Semidistributed hydrological modeling: A "saturation path" perspective on TOPMODEL and VIC

The conceptual foundation, behavior, and implementation of semidistributed hydrological models such as TOPMODEL and VIC are reviewed from a "saturation path modeling" perspective, hereinafter referred to as SPM. A general family of SPM models is analyzed, based on the assumptions that (1) an event-invariant relationship between the saturated area and catchment storage exists (which may include hysteretic and stochastic components) and (2) ponding is negligible and quick flow is generated from precipitation on saturated areas. The VIC and TOPMODEL are then obtained from specific constitutive functions and numerical approximations. In general, SPM leads to compact equations in canonical ODE form, making the behavior of the model transparent and facilitating improvements of both the conceptual model itself and its numerical implementation. A comprehensive numerical analysis of SPM, TOPMODEL, and VIC is presented, providing insight into the timescale dependence of their parameters. It is demonstrated that uncontrolled numerical implementations, particularly traditional fixed-step explicit Euler methods, can introduce considerable artifacts into the behavior of conceptual models such as TOPMODEL, corrupting calibration and prediction.