# A Critical Review of Short-Term Water Demand Forecasting Tools—What Method Should I Use?

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## Abstract

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## 1. Introduction

## 2. Systematic Literature Review: Methodology

## 3. Predictive Methods and Validation

#### 3.1. Impact of Exogenous Factors in Water Demand Models

- Climatic or weather conditions (e.g., temperature, humidity, and precipitation): There is almost an evident correlation between weather and water use, and often this is co-founded to customer behaviour and a general seasonality effect on outdoor activity. However, the exposure to severe weather periods will also have a significant impact on the water demand. Climatic variables are among the most used, along with historical past water consumption, and they have been considered in many studies. For example, Brentan et al. [15] examined the correlation between weather factors with water demand and showed that three factors, temperature, relative humidity, and hour of the day, are the most relevant variables for forecasting water demand. Moreover, Hu et al. [16] used temperatures, dew point, humidity, wind speed, and atmospheric pressure as input variables in the water demand forecasting model.
- Economic inputs (e.g., water price, billing, and income): One of the reasons why economic factors, such as price, can be naturally considered for water demand forecasting is due to the fact that a higher price may lead to lower consumption [14]. In some studies, these factors have been considered too. For example, de Maria André and Carvalho [17] showed that some factors, including water price and household income, have a positive effect on water demand, since an increase in these variables will increase water demand.
- Social-demographic situation (e.g., population, household size, and occupants’ ages) and other household properties (e.g., house type and property value): In this regard, Hussien et al. [18] investigated the effect of social-demographic factors, such as the number of children, adult male members, adult female members, and elderly household occupation, as well as some physical property factors, such as household size, household type, the total built-up area of all floors, garden area per household, number of rooms, and number of floors, on per capita water consumption. Additionally, Bennett et al. [19] has introduced the number of adults, children, and teenagers in a household as independent variables for a model based on neural networks.
- Geographical factors (e.g., urban density, and type of location): In the literature, geographical factors have been shown to have an impact on forecasting water demand, and they should be considered further for efficient water supply planning and management [20]. One of the main examples including geographical factors for water demand forecasting is the work of Bao and Chen [21]. They used spatial econometric models to analyse the influencing factors in water consumption efficiency and found that urbanisation level is one of the most important covariables affecting water consumption among the socio-economic and eco-environmental indicators. Among the more relevant works that include GFs in the methodology development for water demand forecasting, Benítez et al. [22] considered the type of location, including the city centre site, the production site (industrial), and the residential site (suburb) to develop predictive models for water demand.
- Technological factors (e.g., smart meters, sensors, and data loggers): Smart meters are the most widely used technological factor among the others. Hence, they have been included in multiple research endeavours on water demand forecasting models. In these studies, users’ consumption information is collected hourly or even instantaneously through such smart meters and used as consumption input data in the forecasting models [13,23]. Other technology factors, such as high-efficiency fixtures and appliances [24] or alarming display monitors [25], have been shown to also have an impact on water consumption. However, such factors have rarely been used in water demand forecasting models.
- Calendar variables (weekdays, weekends, holidays, and special events): Although calendar information is inherently present in other factors, such as weather, socio-demographic, and geographic factors, it is a good practice to specifically consider its effect on water demand models. Calendar variables can be considered as information at a finer granularity than other related factors, having the potential to increase the accuracy of any predictive method. Among the studies that have specifically considered calendar factors, we highlight the works of Pesantez et al. [13]; Benítez et al. [22]; Antunes et al. [12]; Hu et al. [16]; Brentan et al. [15]; Liu et al. [26]; and Herrera et al. [9].

#### 3.2. Predictive Methods for Forecasting Urban Water Demand

#### 3.2.1. Artificial Neural Networks

#### 3.2.2. Support Vector Machines

#### 3.2.3. Traditional Time Series Analysis

#### 3.2.4. Metaheuristic Algorithms

#### 3.2.5. Regression

#### 3.2.6. Hybrid Methods

#### 3.3. Model Validation

^{2}), mean absolute percentage error (MAPE), mean absolute error (MAE), and Nash–Sutcliffe efficiency (NSE) indices. The lower the RMSE, the better the fit of the model to the observed data. Note that RMSE is scale dependent and it is suitable, in principle, just to compare models using the same dataset. The R

