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Section 1: Map of observation sites and table of site locations, elevations, and corrected temperature data
Figure fs01.jpg: Map of our traverse route in NW
Greenland showing observation sites. Sites named
starting with Benson are coincident with sites from
Benson’s 1952-55 route. Surface elevation contours are
from Howat et al. [2014]
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5
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Table ts01.xls – Site locations, elevation, and temperatures
Date
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Site
Latitude Longitude Elevation (m) 2013 Corrected Temp
1952-55 Corrected Temp
5/9/2013 B 4-275
73.167
41.100
3071.4
-29.39
-29.4
5/10/2013 B4-225
73.873
41.800
2996.2
-29.91
-29.8
5/11/2013 B 4-175
74.590
42.550
2949.3
-31.13
-30.2
5/12/2013 B 4-100
75.637
43.950
2860.4
-31.78
-30.6
5/13/2013 B 4-050
76.317
45.100
2781.3
-30.23
-30.7
5/14/2013 B 4-000
76.965
46.983
2664.2
-31.12
-30.7
5/15/2013 B 2-200
77.058
49.600
2540.7
-28.69
-29.6
5/17/2013 B 2-175
77.057
51.333
2445.6
-25.87
-28.4
5/19/2013 B 2-125
77.042
54.517
2198.7
-24.95
-26.6
5/20/2013 B 2-070
77.093
57.818
1971.3
-21.13
-23.8
5/21/2013 B 2-020
77.217
61.022
1905.8
-23.29
-23.9
5/22/2013 B 1-050
77.150
62.900
1671.7
-19.76
-23.1
5/23/2013 B 1-010
76.803
64.890
1466.2
-14.05
-19.7
5/24/2013 B 1A-20
76.920
62.000
1688.5
-16.97
-22.5
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Section 2: Additional information on temperature corrections applied to observed temperatures:
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Figure fs02 - Graphical representation of seasonal variation in firn temperature and correction process
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The temperature correction we apply simply removes the seasonal variation expected at the time the
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observations were collected. This figure shows seasonal temperature variability at depth predicted using
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methodology from Benson [1962]. Predicted maximum and minimum variation from the mean annual
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temperature at any point in the year are presented in gray solid lines and mean temperature is shown as a
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dashed black line. Four scenarios for the temperature deviation from mean annual temperature that would
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be expected at depth are shown for the first day of spring, summer, fall, and winter. Finally, temperature
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observations, collected at 3m, 4m, and 8m at site 4-150 by Benson are shown along with temperatures
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calculated after seasonal variation is removed. The three corrected temperatures were then averaged to
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produce the mean annual firn temperature at the site, commonly referred to as the ‘10m temperature’. We
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apply the same methodology to our temperature observations, though our temperature corrections are
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typically much smaller than Benson’s. While snow surface temperature can range about from -60C in
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winter to 0C in summer, both direct observations and modeling show that at depths below about 10m in
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dry firn the maximum variation from the mean annual temperature is typically less than 0.5C [Benson,
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1962; Steffen, 1996]. Our results relying primarily on temperature observations below 7.5 m depth,
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collected in May, a time of the year when corrections at these depths are so small (<0.3C) as to be hard to
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see when plotted on this graph.
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Section 3: Placing Firn Temperatures in Context
Firn temperatures high on the ice sheet show no change since Benson’s work, while warming
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observed at lower elevations is attributed entirely to percolation in our paper. At first glance these results
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imply that mean surface temperatures on the interior ice sheet are very similar during the early 2010s to
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those experienced in the early 1950’s. This would be an unexpected conclusion, and therefore bears closer
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examination. Unchanged firn temperatures observed at high elevations can be reconciled with warming
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expected from other observations by modeling the response of firn temperature in a changing climate. By
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modeling the time response of firn in warming and cooling climates, the response lag of firn temperature
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in a non-static climate, therefore, can explain much of the discrepancy between apparently unchanged firn
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temperature and rising observed surface temperatures without impacting our conclusions about enhanced
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percolation warming in the paper.
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Broad analyses of surface temperature observations show that both global and Arctic wide mean
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temperatures declined from the 1950’s until about 1975, and have risen rapidly since [Hansen et al.,
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2010]. The rise since about 1975 dominates net change, such that global temperatures are ~0.6C higher in
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the early 2010’s than in the early 1950’s, and Arctic temperatures are ~1.4C higher [Hansen et al., 2010].
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Analyses of temperatures around the periphery of the ice sheet show similar trajectories [Hanna et al.,
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2012] with a net warming of 1.125C when the 1940-1970 interval is compared to the 2000-2011 interval.
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On the interior ice sheet, observations spanning the 1952-2013 interval are extremely limited, however
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Ohmura [1987] conducted a synthesis reducing early observations to the 1950-1960 standard decade to
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create temperature distribution maps which can be compared to current GC-Net observations [Steffen and
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Box, 2001]. Steffen and Box [2001] analyze these datasets to find a warming of approximately 2C in the
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interior ice sheet from the 1950 standard decade to the late 1990s. We update their analysis with current
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GC-Net data and find a warming of approximately 2.9C over the full 1950’s-2010’s interval.
Figure fs03 – 10m Firn temperature response to
changing mean annual surface temperature
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A warming this large should be apparent in our firn temperature observations unless the
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relationship between firn temperature and surface temperature in the dry snow facies has changed.
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Ohmura [1987] makes a comparison of 10m temperatures with mean annual air temperatures in the dry
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snow facies during the 1950 standard decade and finds firn temperatures, on average, exceed mean annual
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site temperatures by 0.8C, with 14 out of 18 sites showing firn temperatures that exceed air temperatures.
