Application of Bayesian Model Averaging Approach to Multimodel Ensemble Hydrologic Forecasting

Bayesian model averaging (BMA) is a statistical method that can synthesize the advantages of different models or methods. The objective of this research is to explore the use of BMA to forecast combinations among several hydrological models. BMA is a statistical scheme that infers the posterior distribution of forecasting variables by weighing individual posterior distributions based on their probabilistic likelihood measures, with the better performing predictions receiving higher weights than the worse predictions. The Topographic Kinematic Approximation and Integration and Xin’anjiang models were applied to the Dongwan basin, Yellow River, China, for flood simulation. Observed and simulated discharge time series were transformed into normally distributed variables through the normal quantile transform. The Gaussian mixture model was constructed by weighing the posterior distribution of individual hydrological models in the transformed space. The posterior probability measuring samples belonging to each specific hydrological model were treated as the weights. The parameters of the Gaussian mixture model and the weight of each hydrological model were estimated by the expectation maximization algorithm. Thus, the forecast combination in the catchment was obtained from the two hydrological models. For flood forecasting, the results provided not only the mean discharge values, but also quantitative evaluation of forecasting uncertainties (e.g., standard deviation and confidence interval), because the BMA approach calculated the estimation of the probability distribution of forecasted variables.