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Probabilistic modeling and uncertainty estimation of urban water consumption under an incompletely informational circumstance

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Abstract

With a booming development characterized by new urbanization in current China, urban water consumption attracts growing concerns. An efficient and probabilistic prediction of urban water consumption plays a vital role for urban planning toward sustainable development, especially in megacities limited by water resources. However, the data insufficiency issue commonly exists nowadays and seriously restricts further development of urban water simulation. In this article, we proposed a consolidated framework for probabilistic prediction of water consumption under an incompletely informational circumstance to deal with the challenge. The model was constructed based on a state-of-the-art Bayesian neural networks (BNNs) technique. Three dominated influencing factors were identified and included into the BNN model. Future impact factors were generated by using a variety of methods including a quadratic polynomial model, a regression and auto-regressive moving average combination model and a Grey Verhulst model. Thereafter, water consumption projection (2013–2020) and uncertainty estimates was done. Results showed that the model matched well with observations. Through reducing the dependence on large amount of information and constructing a probabilistic means incorporating uncertainty estimation, the new approach can work better than conventional means in support of water resources planning and management under an incompletely informational circumstance.

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References

  • Azadeh A, Neshat N, Hamidipour H (2012) Hybrid fuzzy regression artificial neural network for improvement of short-term water consumption estimation and forecasting in uncertain and complex environments: case of a large metropolitan city. J Water Resour Plan Manag 1385:71–75

    Article  Google Scholar 

  • Beam AL, Motsinger-Reif A, Doyle J (2014) Bayesian neural networks for genetic association studies of complex disease. arXiv:1404.3989v2 [q-bio.GN], 16 Apr 2014

  • Bennett C, Stewart RA, Beal CD (2013) ANN-based residential water end-use demand forecasting model. Expert Syst Appl 40(2013):1014–1023. (Published online in Wiley InterScience (www. interscience.willy.com))

    Article  Google Scholar 

  • Bougadis J, Adamowski K, Diduch R (2005) Short-term municipal water demand forecasting. Hydrol Process 19:137–148. doi:10.1002/hyp.5763

    Article  Google Scholar 

  • Box G, Jenkins G (1970) Time series analysis: forecasting and control. Holden-Day, San Francisco

    Google Scholar 

  • China Meteorological data Sharing Service System (CMDSSS), (2014) Ground meteorological data. http://cdc.cma.gov.cn/home.do

  • Deng JL (2002) The basis of Grey theory. Press of Huazhong University of Science & Technology, Wuhan

    Google Scholar 

  • Dube E, van der Zaag P (2003) Analysing water use patterns for demand management: the case of the city of Masvingo, Zimbabwe. Phys Chem Earth 28:805–815

    Article  Google Scholar 

  • Gianola D, Okut H, Weigel KA, Rosa GJM (2011) Predicting complex quantitative traits with Bayesian neural networks: a case study with Jersey cows and wheat. BMC Genet 2011(12):87

    Article  Google Scholar 

  • Gu JJ, Guo P, Huang GH (2013) Inexact stochastic dynamic programming method and application to water resources management in Shandong China under uncertainty. Stoch Environ Res Risk Assess 27:1207–1219

    Article  Google Scholar 

  • Herrera M, Torgo L, Izquierdo J, Perez-Garcia R (2010) Predictive models for forecasting hourly urban water demand. J Hydrol 387:141–150

    Article  Google Scholar 

  • Holmes CC, Mallick BK (1998) Bayesian radial basis functions of variable dimension. Neural Comput 10(5):1217–1233. doi:10.1162/089976698300017421

    Article  Google Scholar 

  • Jorqensen B, Graymore M, O’Toole K (2009) Household water use behavior: an integrated model. J Environ Manag 91(1):227–236

    Article  Google Scholar 

  • Kayacan E, Ulutas B, Kaynak O (2010) Grey system theory-based models in time series prediction. Expert Syst Appl 37:1784–1789

    Article  Google Scholar 

  • Khan MS, Coulibaly P (2006) Bayesian neural network for rainfall-runoff modeling. Water Resour Res 42(7). doi:10.1029/2005wr003971

  • Kingston GB, Lambert MF, Maier HR (2005) Bayesian training of artificial neural networks used for water resources modeling. Water Resour Res 41(12). doi:10.1029/2005wr004152

