Effect of Time Step and Data Aggregation on Cross Correlation of Residential Demands

Abstract

End-use water demands are one of the most important and vexing inputs to a network hydraulic model. Accurate water demands are essential for meaningful network calibration, validation and simulation exercises as well as for design, analysis and performance assessment. However, assigning water use to network nodes is fraught with many difficulties, including questions about the demand magnitude, the temporal pattern and the cross (i.e., spatial) correlation. It is not unusual in practice to assume that, during extended period simulations, all demand nodes follow the same synchronized hourly demand pattern. In essence, the demands across the distribution system are often taken to be perfectly cross correlated in space. Clearly, the degree of cross correlation between nodal demands (if any exists) could have a profound effect on the results of subsequent hydraulic and water quality simulations. Despite the importance of the water use cross correlation issue, there has been relatively little work on this problem – perhaps due to a lack of field data. This paper seeks to quantify the degree of cross correlation that exists in 365,000 residential water demands collected from 21 single family homes in Milford, Ohio, during a seven month period. This collection of field data represents one of the most extensive high resolution records (one-second interval) of continuous residential water use ever assembled. In particular, the paper investigates two important research questions: (i) How does cross correlation between indoor water demands change with the level of spatial aggregation (e.g., two groups of five or ten homes)? (ii) How does cross correlation between water demands change with the averaging time step (i.e., one second, one minute, one hour, or longer)? This investigation offers empirical insights into the degree of cross correlation between water demands that exists in a small residential neighborhood, including a picture of how the cross correlation between demands is affected by changes in temporal averaging (time step) and spatial aggregation. Principal findings show that cross correlation tends to increase with an increase in spatial and temporal aggregation.