.” Applied Soft Computing, Vol. 19, pp. 372–386, DOI: 10.1016/j.asoc.2014.02.002.
Demirel, M. C., Booij, M. J., and Hoekstra, A. Y. (2013). “Identification of appropriate lags and temporal resolutions for low flow indicators in the River Rhine to forecast low flows with different lead times.” Hydrological Processes, Vol. 27, No. 19, pp. 2742–2758, DOI: 10.1002/hyp.9402.
Deo, R. C. and Sahin, M. (2015). “Application of the artificial neural network model for prediction of monthly standardized precipitation and evapotranspiration index using hydrometeorological parameters and climate indices in eastern Australia.” Atmospheric Research, Vol. 161, pp. 65–81, DOI: 10.1016/j.atmosres.2015.03.018.
Deo, R. C. and Sahin, M. (2016). “An extreme learning machine model for the simulation of monthly mean streamflow water level in eastern Queensland.” Environmental Monitoring and Assessment, Vol. 188, No. 2, pp. 1–24, DOI: 10.1007/s10661-016-5094-9.
Deo, R. C. and Samui, P. (2017). “Forecasting evaporative loss by least-square support-vector regression and evaluation with genetic programming, Gaussian process, and minimax probability machine regression: Case study of Brisbane City.” Journal of Hydrologic Engineering, Vol. 22, No. 6, pp. 05017003, DOI: 10.1061/(ASCE) HE.1943-5584.0001506.
Deo, R. C., Samui, P., and Kim, D. (2016). “Estimation of monthly evaporative loss using relevance vector machine, extreme learning machine and multivariate adaptive regression spline models.” Stochastic Environmental Research and Risk Assessment, Vol. 30, No. 6, pp. 1769–1784, DOI: 10.1007/s00477-015-1153-y.
Dracup, J. A., Lee, K. S., and Paulson, E. G. (1980). “On the definition of droughts.” Water Resources Research, Vol. 16, No. 2, pp. 297–302, DOI: 10.1029/WR016i002p00297.
Giuntoli, I., Renard, B., Vidal, J.-P., and Bard, A. (2013). “Low flows in France and their relationship to large-scale climate indices.” Journal of Hydrology, Vol. 482, pp. 105–118, DOI: 10.1016/j.jhydrol.2012.12.038.
Gustard, A. and Demuth, S. (2009). Manual on low-flow estimation and prediction, Opera.
Haghiabi, A. H. (2016). “Prediction of longitudinal dispersion coefficient using multivariate adaptive regression splines.” Journal of Earth System Science, Vol. 125, No. 5, pp. 985–995, DOI: 10.1007/s12040-016-0708-8.
Haghiabi, A. H. (2017). “Modeling river mixing mechanism using data driven model.” Water Resources Management, Vol. 31, No. 3, pp. 811–824, DOI: 10.1007/s11269-016-1475-7.
Haghiabi, A. H., Azamathulla, H. M., and Parsaie, A. (2017). “Prediction of head loss on cascade weir using ANN and SVM.” ISH Journal of Hydraulic Engineering, Vol. 23, No. 1, pp. 102–110, DOI: 10.1080/09715010.2016.1241724.
Haghiabi, A. H., Nasrolahi, A. H., and Parsaie, A. (2018). “Water quality prediction using machine learning methods.” Water Quality Research Journal, Vol. 53, No. 1, pp. 3–13, DOI: 10.2166/wqrj.2018.025.
Han, D., Chan, L., and Zhu, N. (2007). “Flood forecasting using support vector machines.” Journal of Hydroinformatics, Vol. 9, No. 4, pp. 267–276, DOI: 10.2166/hydro.2007.027.
Hipel, K. W. and McLeod, A. I. (1994). Time series modelling of water resources and environmental systems, Elsevier.
Huang, G.-B., Zhu, Q.-Y., and Siew, C.-K. (2006). “Extreme learning machine: Theory and applications.” Neurocomputing, Vol. 70, Nos. 1–3, pp. 489–501, DOI: 10.1016/j.neucom.2005.12.126
Jha, R. and Smakhtin, V. (2008). A review of methods of hydrological estimation at ungauged sites in India, IWMI.
Jha, R., Sharma, K., and Singh, V. (2008). “Critical appraisal of methods for the assessment of environmental flows and their application in two river systems of India.” KSCE Journal of Civil Engineering, Vol. 12, No. 3, pp. 213–219, DOI: 10.1007/s12205-008-0213-y.
