There is significant uncertainty regarding the spatiotemporal distribution of
seasonal snow on glaciers, despite being a fundamental component of glacier
mass balance. To address this knowledge gap, we collected repeat, spatially
extensive high-frequency ground-penetrating radar (GPR) observations on two
glaciers in Alaska during the spring of 5 consecutive years. GPR
measurements showed steep snow water equivalent (SWE) elevation gradients at
both sites; continental Gulkana Glacier's SWE gradient averaged 115 mm 100 m

Our ability to quantify glacier mass balance is dependent on accurately resolving the spatial and temporal distributions of snow accumulation and snow and ice ablation. Significant advances in our knowledge of ablation processes have improved observational and modeling capacities (Hock, 2005; Huss and Hock, 2015; Fitzpatrick et al., 2017), yet comparable advances in our understanding of the distribution of snow accumulation have not kept pace (Hock et al., 2017). Reasons for this discrepancy are 2-fold: (i) snow accumulation exhibits higher variability than ablation, both in magnitude and length scale, largely due to wind redistribution in the complex high-relief terrain where mountain glaciers are typically found (Kuhn et al., 1995) and (ii) accumulation observations are typically less representative (i.e., one stake in an elevation band of a few 100 m) or less effective than comparable ablation observations (i.e., precipitation gage measuring snowfall vs. radiometer measuring short-wave radiation). This discrepancy presents a significant limitation to process-based understanding of mass balance drivers. Furthermore, a warming climate has already modified – and will continue to modify – the magnitude and spatial distribution of snow on glaciers through a reduction in the fraction of precipitation falling as snow and an increase in rain-on-snow events (McAfee et al., 2013; Klos et al., 2014; McGrath et al., 2017; Beamer et al., 2017; Littell et al., 2018).

Significant research has been conducted on the spatial and, to a lesser degree, the temporal variability of seasonal snow in mountainous and high-latitude landscapes (e.g., Balk and Elder, 2000; Molotch et al., 2005; Erickson et al., 2005; Deems et al., 2008; Sturm and Wagner, 2010; Schirmer et al., 2011; Winstral and Marks, 2014; Anderson et al., 2014; Painter et al., 2016). Although major advances have occurred in applying physically based snow distribution models (i.e., iSnobal, Marks et al., 1999, SnowModel, Liston and Elder, 2006, Alpine 3-D, Lehning et al., 2006), the paucity of required meteorological forcing data proximal to glaciers limits widespread application. Many other studies have successfully developed statistical approaches that rely on the relationship between the distribution of snow water equivalent (SWE) and physically based terrain parameters (also referred to as physiographic or topographic properties or variables) to model the distribution of SWE across entire basins (e.g., Molotch et al., 2005; Anderson et al., 2014; Sold et al., 2013; McGrath et al., 2015).

A major uncertainty identified by these studies is the degree to which these
statistically derived relationships remain stationary in time. Many studies
(Erickson et al., 2005; Deems et al., 2008; Sturm and Wagner, 2010; Schirmer
et al., 2011; Winstral and Marks, 2014; Helfricht et al., 2014) have found
“time-stability” in the distribution of SWE, including locations where wind
redistribution is a major control on this distribution. For instance, a
climatological snow distribution pattern, produced from the mean of nine
standardized surveys, accurately predicted the observed snow depth in a
subsequent survey in a tundra basin in Alaska (

Even fewer studies have explicitly examined the question of interannual
variability in the context of snow distribution on glaciers.
Spatially extensive snow probe datasets are collected by numerous glacier
monitoring programs (e.g., Bauder, 2017; Kjøllmoen et al., 2017;
Escher-Vetter et al., 2009) in order to calculate a winter mass balance
estimate. Although extensive, such manual approaches are still limited by
the number of points that can be collected and uncertainties in correctly
identifying the summer surface in the accumulation zone, where seasonal snow
is underlain by firn. One study of two successive end-of-winter surveys of
snow depth using probes on a glacier in Svalbard found strong interannual
variability in the spatial distribution of snow, and the relationship
between snow distribution and topographic features (Hodgkins et al., 2005).
Elevation was found to only explain 38 %–60 % of the variability in snow
depth, and in one year, snow depth was not dependent on elevation in the
accumulation zone (Hodgkins et al., 2005). Instead, aspect, reflecting
relative exposure or shelter from prevailing winds, was found to be a
significant predictor of accumulation patterns. In contrast, repeat airborne
lidar surveys of a

