Combination of Multiple Data-Driven Models for Long-Term Monthly Runoff Predictions Based on Bayesian Model Averaging

Accurate and reliable long-term runoff forecasting is very important for water resource system planning and management. This study utilized three data-driven models to simulate and forecast the monthly runoff series of the Huangzhuang hydrological station from 1981 to 2017. To improve the accuracy and reduce the uncertainty, two model averaging techniques were applied to merge forecast results of the different models, and 90% confidence intervals were derived using Monte Carlo sampling. Several indices were used to evaluate the results of three data-driven models and two model averaging techniques. Among the many discoveries in this paper, the following stand out: (i) in general, the random forest (RF) algorithm presented nearly the same accuracy as did the artificial neural network (ANN) algorithm, and both were superior to the support vector machine (SVM) method; however, none of the models consistently provided the best result in all months; (ii) the comparison of the deterministic results indicated that Copula-Bayesian model averaging (BMA) exhibited smaller errors than did BMA, especially for the points whose uniform quantiles ranged within (0.125, 0.35) and (0.5, 0.625); and (iii) in most cases, the 90% confidence interval of the Copula-BMA scheme had higher containing ratio values, smaller average relative bandwidth values in the high-flow months, and smaller average relative deviation amplitudes than did BMA.