^{2}is a non-dimensional number between 0 and 1, being the proportion of the observed variability explained by the predictive model. Hence, the closer R

^{2}is to 1, the better the model performance. MAPE considers the error in terms of proportions or percentages, also being a non-dimensional measure. The lower the MAPE value, the better the forecast. The MAE criterion is similar to RMSE but considering the absolute value. Hence, MAE will be more tolerant than RMSE to individual errors in the summation since their values are not squared. NSE represents the gain of using the model vs. using the mean. NSE = 1 is associated with a perfect fit. NSE = 0 indicates that the model has a similar performance as the mean of the historical time series. Abbreviations includes a full list of the validation indicators in the literature.

#### 3.4. Peaks of Water Demand

## 4. Future Directions for Short-Term Water Demand Forecasting

#### 4.1. Upcoming Challenges for Water Demand Forecasting

#### 4.2. So, What Method Should I Use?

- Identification of the temporal scope and (exogenous) factors of influence at each particular use case.
- Objective of the analysis: average vs. peak demand and anomaly detection vs. future prediction.
- Technology available: Requirement of near-real-time models. Solutions for multidimensional data streams.

#### 4.3. Recommended Software: R, Python, Julia

- The R environment for statistical computing is a free software platform used for statistics and data mining [110]. R is widely used for time-series analysis and forecasting; such is the case of the development of predictive models for water demand. The R community is active in providing programming support and in the number and up-to-date quality of the so-called R packages, which are software libraries developed to run specific methods and data analysis. Among them, they highlight the package “neuralnet” to work with ANN [111], “e1071” to work with SVR [112], or “randomForest” to work with RF [113]. An additional advantage of R working with water demand comes thanks to matching data analyses to the Epanet-toolkit R packages “epanetReader” [114] and “epanet2toolkit” [115].
- Python is an interpreted, general-purpose programming language that can provide a multiplatform solution for scientific computing [116]. This is thanks to Python libraries such as “pandas” and “numpy” for data manipulation and basic analysis and “scikit-learn” [117] for machine and statistical learning software development (including functions to work with ANN, SVR, RF, and many more). Python also has the backup of a huge community supporting up-to-date libraries, creating an ideal framework for research and software development. Importantly, there is a Python library to run the Epanet toolkit called “Epanettools” and a library called “WNTR” that is an Epanet-compatible Python library for the simulation and analysis of water distribution systems resilience, developed by the Sandia National Laboratories and the US Environmental Protection Agency (EPA) [118].
- Julia is a high-level programming language that naturally supports concurrent, parallel, and distributed computing [119]. This means that, although Julia is a general-purpose language, it was originally designed for machine learning and statistical programming. Julia is a quite new language, and it is still far from the popularity of R or Python. However, there is foreseen a brilliant future for Julia given its properties of speed, using just-in-time compilers making it as fast as low-level compiled languages such as C. In addition, Julia can be executed in R, Latex, Python, and C, while Julia can also wrap R and Python code, thanks to the libraries “RCall” and “PyCall”, respectively.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

Mean Squared Error | MSE | Comparing with benchmark | B |

Root Mean Squared Error | RMSE | Lagrange multipliers tests | LM |

Relative Root Mean Square Error | RRMSE | Moran-I test | MI |

Normalized Root Mean Square Error | NRMSE | Normal Mean Square Error | NMSE |

Mean Absolute Percentage Error | MAPE | Pearson coefficient | r |

Mean Absolute Error | MAE | Percentage deviation in peak | Pdv |

Coefficient of Determination | R2 | Persistence Index | PI |

Correlation coefficient | CC | Fraction Out of Bounds | FOB |

Nash–Sutcliffe coefficient | NSE | Mean Bias Error | MBE |

Relative Error | RE | Mean absolute scaled error | MASE |

Absolute Relative Error | ARE | Standard Error Prediction | SEP |

Average Absolute Relative Error | AARE | Variance accounted for | VAF |

Average Absolute Error | AAE | Akaike’s Information Criterion | AICc |

Maximal Root Error | MaxRE | Standard Deviation | SDe |

Standard deviation of the absolute relative error | SDARE | Accuracy | Ac |

Mean Absolute Relative Error | MARE | Gini coefficient | GINI |

Mean Relative Error | MRE | Theil’s coefficients | UI & UII |

Efficiency Index | E | Average prediction interval width | AWPI |

Threshold statistic | Ts | Average empirical coverage rate | ECPI |

Descriptive accuracy metrics and formal statistical tests | ST | Negatively-oriented interval score | NOIS |

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**Figure 3.**Main methodologies used in water demand forecasting models and their frequency of use in the literature.

