Detecting British Columbia Coastal Rainfall Patterns by Clustering Gaussian Processes

Functional data analysis is a statistical framework where data are assumed to follow some functional form. This method of analysis is commonly applied to time series data, where time, measured continuously or in discrete intervals, serves as the location for a function's value. Gaussian processes are a generalization of the multivariate normal distribution to function space and, in this paper, they are used to shed light on coastal rainfall patterns in British Columbia (BC). Specifically, this work addressed the question over how one should carry out an exploratory cluster analysis for the BC, or any similar, coastal rainfall data. An approach is developed for clustering multiple processes observed on a comparable interval, based on how similar their underlying covariance kernel is. This approach provides interesting insights into the BC data, and these insights can be framed in terms of El Ni\~{n}o and La Ni\~{n}a; however, the result is not simply one cluster representing El Ni\~{n}o years and another for La Ni\~{n}a years. From one perspective, the results show that clustering annual rainfall can potentially be used to identify extreme weather patterns.