Runoff Hydrograph as a Function of Rainfall Excess

摘要

A set of differential equations has been obtained for the overland runoff from an arbitrary catchment when the rainfall excess over the catchment is known as a function of space and time. An analytical solution is given for a steady rain of finite duration. The differential equations obtained are also solved analytically for a moving top‐hat storm over a plane catchment, and the maximum depth is obtained explicitly as a function of the storm duration and catchment length. The results for all plane catchments with a given resistance formula are reduced to a single curve. It is found that the depth is increased if the storm moves downstream and decreased if the storm moves upstream, the slower the storm the greater being the change. If the storm period exceeds a critical value, with a storm moving downstream, then the depth is increased by a factorn1/n−1for a sufficiently long catchment. The parameternis the exponent of depth in the discharge depth relation. Finally, it is shown that all the results apply qualitatively to open channel flow where the kinematic wave approach is suitable. If the lateral inflow replaces the rainfall excess, it is found that the form of the curve describing the variation of depth with time is a function of the cross‐section geometry but is qualitatively similar to the overland flow curve described