The “time-stability” of snow distribution on glaciers has particularly important implications for long-term glacier mass balance programs, as seasonal and annual mass balance solutions are derived from the integration of a limited number of point observations (e.g., 3 to 50 stakes), and the assumption that stake and snow pit observations accurately represent interannual variability in mass balance rather than interannual variability in the spatial patterns of mass balance. Previous work has shown “time-stability” in the spatial pattern of annual mass balance (e.g., Vincent et al., 2017) and while this is important for understanding the uncertainties in glacier-wide mass balance estimates, the relative contributions of accumulation and ablation to this stability are poorly constrained, thereby hindering a process-based understanding of these spatial patterns. Furthermore, accurately quantifying the magnitude and spatial distribution of winter snow accumulation on glaciers is a prerequisite for understanding the water budget of glacierized basins, with direct implications for any potential use of this water, whether that be ecological, agricultural, or human consumption (Kaser et al., 2010).

To better understand the “time-stability” of the spatial pattern of snow accumulation on glaciers, we present 5 consecutive years of extensive GPR observations for two glaciers in Alaska. First, we use these GPR-derived SWE measurements to train two different types of statistical models, which were subsequently used to spatially extrapolate SWE across each glacier's area. Second, we assess the temporal stability in the resulting spatial distribution in SWE. Finally, we compare GPR-derived winter mass balance estimates to traditional glaciological derived mass balance estimates and quantify the uncertainty that interannual variability in spatial patterns in snow accumulation introduces to these estimates.

During the spring seasons of 2013–2017, we conducted GPR surveys on
Wolverine and Gulkana glaciers, located on the Kenai Peninsula and eastern
Alaskan Range in Alaska (Fig. 1). These glaciers have been studied as part
of the U.S. Geological Survey's Benchmark Glacier (USGS) project since 1966 (O'Neel
et al., 2014). Both glaciers are

Map of southern Alaska with study glaciers marked by red outline. All glaciers in the region are shown in white (Pfeffer et al., 2014).

The primary SWE observations are derived from a GPR measurement of two-way travel time (twt) through the annual snow accumulation layer. We describe five main steps to convert twt along the survey profiles to annual distributed SWE products for each glacier. These include (i) acquisition of GPR and ground-truth data, (ii) calculation of snow density and associated radar velocity, which are used to convert measured twt to annual layer depth and subsequently SWE, and (iii) application of terrain parameter statistical models to extrapolate SWE across the glacier area. We then describe approaches to (iv) evaluate the temporal consistency in spatial SWE patterns and (v) compare GPR-derived SWE and direct (glaciological) winter mass balances.

Box plots of glacier-wide winter balance for Gulkana and Wolverine glaciers between 1966 and 2017. Years corresponding to GPR surveys are shown with colored markers. These values have not been adjusted by the geodetic calibration (see O'Neel et al., 2014).

Common-offset GPR surveys were conducted with a 500 MHz Sensors and Software pulseEKKO Pro system in late spring close to maximum end-of-winter SWE and prior to the onset of extensive surface melt. GPR parameters were set to a waveform-sampling rate of 0.1 ns, a 200 ns time window, and “Free Run” trace increments, where samples are collected as fast as the processor allows, instead of at uniform temporal or spatial increments.

In general, GPR surveys were conducted by mounting a plastic sled behind a
snowmobile and driving at a near-constant velocity of 15 km h

GPR surveys from 2015 at Gulkana

Radargrams were processed using the ReflexW-2D software package (Sandmeier Scientific Software). All radargrams were corrected to time zero, taken as the first negative peak in the direct wave (Yelf and Yelf, 2006), and a dewow filter (mean subtraction) was applied over 2 ns. When reflectors from the base of the seasonal snow cover were insufficiently resolved, gain and band-pass filters were subsequently applied. Layer picking was guided by ground-truth efforts and done semi-automatically using a phase-following layer picker. For further details, please see McGrath et al. (2015).

