A Bayesian joint probability modeling approach for seasonal forecasting of streamflows at multiple sites

Seasonal forecasting of streamflows can be highly valuable for water resources management. In this paper, a Bayesian joint probability (BJP) modeling approach for seasonal forecasting of streamflows at multiple sites is presented. A Box‐Cox transformed multivariate normal distribution is proposed to model the joint distribution of future streamflows and their predictors such as antecedent streamflows and El Niño‐Southern Oscillation indices and other climate indicators. Bayesian inference of model parameters and uncertainties is implemented using Markov chain Monte Carlo sampling, leading to joint probabilistic forecasts of streamflows at multiple sites. The model provides a parametric structure for quantifying relationships between variables, including intersite correlations. The Box‐Cox transformed multivariate normal distribution has considerable flexibility for modeling a wide range of predictors and predictands. The Bayesian inference formulated allows the use of data that contain nonconcurrent and missing records. The model flexibility and data‐handling ability means that the BJP modeling approach is potentially of wide practical application. The paper also presents a number of statistical measures and graphical methods for verification of probabilistic forecasts of continuous variables. Results for streamflows at three river gauges in the Murrumbidgee River catchment in southeast Australia show that the BJP modeling approach has good forecast quality and that the fitted model is consistent with observed data.