# Also in the Article

Winter deformation rates
This protocol is extracted from research article:
Sliding dominates slow-flowing margin regions, Greenland Ice Sheet
Sci Adv, Jul 10, 2019;

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Continuous tilt measurements (θ) recorded by each inclinometer probe were used to estimate the vertical gradients in horizontal velocity (du/dz) across the 2015–2016 winter. The following relation estimates the shear strain rate from inclinometer tilt in the x-z plane$dudz=ΔxΔzΔt≈ΔtanθaΔt$(1)where Δt spans the length of the winter period, and θa is tilt in the direction of ice flow.

The tilt of an inclinometer installed with its cylindrical axis oriented vertically is solely due to vertical shearing of the ice column (37). Once rotated from this vertical orientation, analytical modeling of inclinometers embedded in deforming ice has shown that the rotation rate is influenced by normal strains (37). This can affect the estimate of du/dz using Eq. 1 if field conditions deviate significantly from shear dominated flow. The magnitude of the normal components of the strain rate tensor calculated from the GPS surface array ($ε˙$xx = 0.0006 a−1, $ε˙$yy = 0.0037 a−1, $ε˙$zz = −0.0043 a−1, and $ε˙$xy = 0.0014 a−1) shows that ice deformation is not only due to vertical shearing. This suggests that it is necessary to quantify the impact of normal strains on our estimates of du/dz using Eq. 1.

To do so, we used a sensitivity analysis (Supplementary Analysis) that shows that the tilt rate of near-vertical inclinometers is dominated by the rate of vertical shearing. Specifically, the analysis illustrates that when θ < 3°, Eq. 1 is a robust method to estimate du/dz. When θ < 10°, Eq. 1 is still reliable for estimating du/dz under most conditions expected at the field location. As a metric of data quality, we therefore partition deformation measurements into two sets based on whether the mean inclinometer tilt over the winter period is θ < 3° or θ > 3° when presented in fig. S2.

The instrumental error in the calculated vertical shear strain rates ranges from ±0.5 × 10−5 to 1.7 × 10−5 a−1 (SD). Inclinometers with nonfunctional tilt sensors or those with sensor errors identified by the logger during sampling were not included in the analysis. Uncertainty associated with the effect of normal strains is estimated to be an additional ±10% of the strain rate estimated using Eq. 1 (Supplementary Analysis).

The winter period spans 240 days during the 2015–2016 winter [day of year (DOY) 2015, 255 to 495]. During this period, the velocity field did not undergo any large and rapid variations in time (fig. S4). Air temperatures generally remained below freezing, with the exception of a brief excursion to positive temperatures near the end of the winter (DOY 2015, 466 to 471), which resulted in a minor velocity decrease at the westernmost GPS station. The lack of coherence between GPS stations and small magnitude of the event suggests that this is likely due to coupling to nonlocal flow downgradient of the site.

For most inclinometers, du/dz was estimated using Δt equal to the entire winter period. Discontinuous or intermittent records at specific borehole locations and inclinometers yield some variation in the length of the record used to estimate du/dz. This is documented in table S1.

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