**Figure 4.**Frequency of the validation indicators found in the literature on water demand forecasting.

Journal Name | References | Publisher | Impact Factor (5 year) | Best Quartile |
---|---|---|---|---|

Procedia Engineering | [12] | Elsevier | - | - |

Water Resources Planning and Mgmt. | [11] | ASCE | 3.563 | Q2 |

Water | [8] | MDPI | 3.229 | Q2 |

Environmental Modelling & Software | [7] | Elsevier | 6.036 | Q1 |

Hydrology | [6] | Elsevier | 6.033 | Q1 |

Water Resources Management | [4] | Springer | 3.868 | Q2 |

Water Supply | [3] | IWA Publishing | 1.152 | Q4 |

Water Resources Research | [2] | Wiley | 6.006 | Q1 |

Desalination | [2] | Elsevier | 9.189 | Q1 |

Sustainable Cities and Society | [2] | Elsevier | 7.308 | Q1 |

**Table 2.**Summary of factors affecting water consumption and short-term water demand forecasting models. The symbol ‘*’ means that the column feature is included in the revised literature (in rows).

Authors (Year) | Study Area | Measures of Accuracy | Time Periods | Methods | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Hourly and Less | Daily | Weekly | Monthly | TS | NN | R / RF | Hyb | SVM | MHA | LM | SD | Others | |||

Shirkouhi et al. [29] | Canada | RRMSE, MAPE, and NSE | * | * | * | * | * | ||||||||

Koo et al. [30] | Korea | RMSE, NRMSE, NSE, r, and Residual | * | * | * | * | |||||||||

Pandey et al. [31] | Spain and India | RMSE, MAE, and MAPE | * | * | * | * | * | ||||||||

Rezaali et al. [32] | Iran | RMSE, r, NSE, MAE, and MARE | * | * | * | * | * | ||||||||

Du et al. [33] | China | MAPE, MAPE of peaks, r, and explain variance score (EVS) | * | * | |||||||||||

Hu et al. [34] | China | MAE, RMSE, NSE, and r | * | * | * | ||||||||||

Al-Ghamdi [35] | Saudi Arabian | RMSE | * | * | |||||||||||

Salloom et al. [36] | China | MAPE | * | * | |||||||||||

Pesantez et al. [13] | United States | RMSE | * | * | * | * | * | ||||||||

Bata et al. [37] | Canada | MAPE and NRMSE | * | * | * | * | * | ||||||||

Xenochristou et al. [38] | UK | MAPE, MSE, and R2 | * | * | |||||||||||

Yousefi et al. [39] | Canada | CC, RMSE, and MAE | * | * | * | * | * | ||||||||

Pacchin et al. [40] | Italy | MAE and RMSE | * | * | * | ||||||||||

Villarin and Rodriguez-Galiano [41] | Spain | R2 and RMSE | * | * | |||||||||||

Perea et al. [42] | Spain | SEP and R2 | * | * | * | * | * | ||||||||

Maruyama and Yamamoto [43] | Japan | ARE | * | * | * | ||||||||||

Gharabaghi et al. [44] | Canada | MAPE, R2, VAF, AICc, and UI & UII | * | * | * | * | |||||||||

Banihabib and Mousavi-Mirkalaei [45] | Iran | RMSE, MARE, MaxRE, MBE, and R2 | * | * | * | ||||||||||

Benítez et al. [22] | Spain | MAPE, RMSE, and FOB | * | * | * | ||||||||||

Candelieri et al. [46] | Italy | MAPE | * | * | * | * | |||||||||

Hu et al. [16] | Not mentioned | MAE and MAPE | * | * | * | * | |||||||||

Kozłowski et al. [11] | Poland | R2 | * | * | |||||||||||

Antunes et al. [12] | Portugal | RMSE and NSE | * | * | * | * | * | ||||||||

Vijai and Sivakumar [2] | EU | RMSE, R2, MSE, and MAE | * | * | * | * | * | * | |||||||