We collected extensive ground-truth data to validate GPR surveys, including
probing and snowpits/cores. In the ablation zone of each glacier, we probed
the snowpack thickness every

As snow densities did not exhibit a consistent spatial nor elevation
dependency on the glaciers (e.g., Fausto et al., 2018), we calculated a
single average density,

Extrapolating SWE from point measurements to the basin scale has been a
topic of focused research for decades (e.g., Woo and Marsh, 1978; Elder et
al., 1995; Molotch et al., 2005). Most commonly, the dependent variable SWE
is related to a series of explanatory terrain parameters, which are proxies
for the physical processes that actually control SWE distribution across the
landscape. These include the orographic gradient in precipitation (elevation),
wind redistribution of existing snow (slope, curvature, drift potential),
and aspect with respect to solar radiation and prevailing winds (eastness,
northness). We derived terrain parameters from 10 m resolution digital
elevation models (DEMs) sourced from the ArcticDEM project (Noh and Howat,
2015) for Gulkana and produced from airborne structure from motion
photogrammetry at Wolverine (Nolan et al., 2015). Both DEMs were based on
imagery from August 2015. Specifically, these parameters include elevation,
surface slope, surface curvature, northness (Molotch et al., 2005),
eastness, and snow drift potential (Sb) (Winstral et al., 2002, 2013; Figs. S3, S4). The Sb parameter is commonly used to identify
locations where airflow separation occurs based on both near and far-field
topography and are thus likely locations to accumulate snow drifts (Winstral
et al., 2002). For specific details on this calculation, please refer to
Winstral et al. (2002). In the application of Sb here, we determined the
principal direction by calculating the modal daily wind direction during the
winter (October–May) when wind speeds exceeded 5 m s

Prior to spatial extrapolation, we aggregated GPR observations to the
resolution of the DEM by calculating the median value of all observations
within each 10 m pixel of the DEM. We then utilized two approaches to
extrapolate GPR point observations across the glacier surface: (i) least-squares elevation gradient applied to glacier hypsometry and
(ii) statistical models. For (i), we derived SWE elevation gradients in two ways;
first, solely on observations that followed the glacier centerline and
second, from the entire spatially extensive dataset. For (ii), we utilized
two different models: stepwise multivariable linear regressions and
regression trees (Breiman et al., 1984). All of these approaches produced a
spatially distributed SWE field over the entire glacier area. Individual
points in this field are equivalent to point winter balances (

Additionally, we implemented a cross-validation approach to the statistical
models (multivariable regression and regression tree), whereby 75 % of
the aggregated observations were used for training and 25 % were used for
testing. However, rather than randomly selecting pixels from across the
entire dataset, we randomly selected a single pixel containing aggregated
GPR observations and then extended this selection out along continuous
survey lines until we reached 25 % of the total observational dataset,
thus removing entire sections (and respective terrain parameters) from the
analysis (Fig. S5). This approach provided a more realistic test for the
statistical models, as the random selection of individual cells did not
significantly alter terrain-parameter distributions. For each glacier and
each year, we produced 100 training and test dataset combinations, but rather
than take the single model with the highest

We used a stepwise multivariable linear regression model of the form,

Regression trees (Breiman et al., 1984) provide an alternative statistical approach for extrapolating point observations by recursively partitioning SWE into progressively more homogenous subsets based on independent terrain parameter predictors (Molotch et al., 2005; Meromy et al., 2013; Bair et al., 2018). The primary advantage of the regression tree approach is that each terrain parameter is used multiple times to partition the observations, thereby allowing for non-linear interactions between these terms. In contrast, the MVR only allows for a single “global” linear relationship for each parameter across the entire parameter-space. We implemented a random forest approach (Breiman, 2001) of repeated regression trees (100 learning cycles) in Matlab, using weak learners and bootstrap aggregating (bagging; Breiman, 1996). Each weak learner omits 37 % of observations, such that these “out-of-bag” observations are used to calculate predictor importance. The use of this ensemble bagging approach reduces overfitting and thus precludes having to subjectively prune the tree and provides more accurate and unbiased error estimates (Breiman, 2001). Prior to implementing the regression tree, we removed the SWE elevation gradient from the observations using a least-squares regression. As described in the results, elevation is the dominant independent variable and as our observations (particularly at Wolverine) did not cover the entire elevation range, the regression tree approach was not well suited to predicting SWE at elevations outside of the observational range.

