TCThe CryosphereTCThe Cryosphere1994-0424Copernicus GmbHGöttingen, Germany10.5194/tc-9-2219-2015Observations of seasonal and diurnal glacier velocities at Mount Rainier,
Washington, using terrestrial radar interferometryAllstadtK. E.allstadt@uw.eduSheanD. E.CampbellA.FahnestockM.MaloneS. D.University of Washington, Department of Earth and Space
Sciences, Washington, USAUniversity of Washington, Applied Physics Lab Polar
Science Center, Washington, USAUniversity of Alaska Fairbanks, Geophysical
Institute, Fairbanks, Alaska, USAnow at: USGS Geologic Hazards Science
Center, Golden, CO, USAK. E. Allstadt (allstadt@uw.edu)1December2015962219223516June201531July201511November201516November2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://tc.copernicus.org/articles/9/2219/2015/tc-9-2219-2015.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/9/2219/2015/tc-9-2219-2015.pdf
We present surface velocity maps derived from repeat terrestrial radar
interferometry (TRI) measurements and use these time series to examine
seasonal and diurnal dynamics of alpine glaciers at Mount Rainier,
Washington. We show that the Nisqually and Emmons glaciers have small
slope-parallel velocities near the summit (< 0.2 m day-1), high
velocities over their upper and central regions (1.0–1.5 m day-1), and
stagnant debris-covered regions near the terminus (< 0.05 m day-1).
Velocity uncertainties are as low as ±0.02–0.08 m day-1. We document a
large seasonal velocity decrease of 0.2–0.7 m day-1 (-25 to -50 %) from July
to November for most of the Nisqually Glacier, excluding the icefall,
suggesting significant seasonal subglacial water storage under most of the
glacier. We did not detect diurnal variability above the noise level. Simple
2-D ice flow modeling using TRI velocities suggests that sliding accounts for
91 and 99 % of the July velocity field for the Emmons and Nisqually
glaciers with possible ranges of 60–97 and 93–99.5 %,
respectively, when considering model uncertainty. We validate our
observations against recent in situ velocity measurements and examine the
long-term evolution of Nisqually Glacier dynamics through comparisons with
historical velocity data. This study shows that repeat TRI measurements with
> 10 km range can be used to investigate spatial and temporal
variability of alpine glacier dynamics over large areas, including hazardous
and inaccessible areas.
Introduction
Direct observations of alpine glacier velocity can help improve our
understanding of ice dynamics. Alpine glacier surface velocities are
typically dominated by basal sliding, which is tightly coupled to subglacial
hydrology (Anderson et al., 2014; Bartholomaus et al., 2007). However, the
spatial extent and spatial/temporal resolution of direct velocity
measurements are often limited to short campaigns with sparse point
measurements in accessible regions (e.g., Hodge, 1974; Driedger and Kennard,
1986). Remote sensing can help overcome many of these limitations. Radar
interferometry, a form of active remote sensing, detects millimeter-to-centimeter-scale
displacements between successive images of the same scene and can see
through clouds and fog. In the past few decades, satellite interferometric
synthetic aperture radar, or InSAR (e.g., Massonnet and Feigl, 1998; Burgmann
et al., 2000), has emerged as an invaluable tool for quantifying glacier
dynamics (e.g., Joughin et al., 2010). However, limited data availability and
revisit times limit the application of InSAR for the study of many
short-term processes.
Terrestrial radar interferometry (TRI), also referred to as ground-based
radar interferometry, has recently emerged as a powerful technique for
observing glacier displacement that is not prone to the same limitations
(Caduff et al., 2014). Sets of radar data acquired at intervals as short as
∼1 min from up to several kilometers away allow for observations
of velocity changes over short timescales and large spatial extents.
Stacking these large numbers of interferogram pairs over longer timescales
can significantly reduce noise. Here, we employ this relatively new
technique to provide spatially and temporally continuous surface velocity
observations for several glaciers at Mount Rainier volcano in Washington
State (Fig. 1). Though Rainier's glaciers are among the best-studied alpine
glaciers in the USA (Heliker et al., 1984; Nylen, 2004), there are many
open questions about diurnal and seasonal dynamics that TRI can help
address. Specifically, many aspects of subglacial hydrology and its effects
on basal sliding are poorly constrained, especially for inaccessible
locations like the Nisqually icefall and ice cliff. Our observations provide
new insight into these processes through analysis of the relative magnitude
and spatial patterns of surface velocity over diurnal and seasonal
timescales. To our knowledge, no other studies have investigated seasonal
changes to glacier dynamics using TRI.
Glaciers at Mount Rainier and locations of viewpoints used for
ground-based radar interferometry. Instrument view angle ranges are
indicated by arrows extending away from each viewpoint location. Boxes A–C
show zoom areas for later figures. Inset map shows regional location of
Mount Rainier. Glacier outlines in this and subsequent figures are from
Robinson et al. (2010).
Mount Rainier offers an excellent setting for TRI, with several accessible
viewpoints offering a near-continuous view with ideal line-of-sight vectors
for multiple glaciers, and well-distributed static bedrock exposures for
calibration. The ability to image the velocity field of entire glaciers from
one viewpoint with minimal shadowing sets this study area apart. Most
previous studies only image part of the glaciers under investigation,
usually due to less favorable viewing geometries (e.g., Noferini et al.,
2009; Voytenko et al., 2015; Riesen et al., 2011). However, the steep
topography and local climatic factors at Mount Rainier result in strong
atmospheric variability and turbulence – a major source of noise for radar
interferometry techniques (Goldstein, 1995). Atmospheric noise is a
particular issue for the long ranges (> 10 km) associated with
accessible viewpoints at Mount Rainier. To overcome this limitation, we
successfully combine, expand on, and evaluate noise reduction techniques
such as stacking interferograms (e.g., Voytenko et al., 2015) and deriving
atmospheric noise corrections over static control surfaces (bedrock
exposures) (e.g., Noferini et al., 2009). We demonstrate that these techniques
offer significant uncertainty reductions using a novel bootstrapping
approach.
In the following sections, we provide background on Mount Rainier's
glaciers and detail our sampling methodology and data processing
techniques. We then present TRI results documenting seasonal and diurnal
velocity variations for the Nisqually, Wilson, Emmons, and upper Winthrop
glaciers and quantify measurement uncertainty. Next we examine the
partitioning of observed surface velocities between deformation and basal
sliding at different times of year using a simple 2-D flow model and compare
our observations to other recent and historical velocity measurements. These
comparisons provide ground truth for TRI measurements and new insight into
the evolution of the Nisqually Glacier since the late
1960s.