Brentan et al. [47] | Brazil | SDe | * | * | * | ||||||||||

Sardinha-Lourenço et al. [48] | Portugal | R2 and MAPE | * | * | * | ||||||||||

Shabani et al. [49] | Canada | MAE, RMSE, R2, and MAPE | * | * | * | * | |||||||||

Pacchin et al. [50] | Italy | RMSE and MAE | * | * | |||||||||||

Oliveira et al. [51] | Brazil | MAPE and RMSE | * | * | * | * | |||||||||

Gagliardi et al. [52] | UK | NSE | * | * | * | ||||||||||

Brentan et al. [15] | Brazil | RMSE, MAE, and R2 | * | * | * | * | |||||||||

Candelieri [23] | Italy | MAPE | * | * | * | ||||||||||

Tiwari et al. [3] | Canada | R2, RMSE, Pdv, MAE, and PI | * | * | * | ||||||||||

Arandia et al. [53] | Ireland | RMSE, NRMSE, and MAPE | * | * | * | ||||||||||

Walker et al. [54] | Greece | CC and Sde | * | * | * | * | |||||||||

Candelieri et al. [55] | Italy | MAPE | * | * | * | ||||||||||

Hutton and Kapelan [56] | UK | MAPE | * | * | |||||||||||

Al-Zahrani and Abo-Monasar [57] | Saudi Arabia | MAPE and R2 | * | * | * | ||||||||||

Vijayalaksmi and Babu [58] | India | RMSE, MAPE, and CC | * | * | |||||||||||

Tiwari and Adamowski [59] | Canada | R2, RMSE, Pdv, MAE, and PI | * | * | * | * | * | ||||||||

Bakker et al. [60] | Netherlands | RE, MAPE, and R2 | * | * | * | * | |||||||||

Romano and Kapelan [61] | UK | MAPE and MSE | * | * | * | ||||||||||

Okeya et al. [62] | UK | MAE | * | * | * | ||||||||||

Bai et al. [63] | China | NRMSE, CC, and MAPE | * | * | * | * | |||||||||

Candelieri and Archetti [64] | Italy | MAPE | * | * | * | ||||||||||

Chen and Boccelli [65] | Not mentioned | AARE | * | * | |||||||||||

Alvisi and Franchini [66] | Italy | NSE and RMSE | * | * | * | * | |||||||||

Sampathirao et al. [67] | Spain | Average PMSE24, Average PRMSE24, and Number of Parameters | * | * | * | * | * | * | |||||||

Bennett et al. [19] | Australia | R2, ARE, AAE, RMSE, Mann–Whitney, Wilcoxon (MW), and p-value | * | * | |||||||||||

Liu et al. [26] | China | AARE | * | * | |||||||||||

Khan et al. [68] | Australia | Ac | * | * | * | * | |||||||||

Adamowski et al. [69] | Canada | R2, RMSE, RRMSE, and E | * | * | * | * | * | ||||||||

Azadeh et al. [70] | Iran | MAPE | * | * | * | * | |||||||||

Odan and Reis [71] | Brazil | MAE and r | * | * | * | ||||||||||

Herrera et al. [72] | Spain | RMSE and MAE | * | * | * | * | |||||||||

Herrera et al. [9] | Spain | RMSE and MAE | * | * | * | * | * | ||||||||

Adamowski and Karapataki [73] | Cyprus | R2, RMSE, AARE, and MaxARE | * | * | * | ||||||||||

Caiado [74] | Spain | MSE | * | * | |||||||||||

Wu and Yan [75] | United Kingdom | MSE, RMSE, MRE, and MaxRE | * | * |

**Table 3.**Summary of factors affecting water consumption and medium-term and long-term water demand forecasting models. The ‘*’ symbol means that the column feature is included in the revised literature (in rows).

