This paper presents a comparison of different short-term water demand forecasting models. The comparison regards six models that differ in terms of: forecasting technique, type of forecast (deterministic or probabilistic) and the amount of data necessary for calibration. Specifically, the following are compared: a neural-network based model (ANN_WDF), a pattern-based model (Patt_WDF), two pattern-based models relying on the moving-window technique (αβ_WDF and Bakk_WDF), a probabilistic Markov chain-based model (HMC_WDF) and a naïve benchmark model. The comparison is made by applying the models to seven real-life cases, making reference to the water demands observed over 2 years in district-metered areas/ water distribution networks of different sizes serving a different number and type of users. The models are applied in order to forecast the hourly water demands over a 24-h time horizon. The comparison shows that a) models based on different techniques provide comparable, mediumhigh forecasting accuracies, but also that b) short-term water demand forecasting models based on moving-window techniques are generally the most robust and easier to set up and parameterize.

This paper proposes a short-term water demand forecasting method based on the use of the Markov chain. This method provides estimates of future demands by calculating probabilities that the future demand value will fall within pre-assigned intervals covering the expected total variability. More specifically, two models based on homogeneous and non-homogeneous Markov chains were developed and presented. These models, together with two benchmark models (based on artificial neural network and naïve methods), were applied to three real-life case studies for the purpose of forecasting the respective water demands from 1 to 24 h ahead. The results obtained show that the model based on a homogeneous Markov chain provides more accurate short-term forecasts than the one based on a non-homogeneous Markov chain, which is in line with the artificial neural network model. Both Markov chain models enable probabilistic information regarding the stochastic demand forecast to be easily obtained.

In this paper, two models are set up in order to forecast hourly water demands up to 24 h ahead and are contrasted with each other. The first model (hereinafter referred to as the Patt model) is based on the representation of the periodic patterns that typically characterize water demands, such as seasonal and weekly patterns of daily water demands and daily patterns of hourly water demands. The second model is based on artificial neural networks (hereinafter referred to as ANN models). Both the models have been applied to three case studies, representing water distribution systems managed by HERA S.p.A., characterized by very different numbers of users served, and consequently very different average water demands, ranging from 900 L/s for the first case study (CS1) to about 8 L/s and1.5 L/s for the second (CS2) and third (CS3) case studies, respectively. The results show that in general, both the models, Patt and ANN, provide good accuracy for the CS1. The performances of both the models tend to decrease for CS2 and, particularly, for CS3. In particular, in the validation phase, the Patt model is more accurate than the ANN model for the CS1; for the CS2, the accuracy of the two models are very similar, and for the CS3 the accuracy of the ANN model is slightly higher than that of the Patt model.

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