  • Lampinen J, Vehtari A (2001) Bayesian approach for neural networks- reviews and case studies. Neural Netw 14(3):257–274. doi:10.1016/S0893-6080(00)00098-8

    Article  CAS  Google Scholar 

  • Lee S, Wentz EA, Gober P (2010) Space-time forecasting using soft geostatistics: a case study in forecasting municipal water demand for Phoenix, Arizona. Stoch Environ Res Risk Assess 24:283–295

    Article  Google Scholar 

  • Liang FM (2005) Bayesian neural networks for nonlinear time series forecasting. Stat Comput 15(1):13–29. doi:10.1007/s11222-005-4786-8

    Article  Google Scholar 

  • Liang F, Kuk YCA (2004) A finite population estimation study with Bayesian neural networks. Surv Methodol 30:219–234

    Google Scholar 

  • Liang F, Wong WH (2001) Real-parameter evolutionary sampling with applications in Bayesian mixture models. J Am Stat Assoc 96:653–666. doi:10.1198/016214501753168325

    Article  Google Scholar 

  • Liu J, Hubert HG, Savenije XuJX (2003) Forecast of water demand in Weinan City in China using WDF-ANN model. Phys Chem Earth 28(2003):219–224

    Article  Google Scholar 

  • MacKay DJC (1992) A practical Bayesian framework for backpropagation networks. Neural Comput 4(3):448–472. doi:10.1162/neco.1992.4.3.448

    Article  Google Scholar 

  • Muller P, Insua DR (1998) Issues in Bayesian analysis of neural network models. Neural Comput 10(3):749–770. doi:10.1162/089976698300017737

    Article  Google Scholar 

  • Municipal Water Affairs Bureau of Shenzhen (MWABS) (2011) Basic water regime information for Shenzhen. http://www.szwrb.gov.cn/cn/zwgk_show.asp?id=16069 (in Chinese)

  • Neal RM (1996) Bayesian learning for neural networks. Springer, New York

    Book  Google Scholar 

  • Niu D, Shi H, Wu DD (2012) Short-term load forecasting using Bayesian neural networks learned by hybrid Monte Carlo algorithm. Appl Soft Comput 12(2012):1822–1827

    Article  Google Scholar 

  • Qi Cheng, Chang N (2011) System dynamics modeling for municipal water demand estimation in an urban region under uncertain economic impacts. J Environ Manag 92(2011):1628–1641

    Article  Google Scholar 

  • Shi P, Yang T, Chen X, Yu Z, Acharyad K, Chongyu X (2013) Urban water consumption in a rapidly developing flagship megacity of south china, prospective scenarios and implications. Stoch Environ Res Risk Assess 27:1359–1370

    Article  Google Scholar 

  • Statistics Bureau of Shenzhen (SBS) (2014). http://www.sztj.gov.cn/xxgk/tjsj/tjnj/201404/t20140421_2341137.htm (In Chinese)

  • Wang X, Burgess A, Yang J (2013) A scenario-based water conservation planning support system (SB-WCPSS). Stoch Environ Res Risk Assess 27:629–641. doi:10.1007/s00477-012-0628-3

    Article  Google Scholar 

  • Yurdusev MA, Firat M, Turan ME (2010) Generalized regression neural networks for municipal water consumption prediction. J Stat Comput Simul 80(4):477–478. doi:10.1080/00949650903520118

    Article  Google Scholar 

  • Zhang X, Liang F, Srinivasan R, Van Liew M (2009) Estimating uncertainty of streamflow simulation using Bayesian neural networks. Water Resour Res 45(2):1. doi:10.1029/2008wr007030

    Article  Google Scholar 

Download references

Acknowledgments

The work was jointly supported by a Grant from the National Natural Science Foundation of China (41371051), a key Grant of Chinese Academy of Sciences (KZZD-EW-12), a grant from the Ministry of Science and Technology of China (2013BAC10B01) and a Grant from the Fundamental Research Funds for the Central Universities (2014B34514).

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Correspondence to Tao Yang.

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Yang, T., Shi, P., Yu, Z. et al. Probabilistic modeling and uncertainty estimation of urban water consumption under an incompletely informational circumstance. Stoch Environ Res Risk Assess 30, 725–736 (2016). https://doi.org/10.1007/s00477-015-1081-x

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