Prediction of water consumption by consumer categories: a case study




Water consumption, Time series models, Water consumption forecast, Bayesian model, MCMC methods


This study introduces a new Bayesian model for predicting water consumption in a medium-sized municipality in the State of São Paulo, Brazil. For the study, a stratified random sample of water consumption for consumers in different consumer categories (residential, industrial, public and commercial) is selected for 55 monthly consecutive measurements of water consumption and the proposed model is compared with some usual existing time series models (moving average models and ARIMA models) commonly used in forecasts. The Bayesian model for the consumption data assumes the presence of a random effect that captures the possible dependence between the monthly consumption for the different categories. A hierarchical Bayesian analysis is done using MCMC (Markov Chain Monte Carlo) methods to generate samples of the joint posterior distribution of interest. A detailed discussion of the results obtained is presented, showing the advantages and disadvantages of each model proposed in terms of feasibility for the municipality's water supply company. The results of this study can be generalized to water consumption data for any municipality.


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Author Biographies

Jorge Alberto Achcar, Universidade de São Paulo, Ribeirão Preto, SP

Jorge Alberto Achcar ;BS mathematics, (UNESP), SJRP, SP, 1971, Brazil;  Ms statistics, IME-USP, SP, 1976, Brazil; PhD statistics University of Wisconsin-Madison, USA, 1982

Marcos Valerio Araujo, Universidade de Araraquara, Araraquara, SP

Marcos Valério de Araujo. Possui graduação em tecnologia sanitária pela UNICAMP em 1997, MBA em Gestão Empresarial pela FGV em 2002, aluno do Mestrado Profissional em Engenharia de Produção na UNIARA, atua no setor de saneamento básico por 22 anos onde é responsável pela Operação (captação, tratamento e distribuição de água e coleta, tratamento e destinação do efluente), Gestão dos Serviços, Gestão Comercial e Plano de Negócio da companhia envolvendo todo o planejamento, acompanhamento econômico e financeiro, receitas, custos e programa de investimentos de concessões privadas.

Claudio Luis Piratelli, Universidade de Araraquara, Araraquara, SP

Claudio Luis Piratelli has degree in Production Engineer – UFSCar – Federal University of São CarloS, SP São Carlos, 1998; MSc Regional Development, University of Araraquara, 2005;  PhD in Aeronautical and Mechanics engineering, Production area, Aeronautics Institute of Technology – ITA (2010)

Ricardo Puziol de Oliveira, Universidade de São Paulo, SP

Ricardo Puziol de Oliveira has degree in Mathematics - UEM - Maringá State University; MSc Biostatistics, Maringá State University, 2016; PhD in Biostatistics, Medical School of Ribeirão Preto, University of São Paulo (USP), 2019.


Akgün, B. (2003). Identification of periodic autoregressive moving average models. PhD thesis. Middle East Technical University.

Altunkaynak, A., Özger, M., Çakmakci, M. (2005). Water consumption prediction of istanbul city by using fuzzy logic approach. Water Resources Management, 19(5), 641–654.

Aly, A. H., Wanakule, N. (2004). Short-term forecasting for urban water consumption. Journal of water resources planning and management, 130(5), 405–410.

Amaral, A. M. P., Shirota, R. (2000). Mean residential consumption of treated water: an application of time series models in piracicaba (in portuguese). Revista Agrícola, 49(1), 55–72.

Balling, R. C., Gober, P., Jones, N. (2008). Sensitivity of residential water consumption to variations in climate: An intraurban analysis of Phoenix, Arizona. Water Resources Research, 44(10).

Bell, W. R. (1984). An introduction to forecasting with time series models. Insurance: Mathematics and Economics, 3(4), 241–255.

Bougadis, J., Adamowski, K., Diduch, R. (2005). Short-term municipal water demand forecasting. Hydrological Processes: An International Journal, 19(1), 137–148.

Box, G. E., Jenkins, G. M., Reinsel, G. C., Ljung, G. M. (2015). Time series analysis: forecasting and control. John Wiley & Sons.

Casella, G., George, E. I. (1992). Explaining the Gibbs sampler. The American Statistician, 46(3), 167–174.

Chang, H., Parandvash, G. H., Shandas, V. (2010). Spatial variations of single-family residential water consumption in Portland, Oregon. Urban geography, 31(7), 953–972.

Chib, S., Greenberg, E. (1995). Understanding the Metropolis-Hastings algorithm. The american statistician, 49(4), 327–335.

Crommelynck, V., Duquesne, C., Mercier, M., Miniussi, C. (1992). Daily and hourly water consumption forecasting tools using neural networks. Em: Proc. of the AWWA’s annual computer specialty conference, pp. 665–676.

Dias, D., Martinez, C.B., M., Libanio (2010). Evaluation of the impact of income variation on household consumption of water (in portuguese). Engenharia Sanitária Ambiental, 15(2), 155–166.

