Abstract
Outlet glaciers of the Greenland Ice Sheet exhibit characteristic patterns of motion, in which glacier velocities increase and decrease coherently. In many cases these spatial patterns are driven by time-varying terminus positions or hydrologic forcing. These patterns have been diagnosed using increasingly high resolution remote sensing data-data that are also empowering rapid advances in our understanding of the processes driving glacier change. However, process-oriented studies of glacier motion are frequently challenged by spatial gaps within data. While temporal resolution is in many cases finer than monthly, critical portions of velocity fields may go unmapped due to incoherent surface features, clouds, or processing errors. In this work, we show that spatial patterns of surface motion at individual glaciers are consistent over time, presumably dictated by individual glacier geometry, and that these characteristic patterns of motion can be described by just a handful of empirical orthogonal functions (EOFs). These several EOFs are exceptionally capable of reproducing the dominant patterns of glacier motion. Just the first EOF produced using MEaSUREs TerraSAR-X velocities from the Upernavik Ice Streams captures 2/3rds of the observed variation in glacier motion; this EOF describes the magnitude of seasonal, coherent, terminus acceleration and deceleration. The first four EOFs describe 95% of velocity variations. In this study, we proceed to use these mapped EOFs to diagnose the spatial patterns of glacier motion using spatially gappy data and then empirically synthesize missing data to create time series of complete velocity fields. In experiments where we further censor successfully mapped data, we find that our EOF approach is able to reconstruct the censored data with approximately 5% error. This workflow is demonstrated in an open-source Jupyter Notebook designed for the adoption and customization of our approach. We hope that our study represents a step towards spatially and temporally complete velocity fields of the entire Greenland Ice Sheet, and empower the further expansion of new process-oriented studies.