Predicting the pulse of urban water demand: a machine learning approach to deciphering meteorological influences

Abstract

Objective

This study delves into the impact of urban meteorological elements—specifically, air temperature, relative humidity, and atmospheric pressure—on water consumption in Kamyaran city. Data on urban water consumption, temperature (in Celsius), air pressure (in hectopascals), and relative humidity (in percent) were used for the statistical period 2017–2023. Various models, including the correlation coefficient, generalized additive models (GAM), generalized linear models (GLM), and support vector machines (SVM), were employed to scrutinize the data.

Results

Water consumption increases due to the influence of relative humidity and air pressure when the temperature variable is controlled. Under specific air temperature conditions, elevated air pressure coupled with high relative humidity intensifies the response of water consumption to variations in these elements. Water consumption exhibits heightened sensitivity to high relative humidity and air pressure compared to low levels of these factors. During winter, when a western low-pressure air mass arrives and disrupts normal conditions, causing a decrease in pressure and temperature, urban water consumption also diminishes. The output from the models employed in this study holds significance for enhancing the prediction and management of water resource consumption.

Introduction

Addressing the escalating challenge of urban water scarcity and exploring sustainable management methods stands out as a crucial research imperative on a global scale today [1]. Climate change and heightened global resource utilization, particularly in arid regions like Iran, are contributing to escalating water tensions among various regions and cities. Simultaneously, the surge in urban population over recent decades has led to a doubling of the demand for water resources [2]. Access to water resources emerges as a fundamental challenge in urban management. According to studies, accurately predicting the water demand for a city relies significantly on meteorological variables, in addition to factors such as population, social dynamics, economic conditions, and technological aspects [3].

Water consumption is influenced by human factors like population and technology, but monthly and seasonal patterns depend on meteorological conditions, which drive medium-term fluctuations in consumption [4, 5]. Water scarcity in North America results from climate change and population growth, worsened by overexploitation of water resources. This is compounded by abundant fresh water alongside poor management practices [6].

The significance of meteorological variables in predicting urban water consumption has been underscored as crucial by various studies [7,8,9,10]. Studies have used machine learning methods like artificial neural networks (ANNs) to forecast water demand [9], specifically in relation to climatic factors. They primarily explored potential input variables, employing various statistical techniques to discern the optimal model input and to achieve precise predictions of future urban water demand, considering meteorological factors [11,12,13]. Seasonal climate variations influence water consumption differently throughout the year, with factors like humidity and evaporation affecting end-of-summer usage. Identifying these influences is crucial due to the complexity of urban water consumption pattern [14,15,16].

Effective and sustainable urban water management requires understanding meteorological variables’ identification and impact. Each region has its own water consumption patterns and should be investigated by advance modelling methods to provide an insight into the effects of environmental factors. Therefore, we investigated monthly and seasonal water consumption fluctuations, using Generalized Linear Models (GLM), Generalized Additive Models (GAM), and support vector machines (SVM) in Kamyaran, Iran.

Materials and methods

Data

This study utilized data encompassing urban water consumption, temperature (measured in Celsius), air pressure (measured in hectopascals), and relative humidity (measured in percentage) for the statistical period spanning from 2017 to 2023.

Statistical analysis

The study employed zero-order Pearson correlation to explore linear associations between meteorological variables and water consumption, and first-order partial correlation to assess distinct impacts. A GAM was used to examine non-linear responses. Additionally, GLM and SVM models were constructed to capture both linear and non-linear relationships. The simplex optimizer algorithm was applied to understand the additive and subtractive influences of independent variables.

GLM extends linear models, measuring relationships between variables via regression parameters and confidence intervals, based on provided formulas. The GLM model can be written as $\:g\left(\mu\:\right)=a+\sum\:{\beta\:}_{j}{x}_{j}$ where “g” is a link function from the exponential family, $\:\mu\:$ is the mean response, $\:\beta\:$ is the vector of regression coefficients and $\:x$ is the matrix of predictors.

GAMs are a nonparametric extension of GLMs [17]. GAMs allow the data to determine the shape of the response curve by $\:g\left(\mu\:\right)=a+{\sum\:}_{j=1}^{p}{f}_{j}\left({X}_{j}\right)$. In these models, it is assumed that the dependent variable has a distribution from the exponential family with mean $\:\mu\:=E\left(Y\right|{X}_{1},\dots\:,\:{X}_{p})$, which is linked to the independent variables (X_j) through the link function (g). In fact, GAMs extend the parametric form of the independent variables in the linear model to a nonparametric form.

