Two-Dimensional Hydrodynamic Model for Surface-Flow Routing

A new surface flow routing algorithm based on numerical solutions of shallow water equations and the kinematic wave approximation (SWE-KWA) is proposed in this paper. The shallow water equations are discretized by the first-order Godunov-type finite-volume method. The stability analysis showed that the friction source term increased exponentially as flow depth became very small. This breaks the balance between the friction and the slope source terms. An approximate solution to the kinematic wave equation is introduced to restore this balance. This kinematic wave approximation makes it possible to apply the shallow water equations to both overland and channel flows. Test results show that this algorithm is accurate, robust, and stable for both very shallow overland and concentrated channel flows. The minimum allowable flow depth used in the tests is 10−10 m, two orders of magnitude smaller than the common rainfall excess rate (10−5 to 10−8 m/s). Because this algorithm applies to both the overland and the channel flow, the developed model can directly use the raw digital elevation data as topographic data without a predefined channel network. This feature makes the new algorithm extremely valuable for solving flow routing problems in ungauged watersheds.