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In order to understand the behavior of the glaciers, their mass balance should be studied. The loss of water produced by melting, known as glacier discharge, is one of the components of this mass balance. In this paper, a vine copula structure is proposed to model the multivariate and nonlinear dependence among the glacier discharge and other related meteorological variables such as temperature, humidity, solar radiation and precipitation. The multivariate distribution of these variables is expressed as a mixture of four components according to the presence or not of positive discharge and/or positive precipitation. Then, each of the four subgroups is modelled with a vine copula. The conditional probability of zero discharge for given meteorological conditions is obtained from the proposed joint distribution. Moreover, the structure of the vine copula allows us to derive the conditional distribution of the glacier discharge for the given meteorological conditions. Three different prediction methods for the values of the discharge are used and compared. The proposed methodology is applied to a large database collected since 2002 by the GLACKMA association from a measurement station located in the King George Island in the Antarctica. Seasonal effects are included by using different parameters for each season. We have found that the proposed vine copula model outperforms a previous work where we only used the temperature to predict the glacier discharge using a time-varying bivariate copula.