**1. Introduction**

While water scarcity has become a key concern worldwide, it is particularly so in arid and semiarid regions with limited potable water sources. In designing water distribution systems (WDS), engineers have typically used a "fixture unit" method, which considers the sum of fixture unit demands, facility types, and socioeconomic factors to determine peak de‐ mand. However, this overestimates the actual peak demand by as much as 100% [1]. Due to various uncertainties, including those associated with demand, engineers often include large safety factors when designing WDS. Given that WDS rely mainly on regional energy and resources, an overdesigned system can have environmental impacts that will appear in region(s) beyond the jurisdictional boundaries of the system. While short-term demand forecasts are critical to a WDS daily operations [2], long-term forecasts are required for future planning and management of the systems. In providing an accurate estimate of water demand, a robust demand-forecasting model assists managers in designing a more envi‐ ronmentally sustainable WDS and in managing available water resources more efficiently. When coupled with a water demand management strategy, such models can help manag‐ ers overcome operational problems (e.g., low pressure during peak demands) and issues related to asset management (e.g., nonreplacement of assets or replacement by lower capacity assets reaching the end of their economic life). It has been estimated that a wellpredicted monthly average demand might be up to 400% lower than peak demands that cause low pressure; however, a more realistic model can enhance resource management and operating systems. This will eventually lead to significant savings for water and energy (for running pumps, treatment plants, etc.) industries. Considering weather conditions and population, the prime objective of the present study was to develop a predictive model for monthly average water demand. While the present study proposed a generic framework that could be easily adjusted for any specific case, the City of Kelowna (British Columbia, Canada) was employed as a test case.

### **2. Literature review**

Water demand varies greatly both regionally and seasonally. Increasing urbanization and industrialization as well as emerging issues such as shifting weather patterns and population growth have significant impacts on water demand. The main components in demand predic‐ tion are the explanatory variables and time scales used. Selecting explanatory variables for a predictive model depend on the desired time scale and the availability of data. Simple models using very few explanatory variables have shown promising accuracy for short-term predic‐ tion [3, 4]. In general, the explanatory variables affecting water demand are of two types: weather (e.g., temperature, relative humidity, and rainfall) and socioeconomic (e.g., popula‐ tion and income). Weather conditions affect short-term prediction while their socioeconomic counterparts can affect long-term predictions [5–7]. As has been highlighted by significant worldwide changes in climate, both in terms of weather conditions and global warming, water availability is prone to great uncertainty [8]. Therefore, the impact of evolving weather conditions on long-term water demand predictions should receive greater attention. Further‐ more, researchers who have considered weather conditions in short-term water demand prediction have established that it is not feasible to feed online automated WDS with real time weather information [9]. As a result, limited studies have considered weather conditions in their demand forecasting models [10–12]. **Table 1** summarizes the relevant literature. Tem‐ perature, precipitation, pan evaporation, and number of days since the last rainfall were used in a forecasting model [13]. Another study used temperature, relative humidity, rainfall, wind speed, and air pressure as weather parameters in their hourly water demand model for Sao Paulo, Brazil [12]. **Table 1** shows the previous researchers did not consider socioeconomic and weather conditions simultaneously since their effects are highly dependent on the forecast's time scale. Traditionally, WDS utilities have used historical patterns as explanatory variables in predicting future water demands. Scarce water reserves and the rapid increase in urbani‐ zation have raised awareness and led to implementation of statistical approaches. Multiple linear regression (MLR) and time series were the most popular techniques used in the early stages of demand forecasting [6]. While MLR has been widely used to better understand the determinants of water demand [14–18], its major drawback is the fact that it considers linear relationships among variables and water demand, such relationships are nonlinear by nature. Time series have been introduced along with regression as methods for demand forecasting [10, 19]. Due to the common belief that they can deal with complex systems [20], artificial neural networks (ANNs) have been widely applied in water demand forecasting [21–23, 2]. Com‐ paring regression, univariate time series, and ANN models, one study found ANN models drawing on standard rainfall and maximum temperature data could better predict weekly water demand than other models [6]. Similarly, drawing on temperature and rainfall data in their forecasting models, researchers concluded that ANN models provided more reliable forecasts for peak weekly demand than time series and simple and multiple linear regressions [22]. Results of another study showed ANN models performed better for hourly forecasts, whereas regression models were more accurate in forecasting daily demand [23]. To improve the accuracy and robustness of demand forecasting models, hybrid models combining or modifying ANN, MLR, and time series techniques have been tested [24–27]. However, application of nonlinear regression in demand forecasting has remained limited to studies using support vector machines (SVMs) [28–30] and training nonlinear relationships through linear regression models [6, 31]. The present study compares gene expression programming (GEP) and SVM nonlinear approaches. Inspired by Darwin's theory of evolution, GEP was recently proposed in engineering disciplines to optimize the structure of input variables fed into predictive models [32]. Being a self-learning algorithm, GEP has several advantages over conventional predictive models. GEP defines individual block structures (input variables, response, and function sets) and selects the optimized operating functions and multipliers through the process of learning algorithms. Results of one study indicated GEP models outperformed traditional linear models in the field of hydrology [32]. Since weather informa‐ tion is one of the major determinants of water demand, this research employed GEP to develop a robust and accurate demand-forecasting model.