Study area
With a summit elevation of 4392 m, Mount Rainier (Fig. 1) is the largest
stratovolcano in the Cascades and is considered the most dangerous volcano
in the USA (Swanson et al., 1992). It also holds the largest
concentration of glacial ice in mainland USA (Driedger and
Kennard, 1986) – 87 km2 was covered with perennial snow and ice in 2008
(Sisson et al., 2011). The steep upper sections of the major glaciers are
relatively thin, with typical thicknesses of ∼30–80 m
(Driedger and Kennard, 1986). Thickness increases at lower elevations, with
a maximum of ∼200 m for the Carbon Glacier, although these
estimates likely provide an upper bound, as these glaciers have experienced
significant thinning in recent decades, losing 14 % of their volume
between 1970 and 2008 (Sisson et al., 2011). Mass balance stake measurements
from 2003 to 2010 show that the average winter balance for Nisqually was
2.4 m water equivalent (m w.e.), average summer balance was -3.5 m w.e., and
cumulative net balance was -8.6 m w.e. from 2003 to 2011 (Riedel, 2010; Riedel
and Larrabee, 2015).
The glaciers of Mount Rainier have been of interest to geoscientists for over
150 years and have a long record of scientific observation (Heliker, 1984).
In this study, we focus on large, accessible, well-documented glaciers in
the park: the Nisqually Glacier on the southern flank and Emmons Glacier
on the northeastern flank. Additional glaciers in the field of view are also
captured, including the Wilson Glacier, which flows into the Nisqually
Glacier, the upper Winthrop Glacier, Fryingpan Glacier, upper Kautz Glacier,
and Inter Glacier. All glaciers are labeled in Fig. 1.
The Nisqually Glacier is visible from several viewpoints near the Paradise
Visitor Center, which is accessible year round. The terminus location has
been measured annually since 1918, and three transverse surface elevation
profiles have been measured nearly every year since 1931 (Heliker, 1984).
Veatch (1969) documented a 24-year history of Nisqually's advances and
retreats and other dynamic changes through a meticulous photographic survey
from 1941 to 1965. Hodge (1974) conducted a detailed 2-year field study of the
seasonal velocity cycle for the lower Nisqually. He found that velocities
varied seasonally by about 50 %, with maximum velocities in the spring
(June) and minimum in the fall (November). This finding, and the lack of
correlation between runoff and sliding speeds, advanced the idea that
efficient conduits close as meltwater input decreases in the fall, leading
to distributed subglacial storage through the fall, winter, and spring.
Increased surface melting in spring and summer leads to increased subglacial
discharge and the opening of a more efficient network of conduits capable of
releasing some of this stored water (Hodge, 1974). More recently, Walkup et
al. (2013) tracked the movements of supraglacial rocks with high precision
from 2011 to 2012, yielding velocity vectors for a wide network of points over
the lower parts of Nisqually Glacier.
The Emmons Glacier, visible from the Sunrise Visitors Center, has received
less attention than Nisqually, despite the fact that it is the largest
glacier by area on the mountain (Driedger and Kennard, 1986), mainly because
it is not as easily accessible as Nisqually. A large rock fall
(∼1.1×107 m3) from Little Tahoma in December 1963
covered much of the lower Emmons Glacier with a thick debris layer (Crandell
and Fahnestock, 1965). The insulating debris cover likely contributed to the
advance and thickening of the Emmons Glacier from 1970 to 2008, while all other
glaciers on Mount Rainier experienced significant thinning (Sisson et al.,
2011). The average 2003–2010 winter balance for Emmons was 2.3 m w.e., the average
summer balance was -3.2 m.w.e, and the cumulative net balance was 7.7 m w.e.
from 2003 to 2011 (Riedel, 2010; Riedel and Larrabee, 2015).
The National Park Service's long-term monitoring protocols include both the
Nisqually and Emmons glaciers and involve regular photographs, annual mass
balance measurements, meltwater discharge rates, plus area and volume change
estimates every decade (Riedel, 2010; Riedel and Larrabee, 2015).
GPRI equipment setup during the 27 November 2012 campaign at ROI viewpoint.
MethodsInstrument description
For this study, we used a GAMMA portable radar interferometer (GPRI) (Werner
et al., 2008, 2012) – a ground-based, frequency-modulated
continuous waveform radar that can capture millimeter-scale surface
displacements. The instrument includes three 2 m antennas mounted on a
vertical truss, with one transmit antenna 35 cm above the upper of two
receiving antennas, spaced 25 cm apart (Fig. 2). The transmit antenna
produces a 35∘ vertical beam with 0.4∘ width that
azimuthally sweeps across the scene to build a 2-D radar image as the truss
rotates. The radar operates at a center frequency of 17.2 GHz, with
selectable chirp length of 2–8 ms and bandwidth of 25–200 MHz. The radar
wavelength is 17.6 mm with range resolution of ∼0.75 cm and
one-way interferometric change sensitivity of 8.7 mm cycle-1 of phase
providing < 1 mm line-of-sight precision. Line-of-sight
interferograms are generated by comparing phase differences in successive
acquisitions from the same viewpoint. The interval between acquisitions can
be as short as ∼1 min, allowing for high coherence even in
rapidly changing scenes.
We performed four data collection campaigns in 2012 (Table 1). The first
campaign occurred on 6–7 July 2012. This timing corresponds to just after
the expected peak seasonal glacier velocities at Mount Rainier (Hodge,
1974). Following the success of this study, three subsequent deployments
were performed during the late fall and early winter, which should capture
near-minimum seasonal velocity (Hodge, 1974). These campaigns were timed to
occur before, immediately after, and a few weeks after the first heavy
snowfall of the season (2 and 27 November and 10 December 2012,
respectively).
Three viewpoints were selected for data collection: GLPEEK and ROI, which
overlook the Nisqually, Wilson, and upper Kautz glaciers, and SUNRIZ, which
overlooks the Emmons, upper Winthrop, Inter, and Fryingpan glaciers (Fig. 1).
ROI and SUNRIZ were directly accessible from park roads, which greatly
facilitated instrument deployment, and GLPEEK was accessed on foot. ROI was
occupied during all campaigns, while SUNRIZ and GLPEEK were only occupied
during the July 2012 campaign because of access limitations. Figures A1–A3
in the Appendix show the field of view from each viewpoint.
