Hybrid modified continuous time Markov chain model for daily streamflow generation

A novel hybrid Modified Continuous Time Markov Chain (MCTMC)-based single site stochastic model is proposed for the synthetic generation of daily streamflow sequences. The inherent characteristic of the Continuous Time Markov Chain (CTMC) process to represent the dynamic and continuous behaviour of stochastic systems through discrete states and their persistence in time, has been perceived to be suitable for modelling the daily streamflows. The structure of the original CTMC is modified to model the asymmetry of the daily flow hydrograph and the seasonality characteristics involved. The de-seasonalized streamflow space is discretized into an appropriate number of Markov states and a normal probability distribution (parametric component) is fitted to each state. The state occurrences are modelled using the embedded transition probability matrix within the month and the state holding times. The state holding times are conditioned on the preceding state and the month of occurrence to reflect the inherent historical dependence and the non-homogeneity of the daily streamflows, and are resampled from the observed data. The normal distribution generated values within the state are reshuffled according to the ranks of the resampled historical sequence. The competence of the proposed model is illustrated through its application to the observed daily flows at three rivers in the Colorado basin. The model is shown to reproduce the summary statistics and the distributional characteristics at the daily as well as the aggregated time scales. The short-term and the long-term dependence, the asymmetric shape of the hydrograph as well as the water use statistics are well preserved in the simulations. The efficacy of the proposed model is also brought out through a comparison with the frequency-based model of Brunner et al. (2019).