Analytical Solution of Kinematic Wave Equation for Overland Flow due to Storms Moving at a Velocity Lower than Flow Velocity

Overland flow is often generated by moving rainstorms and is modeled using the kinematic wave theory. In overland flow modeling, it is usually assumed that rainstorms are stationary and occur over the entire watershed. Consequently, studies on overland flow modeling considering moving storms have been limited. Storms may move from upstream to downstream, downstream to upstream, or across stream. Likewise, storms can occur over the entire watershed or a portion thereof, which can be upstream, downstream, in the center, or at different portions. Studies that have considered moving rainstorms have assumed that storm velocity is the same as flow velocity. However, it is not uncommon that storms move at a velocity slower than flow velocity, and such storms have not been considered in the studies. For such storms, the structure of the solution domain and, in turn, of the kinematic wave solution becomes quite different and has not yet been reported in the hydrologic literature. The objective of this paper therefore is to derive an analytical solution of the kinematic wave equation under the condition that a rainstorm is moving at a velocity slower than flow velocity. Field or laboratory observations on storms moving at a velocity slower than flow velocity are not available. Therefore, validation of the derived solution is not the objective here, because without data, the analytical solution cannot be verified.