Distances from the GPRI to the summit were 6.7, 7.6, and 10.8 km from
GLPEEK, ROI, and SUNRIZ, respectively. Radar images were continuously
collected with a 3 min interval for all surveys. Total acquisition time
at each site was dictated by logistics (weather conditions, personnel), with
∼24 h acquisitions at SUNRIZ and ROI to capture diurnal
variability.
The instrument was deployed on packed snow during the 6 July 2012 GLPEEK and
27 November and 10 December 2012 ROI acquisitions. Over the course of the GLPEEK
survey, we noted limited snow compaction and melt beneath the GPRI tripod
with total displacement of ∼2–4 cm over ∼6 h. However, this instrument motion proved to be negligible for the
interferogram interval used (6 min). We did not note significant snow
compaction under the tripod during the fall/winter surveys.
Weather conditions during the July 2012 surveys were clear with
light/variable wind. The 2 November 2012 survey involved high-altitude clouds,
passing showers, and brief interruptions in data collection. Weather
conditions were clear with sun for the 27 November 2012 campaign and fog with
limited visibility on 10 December 2012.
Data processing
All radar data were processed with the GAMMA SAR and Interferometry software
suite. Interferograms were generated from single-look complex SLC products
with a time separation of 6 min, though sometimes longer if acquisition
was interrupted. For example images see Fig. A4. Interferograms were
multi-looked by 15 samples in the range direction to reduce noise. A
correlation threshold filter of 0.7 and an adaptive bandpass filter
with default GAMMA parameters were applied to the interferograms to improve
phase unwrapping. Phase unwrapping was initiated in areas with high
correlation scores and negligible deformation, such as exposed bedrock or
stagnant ice.
Summary of uncertainty estimates of median stacks.
1 Derived from bootstrapping, 95 % confidence, line of sight velocities;
2 correction refers to removing displacements due to atmospheric noise (interpolated over static control surfaces).
Atmospheric noise corrections
Slight changes in the dielectric properties of the atmosphere between the
GPRI and target surfaces can lead to uncertainty in the interferometric
displacement measurements (Zebker et al., 1997; Werner et al., 2008). Changes
in atmospheric humidity, temperature, and pressure can all affect radar
propagation velocity (Goldstein, 1995). These variations are manifested as
phase offsets in the received radar signal, which must be isolated from
phase offsets related to true surface displacements.
This atmospheric noise proved to be significant for the long range (i.e.,
∼22 km two-way horizontal path at SUNRIZ), mountainous
terrain (i.e., ∼2.4 km vertical path from SUNRIZ to summit),
and turbulent atmosphere involved with this study, with the magnitude of
this noise often exceeding that of surface displacement signals. The scale
of the atmospheric noise features we observed in the data was typically much
wider than the width of the glaciers, so in order to minimize this
atmospheric noise in the individual interferograms, we interpolated apparent
displacement values over static control surfaces (e.g., exposed bedrock). To
do this, we fit a surface using Delaunay triangulation to a subset (5 %)
of pixels over exposed bedrock. The subset of pixels was resampled randomly
for each unwrapped interferogram and the interpolated result was smoothed to
reduce artifacts and then subtracted from the interferogram. The corrections
were applied to all individual interferograms, and the resulting products
were stacked to further reduce noise. To stack, we took all the images for a
given time period and computed the mean and median at each pixel. This has
the effect of augmenting signal and canceling out noise. The median is less
affected by outliers and is our preferred result. The median line-of-sight
(LOS) velocities from this stack provide a single measurement with a high
signal-to-noise ratio for the entire sampling period.
In addition to computing the median LOS velocities for the entirety of each
sampling period, we also computed a running mean of the LOS velocities to
characterize any short-term velocity variations in the extended occupation
data sets: 7–8 July SUNRIZ (24 h) and 1–2 November ROI (21 h). The
running mean was computed every 0.3 h with a 2-h centered (acausal)
window, with standard error used to estimate uncertainty.
Interferograms with significant phase unwrapping errors, low correlation, or
anomalous noise were excluded from stacking. We only excluded a few images
for each site with the exception of SUNRIZ, which produced many images with
anomalous noise and unwrapping errors, possibly due to instrument noise
and/or the extended range through significant atmospheric disturbance. For
this reason, more than half of the data from SUNRIZ were excluded from the
analysis (Table 2). For GLPEEK and ROI, interferograms with occasional
localized unwrapping errors were preserved during stacking, as they have
little influence on the final stack median. However, localized areas with
persistent unwrapping errors in the SUNRIZ data were masked using a
threshold standard deviation filter of 0.6 m day-1.
We estimated median LOS velocity uncertainties using a bootstrapping
approach (Efron, 1979). This involved resampling the set of images used in
the stack with replacement 1000 times for each campaign. Then, for each
pixel, the 25th and the 975th ordered values were set as the lower and upper
bounds of the 95 % confidence interval.
Conversion from radar coordinates to map coordinates
We developed a sensor model and tools to terrain-correct the stacked GPRI
data (in original azimuth, range coordinates) using an existing 2 m pixel-1
airborne LiDAR digital elevation model (DEM) acquired in September 2007/2008
(Robinson et al., 2010). While some elevation change has undoubtedly
occurred for glacier surfaces between September 2008 and July 2012, the
magnitude of these changes (< 20 m) is negligible for
orthorectification purposes given the GPRI acquisition geometry. A single
control point identified over exposed bedrock in the LiDAR DEM and the
multi-look image radar data was used to constrain absolute azimuth
orientation information for each campaign. A ∼10 m pixel-1
(mean of azimuth and range sample size) grid in UTM 10N (EPSG: 32610) was
created for each campaign, with extent computed from the GPRI GPS
coordinates, min/max range values, and min/max absolute azimuth values. Each
3-D pixel in this grid was then populated by extracting the radar sample with
corresponding range and azimuth.
Correction to slope-parallel velocities
While the line-of-sight vectors for these surveys are roughly aligned with
surface displacement vectors (median incidence angles for glacier surfaces
are ∼22∘ for GLPEEK, ∼25∘
for SUNRIZ, and ∼26∘ for ROI), glaciological
analyses typically require horizontal and vertical velocity components
relative to the glacier surface. As each GPRI survey offers only a single
look direction, this is not possible. However, we can assume that
displacement is dominated by surface-parallel flow and use the 2007/2008
LiDAR DEM to extract surface slopes needed to estimate 3-D displacement
vectors (e.g., Joughin et al., 1998).
