Stochastic series lumped rainfall–runoff model for a watershed in Taiwan

The purpose of this paper is to develop a stochastic differential equation (SDE) for a lumped rainfall–runoff model and apply it to a watershed that consists of a number of subwatersheds in a series structure in Taiwan. Each subwatershed unit is treated as a two-part tank model. One part is for converting rainfall excess within the subwatershed into outflow at the subwatershed outlet. The other part converts subwatershed outflow into inflow at the next connecting subwatershed inlet. The measured values of rainfall excess are treated as random variables, and are used as input to the rainfall–runoff model. The development of the moment equations of simulated outflow is based on a SDE. The outflow hydrograph is obtained by applying the Laplace transform method to the equations that describe rainfall excess.