Khan, M. S. and Coulibaly, P. (2006). “Application of support vector machine in lake water level prediction.” Journal of Hydrologic Engineering, Vol. 11, No. 3, pp. 199–205, DOI: 10.1061/(ASCE) 1084-0699(2006)11:3(199).
Kim, T.-W. and Valdés, J. B. (2003). “Nonlinear model for drought forecasting based on a conjunction of wavelet transforms and neural networks.” Journal of Hydrologic Engineering, Vol. 8, No. 6, pp. 319–328, DOI: 10.1061/(ASCE)1084-0699(2003)8:6(319).
Komorník, J., Komorníková, M., Mesiar, R., Szökeová, D., and Szolgay, J. (2006). “Comparison of forecasting performance of nonlinear models of hydrological time series.” Physics and Chemistry of the Earth, Parts A/B/C, Vol. 31, No. 18, pp. 1127–1145, DOI: 10.1016/j.pce.2006.05.006.
Kumar, R., Goel, N. K., Chatterjee, C., and Nayak, P. C. (2015). “Regional flood frequency analysis using soft computing techniques.” Water Resources Management, Vol. 29, No. 6, pp. 1965–1978, DOI: 10.1007/s11269-015-0922-1.
Laaha, G. and Blöschl, G. (2005). “Low flow estimates from short stream flow records—a comparison of methods.” Journal of Hydrology, Vol. 306, Nos. 1–4, pp. 264–286, DOI: 10.1016/j.jhydrol.2004.09.012.
Lei, Y., Zhao, D., and Cai, H. (2015). “Prediction of length-of-day using extreme learning machine.” Geodesy and Geodynamics, Vol. 6, No. 2, pp. 151–159, DOI: 10.1016/j.geog.2014.12.007.
Lin, J.-Y., Cheng, C.-T., and Chau, K.-W. (2006). “Using support vector machines for long-term discharge prediction.” Hydrological Sciences Journal, Vol. 51, No. 4, pp. 599–612, DOI: 10.1623/hysj.51.4.599.
MacKay, D. J. (1996). “Bayesian methods for backpropagation networks.” Models of neural networks III. Springer, pp. 211–254, DOI: 10.1007/978-1-4612-0723-8_6.
Müller, K.-R., Smola, A. J., Rätsch, G., Schölkopf, B., Kohlmorgen, J., and Vapnik, V. (1997). “Predicting time series with support vector machines.” International Conference on Artificial Neural Networks. Springer, pp. 999–1004, DOI: 10.1007/BFb0020283.
Najafzadeh, M. and Azamathulla, H. M. (2013). “Group method of data handling to predict scour depth around bridge piers.” Neural Computing and Applications, Vol. 23, Nos. 7–8, pp. 2107–2112, DOI: 10.1007/s00521-012-1160-6.
Najafzadeh, M. and Saberi-Movahed, F. (2018). “GMDH-GEP to predict free span expansion rates below pipelines under waves.” Marine Georesources & Geotechnology, pp. 1–18, DOI: 10.1080/1064119X.2018.1443355.
Najafzadeh, M., Etemad-Shahidi, A., and Lim, S. Y. (2016). “Scour prediction in long contractions using ANFIS and SVM.” Ocean Engineering, Vol. 111, pp. 128–135, DOI: 10.1016/j.oceaneng.2015.10.053.
Najafzadeh, M., Rezaie-Balf, M., and Tafarojnoruz, A. (2018). “Prediction of riprap stone size under overtopping flow using data-driven models.” International Journal of River Basin Management, pp. 1–8, DOI: 10.1080/15715124.2018.1437738.
Najafzadeh, M., Saberi-Movahed, F., and Sarkamaryan, S. (2017). “NFGMDH-Based self-organized systems to predict bridge pier scour depth under debris flow effects.” Marine Georesources & Geotechnology, Vol. 36, No. 5, pp. 589–602, DOI: 10.1080/1064119X.2017.1355944.
Nayak, P. C., Sudheer, K., Rangan, D., and Ramasastri, K. (2004). “A neuro-fuzzy computing technique for modeling hydrological time series.” Journal of Hydrology, Vol. 291, Nos. 1–2, pp. 52–66, DOI: 10.1016/j.jhydrol.2003.12.010.
