Abstract
Forecasting urban water demand can be of use in the management of water utilities. For example, activities such as water-budgeting, operation and maintenance of pumps, wells, reservoirs, and mains require quantitative estimations of water resources at specified future dates. In this study, we tackle the problem of forecasting urban water demand by means of back-propagation artificial neural networks (ANNs) coupled with wavelet-denoising. In addition, non-coupled ANN and Linear Multiple Regression were used as comparison models. We considered the case of the municipality of Syracuse, Italy; for this purpose, we used a 7 year-long time series of water demand without additional predictors. Six forecasting horizons were considered, from 1 to 6 months ahead. The main objective was to implement a forecasting model that may be readily used for municipal water budgeting. An additional objective was to explore the impact of wavelet-denoising on ANN generalization. For this purpose, we measured the impact of five different wavelet filter-banks (namely, Haar and Daubechies of type db2, db3, db4, and db5) on a single neural network. Empirical results show that neural networks coupled with Haar and Daubechies’ filter-banks of type db2 and db3 outperformed all of the following: non-coupled ANN, Multiple Linear Regression and ANN models coupled with Daubechies filters of type db4 and db5. The results of this study suggest that reduced variance in the training-set (by means of denoising) may improve forecasting accuracy; on the other hand, an oversimplification of the input-matrix may deteriorate forecasting accuracy and induce network instability.
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References
Adamowski J (2008) Peak daily water demand forecast modeling using artificial neural networks. J Water Resour Plan Manage 134(2):119–128
Adamowski J, Chan HF (2011) A wavelet neural network conjunction model for groundwater level forecasting. J Hydrol 407(1–4):28–40
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 15:729–743
Adamowski J, Sun K (2010) Development of a coupled wavelet transform and neural network method for flow forecasting of non-perennial rivers in semi-arid watersheds. J Hydrol 390(1–2):85–91
Adamowski K, Prokoph A, Adamowski J (2009) Development of a new method of wavelet aided trend detection and estimation. Hydrol Process Spec Issue Can Geophys Union Hydrol Sect 23:2686–2696
Adamowski J, Fung Chan H, Prasher SO, Ozga-Zielinski B, Sliusarieva A (2012) Comparison of multiple linear and nonlinear regression, autoregressive integrated moving average, artificial neural network, and wavelet artificial neural network methods for urban water demand forecasting in Montreal, Canada. Water Resour Res 48:W01528. doi:10.1029/2010WR009945
Adar E, Neuman SP, Woolhiser DA (1988) Estimation of spatial recharge distribution using environmental isotopes and hydrochemical data: mathematical model and application to synthetic data. J Hydrol 97:251–277
An A, Shan N, Chan C, Cercone N, Ziarko W (1996) Discovering rules from data for water demand prediction: an enhanced rough-set approach. Eng Appl Artif Intell 9(6):645–653
Blatter C (1998) Wavelet: a primer. Peters Natick, Massachusetts
Bougadis J, Adamowski K, Diduch R (2005) Short-term municipal water demand forecasting. Hydrol Process 19:137–148
Cannas B, Fanni A, See L, Sias G (2006) Data preprocessing for river flow forecasting using neural networks: wavelet transforms and data partitioning. Phys Chem Earth 31(18):1164–1171
Chou CM (2011) A threshold based wavelet denoising method for hydrological data modeling. Water Resour Manag 25(7):1809–1830. doi:10.1007/s11269-011-9776-3
Compo GP, Torrence C (1998) A practical guide to wavelet analysis. Bull Am Meteorol Soc 79:61–78
Conover WJ (1980) Practical nonparametric statistics. Wiley, New York
Daubechies I (1992) Ten lectures on wavelets. SIAM, Philadelphia
Foufoula-Georgiou E, Kumar P (1994) Wavelets in geophysics. Academic, San Diego
Grubbs JW (1994) Evaluation of ground-water flow and hydrologic budget for lake Five-O, a seepage lake in Northwestern Florida. U.S. Geological Survey, WRIR 94–4145
Güldal V, Tongal H (2010) Comparison of recurrent neural network, adaptive neuro-fuzzy inference system and stochastic models in Egirdir Lake level forecasting. Water Resour Manag 24:105–128
Hagan MT, Demuth HB, Beale MH (1996) Neural network design. PWS Publishing, Boston
Haykin S (1994) Neural networks, a comprehensive foundation. Macmillan College Publishing Company, New York
