Quantifying predictive uncertainty of streamflow forecasts based on a Bayesian joint probability model

- A novel BJP model post-processing deterministic streamflow forecasts is developed.
- Heteroscedasticity and non-Gaussianity are efficiently addressed.
- The BJP model works in concert with the hydrological and hydro-dynamical models.

SummaryUncertainty is inherent in streamflow forecasts and is an important determinant of the utility of forecasts for water resources management. However, predictions by deterministic models provide only single values without uncertainty attached. This study presents a method for using a Bayesian joint probability (BJP) model to post-process deterministic streamflow forecasts by quantifying predictive uncertainty. The BJP model is comprised of a log-sinh transformation that normalises hydrological data, and a bi-variate Gaussian distribution that characterises the dependence relationship. The parameters of the transformation and the distribution are estimated through Bayesian inference with a Monte Carlo Markov chain (MCMC) algorithm. The BJP model produces, from a raw deterministic forecast, an ensemble of values to represent forecast uncertainty. The model is applied to raw deterministic forecasts of inflows to the Three Gorges Reservoir in China as a case study. The heteroscedasticity and non-Gaussianity of forecast uncertainty are effectively addressed. The ensemble spread accounts for the forecast uncertainty and leads to considerable improvement in terms of the continuous ranked probability score. The forecasts become less accurate as lead time increases, and the ensemble spread provides reliable information on the forecast uncertainty. We conclude that the BJP model is a useful tool to quantify predictive uncertainty in post-processing deterministic streamflow forecasts.