We quantified the stability of spatial patterns in SWE across the 5-year
interval using two approaches: (i) normalized range and (ii) the coefficient
of determination. In the first approach, we first divided each pixel in the
distributed SWE fields by the glacier-wide average,

Beginning in 1966, glacier-wide seasonal (winter,

The integration of these point measurements was accomplished using a
site-index method – equivalent to an area-weighted average (March and
Trabant, 1996; van Beusekom et al., 2010). Beginning in 2009, a more
extensive stake network of seven to nine stakes was established on each
glacier, thereby facilitating the use of a balance profile method for
spatial extrapolation (Cogley et al., 2011). Systematic bias in the
glaciological mass balance time series is removed via a geodetic adjustment
derived from DEM differencing over decadal timescales (e.g., O'Neel et al.,
2014). For this study, glaciological measurements were made within a day of
the GPR surveys, and integrated over the glacier hypsometry using both the
historically applied site-index method (based on the long-term three stake
network) and the more commonly applied balance profile method (based on the
more extensive stake network). We utilized a single glacier hypsometry,
derived from the 2015 DEMs, for each glacier over the entire 5-year
interval. Importantly, in order to facilitate a more direct comparison to
the GPR-derived

Since 1966, Wolverine Glacier's median

Average accumulation season (taken as 1 October–31 May) wind speeds over
the study period were stronger (

SWE from GPR surveys as a function of elevation, along with least squares regression slope and coefficient of determination for each year of the study period. Wolverine is plotted in blue, Gulkana in red.

Glacier-averaged snow densities across all years were 440 kg m

To evaluate model performance in unsampled locations of the glacier, both
extrapolation approaches were run 100 times for each glacier and each year,
each time with a unique, randomly selected training (75 % of aggregated
observations) and test (remaining 25 % of aggregated observations)
dataset. The median and standard deviation of the coefficients of
determination (

Median and standard deviation (error bars) of coefficient of determination (from 100 model runs) for both extrapolation approaches (circles are MVR, triangles are regression tree) developed on training datasets and applied to test datasets. Symbols and error bars are offset from year for clarity.

At Gulkana, the model residuals (Fig. S1) exhibited spatiotemporal
consistency, with positive residuals (i.e., observed SWE exceeded modeled
SWE by

The beta coefficients of terrain parameters from the MVR were fairly consistent from year-to-year at both glaciers (Fig. 6). At Wolverine, elevation was the largest beta coefficient, followed by Sb and curvature. At Gulkana, elevation was also the largest beta coefficient, followed by curvature. Gulkana experiences much greater variability in wind direction during the winter months (Fig. S6), possibly explaining why Sb was either not included or had a very low beta coefficient in the median regression model. As our surveys were completed prior to the onset of ablation, terrain parameters related to solar radiation gain (notably the terms that include aspect: northness and eastness) had small and variable beta coefficients.

Terrain parameter beta coefficients for

A common approach for quantifying snow accumulation variability across a
range of means is the coefficient of variation (CoV), which is calculated as
the ratio of the standard deviation to the mean (Liston et al., 2004;
Winstral and Marks, 2014). The mean and standard deviation of CoVs at
Wolverine were

Qualitatively, both Wolverine and Gulkana glaciers exhibited consistent
spatiotemporal patterns in accumulation across the glacier surface, with
elevation exerting a first-order control (Figs. 8, S7, S8). Overlaid on the
strong elevational gradient are consistent locations of wind scour and
deposition, reflecting the interaction of wind redistribution and complex –
albeit relatively stable year to year – surface topography (consisting of
both land and ice topography). For instance, numerous large drifts
(

Spatial variability in snow accumulation across the glacier quantified by the coefficient of variation (standard deviation/mean) for each glacier across the 5-year interval based on MVR model output.

