Risk Assessment of Urban Water and Energy Supply Using Copula Function: A Water–Energy Nexus Approach in an Arid City

Planning for the future of water and energy supply systems in urban areas requires a thorough assessment of associated risks. In this study, monthly water and energy demand data from 2011 to 2022 in an arid city was used to predict the corresponding demands from 2023 to 2032 using the seasonal auto-regressive integrated moving average (SARIMA) method. The aim is to estimate future water and energy supply risks both individually and jointly, using cumulative distribution functions (CDFs) derived from historical data. The main focus is to calculate the combined risk of water and energy, referred to as the water–energy nexus (WEN) risk. Based on the interdependent relationship between water and energy, the Copula function was utilized to model the bivariate distribution between these two variables. Pearson correlation analysis indicated a strong correlation between water and energy supplies. Among the distributions fitted to the data, the log-normal and gamma distributions were the best fit for water supply and energy supply systems, respectively, with the lowest Akaike information criterion (AIC) values. The Gumbel Copula, with a parameter of 1.66, was identified as the most suitable for modeling the joint distribution, yielding the lowest AIC value. The results indicate that the risks associated with energy supply, water supply, and their joint dependency could exceed 0.8% in the future, highlighting a potentially critical situation for the city. The trend analysis revealed that forecasted water and energy demands and their corresponding risks and the WEN risk are expected to have a significant upward trend in the future. Finally, local authorities need to explore alternative sources to supply water and energy in the future to address the ever-growing water and energy demands.