Abstract
Using a simplified representation of how a river basin stores precipitation, generates runoff, and loses water through evapotranspiration, we derive probabilistic relationships between precipitation, soil moisture deficit, and generated runoff. The “distribution function model” is used to describe the soil moisture storage capacity of the basin: storage capacity, per unit of basin surface area, is regarded as a spatially variable quantity described by a density function. By routing the generated runoff through what is essentially a linear reservoir with stochastic inputs and outputs, we show how the median discharge can be calculated which corresponds to a rainfall input of some specified return period T time intervals. The return period for basin discharge can, with certain assumptions, also be calculated, thereby yielding probability statements relating the T‐period rainfall to its resultant discharge.
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