Applications of functional data analysis to environmental problems.

Functional Data Analysis (FDA) is a relatively recent framework within the statistical sciences, and while it offers compelling benefits to many applications, it has not yet gained widespread applied use. Two important environmental applications, water quality profile forecasting and larval fish photolocomotor response studies, measure functional data and stand to profit from employing FDA. In this work, we present the first application of FDA to these two applications of environmental and biological sciences. Specifically, this dissertation analyzes the most temporally and vertically dense dissolved oxygen lake profiles in the water quality forecasting literature. This is the first work to introduce full function forecasting with exogenous variables, various machine learning approaches, and empirical prediction band construction in the context of functional principal component machine learning hybrid models. Additionally, this research introduces both a new permutation test for two-way functional ANOVA and the first simulation study comparing four global F-based statistics in a two-way functional ANOVA setting.