Multivariate statistical analysis for water demand modelling: implementation, performance analysis, and comparison with the PRP model

Water demand is the driving force behind hydraulic dynamics in water distribution systems. Consequently, it is crucial to accurately estimate the actual water use to develop reliable simulation models. In this study, copula-based multivariate analysis was proposed and used for demand prediction for a given return period. The analysis was applied to water consumption data collected in the water distribution network of Palermo (Italy). The approach produced consistent demand patterns and could be a powerful tool when coupled with water distribution network models for design or analysis problems. The results were compared with those obtained using a classical water demand model, the Poisson rectangular pulse (PRP) model. The multivariate consumption data statistical analysis results were always higher than those of the PRP model but the copula-based method maintained the daily water volume of actual consumptions and provided maximum daily consumption that increased with the return period.

[1]  G. La Loggia,et al.  A WATER DEMAND MODEL BY MEANS OF THE ARTIFICIAL NEURAL NETWORKS METHOD , 2004 .

[2]  T. Mazzuchi,et al.  Urban Water Demand Forecasting: Review of Methods and Models , 2014 .

[3]  Edward C. Waymire,et al.  Scale considerations in the modeling of temporal rainfall , 1984 .

[4]  A. Frigessi,et al.  Pair-copula constructions of multiple dependence , 2009 .

[5]  Fabrizio Durante,et al.  On the return period and design in a multivariate framework , 2011 .

[6]  T. McMahon,et al.  Forecasting operational demand for an urban water supply zone , 2002 .

[7]  I. Vertommen,et al.  Generating Water Demand Scenarios Using Scaling Laws , 2014 .

[8]  David Zimbra,et al.  Urban Water Demand Forecasting with a Dynamic Artificial Neural Network Model , 2008 .

[9]  Shaw-Pin Miaou,et al.  A class of time series urban water demand models with nonlinear climatic effects , 1990 .

[10]  F. Serinaldi,et al.  Design hyetograph analysis with 3-copula function , 2006 .

[11]  Lily House-Peters,et al.  Urban water demand modeling: Review of concepts, methods, and organizing principles , 2011 .

[12]  K. Adamowski,et al.  Short‐term municipal water demand forecasting , 2005 .

[13]  Ashu Jain,et al.  Short-Term Water Demand Forecast Modelling at IIT Kanpur Using Artificial Neural Networks , 2001 .

[14]  A. Bárdossy,et al.  Copula based multisite model for daily precipitation simulation , 2009 .

[15]  Steven G. Buchberger,et al.  Intensity, Duration, and Frequency of Residential Water Demands , 1996 .

[16]  R. Bruce Billings,et al.  STATE-SPACE VERSUS MULTIPLE REGRESSION FOR FORECASTING URBAN WATER DEMAND , 1998 .

[17]  Velitchko G. Tzatchkov,et al.  Modeling of Drinking Water Distribution Networks Using Stochastic Demand , 2012, Water Resources Management.

[18]  M. Babel,et al.  A multivariate econometric approach for domestic water demand modeling: An application to Kathmandu, Nepal , 2007 .

[19]  T. Bedford,et al.  Vines: A new graphical model for dependent random variables , 2002 .

[20]  S. Alvisi,et al.  A Stochastic Model for Representing Drinking Water Demand at Residential Level , 2003 .

[21]  R. Magini,et al.  Spatial and Temporal Scaling Properties of Water Demand , 2008 .

[22]  David R. Maidment,et al.  Transfer Function Models of Daily Urban Water Use , 1985 .

[23]  Joaquín Izquierdo,et al.  Predictive models for forecasting hourly urban water demand , 2010 .

[24]  T. McMahon,et al.  Forecasting daily urban water demand: a case study of Melbourne , 2000 .

[25]  Eric Rothstein.  Water Demand Monitoring in Austin, Texas , 1992 .

[26]  Stefano Alvisi,et al.  A short-term, pattern-based model for water-demand forecasting , 2006 .

[27]  S. Buchberger,et al.  Model for Instantaneous Residential Water Demands , 1995 .

[28]  Robert M. Clark,et al.  Modeling contaminant propagation in drinking-water distribution systems , 1993 .

[29]  Nisai Wanakule,et al.  Short-Term Forecasting for Urban Water Consumption , 2004 .

[30]  Ignacio Rodriguez-Iturbe,et al.  Scale of fluctuation of rainfall models , 1986 .

[31]  B. Schweizer,et al.  Thirty Years of Copulas , 1991 .

[32]  C. M. Fontanazza,et al.  Uncertainty evaluation of design rainfall for urban flood risk analysis. , 2011, Water science and technology : a journal of the International Association on Water Pollution Research.

[33]  H. Joe.  Families of $m$-variate distributions with given margins and $m(m-1)/2$ bivariate dependence parameters , 1996 .

[34]  Roberto Guercio,et al.  Instantaneous residential water demand as stochastic point process , 1970 .

[35]  Andrea Petroselli,et al.  Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation , 2012 .

[36]  John J. Boland,et al.  Forecasting Urban Water Use: the Iwr-Main Model , 1989 .

[37]  Zoran Kapelan,et al.  Adaptive water demand forecasting for near real-time management of smart water distribution systems , 2014, Environ. Model. Softw..

[38]  Roger M. Cooke,et al.  Probability Density Decomposition for Conditionally Dependent Random Variables Modeled by Vines , 2001, Annals of Mathematics and Artificial Intelligence.

[39]  Gabriele Freni,et al.  Multivariate Statistical Analysis for Water Demand Modeling , 2014 .

[40]  Valerie Isham,et al.  Some models for rainfall based on stochastic point processes , 1987, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[41]  P. E. O'Connell,et al.  Stochastic point process modelling of rainfall. I. Single-site fitting and validation , 1996 .

[42]  J. C. van Dijk,et al.  Simulating Nonresidential Water Demand with a Stochastic End-Use Model , 2013 .

[43]  C. De Michele,et al.  Analytical calculation of storm volume statistics involving Pareto‐like intensity‐duration marginals , 2004 .

[44]  M. Bakker,et al.  A fully adaptive forecasting model for short-term drinking water demand , 2013, Environ. Model. Softw..

[45]  Ni-Bin Chang,et al.  System dynamics modeling for municipal water demand estimation in an urban region under uncertain economic impacts. , 2011, Journal of environmental management.

[46]  Gianfausto Salvadori,et al.  Frequency analysis via copulas: Theoretical aspects and applications to hydrological events , 2004 .

[47]  Vicente Juan Garcia,et al.  Stochastic Model to Evaluate Residential Water Demands , 2004 .

[48]  S. Miaou,et al.  Daily Water Use in Nine Cities , 1986 .

[49]  B. Bobée,et al.  Multivariate hydrological frequency analysis using copulas , 2004 .

[50]  C. De Michele,et al.  A Generalized Pareto intensity‐duration model of storm rainfall exploiting 2‐Copulas , 2003 .

[51]  Ashu Jain,et al.  Hybrid neural network models for hydrologic time series forecasting , 2007, Appl. Soft Comput..