The Greenland ice sheet has experienced significant melt over the past six decades, with rare extreme melt events covering large areas of the ice sheet. Melt events are typically analysed using summary statistics from satellite data, but the nature and characteristics of the events themselves are less frequently analysed. In this thesis, we take MODIS satellite temperature data and develop a series of models to build a detailed understanding of temperature, melt, and extreme temperature events on the ice sheet. A core aim of the modelling work is to create and use
models that are statistically robust that also strongly consider the scientific context of the variables and processes being modelled. We first develop a statistical model for temperatures at a single location on the ice sheet. We define a novel method of identifying melt observations using a Gaussian mixture model to capture the distribution of temperatures across the ice sheet in a consistent format. In the next chapter, we begin to examine the spatial trends in the data by examining the mixture
model’s parameters in a spatial setting. We use a regression model to predict the mixture model parameters for a given location based only on geographic spatial variables, allowing us to estimate the distribution of temperatures for any location using only a set of coordinates and information derived from them. We then examine spatial dependence between locations using a Gaussian process. Using the mixture
model as a marginal model and insights from the regression model, we quantify the spatial dependence in the data and simulate temperature realisations for the entire ice sheet. Finally, we use the spatial conditional extremes model to model extreme temperature events. Using the model, we can describe the characteristics of extreme temperature events and simulate and predict them.