A review of integrated surface-subsurface numerical hydrological models

Hydrological modeling, leveraging mathematical formulations to represent the hydrological cycle, is a pivotal tool in representing the spatiotemporal dynamics and distribution patterns inherent in hydrology. These models serve a dual purpose: they validate theoretical robustness and applicability via observational data and project future trends, thereby bridging the understanding and prediction of natural processes. In rapid advancements in computational methodologies and the continuous evolution of observational and experimental techniques, the development of numerical hydrological models based on physically-based surface-subsurface process coupling have accelerated. Anchored in micro-scale conservation principles and physical equations, these models employ numerical techniques to integrate surface and subsurface hydrodynamics, thus replicating the macro-scale hydrological responses of watersheds. Numerical hydrological models have emerged as a leading and predominant trend in hydrological modeling due to their explicit representation of physical processes, heightened by their spatiotemporal resolution and reliance on interdisciplinary integration. This article focuses on the theoretical foundation of surface-subsurface numerical hydrological models. It includes a comparative and analytical discussion of leading numerical hydrological models, encompassing model architecture, numerical solution strategies, spatial representation, and coupling algorithms. Additionally, this paper contrasts these models with traditional hydrological models, thereby delineating the relative merits, drawbacks, and future directions of numerical hydrological modeling.