Here, ${f_j}$ for $j=1,2, \cdots, \, p$are assumed to be unknown and smooth functions, and X_j are independent variables. Specifically, ${f_j}$is estimated from the data using advanced scatterplot smoothing techniques. GAM allows data to shape response curves unlike parametric models, replacing linear functions with smooth functions. These additive functions enable separate investigation of predictor variables’ effects, identifying nonlinear relationships [18, 19].

The SVMs are data-driven algorithms, used for classification and regression problems. SVMs create a hyperplane to maximize the margin between classes, utilizing support vectors for optimization [20]. SVR is used to describe regression [21] in the form of a least squares model. In this regard, there are two types of SVMs called SVM-ɛ and SVM-Nu, and in this study, the SVM-Nu approach is used. In machine learning models, the aim is to estimate the relationship between dependent variable and independent variables, minimizing error while maintaining smoothness.

The Simplex algorithm is a non-gradient search method for minimizing functions with continuous variables. It iteratively tests solutions until an optimal point is found, making no assumptions about the function’s nature [22, 23]. Therefore, in this approach, by applying the Simplex algorithm on the models produced by GLM and SVM-Nu, the simulated water consumption of each of these models was optimized.

Results and discussion

The long-term average of meteorological variables during summer for air temperature (°C), relative humidity (%), and air pressure (hPa) was 8, 60, and 892 respectively. The same for summer was 29, 20, and 880 respectively. Similarly for yearly was 18, 41, and 886.

The results from the Pearson correlation analysis and the nonlinear and significant impact of temperature, pressure, and relative humidity variables at a 99% confidence level on water consumption (depicted in Table 1) reveal a statistically significant relationship between the three meteorological variables and water consumption. Specifically, air temperature exhibits a direct relationship, while air pressure and relative humidity show an inverse relationship with the dependent variable. Continuing the investigation, the study explores the non-linear response of water consumption using the GAM for both individual and cumulative variables, employing the Poisson distribution and the log link function.

Table 1 Zero- and 1-degree correlation coefficient of meteorological variables with water consumption and results of individual and combined fitting of GAM model on meteorological variables against water consumption in Khorram Abad

Figure 1 depicts the nonlinear relationship between water consumption and temperature, humidity, and pressure individually and cumulatively. Individual analysis reveals varying responses compared to the combined state, notably opposite reactions to humidity. In the cumulative state, pressure influences increased consumption, moderated by temperature. However, controlling for humidity and temperature unveils nuanced reactions, with consumption initially increasing with pressure, then decreasing beyond 883 hectopascals. A pattern of increasing-stasis-increasing is observed concerning humidity. Changes in a 5-month moving average indicate an inverse correlation between temperature and pressure, mitigating summer temperature impacts on consumption.

Fig. 1

(a) Cumulative reaction of water consumption to temperature, (b) Separate reaction of water consumption to temperature, (c) Cumulative reaction of water consumption to pressure, (d) Separate reaction of water consumption to pressure, (e) Cumulative reaction of water consumption to relative humidity, (f) Separate reaction of water consumption to relative humidity

A 5-month moving average was applied to the time series to smooth seasonal fluctuations. Winter temperature changes have a larger impact on consumption, while summer sees mitigating effects from air pressure and humidity. Adaptive GAM and SVM models further analyze consumption reactions. Temperature increases correlate with consumption, especially in colder seasons below 11.15 °C, when humidity and air pressure are higher, indicating stronger temperature effects. (Fig. 2).

Fig. 2

Five-month moving average: temperature, pressure, relative humidity

The reaction of water consumption to air temperature, pressure, and humidity in annual status, winter, and summer conditions in GLM and SVM-Nu models was checked (FIG S1). The examination of these graphs reveals a seasonal transition from winter to spring-summer, characterized by a gradual increase in air temperature and a decrease in relative humidity and air pressure. Notably, the composite spline component graphs indicate a positive impact of net pressure, relative humidity, and temperature on water consumption. Therefore, under specific conditions, the combination of these three variables may exert a synergistic effect on water consumption.

