Abstract Reliable streamflow forecasts can be highly valuable for water resources planning and management. In this study, we combined a hidden Markov model (HMM) and Gaussian Mixture Regression (GMR) for probabilistic monthly streamflow forecasting. The HMM is initialized using a kernelized K-medoids clustering method, and the Baum–Welch algorithm is then executed to learn the model parameters. GMR derives a conditional probability distribution for the predictand given covariate information, including the antecedent flow at a local station and two surrounding stations. The performance of HMM–GMR was verified based on the mean square error and continuous ranked probability score skill scores. The reliability of the forecasts was assessed by examining the uniformity of the probability integral transform values. The results show that HMM–GMR obtained reasonably high skill scores and the uncertainty spread was appropriate. Different HMM states were assumed to be different climate conditions, which would lead to different types of observed values. We demonstrated that the HMM–GMR approach can handle multimodal and heteroscedastic data.

中文翻译：

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基于隐马尔可夫模型和高斯混合回归的月流量预测

摘要 可靠的流量预测对于水资源规划和管理非常有价值。在这项研究中，我们结合了隐马尔可夫模型 (HMM) 和高斯混合回归 (GMR) 进行概率月流量预测。HMM 使用核化 K-medoids 聚类方法初始化，然后执行 Baum-Welch 算法以学习模型参数。GMR 导出预测和给定协变量信息的条件概率分布，包括本地站和两个周围站的先行流量。HMM-GMR 的性能基于均方误差和连续排序概率得分技能得分进行验证。通过检查概率积分变换值的均匀性来评估预测的可靠性。结果表明，HMM-GMR 获得了相当高的技能分数，并且不确定性传播是适当的。假设不同的 HMM 状态具有不同的气候条件，这将导致不同类型的观测值。我们证明了 HMM-GMR 方法可以处理多模态和异方差数据。