Mountain and high-mountain watersheds are headwaters of major rivers worldwide. Although they have smaller sizes, these catchments offer significant hydropower potential, transform considerable amount of snow into runoff, provide water for specific mountain ecosystems, and could also be viewed as climate change indicators. Hence, continuous research on this topic is important either in the form of field investigations or computational modelling of natural processes.
In this study, a coupled distributed surface–subsurface flow model of the watershed runoff formation was implemented. For the surface flow, the zero-inertia/diffusive-wave hydrodynamic model was used. For the subsurface flow, the Boussinesq model for saturated flow in porous media was used. Using these models, a two-dimensional transient differential problem was set, consisting of a system of two nonlinear advection partial differential equations. The functions of the solutions for both models are the flow thicknesses (also called flow heights). To improve the numerical stability of the solutions and to use convenient time steps, an implicit scheme was used for the time domain. For the irregular geometries of the real-world watersheds, the Galerkin finite element method was employed. Because of the nonlinear and advective nature of the system, stabilization terms were added to the numerical scheme. These were a streamline–upwind Petrov–Galerkin (SUPG) term and spurious-oscillations-at-layers diminishing (SOLD) term.
Numerical experiments, each one with a simulation time of one hydrological year, were conducted for an example of a high-mountain watershed. The input meteorological data was obtained from stations and was spatially and temporally distributed. The computed river discharge values were compared with the measured ones, and the results were acceptable, although with defects.
Physically based distributed hydrological models are useful, e.g., in the determination of effective areal values of some physical variables, estimation of results of different what-if scenarios, runoff forecasting, etc. Further studies can improve the numerical approaches used in this field.
