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

Leihua Dong,Lihua Xiong,Kun-Xia Yu

doi:10.1155/2013/346045

Abstract

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.

Highlights

To date, various hydrological models have been put forward and widely used in flood forecasting, planning, and water resources management [1, 2]
Bayesian Model Averaging came to prominence in statistics in the mid-1990s, and Madigan and Raftery [8] were the first to propose this method for combining predictions
In order to compare the performance of two Bayesian Model Averaging (BMA) schemes in different flow ranges, according to the characteristics of the streamflow values of Mumahe catchment, data are broken into three flow ranges: high flow, medium flow, and low flow

Summary

Introduction

Various hydrological models have been put forward and widely used in flood forecasting, planning, and water resources management [1, 2]. Bayesian Model Averaging (BMA), a method for averaging over different competing models, has been introduced to ensemble hydrologic predictions. Raftery [9] and Draper [10] gave more detailed discussion about BMA. It has been applied in diverse fields such as economics [11], biology [12], ecology [13], public health [14], toxicology [15], meteorology [16], and management science [17]. BMA produces accurate and reliable predictions and was shown to be a better scheme than other model-combining methods [18,19,20]. Hydrologists have applied BMA to hydrologic modeling, such as groundwater [21] and rainfallrunoff modeling [22,23,24]

Methods

Results

Conclusion