A Hydrologic Uncertainty Processor Using Linear Derivation in the Normal Quantile Transform Space
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A Hydrologic Uncertainty Processor Using Linear Derivation in the Normal Quantile Transform Space Jianzhong Zhou 1,2 & Kuaile Feng 1,2 & Yi Liu 1,2 & Chao Zhou 3 & Feifei He 1,2 & Guangbiao Liu 1,2 & Zhongzheng He 1,2 Received: 5 February 2020 / Accepted: 22 July 2020/ # Springer Nature B.V. 2020
Abstract
Hydrological forecasting plays an important role in basin flood control systems, and the uncertainty of hydrological forecasting is helpful to reveal basin hydrological characteristics and provide support to decision makers in formulating water resources management schemes. The hydrologic uncertainty processor (HUP) has been widely employed in hydrological uncertainty prediction. However, in the HUP normal quantile transform (NQT) space, the posteriori distribution is derived from the Bayesian theory. This increases the difficulty of the theory and calculations. In this paper, a new method is proposed to deduce the posterior residual equation, and the HUP-Gaussian mixture model (HUP-GMM) is adopted to simplify the calculations. By maintaining the original hypothesis, since the posterior residual is known to follow a normal distribution, the posterior linear correlation equation can be directly assumed without prior and likelihood inferences. In particular, the complex Bayesian inference is replaced with simple linear equations. By converting the linear equation into the original space, we obtain a new method consisting of the HUP linear GMM (HUP-LG). In the study area, the parameters of the HUP-LG and HUP-GMM in the NQT space are calculated, and corresponding expressions of the probability density in the original space are obtained. The results reveal that the HUP-LG simplifies the calculation process in the NQT space, and attains the same performance as that of the HUP-GMM. Keywords Hydrological uncertainty . Linear derivation . Normal quantile transform . River discharge
* Jianzhong Zhou [email protected]
1
School of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
2
Hubei Key Laboratory of Digital Valley Science and Technology, Wuhan 430074, China
3
Changjiang Institute of Survey, Planning, Design and Research, Wuhan 430010, China
Zhou J. et al.
1 Introduction Hydrological forecasting plays an important role in basin flood control systems, which include engineering and non-engineering measures(Hao et al. 2012). The prediction of hydrological variables is susceptible to various uncertainties, such as the climate, model structure and parameters, and initial prediction conditions (Kavetski et al. 2006; Chen et al. 2011; Renard et al. 2011; Madadgar et al. 2014; Alvarado-Montero et al. 2017; Jiang et al. 2018). The uncertainty of hydrological forecasting is helpful to reveal the basin hydrological characteristics and provide support to decision makers in the formulation of water resources management schemes (Jia et al. 2019; Zhou et al. 2019). In other words, the uncertainty analysis of hydrological forecasting models is of great theoretical an
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