Explicitly integrating parameter, input, and structure uncertainties into Bayesian Neural Networks for probabilistic hydrologic forecasting


Zhang, Xuesong
Liang, Faming
Yu, Beibei
Zong, Ziliang

KAUST Grant Number


Estimating uncertainty of hydrologic forecasting is valuable to water resources and other relevant decision making processes. Recently, Bayesian Neural Networks (BNNs) have been proved powerful tools for quantifying uncertainty of streamflow forecasting. In this study, we propose a Markov Chain Monte Carlo (MCMC) framework (BNN-PIS) to incorporate the uncertainties associated with parameters, inputs, and structures into BNNs. This framework allows the structure of the neural networks to change by removing or adding connections between neurons and enables scaling of input data by using rainfall multipliers. The results show that the new BNNs outperform BNNs that only consider uncertainties associated with parameters and model structures. Critical evaluation of posterior distribution of neural network weights, number of effective connections, rainfall multipliers, and hyper-parameters shows that the assumptions held in our BNNs are not well supported. Further understanding of characteristics of and interactions among different uncertainty sources is expected to enhance the application of neural networks for uncertainty analysis of hydrologic forecasting. © 2011 Elsevier B.V.

Zhang X, Liang F, Yu B, Zong Z (2011) Explicitly integrating parameter, input, and structure uncertainties into Bayesian Neural Networks for probabilistic hydrologic forecasting. Journal of Hydrology 409: 696–709. Available: http://dx.doi.org/10.1016/j.jhydrol.2011.09.002.

We sincerely appreciate the three anonymous reviewers for their valuable comments that help significantly improve the manuscript, especially those comments on critical posterior analysis, reorganization of the sections, and linkage and difference between the new BNNs and those reported in previous research. Dr. Xuesong Zhang is supported by the DOE Great Lakes Bioenergy Research Center (DOE BER Office of Science DE-FC02-07ER64494, DOE BER Office of Science KP1601050, DOE EERE OBP 2046919145). This research is partially supported by grants from the National Science Foundation (DMS-0607755 and CMMI-0926803) and the award (KUS-C1-016-04) made by King Abdullah University of Science and Technology (KAUST). We thank Mr. David Manowitz at the Joint Global Change Research Institute, Pacific Northwest National Laboratory and University of Maryland for professional editing.

Elsevier BV

Journal of Hydrology


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