This approach is intended for relatively smooth, continuous surface slopes
over length scales > 2–3× ice thickness. It is therefore possible
that the slope-parallel correction can overestimate velocity for steep, high-relief surfaces with significant high-frequency topographic variability
(e.g., icefalls). The slope-parallel assumption also begins to break down
where the vertical flow velocity component becomes significant. This is
expected in the upper accumulation and lower ablation zones, where the
submergence and emergence velocities become more significant, respectively,
but is less important near the equilibrium-line altitude (ELA) or locations
where sliding dominates surface motion. The latter is expected for much of
the Nisqually Glacier at least (Hodge, 1974).
We implement a slope-parallel correction by first downsampling the 2007/2008
LiDAR DEM to 20 m pixel-1 and smoothing with a 15×15 pixel (∼300 m), 5σ Gaussian filter. The slope-parallel velocity (Vsp) is
defined as
Vsp=VLOS(S^⋅L^),
where S^⋅L^ is the dot product between the unit vector
pointing directly downslope from each grid cell (S^) and the unit
vector pointing from each grid cell to the sensor (L^). Regions where
the angle between these two vectors exceeded 80∘ were masked to
avoid dividing by numbers close to 0 which could amplify noise.
Two-dimensional glacier deformation modeling
Surface flow velocity can be partitioned into internal deformation and basal
sliding components. We present a simple, 2-D plane-strain ice deformation
model for a preliminary assessment of the importance of basal sliding for
the glaciers in our study area. The deformation model uses the shallow ice
approximation (SIA) – an approximate solution of the Stokes equations
(Greve and Blatter, 2009; Cuffey and Paterson, 2010). The expected surface
velocity us due to internal deformation from the SIA model is
us=2Asin(α)ρignHn+1n+1,
where ρi represents ice density, g represents gravitational
acceleration, α represents local surface slope, H represents local
ice thickness, A represents an ice softness parameter, and n represents a flow
rate exponent. The coordinate system is vertically aligned.
The SIA is not well suited for narrow mountain glaciers, so we modify it to
simulate the effect of non-local conditions, such as lateral sidewall drag
and longitudinal stretching. The ice thickness H and surface slope α
are smoothed using a weighting function based on Kamb and Echelmeyer (1986).
Kamb and Echelmeyer (1986) calculated a longitudinal coupling length l using
a 1-D force balance approach, for each point in their domain. They
calculated l to be in the range of one to three ice thicknesses for valley
glaciers. We simplified this by using a single value for l over the domain of
model. The longitudinal couple length l is used in a weighting function to
smooth α and H. The weighting function has the form
W(x,y)=e-(x-x′)2+(y-y′)2,l
where x and y represent the horizontal coordinates of the weight position, and x′ and
y′ represent the horizontal coordinates of the reference position. Weights are
calculated at each point in the model domain, over a square reference window
(side length of Aw). H and α are smoothed at the reference
position by normalizing weights over the reference window. We choose a
coupling length l of ∼1.5 ice thickness and an averaging
window size of ∼3 ice thicknesses, consistent with the usage
in Kamb and Echelmeyer (1986). We use a spatially uniform and temporally
constant ice softness parameter suitable for ice at the pressure melting
point of 2.4×10-24 Pa-3 s-1 (Cuffey and Paterson,
2010, p. 75). Ice softness can be affected by several factors (e.g.,
englacial water content and impurities), so we also consider an ice softness
parameter up to twice this best estimate in accounting for model
uncertainties, as described below. Our best estimates of model input
parameters are summarized in Table 3.
Constants used in modeling analysis.
NameSymbolValueUnitsIce softnessparameterA2.4×10-24Pa-3 s-1Side length ofreference windowAw120mAccelerationof gravityg9.81m s-2Coupling lengthl60mFlow law exponentn3dimensionlessDensity of iceρi900kg m-3Density of waterρw1000kg m-3
(a) Median slope-parallel velocity derived from TRI for GLPEEK and
SUNRIZ viewpoints taken on 6–7 July 2011. (b) Width of 95 % confidence
interval (high minus low limits for slope-parallel flow field) of slope-parallel velocities for 6–7 July 011 computed by bootstrapping after
performing atmospheric noise corrections and stacking. Area shown is
indicated by Box A on Fig. 1.
Surface slope (Fig. A1b) was estimated from the 2007/2008 LiDAR DEM
(Robinson et al., 2010). Surface velocities us are the TRI-derived median
slope-parallel velocities. Ice thicknesses H (Fig. A1a) were estimated by
differencing the 2007/2008 LiDAR DEM surface elevations and the digitized
and interpolated bed topography from Driedger and Kennard (1986). The
Driedger and Kennard (1986) bed topography contours were derived from
ice-penetrating radar point measurements and surface contours from aerial
photographs. The published basal contours for Nisqually/Wilson, Emmons, and
Winthrop glaciers were digitized and interpolated to produce a gridded bed
surface using the ArcGIS Topo to Raster utility. The gridded bed elevations
have a root mean squared error of 11 m when compared with the 57
original radar point measurements. A point-to-plane iterative closest point
algorithm (implemented in the NASA Ames Stereo Pipeline pc_align utility;
Shean et al., 2015) was used to coregister the 1986 bed
topography to the 2007/2008 LiDAR topography over exposed bedrock on valley
walls. Mean error over these surfaces was 7.6 m following coregistration,
although some of this error can be attributed to actual surface evolution
near glacier margins (e.g., hillslope processes) from 1986 to 2008. In addition
to these interpolation and coregistration errors, there were likely small
changes in ice thickness during the 4–5 years between the 2007/2008 DEM data
collection and the 2012 TRI observations, as mass balance measurements
suggest that both the Nisqually and Emmons glaciers experienced net mass
loss during this time period (Riedel and Larrabee, 2015). Propagation of
these uncertainties results in estimated ice thickness uncertainties of
∼5–25 %. In order to account for this large uncertainty, we
ran the model with ±25 % ice thickness as well as 2× ice softness
in order to estimate the possible range of expected deformation velocities.
More sophisticated ice flow models (e.g., Gagliardini et al., 2013; Le
Meur et al., 2004; Zwinger et al., 2007) could potentially offer a more
realistic picture of the spatial and temporal variability of glacier
sliding. However, given the poorly constrained model inputs and
observational emphasis for this study, we proceed with the SIA model to
obtain approximate estimates for the deformation and sliding components of
observed velocities.