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Meanwhile, Steffen and Box [2001] conduct a similar analysis during the late 1990’s and find instead that
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firn temperatures are lower than mean annual site air temperatures by an average of 1.5C during the late
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1990s (7 out of 7 stations). Again we update Steffen and Box’s [2001] analysis using GC-Net air and firn
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temperature observations available since their paper was published and find that 10m temperatures at sites
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with minimal percolation (defined here as where mean annual air temperature is <-20C) tend to be lower
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than mean annual air temperature (22 out of 26 site-years) by a mean margin of 1.1C.
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Considering climatic trends prior to our firn observations (cooling for the 1950’s and rapid
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warming for the 2010’s) helps to reconcile the deviation between firn and mean annual air temperatures
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as well as the lack of firn warming with expected changes mean annual surface temperature. In Figure
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fs02 we model the response of firn temperature in a dry snow environment typical of the north-central ice
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sheet near NEEM to changes in surface temperature similar to those expected prior to the 1950’s and
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2010s. If interior conditions mirrored coastal trends, the climate on the interior ice sheet during the 1950s
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would have been cooling from peaks 0.5C to 1C higher in the early 1930’s [Mernild et al., 2010; Hanna et
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al., 2012], while the 2010’s were preceded by warming that is likely at least 1C/decade over the preceding
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30 years [Steffen and Box 2001; Box et al., 2009; Box et al., 2012; Hall et al., 2012; Comiso et al., 2004;
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Hall et al., 2013]. The modeled firn temperature in both cases lags the changing surface temperature,
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producing an expected bias of about +0.4C in the 1950’s and -0.9C in the 2010s, nearly matching
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observed deviations between firn and air temperatures. The response of firn temperature in a non-static
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climate, therefore, can explain much of the discrepancy between apparently unchanged firn temperature
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and rising observed surface temperatures. This minor lag in firn temperature warming behind surface
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observations does not impact our conclusions about enhanced percolation warming made in the paper.
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Section 4: – Description of the 1D Thermodynamic Model
We employ a finite difference scheme to calculate heat transport within the firn on an hourly
𝑑𝑇
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timestep, using Fourier’s Law [𝑞 = −𝑘 (𝑑𝑥)] to calculate heat flux based on the temperature difference
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between adjacent cells of 1cm thickness and iterating a second order backward difference until
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convergence. Thermal conductivity is set as a function of snow density according to the third order
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polynomial of Van Dusen [1929]. Density profile is initialized based on prior observations in the dry
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snow facies [Herron and Langway, 1980] or using our field observations in areas where we initialized
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with a firn column that has experienced past percolation. The density profile is treated as constant with
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time except for additions of mass at depth due to refreezing percolation. In these cases, density is simply
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increased according to the amount of meltwater refrozen in place during percolation events. Density is not
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permitted to exceed 850kg/m3. Percolating meltwater proceeds past any cells that have reached this
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density, so long as there is lower density firn below. This behavior is consistent with field observations
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which indicate that firn columns do not form impermeable layers, and are capable of transitioning to near
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solid ice as percolation increases [Humphrey et al., 2012]. Snow accumulation rate is variable, and set
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according to the accumulation observed in our pits at the site of interest.
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The model is forced by setting snow surface temperature to 2010 hourly air temperature
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observations from NEEM, adjusted for the elevation of the site being modeled by offsetting temperatures
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using the lapse rate 0.75C/100m elevation. Surface temperatures are not permitted to exceed 0C and,
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because the model does conduct a full surface energy balance treatment, meltwater production at the
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surface is prescribed manually. Behavior of the meltwater as it percolates away from the surface can be
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adjusted in several ways. A minimum depth that percolation reaches can be set, matching field
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observations that indicate meltwater often moves vertically through the prior year’s accumulation and
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doesn’t spread out and refreeze until striking the prior year’s summer hoar layer. Below the minimum
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depth, further percolation is governed by requiring latent heat delivery from the percolating water to raise
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each layer of firn to a threshold temperature of -2C before percolation can proceed deeper. The model
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releases all latent heat contained in the meltwater upon deposition of meltwater in a layer, effectively
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refreezing delivered meltwater immediately and warming the firn with the released energy. Field
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observations show that it is not necessary to raise firn temperature to 0C in order for percolation to
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proceed through a layer, and that percolation often occurs in isolated columns passing through firn layers
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as cold as -10C [Benson, 1962]. It may be necessary to execute a more complex modeling scheme to
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represent the percolating water fully, however we found that using a percolation threshold of -2C resulted
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in distributions of refrozen melt similar to that observed in pits along our route, and therefore use that
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value as our threshold for controlling further percolation. We also acknowledge that meltwater which has
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percolated into the upper firn layers has been observed to remain liquid for days, weeks, or, in special
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cases of high accumulation and high melt, even months [e.g. Miller et al., 2013]. The model is not
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sensitive to timing of energy delivery on day to week scales, however, so the approximation of instant
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refreezing and energy release at depth is reasonable for the low percolation cases we model where limited
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amounts of meltwater percolate into relatively cold firn, refreezing within, at most, a few weeks.
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We validated the model in dry snow by setting the temperature profile to that observed by
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Benson at site B 2-200, and fixing the snow surface cell temperature to the air temperature observed by
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the GC-Net station at NEEM and allowing the model to run for several years. After equilibrating, the
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model reproduces the temperatures observed at depth by the GC-Net station well, with largest errors in
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the surface where convection, neglected by the model, is likely important. Temperature evolution below
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5m matches observations within less than 1C. We furthered this validation in the percolation facies by
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comparing the temperature profile produced by the model with profiles measured by Humphrey et al.
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[2012] in the percolation facies during active percolation. Quantitative validation is not possible, because
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precise amounts of percolating meltwater produced are not known, but the character and magnitude of
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temperature warming observed could be reproduced with reasonably expected quantities of meltwater.
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