Abstract The aim of this paper is to investigate the complex relationship between monthly water discharge and suspended sediment load using a flexible statistical model, i.e. a Gaussian Mixture Model. The theoretical principles of this model and its related Expectation- Maximization (E-M) algorithm are briefly analyzed, and subsequently applied to hydrologic data of four medium-sized mountainous rivers of the southern Balkan peninsula (i.e., Acheloos, Arachthos, Aoos and Aliakmon), whose data distribution of the aforementioned variables shows the existence of two sub-populations. A Gaussian Mixture model (GMM) is fitted to the sample points for each river and then its parameters are tuned by comparing different information criteria, in order to determine the optimum parameter settings. These parameters (latent variables) are associated with the generation mechanism of the bivariate distribution, which alternates between two components (regimes), related to the seasonality of the hydrological variables; the latter being characteristic of the Mediterranean environment, comprising of a wet and dry intra-annual variability of water discharge and suspended sediment load. The transitions between the two regimes can be approximated by a Markov chain (switching regression model), which can be used for the estimation of monthly suspended sediment fluxes when the corresponding water discharge is known.

中文翻译：

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拟合高斯混合模型以实现每月河流流量和悬浮沉积物的双变量分布

摘要 本文的目的是使用灵活的统计模型，即高斯混合模型，研究月排水量与悬浮泥沙负荷之间的复杂关系。简要分析了该模型的理论原理及其相关的期望最大化（EM）算法，随后将其应用于巴尔干半岛南部4条中等山区河流（即Acheloos、Arachthos、Aoos和Aliakmon）的水文数据中，其上述变量的数据分布表明存在两个亚群。将高斯混合模型 (GMM) 拟合到每条河流的样本点，然后通过比较不同的信息标准来调整其参数，以确定最佳参数设置。这些参数（潜在变量）与双变量分布的生成机制有关，它在两个分量（制度）之间交替，与水文变量的季节性有关；后者是地中海环境的特征，包括水排放和悬浮泥沙负荷的湿和干年内变化。两种状态之间的转变可以通过马尔可夫链（切换回归模型）来近似，当相应的排水量已知时，该模型可用于估算每月悬浮泥沙通量。包括水流量和悬浮泥沙负荷的湿和干年内变化。两种状态之间的转换可以通过马尔可夫链（切换回归模型）来近似，当相应的排水量已知时，该模型可用于估算每月悬浮泥沙通量。包括水流量和悬浮泥沙负荷的湿和干年内变化。两种状态之间的转变可以通过马尔可夫链（切换回归模型）来近似，当相应的排水量已知时，该模型可用于估算每月悬浮泥沙通量。