A Hydrologic Uncertainty Processor Using Linear Derivation in the Normal Quantile Transform Space

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.