Advances in spatiotemporal multiscale water-energy balance models: A Review

Water and energy balance models have become increasingly important for simulating hydrological and thermal processes, predicting runoff, and managing water resources over the past few decades. Based on the principles of mass and energy conservation, these models describe integrated hydrological and thermal processes across multiple scales in both space and time by analyzing the relationships between key hydrometeorological factors such as precipitation, evapotranspiration, and runoff. This paper provides an overview of water and energy balance models commonly used to model water and thermal dynamics at different spatiotemporal scales. Temporally, these models can be categorized into event-scale, monthly-scale, annual-scale, and multi-year models. Traditional models are typically used for specific temporal scales, such as event, monthly, or annual levels. However, they fail to capture the inherent multiscale nature of hydrological and thermal processes, often overlooking critical factors like inter-basin groundwater exchange and irrigation. We also review advancements in temporal-scale water and energy balance models, including those developed based on Budyko’s theory and the proportional hypothesis. The paper discusses the challenges in the development and application of temporal-scale models, particularly issues related to their uncertainty and accuracy. Additionally, we examine advancements in spatial multiscale models and review key factors—such as inter-basin groundwater interactions and the impact of agricultural land use—that influence the accuracy of multiscale water-energy balance models. Finally, we highlight future directions for the development of multi-scale hydrological and thermal models that can better capture the complex processes involved and improve water resource management across different scales.