Functional data methods for climatological processes

Harris, Trevor Austin

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https://hdl.handle.net/2142/110433 Copy

Description

Title

Functional data methods for climatological processes

Author(s)

Harris, Trevor Austin

Issue Date

2021-04-06

Director of Research (if dissertation) or Advisor (if thesis)

Li, Bo

Doctoral Committee Chair(s)

Li, Bo

Committee Member(s)

• Shao, Xiaofeng
• Narisetty, Naveen N
• Tucker, James D

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• functional data analysis
• climate science, anomaly detection
• paleoclimate

Abstract

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.

Graduation Semester

2021-05

Type of Resource

Thesis

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Copyright and License Information

Copyright 2021 Trevor Harris

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