Results
The median stacks of surface-parallel velocity for all viewpoints and their
respective uncertainty estimates are shown in Figs. 3–6. Overall, our
results show that repeat TRI measurements can be used to document spatial
and temporal variability of alpine glacier dynamics over large areas from
> 10 km away. The atmospheric noise removal approach was
successful in extracting a glacier displacement signal for all campaigns,
with excellent results for Nisqually Glacier due to the shorter range from
ROI and GLPEEK viewpoints and limited glacier width between control
surfaces. Stacking alone was very effective; the velocities of the mean and
median stacks with and without the atmospheric noise correction were very
similar. The main benefit of the extra step of using stable rock points to
subtract an estimate of the atmospheric noise was to significantly reduce
the uncertainties and to reduce the noise where velocities are slow. The
uncertainties before and after atmospheric correction are compared on Table 2.
The median width of the 95 % confidence interval for each corrected,
stacked pixel is plotted in Figs. 3b and 5. Note near-zero values over
exposed bedrock surfaces used to derive atmospheric noise correction. We
were able to reduce uncertainties (half the median confidence interval
width) to about ±0.02 to ±0.08 m day-1 over glacier surfaces for
some campaigns, with uncertainty dependent on the total number of stacked
images, weather conditions, and target range (Table 2). For example, the 6 July 2012
ROI survey had a final confidence interval width of 0.11 m day-1
(∼±0.06 m day-1) while the 10 December 2012 ROI survey had a
final confidence interval width of 0.15 m day-1 (∼±0.08 m day-1)
despite a 50 % increase in stack count. This is likely due to
increased local atmospheric variability, as low-altitude clouds obscured the
surface during 10 December 2012 survey. The 2 November 2012 ROI survey had the highest
stack count (359) with the lowest uncertainty values of ±0.02 m day-1
(Table 2).
(a–d) Median slope-parallel velocities for Nisqually and Wilson
glaciers for four different time periods taken from ROI viewpoint. Dashed
lines on top left panel show locations of profiles taken to create Fig. 6,
markers indicate distance in kilometers. (e–g) Percent change in median
slope-parallel velocity for the Nisqually and Wilson glaciers between time
periods. Blue indicates a velocity decrease and red indicates a velocity
increase relative to the earlier time period; gray polygons indicate areas
where velocity change is significant with 95 % confidence. Area shown is
indicated by Box B on Fig. 1.
July 2012 surface velocities
The 6–7 July 2012 observations show slope-parallel velocities that range
from ∼0.0 to 1.5 m day-1 for both the Nisqually and Emmons
glaciers (Figs. 3a, 4, 6). Both display high velocities over their upper and
central regions that taper into essentially stagnant (< 0.05 m day-1)
debris-covered regions near the terminus. In general, slope-parallel
velocities near the summit are small (< 0.2 m day-1).
On the Nisqually Glacier, a series of local velocity maxima (> 1.0 m day-1)
are associated with increased surface slopes between local
surface highs. Local velocity maxima are also observed for the fast-flowing
Nisqually icefall (western branch of upper Nisqually, see Fig. 3) and above
the Nisqually ice cliff (eastern branch). A relatively smooth velocity
gradient from slow- to fast-moving ice is present upstream of the icefall,
while the velocities above the ice cliff display a steep velocity gradient
(Fig. 3).
Width of 95 % confidence interval (high minus low limits for
slope-parallel velocity) over Nisqually Glacier computed by bootstrapping.
Shown for four sampling periods from the ROI viewpoint. Note that the color
bar is scaled differently than Fig. 3b.
The main (south) branch of the Emmons Glacier displays generally increasing
velocity from the summit to lower elevations. A large high-velocity region
(> 0.7–1.1 m day-1) is present over central Emmons, downstream of
the confluence of upper branches. These elevated velocities decrease at
lower elevations, where ice thickness increases and surface slopes decrease
(Fig. A5). A central “core” of exposed ice displays slightly elevated
velocities relative to surrounding debris-covered ice within ∼1–1.5 km of the terminus.
Velocities exceed 1 m day-1 over the “central” branch of the upper Emmons
Glacier, where flow is restricted between two parallel bedrock ridges, with
local maxima similar to Nisqually. Velocities at higher elevations within
the “central” branch appear slower (< 0.1–0.5 m day-1), separated
from the fast downstream velocities by a small area that was excluded due to
phase unwrapping errors. Photographs show that this area appears heavily
fractured with many large blocks indicative of rapid, discontinuous flow
(Fig. A3).
Smaller, relatively thin glaciers, such as the Fryingpan, upper Kautz, and
Inter glaciers (labeled in Fig. 1), also display nonzero surface velocities
of < 0.1–0.2 m day-1, but with limited spatial variability.
(a) and (c): slope-parallel velocity profiles along the two branches
of Nisqually Glacier (profile lines shown in map view in Fig. 4a) for all
sample time periods and viewpoints. (b) and (d): surface slope and ice thickness
along each profile line. Surface slope is smoothed identically to that used
for slope-parallel corrections (see text); ice thicknesses are estimated
from digitized basal contours from Driedger and Kennard (1986) and surface
elevations from the 2007/2008 LiDAR (Robinson et al., 2010). Refer to Fig. 5 and Table 2 for uncertainty estimates.
Seasonal variability
The repeat observations from the ROI viewpoint provide time series that
capture seasonal velocity variability for the Nisqually, Wilson, and upper
Kautz glaciers. We observe significant velocity changes during the summer to
winter transition and more subtle changes within the winter period. These
changes are shown in map view in Fig. 4 and in profile view with
corresponding slope and ice thickness in Fig. 6.
These data show a velocity decrease of 0.2–0.7 m day-1 (-25 to -50 %) from
July to November 2012 for most of the Nisqually Glacier. This includes
central and lower Nisqually and the ice above the ice cliff. The greatest
velocity decreases are observed near the crest and lee of surface rises
(downstream of data gaps from radar shadows; Fig. 4), where some of the
highest velocities were observed in July. In contrast, the area immediately
downstream of the ice cliff and the area surrounding the icefall both
display an apparent velocity increase for the same time period (Figs. 4, 6).
While the increase is less than the 95 % confidence interval for most
areas, we can confidently state that the icefall and area below the ice
cliff do not display the significant decrease in velocity observed
elsewhere.
The majority of the Wilson Glacier displays a similar ∼0.3–0.7 m day-1 (-40 to -60 %) velocity decrease from July to November.
Interestingly, the steep transition where the Wilson merges with the
Nisqually displays an apparent velocity increase of ∼0.1 m day-1
during this time period (Fig. 4). These data also reveal subtle
velocity increases in the debris-covered ice near the Nisqually terminus and
the upper Kautz Glacier (Fig. 4), though these increases are statistically
insignificant.
LOS velocity time series for areas outlined on maps to the right.