The 5-year mean of normalized distributed SWE for Gulkana

Although the glacier-wide averages between these approaches showed close
agreement, we explored the differences in spatial patterns by calculating a
mean SWE difference map for each glacier by differencing the 5-year mean
SWE produced by the regression tree model from the same produced by the MVR
model (Fig. 10). As such, locations where the MVR exceeded the regression
tree are positive (yellow). At Gulkana, where the two approaches showed
slightly better glacier-wide

We used two different approaches to quantify the “time-stability” of spatial
patterns across these glaciers. By the first metric, normalized range, we
found that both glaciers exhibited very similar patterns (Fig. 11), with
either

Comparing statistical models for GPR-derived glacier-wide winter
balances for both Wolverine (blue) and Gulkana (red) glaciers. For each year
and each glacier, two box plots are shown. The first shows multivariable
regression model (MVR) output and the second shows regression tree output
(tree). The

SWE differences between statistical models for Gulkana

In order to examine systematic variations between the approaches we outlined
in Sect. 3 for calculating the glacier-wide winter balance,

Interannual variability of the SWE accumulation field from
2013–2017, quantified via normalized range

Interannual variability of the SWE accumulation pattern as a
function of cumulative glacier area, shown as

To examine the systematic difference between the glaciological site-index
method and GPR-based MVR approach, we compared stake-derived

Percent deviation for each estimate from the six-method mean of

Spatial variability in snow accumulation for individual years
(2013–2017) by elevation (lower, middle, upper) compared to stake
measurements. Box plot of all distributed SWE values (from multivariable
regression) for each index zone of the glacier for Gulkana

Interannual variability in the spatial pattern of snow
accumulation at long-term mass balance stake locations for Wolverine and
Gulkana glaciers using

In situ stake and pit observations traditionally serve as the primary tool for
deriving glaciological mass balances. However, in order for these
observations to provide a systematic and meaningful long-term record, they
need to record interannual variability in mass balance rather than
interannual variability in spatial patterns of mass balance. To assess the
performance of the long-term stake sites, we examined the interannual
variability metrics for the stake locations. By both metrics (normalized
absolute range and

Each glacier exhibited consistent normalized SWE spatial patterns across the 5-year study, reflecting the strong control of elevation and regular patterns in wind redistribution in this complex topography (Figs. 11, S7, S8). This is particularly notable given the highly variable magnitudes of accumulation over the 5-year study and the contrasting climate regions of these two glaciers (wet, warm maritime and cold, dry continental), with unique storm paths, timing of annual accumulation, wind direction and wind direction variability, and snow density. At both glaciers, the lowest interannual variability was found away from locations with complex topography and elevated surface roughness, such as crevassed zones, glacier margins, and areas near peaks and ridges.

In the most directly comparable study, which used repeat GPR surveys on Switzerland's Findel Glacier, 86 % of the glacier area experienced less than 25 % range in relative normalized accumulation over a three-year interval (Sold et al., 2016). As noted in Sect. 3.4., we reported an absolute normalized range, whereas Sold et al. (2016) reported a relative normalized range. Following their calculation, we found that 81 % and 82 % of Wolverine and Gulkana's area experienced a relative normalized range less than 25 %. Collectively, our results add to the growing body of evidence (e.g., Deems et al., 2008; Sturm and Wagner, 2010; Schirmer et al., 2011; Winstral and Marks, 2014) suggesting “time-stability” in the spatial distribution of snow in locations that span a range of climate zones, topographic complexity, and relief. While the initial effort required to constrain the spatial distribution over a given area can be significant, the benefits of understanding the spatial distribution are substantial and long lasting, and have a wide range of applications.

