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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 346045, 11 pages
Research Article

Uncertainty Analysis of Multiple Hydrologic Models Using the Bayesian Model Averaging Method

1State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
2National Research Center for Sustainable Hydropower Development, China Institute of Water Resources and Hydropower Research, Beijing 100038, China

Received 30 August 2013; Accepted 6 November 2013

Academic Editor: Y. P. Li

Copyright © 2013 Leihua Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Since Bayesian Model Averaging (BMA) method can combine the forecasts of different models together to generate a new one which is expected to be better than any individual model’s forecast, it has been widely used in hydrology for ensemble hydrologic prediction. Previous studies of the BMA mostly focused on the comparison of the BMA mean prediction with each individual model’s prediction. As BMA has the ability to provide a statistical distribution of the quantity to be forecasted, the research focus in this study is shifted onto the comparison of the prediction uncertainty interval generated by BMA with that of each individual model under two different BMA combination schemes. In the first BMA scheme, three models under the same Nash-Sutcliffe efficiency objective function are, respectively, calibrated, thus providing three-member predictions ensemble for the BMA combination. In the second BMA scheme, all three models are, respectively, calibrated under three different objective functions other than Nash-Sutcliffe efficiency to obtain nine-member predictions ensemble. Finally, the model efficiency and the uncertainty intervals of each individual model and two BMA combination schemes are assessed and compared.