Shaded region around each line represents ± 1 standard error for a
2-h running mean. (a) 24-h time series at SUNRIZ on 7–8 July 2012, gray
box indicates the period with poor data quality (see text for details).
(b) 22-h time series at ROI on 1–2 November 2012.
The repeat winter observations of Nisqually show relatively constant
velocities with some notable variability. Analysis of the 2 November to
10 December observations reveals a statistically significant -0.1 m day-1 (-50 %)
velocity decrease ∼1 km upstream of the terminus (centered on
∼0.7 km in Fig. 6a profile), a +0.1 to +0.2 m day-1 (+20
to +30 %) increase over central Nisqually centered on ∼ 3.5 km in the Fig. 6d profile, and an apparent +0.2 m day-1 (+130 %)
increase over upper Wilson. In the latter case, the 10 December velocities
are actually higher than those observed in July. The slowdown over lower
Nisqually appears robust, but other trends have amplitudes that are mostly
below the 95 % confidence interval for the 27 November and 10 December
observational campaigns (Fig. 4).
Diurnal variability
We collected ∼21 and ∼24 h time series for
the Emmons and Nisqually/Wilson glaciers (Table 1) in July and November,
respectively, and looked at changes throughout the day. Although uncertainties
are large, we present the time series in Fig. 7.
Comparison between Walkup et al. (2013) and TRI velocities at Walkup
et al. (2013) sample locations (Fig. 8).
Velocity magnitude (cm day-1) Angular difference from Walkup et al. (2013) (degrees) SourceMeanMedianMaxMinMeanMedianMaxMinWalkup et al. (2013)22.316.664.41.8––––GLPEEK July20.810.582.90.115.812.055.80.7ROI Nov14.610.451.40.315.812.055.80.7
In general, velocities for these regions remain relatively constant during
their respective sampling periods. The Emmons time series shows an apparent
decrease in velocity over the central, fast-flowing regions (B, C, D in Fig. 7a)
from ∼18:00 to 21:00 LT and an apparent increase
between ∼07:00 and 09:00 LT (Fig. 7a). The Nisqually
time series shows an apparent decrease from ∼06:00 to 11:00 LT
for the icefall and ice cliff and an apparent decrease for
several areas of the glaciers followed by an increase (Fig. 7b). However,
uncertainties are large and none of these are statistically significant.
Comparison of average azimuth and velocities measured by Walkup et
al. (2013) between 19 July and 11 October 2012 (black) compared to TRI
slope-parallel velocities derived from this study at the same locations for
two time periods that bracket the time period measured by Walkup et al. (2013).
See Table 4 for comparison statistics and Box C in Fig. 1 for
context.
Comparison with independent velocity measurements
We now compare our TRI results with independent velocity measurements for an
overlapping time period. Walkup et al. (2013) performed repeat total station
surveys to document the location of sparse supraglacial cobbles and boulders
on the lower Nisqually Glacier from 2011 to 2012. While measurement errors
(e.g., cobble rolling/sliding) for these observations are difficult to
document, the large sample size and relatively long measurement intervals
allow for accurate surface velocity estimates.
Figure 8 shows average velocity vectors measured by Walkup et al. (2013) for
the period between 19 July and 11 October 2012, with corresponding
surface-parallel velocity vectors from the 7 July and 2 November TRI
surveys. This comparison is summarized on Table 4. In general, the velocity
magnitudes are similar, with the overall mean of the Walkup et al. (2013)
measurements slightly higher on average but often falling between the 7 July and
2 November GPRI magnitudes, as would be expected of a mean velocity
spanning approximately the same period. The velocity directions are also
relatively consistent, with a median angular difference of 12∘.
The greatest deviations are observed near the ice margins and over
small-scale local topography (e.g., ice-cored moraine near western margin),
where surface-parallel flow assumptions break down. In general, the two
techniques provide similar results and offer complementary data validation.
However, since the Walkup et al. (2013) measurements were limited to
accessible areas, they cannot be used to validate TRI observations for
heavily crevassed areas, icefalls, and other hazardous dynamic areas
generally higher on the mountain.
Model results for summer (6 July 2012) and a late fall (2 November 2012)
time period for Nisqually and Wilson glaciers. (a, d) Modeled surface
velocity for internal deformation; (b, e) sliding residual (observed slope-parallel velocity minus the modeled deformation velocity);
(c, f) estimate of
the sliding percentage (sliding residual divided by total slope-parallel
velocity).
Same as Fig. 9 but for Emmons Glacier.
Two-dimensional flow modeling
Figure 9 shows modeled deformation, sliding velocity residual (observations–deformation model),
and sliding percent (sliding velocity residual as
percentage of total velocity) with best estimate model parameters for
Nisqually Glacier in July and November. Figure 10 shows corresponding output
for Emmons. The SIA deformation models suggest that most areas of both
glaciers are moving almost entirely by sliding. The modeled glacier
deformation alone is unable to account for the observed surface velocity
during any of the observation periods. Only a median of 1 % of the
velocity field over the Nisqually Glacier area can be explained by internal
deformation in July and only 2 % in November. If we consider ±25 % ice thickness and up to 2× the ice softness, the possible range of
the median deformation contribution is still small: 0.5–7 % in July and
0.5–8 % in November. If we consider only ±25 % ice thickness
and do not change the ice softness, the range narrows to 0.5–4 % in
both cases. Using stake measurements, Hodge (1974) estimated deformation
contributed ∼5–20 % of the velocity for the upper third of
the ablation area of the Nisqually Glacier. He did not study any areas above
the equilibrium line, so to compare directly to Hodge's (1974) numbers, we
take the median deformation percentage over approximately the upper third of
the ablation area and find a best estimate of 1 % (range 0.3–5 %) for
July and 2 % (range 0.5–7 %) for November. These numbers suggest that
sliding is even more dominant than Hodge (1974) estimated in this area,
though it is difficult to say whether the differences are real (i.e., sliding was
higher in 2012 than it was 4 decades ago) or just due to differences in
methods and assumptions.
The model results for Emmons suggest that deformation is more important for
the Emmons Glacier than for Nisqually. A median of 9 % of the July
velocity field of Emmons can be explained by deformation, with a possible
range of 3–40 % when considering ±25 % ice thickness and up to
2× the ice softness. When we consider only ±25 % ice thickness, the
range narrows to 3–20 %.
There are a few regions where the observed surface velocity can be explained
entirely or nearly entirely by internal deformation. These include the area
within ∼1–2 km of the Nisqually and Emmons Glacier terminus,
where ice is relatively thick and observed velocities are small.
