One-Dimensional Linear Kinematic Wave Solution for Overland Flow under Moving Storms Using the Method of Characteristics

The kinematic wave theory has been a widely accepted technique for modeling overland flow. Although it is recognized that overland flow is nonlinear, linear approximations have nonetheless been applied and found to be satisfactory on small impermeable areas such as those found in the urban environment as well as on steep slopes. Linear approximation also holds for floods, which may explain the popularity of the unit hydrograph method. This study derives analytical solutions of one-dimensional (1D) kinematic wave equations for overland flow on a plane subjected to moving storms using the method of characteristics. Two cases of storm movement are considered: a storm moving downstream and a storm moving upstream. The 1D solutions are compared with other analytical solutions and with the laboratory simulation. The proposed analytical solution, despite the simplifications embedded therein, suggests that it can be useful for engineering purposes. It clearly shows the flow characteristics during the rising limb, at equilibrium (constant discharge achieved), and during the recession limb of the hydrograph. Also, it can be used to quantify the error resulting from the assumption of a stationary storm covering the entire watershed, which seldom happens.