Vine copula models for predicting water flow discharge in Antarctic glaciers

In order to understand the future behavior of the glaciers, their mass balance must 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 divided in four cases according to the presence or not of positive discharge and/or positive precipitation. Then, each different case 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 for the glacier discharge for the given meteorological conditions. Three different prediction methods are used and compared for the future values of the discharge. The proposed methodology is applied to a large data base 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 our proposed vine copula model outperforms the standard results obtained with the classical degree-day models in all cases for both the probability of positive discharge and the discharge amount predictions.