Cross Correlation of Demands in Water Distribution Network Design Yves Filion 1 ; Barry Adams, M.ASCE 2 ; and Bryan Karney, M.ASCE 3 Abstract: The aim of water distribution design is to size and configure a system so that it meets existing and future demands while providing pressures above a minimum level for service and fire protection. Extended period simulation EPS is used in design to determine network pressures under varied diurnal demand patterns. In EPS, diurnal demands are almost invariably assumed to change in unison, or in statistical terms, to be strongly correlated in space. This paper first tests this common assumption by investigating the extent to which cross correlation in demand affects the mean and standard deviation of pressure heads in water networks, and then investigates how cross correlated demands can influence capital costs in network design. Preliminary findings from two examples indicate that the standard deviation of pressure head and capital costs can be sensitive to the level of cross correlation between nodal demands. Thus a realistic assessment of cross correlation in demand can lead to a more economical design. DOI: 10.1061/ASCE0733-94962007133:2137 CE Database subject headings: Water distribution systems; Stochastic processes; Correlation; Design. Introduction Modeling current and future water demand remains the most chal- lenging activity in water distribution system design. To facilitate the process somewhat, geographic information systems GIS are increasingly being co-opted to assign water demand to network nodes based on user classifications e.g., residential, commercial, industrial, institutional, etc.. When data on individual users is scarce, it is common to assign identical diurnal demand curves to all users of the same type. For example, all residential water users might be assigned a diurnal curve characterized by large peaks at the start and end of the work day, with slack periods during the early morning and mid-afternoon Fig. 1. Similarly, all commer- cial users are assigned a diurnal curve that rises and falls sharply, and that is flat during the workday period Fig. 1. In reality, each house, business, manufacturing plant, etc. has a unique diurnal curve Boulos et al. 2004 that reflects the specific water needs and preferences of that user. Recent studies have shown that residential water demand makes up the majority of water use in an urban water distribution network. Billings and Jones 1996 found that at the national level, residential demand accounts for 50–60% of total municipal water use in the United States. Studies by Flack 1982 and Rafte- lis Financial Consultants et al. 2000 found that residential water use can be as high as 75% in some systems. These statistics imply that the residential user type, and its diurnal pattern, often domi- nates the overall diurnal demand variation in many network mod- els. This regime creates a situation in which the majority of nodal demands in a network model are synchronous. In statistical terms, nodal demands in a network model are often perfectly correlated in space. Applying a single diurnal pattern to residential users in a net- work model implies that residential users—and thus the majority of users—react simultaneously and in exactly the same way to normal and peak demand conditions. In real systems, users re- spond to normal and peak conditions e.g., hot summer day based on their particular preferences, social habits, financial con- straints, etc. which are partially independent of the preferences of others. Most of the time, users have little information about what is happening elsewhere or about the water-consumption patterns of others. Together, all these considerations imply that demands at individual consumption points in real water distribution networks are imperfectly correlated under normal and peak conditions. The term “imperfectly correlated” implies that demand pairs are not exactly synchronous. The aim of this paper is to explore and partly challenge the common design assumption that most users draw water from a network in accordance with a single diurnal pattern, or in statis- tical terms, that demands are perfectly correlated in space during normal and peak conditions. Specifically, the paper explores to what extent cross correlation between demands influences the hy- draulic performance of a system, namely in the mean and stan- dard deviation of pressure head. This analysis is directed towards large systems i.e., transmission and network trunk mains where municipal demands dominate the design, and where fire flow con- siderations play only a minor role fire flows are thus not consid- ered in this paper. The second objective is to investigate to what extent cross correlated demands influence the pipe cost of a net- work to achieve a desired level of hydraulic reliability. Indeed, a clearer picture of the spatial correlation between pairs of demands at the design stage can lower network costs. It thus follows that 1 Assistant Professor, Dept. of Civil Engineering, Queen’s Univ., Kingston, Canada K7L 3N6. E-mail: yves.filion@civil.queensu.ca 2 Professor, Dept. of Civil Engineering, Univ. of Toronto, Toronto, Canada M5S 1A4. E-mail: adams@ecf.utoronto.ca 3 Professor, Dept. of Civil Engineering, Univ. of Toronto, Toronto, Canada M5S 1A4 corresponding authors. E-mail: karney@ ecf.utoronto.ca Note. Discussion open until August 1, 2007. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and pos- sible publication on May 7, 2004; approved on November 14, 2005. This paper is part of the Journal of Water Resources Planning and Manage- ment, Vol. 133, No. 2, March 1, 2007. ©ASCE, ISSN 0733-9496/2007/ 2-137–144/$25.00. JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT © ASCE / MARCH/APRIL 2007 / 137 J. Water Resour. Plann. Manage. 2007.133:137-144. Downloaded from ascelibrary.org by Toronto University Of on 10/04/12. For personal use only. No other uses without permission. Copyright (c) 2012. American Society of Civil Engineers. All rights reserved.