Stochastic recession rates and the probabilistic structure of stream flows

Abstract

This paper investigates the impact of interevent variability of streamflow recession rates on two key streamflow statistics, namely, the equilibrium probability density function (pdf) and the autocorrelation. The relevance of the problem lies in the need to quantify and predict streamflow availability, on the basis of measurable rainfall and landscape attributes, by explicitly incorporating the stochasticity of the underlying climate and transport processes. Novel expressions for the seasonal pdf and the autocorrelation of the daily streamflows are derived by incorporating the randomness of the recession rates into a probabilistic framework where the streamflow fluctuations are explicitly related to the intermittency of the rainfall forcing. The presence of stochastic recession time constants is shown to impact only the third‐ and higher‐order moments of the probability density function of the daily streamflows, without altering the mean and the variance of the pdf. A remarkable effect is instead produced on the correlation structure, which may exhibit long‐term persistence even in the presence of a weak randomness of the recession rate. A relevant case study is then discussed to show that incorporating the stochasticity of the recession time constant leads to an improvement of the model ability to capture the behavior of the equilibrium streamflow pdf and of the underlying correlation function.