Nikbakht, S. A., Zahraie, B., and Nasseri, M. (2012). “Seasonal meteorological drought prediction using support vector machine.” Vol. 23, No. 2, pp. 72–84.
Okkan, U. and Inan, G. (2014). “Bayesian learning and relevance vector machines approach for downscaling of monthly precipitation.” Journal of Hydrologic Engineering, Vol. 20, No. 4, pp. 04014051, DOI: 10.1061/(ASCE)HE.1943-5584.0001024.
Osuna, E., Freund, R., and Girosi, F. (1997). Support vector machines: Training and applications.
Parsaie, A. and Haghiabi, A. H. (2017a). “Computational modeling of pollution transmission in rivers.” Applied water science, Vol. 7, No. 3, pp. 1213–1222, DOI: 10.1007/s13201-015-0319-6.
Parsaie, A. and Haghiabi, A. H. (2017b). “Improving modelling of discharge coefficient of triangular labyrinth lateral weirs using SVM, GMDH and MARS Techniques.” Irrigation and Drainage, Vol. 66, No. 4, pp. 636–654, DOI: 10.1002/ird.2125.
Parsaie, A. and Haghiabi, A. H. (2017c). “Mathematical expression of discharge capacity of compound open channels using MARS technique.” Journal of Earth System Science, Vol. 126, No. 2, p. 20, DOI: 10.1007/s12040-017-0807-1.
Parsaie, A., Azamathulla, H. M., and Haghiabi, A. H. (2017a). “Physical and numerical modeling of performance of detention dams.” Journal of Hydrology, DOI: 10.1016/j.jhydrol.2017.01.018.
Parsaie, A., Ememgholizadeh, S., Haghiabi, A. H., and Moradinejad, A. (2018a). “Investigation of trap efficiency of retention dams.” Water Science and Technology: Water Supply, Vol. 18, No. 2, pp. 450–459, DOI:10.2166/ws.2017.109.
Parsaie, A., Haghiabi, A. H., Saneie, M., and Torabi, H. (2018b). “Prediction of energy dissipation of flow over stepped spillways using data-driven models.” Iranian Journal of Science and Technology, Transactions of Civil Engineering, Vol. 42, No. 1, pp. 39–53, DOI: 10.1007/s40996-017-0060-5.
Parsaie, A., Haghiabi, A. H., Saneie, M., and Torabi, H. (2016). “Applications of soft computing techniques for prediction of energy dissipation on stepped spillways.” Neural Computing and Applications, Vol. 29, No. 12, pp. 1393–1409, DOI: 10.1007/s00521-016-2667-z.
Parsaie, A., Yonesi, H., and Najafian, S. (2017b). “Prediction of flow discharge in compound open channels using adaptive neuro fuzzy inference system method.” Flow Measurement and Instrumentation, Vol. 54, pp. 288–297, DOI: 10.1016/j.flowmeasinst.2016.08.013.
Pyrce, R. (2004). Hydrological low flow indices and their uses, Watershed Science Centre (WSC) Report.
Qishlaqi, A., Kordian, S., and Parsaie, A. (2017). “Hydrochemical evaluation of river water quality—a case study.” Applied Water Science, Vol. 7, No. 5, pp. 2337–2342, DOI: 10.1007/s13201-016-0409-0.
Rajesh, R. and Prakash, J. S. (2011). “Extreme learning machines-a review and state-of-the-art.” International journal of wisdom based computing, Vol. 1, No. 1, pp. 35–49.
Rezaie-Balf, M. and Kisi, O. (2017). “New formulation for forecasting streamflow: Evolutionary polynomial regression vs. extreme learning machine.” Hydrology Research, Vol. 49, No. 3, pp. 939–953, DOI: 10.2166/nh.2017.283.
Salas, J. D. (1993). “Analysis and modeling of hydrologic time series.” Handbook of Hydrology, Vol. 19, pp. 1–72.
Seo, Y., Kim, S., and Singh, V. P. (2015). “Multistep-ahead flood forecasting using wavelet and data-driven methods.” KSCE Journal of Civil Engineering, Vol. 19, No. 2, pp. 401–417, DOI: 10.1007/s12205-015-1483-9.
