# Overview, Comparative Assessment and Recommendations of Forecasting Models for Short-Term Water Demand Prediction

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## Abstract

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## 1. Introduction

- explaining day-to-day demand variations
- minimising the operating cost of pumping stations
- pinpointing possible network failures (e.g., water leaks and pipe bursts)
- helping utilities plan and manage water demands for near-term events
- optimizing daily operations of the infrastructure (e.g., pump scheduling, control of reservoirs volume, pressure management, and water conservation program)

## 2. Overview of STWD Forecasting Methods

#### 2.1. UTS Forecasting Methods

#### 2.2. Time Series Regression (TSR) Forecasting Methods

#### 2.3. Artificial Neural Network (ANN) Forecasting Methods

#### 2.4. Hybrid Forecasting Methods

## 3. Presentation and Discussion of Results

## 4. Recommendations of STWD Forecasting Models and Future Work

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Forecasts generated using (

**a**,

**b**) AR model and (

**c**,

**d**) MA model. The best model orders, AR(p = 2) and MA(q = 3), were determined based on Akaike information criterion (AIC) computation [40]. MAPE: mean absolute percentage error; NS: Nash–Sutcliffe; RMSE: root mean square error.

**Figure 3.**Forecasts generated using (

**a**,

**b**) ARMA model and (

**c**,

**d**) ARMAX model. Using AIC, the best model orders are ARMA(p = 1, q = 1) and ARMAX(p = 1, q = 1, b = 1).

**Figure 4.**Forecasts generated using (

**a**,

**b**) FFBP-NN model and (

**c**,

**d**) Hybrid model. The hybrid forecast was obtained by the combined forecast from ARMA and FFBP-NN.

**Figure 5.**Comparative assessments of the STWD forecasting models using (

**a**) RMSE; (

**b**) MAPE; and (

**c**) NS. (

**d**) Estimated quality of AR, MA, ARMA, ARMAX, and FFBP-NN using AIC value.

**Table 1.**Brief summary of short-term water demand (STWD) forecasting methods and models. UTS: univariate time series; MA: moving average; AR: autoregressive; ARIMA: autoregressive integrated moving average; ARMA: autoregressive-moving average; SARIMA: seasonal ARIMA; TSR: time series regression; MNLR: multiple and nonlinear regression; ARMAX: ARMA with exogenous variable; MLR: multiple linear regression; ARIMAX: ARIMA with exogenous variable; ANN: artificial neural network; FFBP-NN: feed-forward back-propagation neural network; GRNN: generalized regression neural network; RBNN: radial basis neural network; DAN2: dynamic artificial neural network; GARCH: generalized autoregressive conditional heteroskedasticity.

Forecasting Methods and Models | Quantitative Assessment of Forecast Accuracy | Forecast Purpose |
---|---|---|

UTS models [18,27,29]: MA, AR, ARIMA, exponential smoothing, ARMA, SARIMA | It can exhibit more complex profiles. However, it does not account for the effect of exogenous variables (e.g., weather data or price) [11]. | Useful for short-term operational forecasts (i.e., to minimise the operating cost of pumping stations, etc.) |

TSR models [1,25,26]: MNLR, ARMAX, MLR and ARIMAX | TSR models produce forecasts on the basis of the relationship between water demand and its determinants (e.g., weather data, income, demographics) [19]. | Useful for better prediction of daily water demand [24]. Relevant for setting water rates, revenue forecasting, and financial planning exercises. |

ANN models: FFBP-NN, GRNN, RBNN, DAN2 [5,35] | Used with TSR models [1,24,25,26,27], with UTS models [27], or with both UTS and TSR models [5,28,29]. According to [11], ANN outperforms UTS and TSR models. However, the results of [24,25] were inconclusive. | Useful for a better prediction of peak daily water demand. To inform optimal operating policy as well as pumping and maintenance scheduling. |

Hybrid models: FFBP-NN and AR [36], Holt–Winters, ARIMA, and GARCH [37], Fuzzy logic and AR [38] | Different forecasting models are able to capture different aspects of the information available for prediction [11]. As a result, leading to better forecasting performance [33,36] | Useful for real-time, near-optimal control of water distribution systems (WDS) [6]. Necessary for operational purposes [33,36]. |

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**MDPI and ACS Style**

Anele, A.O.; Hamam, Y.; Abu-Mahfouz, A.M.; Todini, E.
Overview, Comparative Assessment and Recommendations of Forecasting Models for Short-Term Water Demand Prediction. *Water* **2017**, *9*, 887.
https://doi.org/10.3390/w9110887

**AMA Style**

Anele AO, Hamam Y, Abu-Mahfouz AM, Todini E.
Overview, Comparative Assessment and Recommendations of Forecasting Models for Short-Term Water Demand Prediction. *Water*. 2017; 9(11):887.
https://doi.org/10.3390/w9110887

**Chicago/Turabian Style**

Anele, Amos O., Yskandar Hamam, Adnan M. Abu-Mahfouz, and Ezio Todini.
2017. "Overview, Comparative Assessment and Recommendations of Forecasting Models for Short-Term Water Demand Prediction" *Water* 9, no. 11: 887.
https://doi.org/10.3390/w9110887