Functional clustering of time series: An insight into length scales in subglacial water flow

Abstract

We analyzed water pressure measurements taken at 10‐min intervals over 49 days in an array of 16 boreholes penetrating a small mountain glacier. We sought temporal and spatial patterns that would define clusters of boreholes that behaved similarly. Because we are interested primarily in changes in pressure with time, we used functional data analysis, which involves fitting mathematical functions to the time series, in order to smooth out the otherwise noisy first derivatives in the time series. Our objective of the analysis is to identify clusters of boreholes with similar behavior, in this case similar rate of change of water pressure, to help elucidate poorly understood subglacial water flow. Though the data are collected over time, treating these time series as functional data allows for a computationally intensive but relatively simple exploratory cluster analysis. The functional cluster analysis reveals a spatially and temporally complex basal water system. We use the clustering to infer evolving regions of local connectivity in the basal water systems and additionally infer a connected englacial water system. The spatial scale of the borehole clusters is of order 50 m, while the time scale is less than 9 days, although not well constrained by our cluster sampling interval.