Forecasting Hourly Water Demands With Seasonal Autoregressive Models for Real-Time Application

Consumer water demands are not typically measured at temporal or spatial scales adequate to support real-time decision making, and recent approaches for estimating unobserved demands using observed hydraulic measurements are generally not capable of forecasting demands and uncertainty information. While time series modeling has shown promise for representing total system demands, these models have generally not been evaluated at spatial scales appropriate for representative real-time modeling. This study investigates the use of a double-seasonal time series model to capture daily and weekly autocorrelations to both total system demands and regional aggregated demands at a scale that would capture demand variability across a distribution system. Emphasis was placed on the ability to forecast demands and quantify uncertainties with results compared to traditional time series pattern-based demand models as well as nonseasonal and single-seasonal time series models. Additional research included the implementation of an adaptive-parameter estimation scheme to update the time series model when unobserved changes occurred in the system. For two case studies, results showed that (1) for the smaller-scale aggregated water demands, the log-transformed time series model resulted in improved forecasts, (2) the double-seasonal model outperformed other models in terms of forecasting errors, and (3) the adaptive adjustment of parameters during forecasting improved the accuracy of the generated prediction intervals. These results illustrate the capabilities of time series modeling to forecast both water demands and uncertainty estimates at spatial scales commensurate for real-time modeling applications and provide a foundation for developing a real-time integrated demand-hydraulic model.