Shiri, J. and Kisi, Ö. (2011). “Application of artificial intelligence to estimate daily pan evaporation using available and estimated climatic data in the Khozestan Province (South Western Iran).” Journal of Irrigation and Drainage Engineering, Vol. 137, No. 7, pp. 412–425, DOI: 10.1061/(ASCE)IR.1943-4774.0000315.
Sivapragasam, C. and Muttil, N. (2005). “Discharge rating curve extension–a new approach.” Water Resources Management, Vol. 19, No. 5, pp. 505–520, DOI: 10.1007/s11269-005-6811-2.
Sivapragasam, C., Maheswaran, R., and Venkatesh, V. (2008). “Genetic programming approach for flood routing in natural channels.” Hydrological Processes, Vol. 22, No. 5, pp. 623–628, DOI: 10.1002/hyp.6628.
Srikanthan, R. and McMahon, T. (2001). “Stochastic generation of annual, monthly and daily climate data: A review.” Hydrology and Earth System Sciences Discussions, Vol. 5, No. 4, pp. 653–670, DOI: 10.5194/hess-5-653-2001.
Sudheer, K. and Jain, A. (2004). “Explaining the internal behaviour of artificial neural network river flow models.” Hydrological Processes, Vol. 18, No. 4, pp. 833–844, DOI: 10.1002/hyp.5517.
Sudheer, K., Gosain, A., and Ramasastri, K. (2002). “A data-driven algorithm for constructing artificial neural network rainfall-runoff models.” Hydrological Processes, Vol. 16, No. 6, pp. 1325–1330, DOI: 10.1002/hyp.554.
Tao, W., Kailin, Y., and Yongxin, G. (2008). “Application of artificial neural networks to forecasting ice conditions of the Yellow River in the Inner Mongolia Reach.” Journal of Hydrologic Engineering, Vol. 13, No. 9, pp. 811–816, DOI: 10.1061/(ASCE)1084-0699(2008) 13:9(811).
Tiwari, M. K. and Adamowski, J. (2013). “Urban water demand forecasting and uncertainty assessment using ensemble wavelet-bootstrap-neural network models.” Water Resources Research, Vol. 49, No. 10, pp. 6486–6507, DOI: 10.1002/wrcr.20517.
Tokar, A. S. and Johnson, P. A. (1999). “Rainfall-runoff modeling using artificial neural networks.” Journal of Hydrologic Engineering, Vol. 4, No. 10, pp. 232–239, DOI: 10.1061/(ASCE)1084-0699(1999) 4:3(232).
Toth, E., Brath, A., and Montanari, A. (2000). “Comparison of shortterm rainfall prediction models for real-time flood forecasting.” Journal of Hydrology, Vol. 239, Nos. 1–4, pp. 132–147, DOI: 10.1016/S0022-1694(00)00344-9.
Vapnik, V. (1998). Statistical learning theory, Wiley, New York.
Wang, W.-C., Chau, K.-W., Cheng, C.-T., and Qiu, L. (2009). “A comparison of performance of several artificial intelligence methods for forecasting monthly discharge time series.” Journal of Hydrology, Vol. 374, Nos. 3–4, pp. 294–306, DOI: 10.1016/j.jhydrol.2009.06.019.
Williams, C. K. and Rasmussen, C. E. (1996). “Gaussian processes for regression.” Advances in Neural Information Processing Systems, pp. 514–520.
Wu, C. and Chau, K.-W. (2010). “Data-driven models for monthly streamflow time series prediction.” Engineering Applications of Artificial Intelligence, Vol. 23, No. 8, pp. 1350–1367, DOI: 10.1016/j.engappai.2010.04.003.
Yu, P.-S., Chen, S.-T., and Chang, I.-F. (2006). “Support vector regression for real-time flood stage forecasting.” Journal of Hydrology, Vol. 328, Nos. 3–4, pp.704–716, DOI: 10.1016/j.jhydrol.2006.01.021.
Zahiri, A. and Najafzadeh, M. (2018). “Optimized expressions to evaluate the flow discharge in main channels and floodplains using evolutionary computing and model classification.” International Journal of River Basin Management, Vol. 16, No. 1, pp. 123–132, DOI: 10.1080/15715124.2017.1372448.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sahoo, B.B., Jha, R., Singh, A. et al. Application of Support Vector Regression for Modeling Low Flow Time Series. KSCE J Civ Eng 23, 923–934 (2019). https://doi.org/10.1007/s12205-018-0128-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-018-0128-1