Markov chain formulations for annual streamflow simulation

This study evaluates first-order discrete-time (DTMC) and continuous-time (CTMC) Markov chain models for simulating annual streamflow, with emphasis on reproducing drought characteristics and hydrologic persistence. The models are applied to three rivers representing distinct flow regimes and dependence structures. In the DTMC framework, annual streamflows are discretized into finite states with transition probabilities estimated from observations. The CTMC formulation explicitly represents state residence times, allowing more flexible characterization of persistence and variability. Synthetic streamflow sequences generated by both models are assessed using statistical moments, marginal distributions and drought metrics. Results show that while both approaches reproduce basic statistical properties, the CTMC model more accurately represents marginal distributions and multi-year drought behaviour. This improvement arises from its explicit treatment of state duration. The findings demonstrate the advantages of continuous-time Markov chains for long-term streamflow simulation and water resources planning applications.