Stochastic simulation of daily streamflow sequences using a hidden Markov model

Abstract

Estimation of daily streamflow time series is of paramount importance for the design and implementation of river engineering and management projects (e.g., restoration, sediment-transport modelling, hydropower). Traditionally, indirect approaches combining stochastic simulation of rainfall with hydrological rainfall–runoff models are used. However, these are limited by uncertainties in model calibration and computational expense. Thus, this paper demonstrates an alternative, direct approach, for stochastic modelling of daily streamflow data, specifically seeking to address well-known deficiencies in model capability to capture extreme flow events in the simulated time series. Combinations of a hidden Markov model (HMM) with the generalised extreme value (HMM-GEV) and generalised Pareto (HMM-GP) distributions were tested for four hydrologically contrasting catchments in the UK (Rivers Dee, Falloch, Caldew and Lud), with results compared to recorded flow data and estimations obtained from a simpler autoregressive-moving-average (ARMA) model. Results show that the HMM-GP method is superior in performance over alternative approaches (relative mean absolute differences (RMAD) of <2% across all catchments), appropriately captures extreme events and is generically applicable across a range of hydrological regimes. In contrast, the ARMA model was unable to capture the flow regime successfully (average RMAD of 14% across all catchments).