Functional data methods for climatological processes

Many climatological and environmental processes take the form of trajectories or surfaces. In the language of Statistics, these observations can be considered as functional data and the tools for studying the behavior of functional data define a framework known as Functional Data Analysis (FDA). In the following Chapters we will propose three FDA methods to model three different climatological phenomena. Chapter 1 will develop a robust test statistic for differentiating between two ensembles of spatial processes. We use this method to test for significant influence of historical proxy observations in paleoclimate reconstructions. Chapter 2 introduces a new class of functional data depths and a rigorous shape outlier detector based on elastic distance. This method handled functional data observed on nonlinear manifolds, such as spheres, which allows us to identify anomalously shaped hurricane trajectories in the Atlantic. Finally, in Chapter 3 we propose a computationally efficient and robust changepoint detector for functional data. We use this to test for, and estimate, changepoints in a long sequence of atmospheric interferometer profile measurements