Abstract
To describe runoff precisely, we have no choice but to use a distributed parameter model. Subdividing a whole basin into many sub-basins, the distributed runoff model estimates the runoff in the whole basin by summing the runoff from all the sub-basins. Because of a long computation time, using the distributed parameter runoff model to estimate runoff of sub-basins is not a good idea We obtained the storage function runoff model, a lumped parameter model, from the distributed parameter model by lumping. Storage coefficients can be expressed by using the area, the slope and the geological characteristics of sub-basins. When we consider many sub-basins, we can define the storage coefficient as a random variable distributed around the mean value. Rainfall can also be defined as a random variable rather than a deterministic function. In this paper, we derive differential equations to calculate the first through fourth moments of runoff when the coefficients and the forcing term of the storage function runoff model are treated as random variables.
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