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Supplementary Material
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Rapid Submarine Melting Driven by Subglacial Discharge, LeConte Glacier, Alaska
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Authors: Roman J Motyka1,2*, William P Dryer1,2, Jason Amundson2, Martin Truffer1, and Mark
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Fahnestock1
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99775
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Juneau, AK 99801
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*rjmotyka@uas.alaska.edu
Geophysical Institute, University of Alaska Fairbanks; 903 Koyukuk Drive, Fairbanks, AK
Department of Natural Sciences , University of Alaska Southeast; 11120 Glacier Hwy(SOB1),
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1. Heat and Salt Balances
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[1] Determination of water and heat fluxes followed methodology presented in Motyka et al.
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[2003] and later used by Rignot et al. [2010]. This method utilizes the fact that melting of
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glacier ice absorbs considerable thermal energy, the source of which is inferred to be incoming
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warm “ambient” seawater at depth (Figure 2). The benefit of this method is that the details of
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convection and heat transfer along the face do not have to be known in order to determine the
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amount of submarine melting. Our analysis focuses on the outflow plume and uses 600 kHz
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ADCP measurements to depths of 70 m with 2-m bins to evaluate fluxes in the outflow plume.
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The 2-m-bin data were linearly interpolated vertically to one meter intervals and horizontally
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between stations to 10 m intervals. Currents for the top 4 m cannot be resolved by the ADCP; we
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therefore used the data trends from the bins below 4 m to extrapolate to the surface. To
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determine the depth of the outflow plume (Table S1), we used current, salinity, and temperature
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profiles. We also used a Gade melt line analyses described in Mortensen et al. [2011] to
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determine the fraction of submarine glacier meltwater in the water column.
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[2] Spacing between stations was a compromise between temporal and spatial resolution. In
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order to resolve tidal effects, we strove to complete each transect in 2 hr or less. To provide
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adequate spatial resolution, we attempted to space our stations about 200 m apart or less. In
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practice, time per station and distance between stations averaged 2.2 hr and 190 m respectively
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(Table S2). The number of stations occupied per transect varied from 5 to 7.
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1.1 Salt Balance
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[3] The total water flux in the outflow plume, Qp, was calculated by numerically integrating the
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measured, interpolated, and extrapolated currents across the flux gate:
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Qp = WD ui(x,z) dxdz
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(1)
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where ui(x,z) are the 600 kHz ADCP velocities, D is the plume depth, and W the width of the
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flux gate. Some flow along the walls is missed by our stations.
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[4] The water discharge in the outflowing plume, Qp, has both seawater, Qsw, and freshwater,
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Qfw, components:
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Qp = Qsw + Qfw = Qsw + Qsg + Qm
(2)
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where Qsg and Qm are the subglacial discharge and terminus ice melt, respectively. The fraction
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of seawater in the overflow plume was determined from the salinity. Subglacial discharge, Qsg,
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and glacier melt Qm, are assumed to have zero salinity and to be at the pressure melting point.
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We used Ssw = 28 PSU and Tsw = 6.8 °C for ambient seawater salinity and temperature; these
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were the average salinity and temperature in the lowest part of the water column (~ 170 – 180
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m). We estimated the fraction of seawater (s ) in the plume at a depth z from
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s = Sp(z)/Ss
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(3)
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where Sp is the measured salinity in the plume. The seawater flux in the outflow plume is then
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given by
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Qsw = WD ui(x,z)  si(x,z) dxdz
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(4)
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Equation (4) was numerically integrated using 600 kHz ADCP velocities, ui(x,z), and Spi(x,z)
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obtained from CTD casts.
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[5] The freshwater flux in the outflow plume, Qfw, was determined from eqn. 2.
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1.2 Heat Balance
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[6] From conservation of mass, the incoming deep ambient seawater flux must be equal to the
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flux of seawater in the outgoing plume and we use Qsw to evaluate Qm. From conservation of
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energy, the heat coming into the system via the warm seawater, Hsw, and via the subglacial water,
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Hsg, must equal the heat leaving the system in the plume, Hp, plus the latent heat lost to melting
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ice, Hm:
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Hm = H = Hsw + Hsg - Hp
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(5)
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Here we neglect heat generated by friction and heat lost to the atmosphere, and we assume that
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Hsg = 0 because the ice and subglacial water are at 0 C, which is our reference state. We
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determine the incoming heat flow from
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Hsw = sw Qsw Csw Tsw
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(6)
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where Csw is the specific heat (3990 J kg-1 K-1), sw is the density (1022 kg m-3), Tsw is the
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temperature of the deep seawater (6.8 C) and where, from conservation of seawater in the fjord,
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the rate of seawater inflow near the terminus is assumed to be equal to outflow of seawater in the
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plume, Qsw, which was calculated above.
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[7] Heat carried away from the terminus by the overflow plume was computed by numerically
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integrating across the flux gate:
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H p = WD ( pi ui C p T pi )dx dz
(7)
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using the measured and interpolated values of mixed-water density, temperature, and velocity
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within the plume. The heat capacity of the plume water was taken to be that of seawater, Csw.
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The rate of ice melt, Qm, is then computed from:
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Qm = Hm L-1
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(8)
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where L is the latent heat of fusion for ice. An adjustment for saltwater melting-point depression
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of approximately -1.0 C was included in this calculation. Qsg is then evaluated from Qfw and Qm
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(eqn. 2).