Elevation explained between 50 % and 83 % of the observed SWE variability
at Gulkana and Wolverine, making it the most significant terrain parameter
at both glaciers every year (Figs. 4, 6). Steep winter SWE gradients
characterized both glaciers throughout the study period (115–440 mm 100 m

Wolverine and Gulkana glaciers exhibited opposing SWE gradients at their highest elevations, with Wolverine showing a sharp non-linear increase in SWE, while Gulkana showed a gradual decrease. This non-linear increase was also noted at two maritime glaciers (Scott and Valdez) in 2013 (McGrath et al., 2015), and perhaps reflects an abundance of split precipitation phase storms in these warm coastal regions. The cause of the observed reverse gradient at Gulkana may be the result of wind scouring at the highest and most exposed sections of the glacier, or in part, a result of where we were able to safely sample the glacier. For instance, in 2013, when we were able to access the highest basin on the glacier, the SWE elevation gradient remained positive (Fig. 4). Reductions in accumulated SWE at the highest elevations have also been observed at Lemon Creek Glacier in southeast Alaska and Findel Glacier in Switzerland (Machguth et al., 2006), presumably related to wind scouring at these exposed elevations.

Both statistical extrapolation approaches found terrain parameters Sb and
curvature, proxies for wind redistribution, to have the largest beta
coefficients after elevation (Figs. 6, S9). The spatial pattern of SWE
estimated by each model clearly reflects the dominant influence of wind
redistribution and elevation (Fig. 8), as areas of drift and scour are
apparent, especially at higher elevations. However, these terms do not fully
capture the redistribution process, as the model residuals (Figs. S1, S2)
show sequential positive and negative residuals associated with drift and scour
zones. There are a number of reasons why this might occur, including
variable wind directions transporting snow (this is likely a more
significant issue at Gulkana, which experiences greater wind direction
variability, Fig. S6), complex wind fields that are not well represented by
a singular wind direction (Dadic et al., 2010), changing surface topography
(the glacier surface is dynamic over a range of temporal scales, changing
through both surface mass balance processes and ice dynamics), and widely
varying wind velocities. This is particularly relevant at Wolverine, where
wind speeds regularly gust over 30 m s

Although our GPR surveys did not regularly include non-glaciated regions of these basins, a few key differences are worth noting. First, the length scales of variability on and off the glacier were distinctly different, with shorter scales and greater absolute variability (snow-free to > 5 m in less than 10 m distance) off glacier (Fig. S10). This point has been clearly shown using airborne lidar in a glaciated catchment in the Austrian Alps (Helfricht et al., 2014). The reduced variability on the glacier is largely due to surface mass balance and ice flow processes that act to smooth the surface, leading to a more spatially consistent surface topography, and therefore a more spatially consistent SWE pattern. For this reason, establishing a SWE elevation gradient on a glacier is likely much less prone to terrain-induced outliers compared to off-glacier sites, although the relationship of this gradient to off-glacier gradients is generally unknown.

The two statistical extrapolation approaches yielded comparable large-scale spatial distributions and glacier-wide averages, although there were some notable spatial differences (Fig. 10). The systematic positive bias of the MVR approach over the regression tree at Wolverine was due to three sectors of the glacier with both complex terrain (i.e., icefalls) and large data gaps (typically locations that are not safe to access on ground surveys). The difference in predicted SWE in these locations is likely due to how the two statistical extrapolation approaches handle unsampled terrain parameter space. The MVR extrapolates based on global linear trends, while the regression tree assigns SWE from terrain that most closely resembles the under-sampled location. Anecdotally, it appears that the MVR may overestimate SWE in some of these locations, which is most evident in Wolverine's lower icefall, where bare ice is frequently exposed at the end of the accumulation season (Fig. S11) in locations where the MVR predicted substantial SWE. Likewise, the regression tree models could be underestimating SWE in these regions, but in the absence of direct observations the errors are inherently unknown. The regression tree model captures more short length scale variability while the MVR model clarifies the larger trends. Consequently, smaller drifts and scours are captured well by the regression tree model in areas where the terrain parameter space is well surveyed, but the results become progressively less plausible as the terrain becomes distinctly different from the sampled terrain parameter space. In contrast, the MVR model appears to give more plausible results at larger spatial scales. This suggests that there is some theoretical threshold where the regression tree is more appropriate if the terrain parameter space is sampled sufficiently, but that for many glacier surveys the MVR model would be more appropriate.

