Abstract
In this article, a model for forecasting water demands over a 24-h time window using solely a pair of coefficients whose value is updated at every forecasting step is presented. The first coefficient expresses the ratio between the average water demand over the 24 h that follow the time the forecast is made and the average water demand over the 24 h that precede it. The second coefficient expresses the relationship between the average water demand in a generic hour falling within the 24-h forecasting period and the average water demand over that period. These coefficients are estimated using the information available in the weeks prior to the time of forecasting and, therefore, the model does not require any actual calibration process. The length of the time series necessary to implement the model is thus just a few weeks (3–4 weeks) and the model can be parameterized and used without there being any need to collect hourly water demand data for long periods. The application of the model to a real-life case and a comparison with results provided by another model already proposed in the scientific literature show it to be effective, robust, and easy to use.
Highlights
Water demands represent the driver of water distribution systems, and reliable demand forecasting represents a valid aid in simulating and managing such systems
If the forecasting time t corresponds to an hour of a holiday falling on a weekday, the moving window will be shorter than n weeks; if the forecasting time t corresponds to an hour of a weekday, but a holiday has fallen on the same type of weekday in the n previous weeks, that day cannot be included in the set S, making it necessary to lengthen the series by going back an additional week
D t over the K = 24 h following the time t still estimated as provided in Equation (2), with αt estimated f or by means of Equation (5)—the hourly water demand Qt+k for the hour corresponding to t+ k can be estimated using Equation (3), but in this case the coefficients βt,k will be estimated on the basis of the data recorded for the forecasted hour corresponding to t + k on the same holiday in the m previous years
Summary
Water demands represent the driver of water distribution systems, and reliable demand forecasting represents a valid aid in simulating and managing such systems. If the forecasting time t corresponds to an hour of a holiday falling on a weekday, the moving window will be shorter than n weeks; if the forecasting time t corresponds to an hour of a weekday, but a holiday has fallen on the same type of weekday in the n previous weeks, that day cannot be included in the set S, making it necessary to lengthen the series by going back an additional week Having clarified these points, the coefficient αt can be estimated in the following manner: obs 1 sn D s j αt =. A numerical example of estimation of the coefficients αt and βt,k is provided in Appendix A
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