The rapid flow model (equivalent to the distributed delayed Muskingum model) is an attractive linear flood routing model meeting the conflicting demands of physical significance and simplicity. After having relaxed the assumption of negligible lateral inflow, made in former studies, the impulse response of the above model with lateral inflow is derived in the analytical (series) form. The cumulants of the impulse response of the model are developed. Although the results presented were obtained for the spatially uniform distribution of lateral inflow, it is possible to solve it also for non-uniform lateral inflows, at the cost of additional algebra.

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