Feil, A., Haetinger, C. (2014). Prediction of water consumption via mathematical modeling of water supply system (in portuguese). Revista DAE, 195, 32–46.

Fortin, V., Perreault, L., Salas, J. (2004). Retrospective analysis and forecasting of streamflows using a shifting level model. Journal of Hydrology, 296(1-4), 135–163.

Gelfand, A. E., Smith, A. F. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85(410), 398–409.

Gwaivangmin, B., Jiya, J. (2017). Water demand prediction using artificial neural network for supervisory control. Nigerian Journal of Technology, 36(1), 148–154.

Ho, S., Xie, M. (1998). The use of arima models for reliability forecasting and analysis. Computers & Industrial Engineering, 35(1-2), 213–216.

House-Peters, L., Pratt, B., Chang, H. (2010). Effects of urban spatial structure, sociodemographics, and climate on residential water consumption in Hillsboro, Oregon. Journal of the American Water Resources Association, 46(3), 461–472.

Jain, A., Ormsbee, L. E. (2002). Short-term water demand forecast modeling techniques: Conventional methods versus AI. Journal-American Water Works Association, 94(7), 64–72.

Kher, L. K., Sorooshian, S. (1986). Identification of water demand models from noisy data. Water Resources Research, 22(3), 322–330.

Ljung, G. M., Box, G. E. (1978). On a measure of lack of fit in time series models. Biometrika, 65(2), 297–303.

Maidment, D. R., Parzen, E. (1984). Cascade model of monthly municipal water use. Water Resources Research, 20(1), 15–23.

Makki, A. A., Stewart, R. A., Panuwatwanich, K., Beal, C. (2013). Revealing the determinants of shower water end use consumption: enabling better targeted urban water conservation strategies. Journal of Cleaner Production, 60, 129–146.

Montgomery, D. C., Runger, G. C. (2010). Applied statistics and probability for engineers. John Wiley & Sons.

Montgomery, D. C., Jennings, C. L., Kulahci, M. (2015). Introduction to time series analysis and forecasting. John Wiley & Sons.

Morettin, P. A., Toloi, C. M. (1987). Time series forecast (in Portuguese). Atual.

Muhammad, M. K. I. B. (2012). Time Series Modeling Using Markov and Arima Models. PhD thesis. Universiti Teknologi Malaysia.

Narchi, H. (1989). Domestic demand for water (in portuguese). Revista DAE, 154, 1–7.

Nucci, N. L. R. (1983). Assessment of urban water demand. economic and urban aspects. the built area as a possible explanatory and prospective factor (in portuguese). Revista DAE, 135, 22–49.

Perry, P. F. (1981). Demand forecasting in water supply networks. Journal of the Hydraulics Division, 107(9), 1077–1087.

Rhoades, S. D., Walski, T. M. (1991). Using regression analysis to project pumpage. Journal-American Water Works Association, 83(12), 45–50.

Silva, C. S. (2003). Multivariate prediction of hourly water demand in urban water supply systems. PhD thesis. University of São Paulo.

Silva, W. T. P., Silva, L. M., Chichorro, J. F. (2008). Water resources management: Per capita water consumption perspectives in Cuiabá (in portuguese). Engenharia Sanitaria Ambiente, 13(1), 8–14.

Smith, J. A. (1988). A model of daily municipal water use for short-term forecasting. Water Resources Research, 24(2), 201–206.

Spiegelhalter, D., Thomas, A., Best, N., Lunn, D. (2003). Winbugs user manual.

Stark, H.L., Stanley, S.J., Buchanan, I.D., (2000). The Application of Artificial Neural Networks to Water Demand Modelling. In: CSCE 28th Annual Conference, London, Ont. , 7-10.

Thomas, S. P. (2000). Prediction of Water Consumption: Interface of Water and Sewage Installations with public services (in Portuguese). Navegar Editora.

Willis, R. M., Stewart, R. A., Giurco, D. P., Talebpour, M. R., Mousavinejad, A. (2013). End use water consumption in households: impact of socio-demographic factors and efficient devices. Journal of Cleaner Production, 60, 107–115.

Wong, J. S., Zhang, Q., Chen, Y. D. (2010). Statistical modeling of daily urban water consumption in hong kong: Trend, changing patterns, and forecast. Water resources research, 46(3).

Zhou, S., McMahon, T., Walton, A., Lewis, J. (2002). Forecasting operational demand for an urban water supply zone. Journal of hydrology, 259(1-4), 189–202.

Zhou, S. L., McMahon, T. A., Walton, A., Lewis, J. (2000). Forecasting daily urban water demand: a case study of melbourne. Journal of hydrology, 236(3-4), 153–164.




How to Cite

Achcar, J. A., Araujo, M. V., Piratelli, C. L., & Oliveira, R. P. de. (2020). Prediction of water consumption by consumer categories: a case study. Ciência E Natura, 42, e110.