Cross Correlation Analysis of Residential Demand in the City of Milford, Ohio

Estimating future demands with a high degree of accuracy in water distribution network design remains an elusive goal. The desired outcome is to match the design demands to the demands that are eventually "realized" in the built system. To this end, this paper explores the cross correlation between demands in an existing system in order to gain a better picture of the representative spatial and temporal patterns of design demands. The aim of the paper is to analyze the cross correlation in the residential demand data collected in the city of Milford, Ohio. More specifically, the paper begins to answer five important questions concerning the cross correlation of the Milford demand data: how strongly cross correlated are indoor, residential demands? How strongly correlated is the deterministic, diurnal component of residential demand? How strongly correlated is the random noise component of residential demand? To what extent does the choice of time step influence the strength of correlation between these 3 demand components? Does the correlation between these 3 demand components differ significantly between weekdays and weekends? To answer these questions, aperiodic regression model was used to isolate the deterministic and the random noise components from the residential demand data collected in Milford. Correlation indices were formulated to measure the cross correlation of residential demand, its deterministic, diurnal component, and its random noise component. The Milford results pointed to a number of preliminary findings: (1) both residential demand and its deterministic, diurnal component had a positive and moderate to high correlation, while the random noise component of demand had a low level of correlation for the cases investigated; (2) increasing the time step length (from 600 s to 3,600 s) did increase the strength of the correlation in residential demand and its deterministic, diurnal component. This suggests that a longer time step increases both the coherence in diurnal demand patterns and their synchronicity. It is unclear whether time step length had any influence on the correlation of the random noise component of demand; (3) both residential demand and its deterministic, diurnal component were more strongly correlated during weekend periods than during weekday periods. This finding suggests that weekend periods may be characterized by less erratic water use patterns between customers leading to more coherent and synchronous diurnal patterns. It is unclear whether the random noise component was influenced by day-of-week effects. The implications of these preliminary results are discussed in the context of extended period simulation (EPS) and water quality modeling as they pertain to cost-effective design. This paper was presented at the 8th Annual Water Distribution Systems Analysis Symposium which was held with the generous support of Awwa Research Foundation (AwwaRF).