Herrera M, Torgob L, Izquierdo J, Pérez-García R (2010) Predictive models for forecasting hourly urban water demand. J Hydrol 387(1–2):141–150
Holder RL (1985) Multiple regression in hydrology. Institute of hydrology, Crowmarsh Gifford
Holschneider M (1995) Wavelets: an analysis tool. Oxford Mathematical Monograph, Clarendon Press
Issar AS, Zohar M (2009) Climate change impacts on the environment and civilization in the near East. In: Brauch HG, Spring ÚO, Grin J, Mesjasz C, Kameri-Mbote P, Behera NC, Chourou B, Krummenacher H (eds) Facing global environmental change. Springer, Berlin, pp 119–130
Jain A, Ormsbee LE (2002) Short-term water demand forecasting modeling techniques: conventional versus AI. J Am Water Works Assoc 94(7):64–72
Jowitt PW, Xu C (1992) Demand forecasting for water distribution systems. Civ Eng Syst 9:105–121
Kisi O (2008) Stream flow forecasting using neuro-wavelet technique. Hydrol Process 22:4142–4152
Kisi O (2009) Neural networks and wavelet conjunction model for intermittent stream flow forecasting. J Hydrol Eng 14(8):773–782
Labat D (2005) Recent advances in wavelet analyses, part 1: a review of concepts. J Hydrol 314(1–4):275–288
Labat D (2008) Wavelet analysis of the annual discharge records of the world’s largest rivers. Adv Water Resour 31:109–117
Maidment DR, Miaou SP (1986) Daily water use in nine cities. Water Resour Res 22(6):845–851
Mallat S (1999) A wavelet tour of signal processing, 2nd edn. Academic, San Diego
Meyer Y (1992) Wavelets and operators. Cambridge Studies in Advanced Mathematics, Cambridge University Press
Msiza IS, Nelwamondo FV, Marwala T (2007) Artificial neural networks and support vector machines for water demand time series forecasting. Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, 7–10 October, Montreal, Canada, 638–643
Nourani V, Komasi M, Mano A (2009) A multivariate ANN-wavelet approach for rainfall-runoff modeling. Water Resour Manag 23(14):2877–2894
Oron G, Campos C, Gillerman L, Salgot M (1999) Wastewater treatment, renovation and reuse for agricultural irrigation in small communities. Agr Water Manag 38(3):223–234
Partal T, Cigizoglu HK (2008) Estimation and forecasting of the daily suspended sediment data using wavelet-neural networks. J Hydrol 358(3–4):317–331
Renaud O, Starck JL, Murtagh F (2005) Wavelet-Based Combined signal filtering and prediction. IEEE T Syst Man Cy B 35(6):1241–1251
Rioul O, Vetterli M (1991) Wavelet and signal processing. IEEE Signal Proc Mag 8:14–38
Rumelhart DE, Hinton GE, Williams RJ (1986) Learning representations by back-propagating errors. Nature 323:533–536
Shirsath PB, Singh AK (2010) A comparative study of daily pan evaporation estimation using ANN, regression and climate based models. Water Resour Manag 24(8):1571–1581
Smith J (1988) A model of daily municipal water use of short term forecasting. Water Resour Res 24(2):201–206
Strang G, Nguyen T (1996) Wavelets and filter banks. Wellesley-Cambridge Press
Wang W, Jin J, Li Y (2009) Prediction of inflow at three gorges dam in Yangtze River with wavelet network model. Water Resour Manag 23(13):2791–2803
Widrow B, Lehr MA (1990) 30 years of adaptive neural networks: perceptron, madaline, and backpropagation. Proc IEEE 78(9):1415–1441
Zhang GP (2003) Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing 50:159–175
Zhang GP, Patuwo EB, Hu MY (1998) Forecasting with artificial neural network: the state of the art. Int J Forecast 14:35–62
Zhang GP, Patuwo BE, Hu MY (2001) A simulation study of artificial neural networks for nonlinear time-series forecasting. Comput Oper Res 28(4):381–396
Zhou H, Peng Y, Liang G (2007) The research of monthly discharge predictor-corrector model based on wavelet decomposition. Water Resour Manag 22(2):217–227
Acknowledgments
This study was supported by the Norman Zavalkoff Foundation whose help is greatly appreciated. This study was also partially funded by a NSERC Discovery Grant held by Jan Adamowski, and by the IWRM-SMART project of The Federal Ministry of Education and Research, Germany, and The Ministry of Science and Technology (MOST) of the State of Israel. The authors would also like to thank the anonymous reviewers for their valuable comments.
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Campisi-Pinto, S., Adamowski, J. & Oron, G. Forecasting Urban Water Demand Via Wavelet-Denoising and Neural Network Models. Case Study: City of Syracuse, Italy. Water Resour Manage 26, 3539–3558 (2012). https://doi.org/10.1007/s11269-012-0089-y
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DOI: https://doi.org/10.1007/s11269-012-0089-y