Effect of Pruning and Smoothing while Using M5 Model Tree Technique for Reservoir Inflow Prediction
Publication: Journal of Hydrologic Engineering
Volume 16, Issue 7
Abstract
This study reports the performance of an M5 model tree (MT) and the effects of pruning and smoothing applied to reservoir inflow prediction. The full year and seasonal monthly time step MT predictions were compared with conventional univariate autoregressive integrated moving average (stochastic) models. It was found that stochastic models could not predict the future inflows in a better way, because the observed series had not followed any particular distribution. However, it was found that the stochastic models showed better improvement using a logarithmic-transformed series, but the logarithmic-transformed MT results showed otherwise. The model validation was performed using the comparison of goodness of fit measures, standard statistics, time series, and scatter plots of predicted inflows with observed inflows. The effect of pruning each leaf in the MT model was also studied. Instead of pruning all the leaves, leading to lesser predictive accuracy, selective pruning was carried out based on the importance of the processes, for example, peak and low flow. The performance of both stochastic and MT models showed that seasonal monthly prediction was superior to full-year monthly prediction because of large zero values in latter data set. Encouraging results indicated that the seasonal nontransformed selective-pruned MT models performed better and produced reliable forecasts of high and low inflows than the stochastic models. A pruned and smoothed MT model (PSMT) performed 79% better than the stochastic models in terms of mean square error (MSE). On the other hand, MSE was 98% better than the stochastic model in an unpruned and unsmoothed MT (UPUSMT) model. Because of better peak prediction by UPUSMT model, the MSE was 90% better than the PSMT models. The other advantage of an MT was having a set of equations and if-then rules to predict the inflow as well as peak inflow into the Pawana reservoir.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors would like to thank authorities of Irrigation Department (Pawana circle), Pune, and the Government of Maharashtra, India, for providing the data to carry out this work. We gratefully acknowledge the anonymous reviewers and editors for their valuable reviews and suggestions, which brought out the real thinking of using wet period data.
References
Ahmad, S., Khan, I. H., and Parida, B. P. (2001). “Performance of stochastic approaches for forecasting river water quality.” Water Resour., 35(18), 4261–4266.
Ahmad, S., and Simonovic, S. P. (2005). “An artificial neural network model for generating hydrograph from hydro-meteorological parameters.” J. Hydrol. (Amsterdam), 315, 236–251.
Ahmed, J. A., and Sarma, A. K. (2007). “Artificial neural network model for synthetic streamflow generation.” Water Resour. Manage., 21(6), 1015–1029.
Akaike, H. (1974). “A new look at the statistical model identification.” IEEE Trans. Autom. Control, 19(6), 716–723.
Bhattacharya, B., Price, R. K., and Solomatine, D. P. (2004). “A data mining approach to modeling sediment transport.” Proc., 6th Int. Conf. on Hydroinformatics, World Scientific, Singapore, 1663–1670.
Bhattacharya, B., and Solomatine, D. P. (2002). “Application of artificial neural networks and M5 model tree to modeling stage-discharge relationship.” Proc., 2nd Int. Symp. on Flood Defence, B. S. Beijing, Z. Y. Wu, G. Q. Wang, G. H. Wang, Huang, and J. C. Huang, eds., Science Press, New York.
Bhattacharya, B., and Solomatine, D. P. (2005). “Neural networks and M5 model tree in modeling water level-discharge relationship.” Neurocomputing; Var. Star Bull., 63, 381–396.
Bhattacharya, B., and Solomatine, D. P. (2006). “Improving empirical models with machine learning.” Proc., 6th Int. Conf. on Neural Networks, IEEE, Vancouver, BC, Canada.
Box, G. E. P., and Jenkins, G. M. (1976). Time series analysis, forecasting and control, Holden Day, San Francisco.
Campolo, M., Andreussi, P., and Soldati, A. (1999). “River flood forecasting with a neural network model.” Water Resour. Res., 35(4), 1191–1197.
Chiang, Y. M., and Chang, F. J. (2009). “Integrating hydrometeorological information for rainfall-runoff modeling by artificial neural networks.” Hydrol. Processes, 23(11), 1650–1659.
Coulibaly, P., Anctil, F., and Bobee, B. (2000). “Daily reservoir inflow forecasting using artificial neural networks with stopped training approach.” J. Hydrol. (Amsterdam), 230, 244–257.
Coulibaly, P., Hache, M., Fortin, V., and Bobee, B. (2005). “Improving daily reservoir inflow forecasts with model combination.” J. Hydrol. Eng., 10(2), 91–99.
Hsu, K. L., Gupta, H. V., and Sorooshian, S. (1995). “Artificial neural network modeling of the rainfall-runoff process.” Water Resour. Res., 31(10), 2517–2530.