The moving average charts depict an inverse relationship between temperature and air pressure-relative humidity trends. While rising temperatures increase water consumption, the influence diminishes in summer due to air pressure and humidity acting as mitigating factors. Consequently, the impact of temperature changes on consumption is more pronounced in cold seasons. Both SVMs (non-linear) and GAM (linear) models were employed to estimate seasonal effects on urban water consumption, revealing nonlinear reactions to meteorological variables and reducing linear correlations.

Nonlinear models generally outperform linear ones in the study. For instance, the impact of air temperature on water consumption, controlled for pressure and humidity, showed nonlinear reactions in winter and annually, but linear in summer. This highlights winter’s heightened responsiveness to temperature changes due to humidity and pressure moderating summer consumption. Air pressure’s effect on consumption varies, with winter conditions showing lower impact than summer. Similarly, relative humidity’s impact, estimated by both linear and nonlinear models, is more pronounced in summer than winter. Overall, nonlinear models provide superior insights, indicating seasonal variations in water consumption’s sensitivity to temperature, pressure, and humidity in Kamyaran’s urban water management.

Discussion and conclusion

The study in Kamyaran investigates the influence of meteorological factors on urban water consumption, highlighting the interplay between temperature, pressure, and humidity. Linear and nonlinear models reveal that all three factors increase water consumption, but air pressure and humidity have a diminishing effect on the temperature-water consumption relationship. This inverse relationship is attributed to the law of gases, where temperature influences pressure and humidity. Analysis using a 6-month moving average further elucidates these trends.

GLM and SVM models predict water consumption based on temperature, pressure, and humidity, showing stronger effects of humidity and pressure in summer and temperature in winter due to regional climate dynamics. External factors like western waves and cyclones also affect local climate, creating unique conditions where the combined effect of temperature, humidity, and pressure significantly influences water consumption, emphasizing the complexity of managing water resources in arid regions.

The absolute and relative position of the city of Kamyaran, which is influenced by the migrating western and southwestern weather systems, and with the arrival of short waves and rainy systems in the west and in the cold season, the climate of Kamyaran is subject to change. Based on the results of the partial correlation coefficient, it is expected that the entry of low-pressure air masses will have a greater effect on reducing consumption than high-pressure air masses. This is because the values of temperature and pressure in the former mass lead to a decrease in the amount of water consumption, while these two variables act against each other in the latter mass. Such results are contrary to reality and the usual and standard state of the air in Kamyaran, in which high pressure in the cold season is based on low temperatures and minimum air pressure in the hot season is based on high temperatures. Such conditions indicate the nonlinear reactions of the amount of water consumption if the effects of other variables are not kept constant. Brentan et al. [24] also showed in a study that water consumption has a positive relationship with temperature and a negative relationship with air pressure and relative humidity. Since the air pressure and relative humidity are low in the hot season in Kamyaran, the amount of water consumption also has an upward trend.

This achievement confirms the findings by Abbasi et al. [4] who reported a threshold temperature of 15 degrees Celsius for the city of Khorramabad, which is in a similar climatic and geographical situation. Similarly, Aqeeluko and Draper [25] reported a threshold temperature of 15 degrees Celsius for the city of Calgary (Alberta, Canada), Gato et al. [26] reported a threshold temperature of 27.5 degrees Celsius for Melbourne (Australia), and Sarker et al. [27] reported a threshold temperature of 35.5 degrees Celsius for Melbourne (Australia). The research findings consistently indicate that water consumption does not exhibit a significant response to temperature increases below these identified thresholds. Maidment and Miao [28] also showed that in the states of Texas, Florida, and Pennsylvania, the reaction of water consumption to temperatures between 29 degrees Celsius and 32 degrees Celsius is about 3 to 5 times greater than temperatures below 29 degrees Celsius. Temperature thresholds were calculated individually, revealing nonlinear water consumption reactions. However, these findings lack control over other variables, showing only the individual model’s effect.

Limitations

Our findings were subjected to some limitations. Shortcomings that occurred during data collection may have influenced the reliability of the results. Additionally, the small sample size was small which may limit the generalizability of our conclusions, as it may not adequately represent the broader population. Furthermore, this study does not establish causality. Without a clear causal framework, it is difficult to determine whether changes in risk factors directly influence water consumption or if other underlying factors are at play.