Spatial correlation analysis of stochastic residential water demands

This paper investigates spatial correlations in stochastic residential water demands that follow a non-homogeneous Poisson Rectangular Pulse (PRP) process. This investigation provides preliminary insights into the cross-correlation structure of stochastic water demands at various levels of temporal-spatial aggregation. Analytical expressions for cross correlation of PRP water demands are established and corroborated numerically through Monte Carlo simulations. Results show that water use for homogeneous PRP random demands is uncorrelated at all levels of spatial and temporal aggregation. For non-homogeneous PRP water demands, however, cross correlation increases with increasing levels of spatial and temporal aggregation. In addition, analytical estimates of the correlation coefficient agree reasonably well with values computed from field observations. Findings will be used to establish an appropriate level of cross correlation between pairs of water demands at network nodes for a desired level of temporal-spatial aggregation.