Climate is a key factor affecting water and energy resources. To quantify its effect, researchers have developed statistical and mechanistic models that simulate the interactions of the Water-Energy-Climate Nexus (WECN). In this work, we address two limitations of current WECN models, including the need to (1) account for the impact of climate on both demand and supply of water and energy, and (2) consider the influence of multiple climate variables in addition to temperature and precipitation. For this aim, we build upon our existing model that simulates in coupled fashion the water and energy systems of the metropolitan region of Phoenix, AZ. We design multidecadal storylines of future climate using an ensemble of downscaled general circulation models from CMIP6, along with possible energy infrastructure expansion scenarios. We develop a hydrologic model to account for the climate impacts on surface water supply sources. We constrain electricity supply based on water availability and temperature-dependent water intensities for power production. In parallel, we consider the effect of climate on demand through multilinear regressions between per-capita water and energy demand and several climate variables. This work advances the simulation of WECN interactions by integrating statistical and mechanistic models of water and energy systems with climate and hydrologic models. While the modeling framework is tested in the Phoenix metropolitan region, our findings provide useful insights that support WECN modeling efforts in other regions.