A Bayesian Hierarchical Framework for Postprocessing Daily Streamflow Simulations across a River Network

Despite the potential and increasing interest in physically based hydrological models for streamflow forecasting applications, they are constrained in terms of agility to generate ensembles. Hence, we develop and test a Bayesian hierarchical model (BHM) to postprocess physically based hydrologic model simulations at multiple sites on a river network, with the aim to generate probabilistic information (i.e., ensembles) and improve raw model skill. We apply our BHM framework to daily summer (July-August) streamflow simulations at five stations located in the Narmada River basin in central India, forcing the Variable Infiltration Capacity (VIC) model with observed rainfall. In this approach, daily observed streamflow at each station is modeled with a conditionally independent probability density function with time varying distribution parameters, which are modeled as a linear function of potential covariates that include VIC outputs and meteorological variables. Using suitable priors on the parameters, posterior parameters and predictive posterior distributions-and thus ensembles-of daily streamflow are obtained. The best BHM model considers a gamma distribution and uses VIC streamflow and a nonlinear covariate formulated as the product of VIC streamflow and 2-day precipitation spatially averaged across the area between the current and upstream station. The second covariate enables correcting the time delay in flow peaks and nonsystematic biases in VIC streamflow. The results show that the BHM postprocessor increases probabilistic skill in 60% compared to raw VIC simulations, providing reliable ensembles for most sites. This modeling approach can be extended to combine forecasts from multiple sources and provide skillful multimodel ensemble forecasts.

Automated summary

In this study, a Bayesian hierarchical model (BHM) was developed and tested to improve the predictions of physically based hydrological models and generate ensemble forecasts. The results showed that the BHM model increased probabilistic skill and provided reliable ensemble forecasts for multiple sites.