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.

水文预报在流域防洪体系中发挥着重要作用，水文预报的不确定性有助于揭示流域水文特征，为决策者制定水资源管理方案提供支持。水文不确定度处理器（HUP）已广泛应用于水文不确定度预测中。但是，在HUP正态分位数变换（NQT）空间中，后验分布是根据贝叶斯理论得出的。这增加了理论和计算的难度。本文提出了一种推导后验残差方程的新方法，并采用了HUP-Gaussian混合模型（HUP-GMM）简化了计算。通过维持原始假设，由于已知后验残差遵循正态分布，可以直接假定后线性相关方程，而无需先验和似然推断。特别是，复杂的贝叶斯推断被简单的线性方程式所代替。通过将线性方程转换为原始空间，我们获得了一种由HUP线性GMM（HUP-LG）组成的新方法。在研究区域，计算了NQT空间中HUP-LG和HUP-GMM的参数，并得到了原始空间中概率密度的对应表达式。结果表明，HUP-LG简化了NQT空间中的计算过程，并获得了与HUP-GMM相同的性能。通过将线性方程转换为原始空间，我们获得了一种由HUP线性GMM（HUP-LG）组成的新方法。在研究区域，计算了NQT空间中HUP-LG和HUP-GMM的参数，并得到了原始空间中概率密度的对应表达式。结果表明，HUP-LG简化了NQT空间中的计算过程，并获得了与HUP-GMM相同的性能。通过将线性方程转换为原始空间，我们获得了一种由HUP线性GMM（HUP-LG）组成的新方法。在研究区域，计算了NQT空间中HUP-LG和HUP-GMM的参数，并得到了原始空间中概率密度的对应表达式。结果表明，HUP-LG简化了NQT空间中的计算过程，并获得了与HUP-GMM相同的性能。