Discussion
The continuous coverage of the TRI provides information about the spatial
distribution of surface velocities. Several local velocity maxima are
apparent along the centerline of the Nisqually Glacier and the central
branch of the Emmons Glacier. These velocity maxima are associated with
surface crevasses and increased surface slopes, with peak velocities
typically observed just upstream of peak slope values (Fig. 6). They are
likely related to accelerated flow downstream from local bedrock
highs.
However, the local velocity maxima at ∼2.1 km in Fig. 6
corresponds to a region of decreased surface slopes and increased ice
thickness. This location also displayed significant seasonal velocity
change, which could be related to variations in local subglacial hydrology
(e.g., reservoir drainage) during this time period.
Icefall and ice cliff dynamics
Terrestrial radar interferometry offers new observations over dynamic,
inaccessible areas that have received limited attention in previous studies
(e.g., icefalls, ice cliffs). For example, the velocities above the
Nisqually ice cliff display an abrupt transition from slow- to fast-moving
ice (Fig. 4). This rapid change from slow to fast favors crevasse opening
and “detached slab” behavior rather than continuous flow, which is
reflected in the heavily crevassed surface at this location.
Our results show that the Nisqually icefall and the icefall at the
convergence of the Wilson and Nisqually glaciers show a slight increase in
velocity from July to the winter months. This suggests that the icefalls may
not be susceptible to the same processes that caused the seasonal velocity
decrease over much of the rest of the glacier. This may indicate that there
is a lack of local continuity through icefalls, which appears to prevent or
dampen propagation of downstream seasonal velocity decreases. It could also
indicate that the icefall is relatively well drained year round and is not
significantly affected by seasonal changes in subglacial hydrology. A
potential explanation for the observed minor increase in velocity could be
early winter snow accumulation on blocks within the icefall.
Interestingly, in contrast to the icefall, the hanging glacier above the
Nisqually ice cliff displayed a significant velocity decrease from July to
November despite similar steep surface slopes and crevasse density. This
could potentially be related to the lack of backstress from downstream ice
and an increased sensitivity to minor fluctuations in subglacial hydrology.
Hanging glaciers are also thought to be the source of some of the repeating
glacial earthquakes that are triggered by snow loading (Allstadt and Malone,
2014), which highlights their sensitivity to minor perturbations.
Lack of significant diurnal variability
We expected to see significant variability over the 24-h July time series
for Emmons, as atmospheric temperatures varied from 16 to
27 ∘C at Paradise Visitors Center (∼1600 m a.s.l),
and skies remained cloud free during data collection. We hypothesized that
the resulting increase in meltwater input from late morning through late
afternoon might produce an observable increase in sliding velocity. While
the results potentially show a slight velocity decrease at higher elevations
overnight, and a slight velocity increase in the morning (Fig. 7a, A–D),
these changes are not statistically significant nor coincident with times
expected to have highest melt input. The lack of a significant diurnal
speedup suggests that the subglacial conduits are relatively mature by July
and are capable of accommodating the diurnal variations in meltwater flux
without affecting basal sliding rates.
We did not expect to see significant diurnal changes in the 21-h November
time series for Nisqually (Fig. 7a), as atmospheric temperatures ranged
between 2 and 6 ∘C at Paradise Visitors Center
(∼1600 m a.s.l.) and skies were partly cloudy to overcast
during data collection, so surface meltwater input should have been minimal.
Our results show only a minor velocity decrease higher on the glacier in the
morning hours but it is not statistically significant and does not occur at
times when we would expect increased meltwater.
Though some of the subtle changes in the extended time series may reflect
actual diurnal velocity variability, we cannot interpret these with
confidence. This suggests that the magnitude of diurnal variability, if it
exists, during these time periods is minor when compared to the observed
seasonal changes. It also implies that other stacks derived from a subset of
the day can be considered representative of the daily mean and can be
compared for seasonal analysis.
July and November 1969 surface velocities measured by Hodge
(1974; digitized from Hodge, 1972) at 19 stake locations along lower
Nisqually profile (circles), compared with sampled 2012 slope-parallel
velocities for corresponding locations/seasons (triangles). Stake locations
are labeled and indicated with dotted lines and are shown in map view at
right (same map extent as Fig. 8).
Seasonal velocity changes
The observed seasonal velocity changes from July to November can likely be
attributed to changes in glacier sliding, which in turn are driven by
evolving englacial and subglacial hydrology (Fountain and Walder, 1998).
During the spring–summer months, runoff from precipitation (i.e., rain) and
surface snow/ice melt enters surface crevasses, moulins, and/or conduits
near the glacier margins. This water travels through a series of englacial
fractures, reservoirs, and conduits and eventually ends up in a subglacial
network of channels and reservoirs between the ice and bed. Storage time and
discharge rates within the subglacial system are variable, with water
finally exiting the system through one or more proglacial streams at the
terminus. This dynamic system is continuously evolving due to variable
input, storage capacity, and output. In early July, ongoing snowmelt should
produce high meltwater discharge that travels through a relatively efficient
network of mature conduits. As discharge decreases later in the summer,
these subglacial conduits/reservoirs close due to ice creep without high
flow to keep them open through melting due to heat from viscous dissipation.
By November, there should be little or no surface meltwater input and we
would expect to see a minimum in basal sliding velocity (Hodge, 1974). This
is consistent with the observed velocity decrease in Fig. 4. However, the
deformation modeling results (Fig. 9) show that a significant sliding
component is still present for most of the Nisqually Glacier in November and
December, when minimum surface velocities are expected.
The spatial patterns of the velocity change observed between July and
November can be used to infer the extent of basal sliding. This may provide
some insight into subglacial water storage, since the deformation component
of surface velocity should remain nearly the same year round. Figure 4
indicates that almost the entire Nisqually Glacier slows down significantly
between July and November, suggesting that storage is occurring under most
of the glacier below the icefall and ice cliff. Significant velocity
decreases are observed near local surface rises (Fig. 4), where some of the
highest velocities were observed in July. This suggests that there are
likely subglacial cavities downstream of these areas with high basal water
pressures that can support enhanced sliding during the summer.
Hodge (1974) interpreted a delay in both the maximum summer velocity and
minimum winter velocity between the terminus and ELA as a propagating
“seasonal wave” traveling ∼55 m day-1. While our sampling is
limited, the continued 2–27 November slowdown over the lower
Nisqually near the terminus (Fig. 4f) could represent a delayed response to
the significant slowdown over central Nisqually. This might be expected, as
surface velocities near the terminus are dominated by internal deformation
and should respond more slowly than areas dominated by basal sliding.