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2. Error Analysis
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[8] The SeaCAT temperature and salinity values are highly accurate, ±0.005 °C and ±0.007 PSU
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respectively; thus the primary sources of uncertainty in our methods stem from current
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measurements, interpolations, and extrapolations. The accuracy for ADCP current
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measurements is reported to be 1 cm/s when averaging 50 pings [RDI, pers. comm., 2012]. We
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preformed a sensitivity analysis on our 600 kHz ADCP data sets, each of which usually consisted
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of 200+ pings. We divided data for each 2-m bin into two populations, odd and even numbered
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(or every other ping), and then computed the average velocity, Uodd and Uev, of each data set of
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100+ pings for each bin. Uodd and Uev for each bin were then differenced for all ADCP casts
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(1250 total bins). The results produced a normal distribution with a mean of ~ 0 and a standard
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deviation, σ, of 1.5 cm/s. We interpret this σ to be a measure of variance in currents due to
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inherent fluctuations. We opted to use 2σ as a conservative estimate of uncertainties for each
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individual current measurement. Given the normal distribution of the comparison, we consider
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the error to be random. Therefore, to estimate total uncertainty in flux through the gate, we used
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σ1 = 2σ√n2, where n is the number of current measurements made across the gate. These
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uncertainties ranged from 3% to 6.5% of the total flux values. Additional uncertainties accrue
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from horizontal interpolations and extrapolations. Temperature and salinity varied little
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horizontally across the transects, so linear interpolation of T and S is unlikely to introduce
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significant errors. There was variation in currents across the gate; however distances between
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stations were small enough that we consider linear interpolation to be a reasonable
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approximation. To be conservative, we added an additional 5% uncertainty to our flux estimates
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to account for potential uncertainties in our interpolations and extrapolations. These uncertainties
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apply to the temporal (~2 hr) and spatial (~ 90 m wide swath) averages of each survey.
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Table S1. Characteristics of outflow plume.
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Transect
Peak
Depth of
Width of
Depth of
Tide
Time local
velocity,
peak vel,
plume,
plume,
stage
cm/s
m
m
m
T3, 9/7
40
27
450
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↑
T4, 9/7
31
28
40
↑
T5, 9/8
44
13
400
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─↓
9 - 10.7
T6, 9/8
50
5
400
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↓─
10.7-12.3
T7, 9/8
45
5
450
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─↑
12.3 - 14.6
T8, 9/8
52
5
450
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↑
14.6 - 16.5
T9, 9/9
61
9
450
50
─↓
9 - 11.5
T10, 9/9
58
7
500
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↓─
11.5 - 14.2
14 - 16.9
T11, 9/10
68
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500
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─↓
12.8 - 15.7
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Table S2. Characteristics of transects.
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Transect
T3
T5
T6
T7
T8
T9
T10
T11
Average
Average
spacing, m
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228
231
183
196
213
167
179
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Average Drift,
m
71
93
92
93
71
112
138
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Average time,
hr
2.8
1.8
1.6
2.3
2.0
2.5
2.6
2.8
2.2
Number of
Stations
7
5
5
6
6
6
7
7
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Supplementary Figures
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Figure S1. Climate data from Petersburg weather station during period of hydrographic surveys
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at LeConte Glacier and Bay.
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Figure S2. Hydrographic cross-sections for Day 1 surveys. Top panel shows tide with red boxes
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marking the surveys. Left panels show results of ADCP measurements; the 600 ADCP was not
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used for first two surveys. Right panels show salinity and temperature cross-sections.
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Figure S2, con’t. Hydrographic cross-sections for Day 1 surveys, continued. Left panels show
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turbidity in NTU, log scale. Right panels show percentage melt water and subglacial discharge
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using methods in Mortensen et al. [2013]. .
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Figure S3. Hydrographic cross-sections for Day 2 surveys. Top panel shows tide with red boxes
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marking the surveys. Left panels show results of ADCP measurement. Right panels show
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salinity and temperature cross-sections.
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Figure S3, con’t. Hydrographic cross-sections for Day 2 surveys, continued. Left panels show
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turbidity in NTU, log scale. Right panels show percentage melt water and subglacial discharge
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using methods in Mortensen et al. [2013]. .
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Figure S4. Hydrographic cross-sections for Day 3 surveys. Top panel shows tide with red boxes
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marking the surveys. Upper left panels show results of ADCP measurements. Upper right panels
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show salinity and temperature cross-sections. Lower left panels show turbidity in log scale.
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Lower right panels show percentage melt water and subglacial discharge using methods in
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Mortensen et al. [2013].
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Figure S5. Hydrographic cross-sections for Day 4 survey. Top panel shows tide with red boxes
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marking the survey. Upper left panels show results of ADCP measurements. Upper right panel
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shows salinity and temperature cross-sections. Lower left panel show turbidity in log scale.
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Lower right panel shows percentage melt water and subglacial discharge using methods in
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Mortensen et al. [2013].
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Supplementary References
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Motyka, R., Hunter, L., Echelmeyer, K. & Connor, C., 2003, Submarine melting at the terminus
of a temperate tidewater glacier, Leconte Glacier, Alaska, USA. Ann. Glaciol. 36, 57-65.
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Rignot, E., Koppes M., and Velicogna, I., 2010, Rapid submarine melting of the calving faces of
West Greenland glaciers. Nature Geosci., 3, 187-191.
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Mortensen, J., J. Bendtsen, R. J. Motyka, K. Lennert, M. Truffer, M. Fahnestock, and S.
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Rysgaard, 2013, On the seasonal freshwater stratification in the proximity of fast-flowing
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tidewater outlet glaciers in a sub-Arctic sill fjord. J. Geophys. Res. Oceans, 118, 1382–1395,
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doi:10.1002/jgrc.20134.