Ljung, G. M., and Box, G. E. P. (1978). “On a measure of lack of fit in time series models.” Biom. J., 65(2), 297–303.
Makridakis, S., Wheelwright, S. C., and Hyndman, R. J. (1998). Forecasting: Methods and applications, Wiley, New York.
Minns, A., and Hall, M. (1996). “Artificial neural networks as rainfall-runoff models.” Hydrol. Sci. J., 41(3), 399–417.
Muluye, G. Y., and Coulibaly, P. (2007). “Seasonal reservoir inflow forecasting with low-frequency climatic indices: A comparison of data-driven methods.” Hydrol. Sci. J., 52(3), 508–522.
Nash, J. E., and Sutcliffe, J. V. (1970). “River flow forecasting through conceptual models Part 1—A discussion of principles.” J. Hydrol. (Amsterdam), 10(3), 282–290.
Nokes, D. J., Mcleod, I., and Hipel, K. W. (1985). “Forecasting monthly river flow time series.” Int. J. Forecasting, 1, 179–190.
Preis, A., and Ostfeld, A. (2005). “A hybrid (MT-LP) approach to water distribution systems inverse modeling.” Proc., 2005 World Water and Environmental Resources Congress, ASCE, Reston, VA.
Quinlan, J. R. (1992). “Learning with continuous classes.” Proc., 5th Australian Joint Conf. on Artificial Intelligence, A. Adams and L. Sterling, eds. World Scientific, Singapore, 343–348.
Raghuwanshi, N. S., Singh, I., and Reddy, L. S. (2006). “Runoff and sediment yield modeling using artificial neural networks: Upper Siwane River, India.” J. Hydrol. Eng., 11(1), 71–79.
Salas, J. D., Delleur, V., Yevjevich, V., and Lane, W. L. (1980). Applied modeling of hydrologic time series, Water Resources Publication, CO.
Senthilkumar, A. R., Sudheer, K. P., Jain, S. K., and Agarwal, P. K. (2005). “ANN based rainfall-runoff modeling: Comparison of network types.” Hydrol. Processes, 19(6), 1277–1291.
Sivapragasam, C., Vincent, P., and Vasudevan, G. (2007). “Genetic programming model for forecast of short and noisy data.” Hydrol. Processes, 21(2), 266–272.
Solomatine, D. P. (2002a). “Applications of data-driven modeling and machine learning in control of water resources.” Computational intelligence in control of water resources, M. Mohammadian, R. A. Sarkar, and X. Yao, eds., Idea Group Publishing, Hershey, PA, 197–217.
Solomatine, D. P. (2002b). “Data-driven modeling: Paradigm, methods, experiences.” Proc., 5th Int. Conf. on Hydroinformatics, IWA Publishing, London.
Solomatine, D. P. (2005). “Local and hybrid learning models in forecasting natural phenomena.” Proc., Int. IEEE Conf. on Neural Networks, IEEE, Montreal, Canada.
Solomatine, D. P., and Dulal, K. N. (2003). “Model tree as an alternative to neural networks in rainfall-runoff modeling.” Hydrol. Sci. J., 48(3), 399–411.
Solomatine, D. P., and Siek, M. B. (2003). “Flexibility and optimality in M5 model tree.” Proc., 3rd Int. Conf. on Hybrid Intelligent Systems, IOS Press, Amsterdam, Netherlands.
Solomatine, D. P., and Xue, Y. (2004). “M5 model tree and neural networks: Application to flood forecasting in the upper reach of the Huai River in China.” J. Hydrol. Eng., 9(6), 491–501.
Štravs, L., and Brilly, M. (2007). “Development of a low-flow forecasting model using the M5 machine learning method.” Hydrol. Sci. J., 52(3), 466–477.
Sudheer, K. P., and Jain, A. (2004). “Explaining the internal behaviour of artificial neural network river flow models.” Hydrol. Processes, 18, 833–844.
Sveinsson, O. G. B., et al. (2008). “Forecasting spring reservoir inflows in Churchill Falls basin in Quebec, Canada.” J. Hydrol. Eng., 13(6), 426–437.
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.” J. Hydrol. (Amsterdam), 374(3–4), 294–306.
Xu, Z. X., and Li, J. Y. (2002). “Short-term inflow forecasting using an artificial neural network model.” Hydrol. Processes, 16, 2423–2439.
Yurekli, K., Kurunc, A., and Simsek, H. (2004). “Prediction of daily maximum streamflow based on stochastic approaches.” J. Spa. Hydrol., 4(2), 1–12.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 16 • Issue 7 • July 2011
Pages: 563 - 574
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Jun 28, 2009
Accepted: Oct 9, 2010
Published online: Oct 28, 2010
Published in print: Jul 1, 2011
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.