Bayesian prediction of glacial discharge in antarctica using copulas

Resumen

Glaciers are considered sensors of the Global Warming. The study of their mass balance is essential to understand their future behaviour. One of the components of this mass balance is the loss of water produced by melting, this is known as the glacier discharge. The aim of this work is to analyse the relationship among the glacier discharge and other meteorological variables such as temperature, humidity, solar radiation and precipitation, and to find a model that allow us to forecast future values of the glacier discharge. In Chapter 2, we propose the use of time-varying copula models for analysing the relationship between air temperature and glacier discharge, which is clearly non constant and non-linear through time. A bivariate copula model is defined, where both the marginal and copula parameters vary periodically along time following a seasonal dynamic. Full Bayesian inference is performed such that the marginal and copula parameters are estimated in a one single step, in contrast with the usual two-step approach. Bayesian prediction and model selection are also carried out for the proposed model such that Bayesian credible intervals can be obtained for the conditional glacier discharge given a value of the temperature at any time point. In Chapter 3, as a second model, a vine copula structure is proposed to model the multivariate and nonlinear dependence among the glacier discharge and the other related meteorological variables. 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. Seasonal effects in this second model are captured by using different parameters for each season. 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. In order to improve the second model, Chapter 4 proposes a hierarchical structure where the relationships between the meteorological variables in each season and in each case are led by common hyperparameters. Bayesian inference is performed over the hierarchical structure with the help of Approximate Bayesian Computation (ABC) techniques. All the proposed methodologies are 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 which records values of the liquid discharge from the Collins glacier.