Abstract. This study proposes a stochastic framework for a linear lumped rainfall-runoff problem at the catchment scale. An autoregressive (AR) model is adopted to account for the temporal variability of the rainfall process. For a stochastic description, solutions of the surface flow problem are derived in terms of first two statistical moments of the runoff discharge through the nonstationary Fourier-Stieltjes representation approach. The closed-form expression for the variance of runoff discharge allows to assessing the impacts of rainfall and storage parameters, respectively, on the discharge variability. It is found that the temporal variability of the runoff discharge induced by a random rainfall process persists longer for smaller values of the storage or rainfall parameters.