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Stream runoff is perhaps the most poorly represented process in ecohydrological stochastic soil moisture models. Here we present a rainfall-runoff model with a new stochastic description of runoff linked to soil moisture dynamics. We describe the rainfall-runoff system as the joint probability density function (PDF) of rainfall, soil moisture and runoff forced by random, instantaneous jumps of rainfall. We develop a master equation for the soil moisture PDF that accounts explicitly for a general state-dependent rainfall-runoff transformation. This framework is then used to derive the joint rainfall-runoff and soil moisture-runoff PDFs. Runoff is initiated by a soil moisture threshold and a linear progressive partitioning of rainfall based on the soil moisture status. We explore the dependence of the PDFs on the rainfall occurrence PDF (homogeneous or state-dependent Poisson process) and the rainfall magnitude PDF (exponential or mixed-exponential distribution). We calibrate the model to 63 years of rainfall and runoff data from the Upper Little Tennessee watershed (USA) and show how the new model can reproduce the measured runoff PDF.

Stochastic rainfall-runoff model with explicit soil moisture dynamics