Analytically Derived Runoff Models Based on Rainfall Point Processes

This work introduces four stochastic and lumped in space rainfall‐runoff models. They arise combining two stochastic rainfall models with two conceptualizations of a basin's response. Rainfall is given by rectangular pulses whose arrivals are described by Poisson and Neyman‐Scott models. Runoff is obtained routing such pulses via two alternative conceptualizations, both based on simple linear reservoirs. General expressions for the first‐ and second‐order moments are given for both the instantaneous and locally averaged processes. The mathematical structure of the alternative parameterizations is illustrated via computer simulations.