Fitting a Gaussian mixture model to bivariate distributions of monthly river flows and suspended sediments

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.