Ice discharge error estimates using different cross-sectional area approaches: a case study for the Canadian High Arctic, 2016/17

Abstract

We analyse the various error sources in the estimation of ice discharge through flux gates, distinguishing the cases with ice-thickness data available for glacier cross-sections or only along the centreline. For the latter, we analyse the performance of three U-shaped cross-sectional approaches. We apply this methodology to glaciers of the Canadian High Arctic. The velocity field is the main error source for small and medium-size glaciers (discharge <100 Mt a−1) with low velocities (<100 m a−1), while for large glaciers (discharge >100 Mt a−1) with high velocities (>100 m a−1) the error in cross-sectional area dominates. Thinning/thickening between ice-thickness and velocity measurements should be considered, as it implies systematic errors up to 8% in our study. The U-shaped parabolic approach, which allows for an adjusted estimation when the ice-thickness measurement point is displaced from the glacier centreline, performs best, with small bias and admissible standard error. We observe an increase of ice discharge from the main glaciers (Trinity and Wykeham) of the Prince of Wales Icefield from 2015 to 2016, by 5 and 20%, respectively, followed by a decrease in 2017, by 10 and 15%, respectively. Belcher Glacier, of the Devon Ice Cap, maintains similar discharges during 2015–17.

Intra- and inter-annual variability in dynamic discharge from the Academy of Sciences Ice Cap, Severnaya Zemlya, Russian Arctic, and its role in modulating mass balance

“…Errors in ice discharge were estimated following Sánchez-Gámez and Navarro (2018). Applying error propagation to Eqn (3) yields where each term is of the form (taking as an example) In Eqn (4) we have omitted the term because the bin-width L i is assumed to be error-free.…”

Quality Assessment and Glaciological Applications of Digital Elevation Models Derived from Space-Borne and Aerial Images over Two Tidewater Glaciers of Southern Spitsbergen

“…Such DEMs have been used to measure elevation changes of glaciers worldwide in recent years [12][13][14]. In particular, the freely available and continuously updated ArcticDEM [15], (https://www.pgc.umn.edu/data/arcticdem/) provides a potent new source of glacier volume change (e.g., [16][17][18][19][20])…”

Uncertainty Assessment of Ice Discharge Using GPR-Derived Ice Thickness from Gourdon Glacier, Antarctic Peninsula

“…For grounded parts of the glacier, the ice discharge Φ can be calculated with the following formula as the mass flux through a given surface S approximated per area bin n (after [37]):…”

“…More details e.g., to the location of the stable areas can be found in Lippl et al [23]. The error in the velocity direction ∆α i is estimated similar to Sánchez-Gámez and Navarro [37] as the standard deviation of α j for j ∈ i − 4, i + 4. In Figure A2c it is visible that the calculated directions of the velocity vector are relatively constant at the lower part of the glacier.…”

“…Following the approach from Sánchez-Gámez and Navarro [37], we assume L n to be free of errors, especially in the case of Gourdon Glacier. The glacier border at the northern side can be differentiated very sharply from the cliff, and the influence at the southern border can be neglected due to the measured low ice thickness values.…”