Comparison with historical velocity measurements
As described earlier, Hodge (1972, 1974) measured surface velocity for a
network of centerline stakes on the lower Nisqually from 1968 to 1970. He
documented a significant seasonal cycle with minimum velocities in November
and maximum velocities in June.
To put our velocity data in historical context, we digitized Hodge's (1972)
July and November 1969 surface velocity data at 19 stake locations along a
profile of the lower half of the Nisqually Glacier. We then sampled the 2012
TRI slope-parallel velocities at these locations (Fig. 11). Remarkably, in
spite of significant terminus retreat of up to ∼360 m and
surface elevation changes of approximately -20 m (Sisson et al., 2011), the
November 1969 and November 2012 surface velocities are almost identical at
stakes 12–20, suggesting that bed properties and local geometry have greater
influence over sliding velocity than ice thickness or relative distance from
the terminus. In contrast, the July 2012 velocities at stakes 12–20 are
8–33 % faster than the July 1969 velocities. The ice is mostly sliding at
these locations, so the change could be related to a difference in the
timing of the peak summer velocities or potentially enhanced sliding in
2012. The nearly identical surface velocities in November 1969 and 2012
suggest that the discrepancy between Hodge's sliding percentage estimates
and our estimates (Sect. 4.5) is likely related to different methodology
and assumptions rather than actual changes in sliding since 1969.
The most notable difference between the profiles is observed closer to the
terminus at stakes 7–12. At these locations, the July and November 2012
velocities are both < 0.05 m day-1, whereas July and November 1969
velocities are ∼0.2 and ∼0.1 m day-1,
respectively, with significant seasonal variability. This suggests that the
ice near the present-day terminus is essentially stagnant and no longer
strongly influenced by changes in subglacial hydrology.
Conclusions
In this study, we used repeat TRI measurements to document spatially
continuous velocities for numerous glaciers at Mount Rainier, WA, focusing
primarily on the Emmons and Nisqually glaciers. We produced surface velocity
maps that reveal speeds of > 1.0–1.5 m day-1 over the upper and
central regions of these glaciers, < 0.2 m day-1 near the summit, and
< 0.05 m day-1 over the stagnant ice near their termini. Novel data
processing techniques reduced uncertainties to ±0.02–0.08 m day-1, and
the corrected, surface-parallel TRI velocities for Nisqually display similar
magnitude and direction with a set of sparse interannual velocity
measurements (Walkup et al., 2013).
Repeat surveys show that Nisqually Glacier surface velocities display
significant seasonal variability. Most of the glacier experienced a
∼25–50 % velocity decrease (up to -0.7 m day-1) between July
and November. These seasonal variations are most likely related to changes
in basal sliding and subglacial water storage. Interestingly, the steep
icefall displays no velocity change or even a slight velocity increase over
the same time period. We documented no statistically significant diurnal
velocity variations in ∼24-h data sets for Nisqually and
Emmons, suggesting that subglacial networks efficiently handled diurnal
meltwater input. Comparisons with 1969 velocity measurements over the Lower
Nisqually (Hodge, 1972, 1974) reveal similar November velocities in both
2012 and 1969 and faster July velocities in 2012.
Using a simple 2-D ice flow model, we estimate that basal sliding is
responsible for most of the observed surface velocity signal except in a few
areas, mainly near the termini. The model suggests that about 99 % of the
July velocity field for the Nisqually Glacier is due to sliding. Even when
we account for the large uncertainties in ice thickness and ice softness,
the possible range of sliding percentage is still narrow: 93–99.5 %.
Deformation is more important for the Emmons Glacier, where we estimate
91 % of the observed motion is due to sliding, with a much wider possible
range of 60–97 % when accounting for uncertainties.
In summary, TRI presents a powerful new tool for the study of alpine glacier
dynamics. With just a few hours of fieldwork for each survey, we were able
to document the dynamics of several glaciers at Mount Rainier in
unprecedented extent and detail from up to 10 km away. TRI is particularly
well suited for examining diurnal and seasonal glacier dynamics, especially
for areas that are difficult to access directly (e.g., icefalls), like many
parts of the glaciers at Mount Rainier. Repeat surveys provide precise
surface displacement measurements with unprecedented spatial and temporal
resolution, offering new insight into complex processes involving subglacial
hydrology and basal sliding. Future studies involving coordinated, multi-day
TRI occupations during critical seasonal transition periods could
undoubtedly provide new insight into these and other important aspects of
alpine glaciology.
Photomosaic acquired from ROI viewpoint on 5 July 2012.
Approximate glacier outlines shown in red.
Photomosaic acquired from GLPEEK viewpoint on 6 July 2012.
Approximate glacier outlines shown in red.
Photomosaic acquired from SUNRIZ viewpoint on 7 July 2012.
Approximate glacier outlines shown in red.
Pair of multi-look intensity radar images from ROI
viewpoint (left and center) generated from original single-look complex
(SLC) images multi-looked by 15 samples in range and multi-looked
interferogram generated from the SLC images (right).
(a) Filtered ice thickness and (b) filtered slope used as model
inputs.
K. E. Allstadt coordinated the effort, developed methods, performed data
acquisition and processing, made the figures, and prepared the manuscript.
D. E. Shean developed methods, performed data acquisition, processing,
analysis, and interpretation of results, and contributed significantly to
the manuscript. A. Campbell performed modeling experiments and contributed
the related section of the manuscript. M. Fahnestock and S. Malone
contributed significantly to experiment design, establishment of objectives,
data acquisition, and manuscript review.
Acknowledgements
Many thanks to the National Park Service staff at Mount Rainier National
Park, in particular Scott Beason, Laura Walkup, and Barbara Samora. Justin
Sweet and Zach Ploskey provided field assistance. Ryan Cassotto and David
Schmidt provided data processing guidance. The University of Washington
Glaciology group provided useful discussions. Thanks to M. Luthi and A. Vieli
for their thoughtful reviews and suggestions, which have significantly
improved the manuscript. Original data used in this analysis are available
upon request from the corresponding author. This work was supported in part
by the US Geological Survey under contract G10AC00087 to the Pacific
Northwest Seismic Network, the University of Washington Earth and Space
Sciences Department Awards, the Colorado Scientific Society, the Gordon and
Betty Moore Foundation (Grants 2626 and 2627), and the National Science
Foundation under award no. 1349572 during the final part of manuscript
preparation.
Edited by: O. Gagliardini
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