Proper orthogonal decomposition of ice velocity identifies drivers of flow variability at Sermeq Kujalleq (Jakobshavn Isbræ)

Abstract

Abstract. The increasing volume and spatio-temporal resolution of satellite-derived ice velocity data have created new exploratory opportunities for the quantitative analysis of glacier dynamics. One potential technique, proper orthogonal decomposition (POD), also known as empirical orthogonal functions, has proven to be a powerful and flexible technique for revealing coherent structures in a wide variety of environmental flows. In this study we investigate the applicability of POD to an openly available TanDEM-X/TerraSAR-X-derived ice velocity dataset from Sermeq Kujalleq (Jakobshavn Isbræ), Greenland. We find three dominant modes with annual periodicity that we argue are explained by glaciological processes. The primary dominant mode is interpreted as relating to the stress reconfiguration at the glacier terminus, known to be an important control on the glacier's dynamics. The second and third largest modes together relate to the development of the spatially heterogenous glacier hydrological system and are primarily driven by the pressurisation and efficiency of the subglacial hydrological system. During the melt season, variations in the velocity shown in these two subsidiary modes are explained by the drainage of nearby supraglacial melt ponds, as identified with a Google Earth Engine Moderate Resolution Imaging Spectroradiometer (MODIS) dynamic thresholding technique. By isolating statistical structures within velocity datasets and through their comparison to glaciological theory and complementary datasets, POD indicates which glaciological processes are responsible for the changing bulk velocity signal, as observed from space. With the proliferation of optical- and radar-derived velocity products (e.g. MEaSUREs, ESA CCI, PROMICE), we suggest POD, and potentially other modal decomposition techniques, will become increasingly useful in future studies of ice dynamics.

Seasonal flow types of glaciers in Sermilik Fjord, Greenland, over 2016–2021

“…4.1.2 Role of higher-order modes EOF/PC decomposition of three years of glacier speed data in a 2.5 × 4 km area on Jakobshavn Isbrae by Ashmore et al (2021) revealed similar results as we find here: a strong first mode (98%) followed by higher-order modes with coherent spatial and temporal patterns. However, Ashmore et al (2021) discovered that modes 2 and 3 were paired:…”

“…The leading modes (highest variance explained) often, but are not mathematically required to, represent a distinct phenomenon that gives rise to a unique spatio-temporal pattern. For example, the Arctic Oscillation is the first mode of the wintertime sea-level pressure field in the northern hemisphere (Lorenz, 1951;Thompson & Wallace, 1998), and the first mode of ice flow speed in a specific area of Jakobshavn Isbrae captures the effects of seasonal stress changes at the glacier terminus (Ashmore et al, 2021).…”

“…To date, the application of EOF / PC analysis within glaciology has been somewhat limited: only Mair (2002); Campbell et al (2017); Ashmore et al (2021) have used this technique to interpret glacier flow. Campbell et al (2017) analyzed the modeled rates of change of ice-surface elevation and speed on Byrd Glacier, Antarctica, over 800-year runs of an ice-flow model.…”

“…Campbell et al (2017) analyzed the modeled rates of change of ice-surface elevation and speed on Byrd Glacier, Antarctica, over 800-year runs of an ice-flow model. Ashmore et al (2021) inferred the contributions of terminus position and runoff forcing on a 2.5 × 4 km area of the main trunk of Jakobshavn Isbrae, approximately 8 km from the terminus. Mair (2002) achieved a similar result on a 0.6 × 1 km reach of Haut Glacier d'Arolla, Switzerland.…”

“…Mair (2002) achieved a similar result on a 0.6 × 1 km reach of Haut Glacier d'Arolla, Switzerland. Here, we run a similar EOF (Joughin, 2021) / PC analysis of ice speed as Mair (2002); Ashmore et al (2021), but do so over full-glacier analysis domains sized 150-350 km 2 .…”