Retrospective analysis and forecasting of streamflows using a shifting level model

Shifting level models have been suggested in the literature since the late 1970ʹs for stochastic simulation of streamflow data. Parameter estimation for these models has been generally based on the method of moments. While this estimation approach has been useful for simulation studies, some limitations are apparent. One is the difficulty of evaluating the uncertainty of the model parameters, and another one is that the proposed model is not amenable to forecasting because the underlying mean of the process, which changes with time, is not estimated. In this paper, we reformulate the original shifting level model to conform to the so-called Hidden Markov Chain models (HMMs). These models are increasingly used in applied statistics and techniques such as Monte-Carlo Markov chain, and in particular Gibbs sampling, are well suited for estimating the parameters of HMMs. We use Gibbs sampling in a Bayesian framework for parameter estimation and show the applicability of the reformulated shifting level model for detection of abrupt regime changes and forecasting of annual streamflow series. The procedure is illustrated using annual flows of the Senegal River in Africa.