The escalating residential water consumption necessitates a deeper understanding of its influencing factors to support effective infrastructure management and municipal planning. While numerous studies have explored various features (water-use related, demographic, economic, and housing information) and techniques (OLS, ARIMA, ANNs, tree-based models) to explain household water consumption, a significant portion of the variability remains unexplained (average R² < 0.50). This study posits that the water-energy nexus—the interconnectedness of water and energy consumption—is a key factor in this unexplained variability. Household water and energy are often concurrently used (e.g., laundry, bathing, cooking), and ignoring this nexus has limited the explanatory power of previous models. Previous studies have either overlooked the nexus or limited its consideration to specific appliances. This research aims to fill this gap by explicitly incorporating energy-related features (energy use patterns and total electricity consumption) into household water consumption models, using data from Beijing, China, to determine whether considering the water-energy nexus enhances the models' explanatory power.

Existing research on household water consumption has explored various factors influencing consumption, including water-use related features, household demographics and economics (population, income, education), and housing characteristics (area, type). Multiple techniques, ranging from traditional statistical methods like OLS and ARIMA to machine learning approaches like ANNs and tree-based models, have been employed. Despite this, a substantial amount of variability in water consumption remains unexplained, typically indicated by low R² values (less than 0.50). This highlights a gap in understanding the key factors driving household water consumption. Although the water-energy nexus has been recognized, its incorporation into comprehensive household water consumption models remains limited, with previous studies either neglecting it or focusing only on a few specific appliances or behaviors.

This study utilized data collected from a survey of 1320 households in Haidian and Tongzhou Districts in Beijing, China, in 2020. The survey included 78 questions covering household information (HI), water use (WU), energy use (EU), and electricity consumption (EC), resulting in 24 features for modeling. Data cleaning involved verifying questionnaire completion, cross-checking water consumption data, and using the 3-sigma principle to remove outliers. LASSO regression was used to address potential multicollinearity. A stepwise-like approach was implemented to build four models: Model (1) using HI and WU; Model (2) using HI and EU; Model (3) using HI, WU, and EU; and Model (4) using HI, WU, EU, and EC. Three modeling techniques—OLS, Random Forest (RF), and XGBoost—were employed for each model. Model performance was evaluated using R², RMSE, and MAPE. The explanatory power of individual features was assessed by removing each feature from Model (4) (using XGBoost) and observing the changes in model performance metrics. Feature importance was determined using XGBoost’s built-in feature importance calculation.

The inclusion of energy-related features (EU and EC) significantly improved the models' performance. On average, the R² value increased by 34.0% when compared to models without energy-related features. XGBoost consistently outperformed OLS and RF, achieving the highest R² values. Model (4), incorporating HI, WU, EU, and EC features, using XGBoost reached an optimized R² of 0.55 and an average R² of 0.52 over 500 repeated runs. This represents a substantial improvement compared to previous studies with similar sample sizes, where the highest reported R² value was 0.42. Energy-related features demonstrated greater explanatory power and importance than water-related features. Specifically, electricity consumption (EC) exhibited the highest explanatory power and feature importance, followed by energy use (EU) features. Among the HI features, family size and housing location were the most important predictors. Among WU features, the frequency of bathing, mopping, and laundry were important. Among EU features, the power of the water heater, cooking duration, and air conditioning duration were important. The study significantly improved the explained variance in household water consumption by at least 23.8% compared to prior studies with similar sample sizes.

The results strongly support the importance of considering the water-energy nexus when modeling household water consumption. The significant increase in R² values when including energy-related features demonstrates that the water-energy nexus acts as a proxy for the unexplained variability in traditional water consumption models. The higher explanatory power and importance of energy-related features compared to water-related features further underscores this point. This suggests a need for future research focusing on residents' water and energy use behaviors and corresponding interventions to control household water consumption. The superior performance of XGBoost indicates its suitability for capturing the non-linear relationships between features and household water consumption.

This study provides compelling evidence for the importance of integrating the water-energy nexus into household water consumption models. The significant increase in model accuracy achieved by including energy-related features offers a more comprehensive understanding of household water use patterns and a more robust basis for water resource management. Future research should investigate the applicability of these findings to other regions and temporal scales, consider the influence of factors like the COVID-19 pandemic, and explore causal relationships between features and water consumption through interventions and social experiments.

The study utilizes cross-sectional data, limiting the ability to analyze temporal trends in water and energy consumption. The COVID-19 pandemic might have influenced water and energy usage behaviors, an impact not fully addressed in this study. The model's predictive capability may vary in different regions due to differing population structures, water use behaviors, and strength of the water-energy relationship. Further research is needed to confirm these findings over longer time periods and to explore causal relationships.