Authors (Year) | Study Area | Measures of Accuracy | Time Periods | Methods | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Monthly | Quarterly | Yearly | TS | ANN | R/RF | Hyb | SVM | MHA | LM | SD | Others | |||

Shuang and Zhao [76] | China | MSE–MAE-R2 | * | * | * | * | ||||||||

Ristow et al. [77] | Brazil | MAPE | * | * | ||||||||||

Karamaziotis et al. [78] | Greece | MAE, MASE, RMSE, and MAPE | * | * | ||||||||||

Sanchez et al. [79] | United States | ST | * | * | * | |||||||||

Guo et al. [80] | China | B, RE, and MRE | * | * | ||||||||||

Rasifaghihi et al. [81] | Canada | Silhouette coefficient | * | * | * | * | ||||||||

Duerr et al. [82] | United States | RMSE, GINI, AWPI, ECPI, and NOIS | * | * | * | * | ||||||||

Sharvelle et al. [83] | United States | MRE, bias fraction (BIAS), and NSE | * | * | ||||||||||

Haque et al. [84] | Brazil | R2, RMSE, MARE, and NSE | * | * | ||||||||||

Shabani et al. [85] | Canada | R2 and RMSE | * | * | ||||||||||

Yousefi et al. [86] | Canada | R2, RMSE, and MAE | * | * | ||||||||||

Nassery et al. [87] | Iran | ME, MAE, MAPE, and RMSE | * | * | * | |||||||||

Altunkaynak and Nigussie [88] | Turkey | RMSE and NSE | * | * | * | * | ||||||||

Vani [89] | India | - | * | * | ||||||||||

Fullerton Jr et al. [90] | United States | B and ST | * | * | ||||||||||

Peña-Guzmán et al. [91] | Colombia | RMSE, AARE, and R2 | * | * | * | |||||||||

Shabani et al. [92] | Canada | R2, MAE, RMSE, and NSE | * | * | * | |||||||||

Shabri et al. [93] | Malaysia | RMSE, MAE, and CC | * | * | * | |||||||||

Kofinas et al. [94] | Greece | R2, MAPE, RMSE, and MAE | * | * | * | * | ||||||||

de Maria André and Carvalho [17] | Brazil | LM, Moran-I test, and R2 | * | * | * | * | ||||||||

Yang et al. [95] | Not mentioned | - | * | * | ||||||||||

Almutaz et al. [96] | Saudi Arabia | SDe | * | * | ||||||||||

Nasseri et al. [97] | Iran | B, NMSE, and R2 | * | * | * | * | * | |||||||

Qi and Chang [98] | United States | Compared with Real-world water demand data | * | * | ||||||||||

Firat et al. [99] | Turkey | AARE, NRMSE, and Ts | * | * | * | |||||||||

Varahrami [100] | Iran | RMSE, MAE, and MAPE | * | * | * | * | ||||||||

Mohamed and Al-Mualla [101] | Emirates | AARE, ARE, and SDARE | * | * | * |

**Table 4.**Advantages and disadvantages of the main categories for predictive methods in water demand forecasting.

Method | Data Requirements | Accuracy | Interpretability | Efficiency | Adaptability |
---|---|---|---|---|---|

ANN-like | High | High | Low | Low | Medium |

SVR-like | High | High | Medium | Low | Medium |

ARIMA(X) | Low | Low | High | High | Low |

Metaheuristics | High | Medium | Low | Low | Low |

Regression | Low | Medium | High | High | Low |

Hybrid | High | High | Medium | Medium | High |

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**MDPI and ACS Style**

Niknam, A.; Zare, H.K.; Hosseininasab, H.; Mostafaeipour, A.; Herrera, M.
A Critical Review of Short-Term Water Demand Forecasting Tools—What Method Should I Use? *Sustainability* **2022**, *14*, 5412.
https://doi.org/10.3390/su14095412

**AMA Style**

Niknam A, Zare HK, Hosseininasab H, Mostafaeipour A, Herrera M.
A Critical Review of Short-Term Water Demand Forecasting Tools—What Method Should I Use? *Sustainability*. 2022; 14(9):5412.
https://doi.org/10.3390/su14095412

**Chicago/Turabian Style**

Niknam, Azar, Hasan Khademi Zare, Hassan Hosseininasab, Ali Mostafaeipour, and Manuel Herrera.
2022. "A Critical Review of Short-Term Water Demand Forecasting Tools—What Method Should I Use?" *Sustainability* 14, no. 9: 5412.
https://doi.org/10.3390/su14095412