An Empirical Approach for Estimating Stress-Coupling Lengths for Marine-Terminating Glaciers

Abstract

Despite an increase in the abundance and resolution of observations, variability in the dynamic behavior of marine-terminating glaciers remains poorly understood. When paired with ice thicknesses, surface velocities can be used to quantify the dynamic redistribution of stresses in response to environmental perturbations through computation of the glacier force balance. However, because the force balance is not purely local, force balance calculations must be performed at the spatial scale over which stresses are transferred within glacier ice, or the stress-coupling length (SCL). Here we present a new empirical method to estimate the SCL for marine-terminating glaciers using high-resolution observations. We use the empirically-determined periodicity in resistive stress oscillations as a proxy for the SCL. Application of our empirical method to two wellstudied tidewater glaciers (Helheim Glacier, SE Greenland, and Columbia Glacier, Alaska, USA) demonstrates that SCL estimates obtained using this approach are consistent with theory (i.e., can be parameterized as a function of the ice thickness) and with prior, independent SCL estimates. In order to accurately resolve stress variations, we suggest that similar empirical stress-coupling parameterizations be employed in future analyses of glacier dynamics.

Evolving Environmental and Geometric Controls on Columbia Glacier's Continued Retreat

“…Ice surface velocities were computed from TerraSAR‐X and TanDEM‐X SAR data, using standard speckle‐tracking methods (Joughin, ). The 100‐m posted (true resolution is ~300 m) velocities were resampled to the 150‐m resolution bed elevation map postings using a linear distance‐weighted approach (Enderlin et al, ).…”

“…High‐resolution (2 m) DEMs were produced from the stereo images (Shean et al, ) and vertically coregistered using bedrock outcrops spanning the near‐terminus regions of both glacier tributaries. Following coregistration, DEMs were downsampled to the common 150‐m postings using a linear distance‐weighted approach, which also smooths the data and minimizes random errors (Enderlin et al, ). Manual inspection of the 2‐m resolution DEMs indicates that horizontal offsets between DEMs are a few pixels or less and have negligible influence on surface elevations extracted from the downsampled DEMs, particularly in the low‐slope regions that are the focus of our analysis.…”

“…We merged the two most recent mass‐conserving bed‐elevation maps constructed for Columbia Glacier (Enderlin et al, ; McNabb et al, ) and further refined the composite bedmap using a flotation‐based criterion over the recently opened inner fjord (Figure a). The bed elevation map from McNabb et al (), hereafter called the M12 bedmap, covers the entirety of the Columbia and Post catchment areas but is only loosely constrained by radar‐derived bed elevation observations.…”

“…The more recent mass‐conserving bedmap from Enderlin et al (; E16 bedmap) incorporates decluttered and reprocessed radar profiles collected during 2012 (Rignot et al, ) that are less prone to errors than the earlier radar observations available to McNabb et al (). However, this more accurate map only covers the trunk of Columbia Glacier over the lowest ~10 km of its two major tributaries (Figure a); Post Glacier is not included in this product.…”

A Plastic Network Approach to Model Calving Glacier Advance and Retreat

“…Overall, the plastic model fit to observed surface elevation as measured by CV RMS is good along the main and west branches (CV RMS = 6.2% and 9.5%, respectively) but weaker along the east branch (19.9%). The east branch, where our model tends to overestimate ice thickness by 50% or more, has seldom been directly studied (Krimmel, 2001), although recent radar-sounding and bed-mapping efforts (Rignot et al, 2013;Enderlin et al, 2016) have better constrained the bed topography there and can be applied in future use of our model. We note also that the stretch of the main branch with the poorest fit to observation is the location of a sharp drop in the bedrock, where we might expect problems with the plastic model due to its strong dependence on bed topography.…”