On average, all methods for estimating

The biggest differences occurred between the GPR-forced MVR model and the
glaciological site-index method, which we have shown is attributed to the
upper stake (with the greatest weight) underestimating the median SWE for
that index zone (Fig. 14). The upper stake location was established in 1966
at an elevation below the median elevation of that index zone, which given
the strong elevation control on SWE, is a likely reason for the observed
difference. At Gulkana, the relationship between the upper index site and
the GPR-forced MVR model is more variable in large part due to observed
differences in the accumulation between the main branch (containing the
index site) and the west branch of the glacier (containing additional stakes
added in 2009). Such basin-scale differences are likely present on many
glaciers with complex geometry, and thus illustrate potential uncertainties
of using a small network of stakes to monitor the mass balance of these
glaciers. In the context of the MVR model, this manifests as a change in
sign in the eastness coefficient (which separates the branches in parameter
space; Fig. S4). Notably, in the two years where the site-index estimate was
most negatively biased at Gulkana (2015 and 2016), the glaciological profile
method, relying on the more extensive stake network (which includes stakes
in the west branch of the glacier), yielded

These GPR-derived

Understanding the spatiotemporal distribution of SWE is useful for informing stake placements and also for quantifying the uncertainty that interannual spatial variations in SWE introduce to historic estimates of glacier-wide mass balance, particularly when long-term mass balance programs rely on limited numbers of point observations (e.g., USGS and National Park Service glacier monitoring programs; O'Neel et al., 2014; Burrows, 2014). Our winter balance results illustrate that stakes placed at the same elevation are not directly comparable, and hence are not necessarily interchangeable in the context of a multi-year mass balance record. Most locations on the glacier exhibit bias from the average mass balance at that elevation and our results suggest interannual consistency in this bias over sub-decadal time scales. As a result, constructing a balance profile using a small number of inconsistently located stakes is likely to introduce large relative errors from one year to the next.

Considering this finding, the placement of stakes to measure snow
accumulation is dependent on whether a single glacier-wide winter mass
balance value (

We assess the uncertainty that interannual variability in the spatial
distribution of SWE introduces to the historic index-method (March and
Trabant, 1996) mass balance solutions by first calculating the
uncertainty,

We collected spatially extensive GPR observations at two glaciers in Alaska
for five consecutive winters to quantify the spatiotemporal distribution of
SWE. We found good agreement of glacier-average winter balances,

In total, six different methods (four based on GPR measurements and two
based on stake measurements) for estimating the glacier-wide average agreed
within

We found the spatial patterns of snow accumulation to be temporally stable
on these glaciers, which is consistent with a growing body of literature
documenting similar consistency in a wide variety of environments. The
long-term stake locations experienced low interannual variability in
normalized SWE, meaning that stake measurements tracked the interannual
variability in SWE, rather than interannual variability in spatial patterns.
The uncertainty associated with interannual spatial variability is only
4 %–10 % of the glacier-wide

The GPR and associated observational data used in this study can be
accessed on the USGS Glaciers and Climate Project website
(

The supplement related to this article is available online at:

SO, DM, LS, and HPM designed the study. DM performed the analyses and wrote the manuscript. LS contributed to the design and implementation of the analyses and CM, SC, and EHB contributed specific components of the analyses. All authors provided feedback and edited the manuscript.

The authors declare that they have no conflict of interest.

This work was funded by the U.S. Geological Survey Land Change Science Program, USGS Alaska Climate Adaptation Science Center, and DOI/USGS award G17AC00438 to Daniel McGrath. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. We acknowledge the Polar Geospatial Center (NSF-OPP awards 1043681, 1559691, and 1542736) for the Gulkana DEM. We thank Caitlyn Florentine, Jeremy Littell, Mauri Pelto, and an anonymous reviewer for their thoughtful feedback that improved the manuscript. Edited by: Nanna Bjørnholt Karlsson Reviewed by: Mauri Pelto and one anonymous referee