**1. Introduction**

100 Water Stress in Plants

Canada) was employed as a test case.

**2. Literature review**

While water scarcity has become a key concern worldwide, it is particularly so in arid and semiarid regions with limited potable water sources. In designing water distribution systems (WDS), engineers have typically used a "fixture unit" method, which considers the sum of fixture unit demands, facility types, and socioeconomic factors to determine peak de‐ mand. However, this overestimates the actual peak demand by as much as 100% [1]. Due to various uncertainties, including those associated with demand, engineers often include large safety factors when designing WDS. Given that WDS rely mainly on regional energy and resources, an overdesigned system can have environmental impacts that will appear in region(s) beyond the jurisdictional boundaries of the system. While short-term demand forecasts are critical to a WDS daily operations [2], long-term forecasts are required for future planning and management of the systems. In providing an accurate estimate of water demand, a robust demand-forecasting model assists managers in designing a more envi‐ ronmentally sustainable WDS and in managing available water resources more efficiently. When coupled with a water demand management strategy, such models can help manag‐ ers overcome operational problems (e.g., low pressure during peak demands) and issues related to asset management (e.g., nonreplacement of assets or replacement by lower capacity assets reaching the end of their economic life). It has been estimated that a wellpredicted monthly average demand might be up to 400% lower than peak demands that cause low pressure; however, a more realistic model can enhance resource management and operating systems. This will eventually lead to significant savings for water and energy (for running pumps, treatment plants, etc.) industries. Considering weather conditions and population, the prime objective of the present study was to develop a predictive model for monthly average water demand. While the present study proposed a generic framework that could be easily adjusted for any specific case, the City of Kelowna (British Columbia,

Water demand varies greatly both regionally and seasonally. Increasing urbanization and industrialization as well as emerging issues such as shifting weather patterns and population growth have significant impacts on water demand. The main components in demand predic‐ tion are the explanatory variables and time scales used. Selecting explanatory variables for a predictive model depend on the desired time scale and the availability of data. Simple models using very few explanatory variables have shown promising accuracy for short-term predic‐ tion [3, 4]. In general, the explanatory variables affecting water demand are of two types: weather (e.g., temperature, relative humidity, and rainfall) and socioeconomic (e.g., popula‐ tion and income). Weather conditions affect short-term prediction while their socioeconomic counterparts can affect long-term predictions [5–7]. As has been highlighted by significant worldwide changes in climate, both in terms of weather conditions and global warming, water availability is prone to great uncertainty [8]. Therefore, the impact of evolving weather


**Table 1.** Literature on water demand forecasting.
