Meltwater and sediment-laden plumes at tidewater
glaciers, resulting from the localized subglacial discharge of surface melt,
influence submarine melting of the glacier and the delivery of nutrients to
the fjord's surface waters. It is usually assumed that increased subglacial
discharge will promote the surfacing of these plumes. Here, at a western
Greenland tidewater glacier, we investigate the counterintuitive observation
of a non-surfacing plume in July 2012 (a year of record surface melting)
compared to the surfacing of the plume in July 2013 (an average melt year).
We combine oceanographic observations, subglacial discharge estimates and an
idealized plume model to explain the observed plumes' behavior and evaluate
the relative impact of fjord stratification and subglacial discharge on
plume dynamics. We find that increased fjord stratification prevented the
plume from surfacing in 2012, show that the fjord was more stratified in
2012 due to increased freshwater content and speculate that this arose from
an accumulation of ice sheet surface meltwater in the fjord in this record
melt year. By developing theoretical scalings, we show that fjord
stratification in general exerts a dominant control on plume vertical extent (and thus
surface expression), so that studies using plume surface expression as a
means of diagnosing variability in glacial processes should account for
possible changes in stratification. We introduce the idea that, despite
projections of increased surface melting over Greenland, the appearance of
plumes at the fjord surface could in the future become less common if the
increased freshwater acts to stratify fjords around the Greenland ice sheet.
We discuss the implications of our findings for nutrient fluxes, trapping of
atmospheric CO2 and the properties of water exported from Greenland's
fjords.
Introduction
Over the last 2 decades, the rate of mass loss from the Greenland ice
sheet (GrIS) has quadrupled
(Rignot
et al., 2011; Shepherd et al., 2012). Approximately 60 % of this ice loss
is attributed to increased ice sheet surface melting, while the remaining
40 % is due to marine-terminating glacier acceleration and retreat
(Jiskoot et
al., 2012; Moon et al., 2012) that is thought to result from increased
iceberg calving and submarine melting at the glacial fronts
(Bamber
et al., 2012; van den Broeke et al., 2009; Enderlin et al., 2014). Thus,
understanding processes at the glaciers' fronts is key if we are to
understand ongoing changes and generate future projections.
Among the important processes occurring at the tidewater glacier–ocean
boundary, we focus here on buoyant plumes. Buoyant plumes typically occur in
localized areas along the glacier front, at times visible on the fjord
surface as patches of turbid water
(e.g., How et al., 2019;
Mankoff et al., 2016). Since they are driven primarily by subglacial
discharge deriving from ice sheet surface melting, their appearance is
limited mainly to summer
(e.g., Motyka et
al., 2013; Schild et al., 2016), and, due to the sediments they carry, they
control sedimentation rates and distribution in the vicinity of the glacier
front (Mugford and Dowdeswell, 2011). As they
rise up the calving front, plumes entrain large volumes of ambient fjord
waters, increasing their initial volume by more than an order of magnitude
(Mankoff et al., 2016; Mortensen et al., 2013) and
acting as the engine of convective-driven circulation in the fjords. Through
their vigorous turbulent nature, they enable the transfer of ocean heat to
the ice, enhancing submarine melting of the glacial front
(Kimura
et al., 2014; Sciascia et al., 2013; Slater et al., 2015, 2018; Xu et al.,
2013). In addition, they likely affect calving rates by incising undercut
notches into the terminus, altering the stress distribution of ice near the
terminus
(De
Andrés et al., 2018; How et al., 2019; Luckman et al., 2015; O'Leary and
Christoffersen, 2013; Schild et al., 2018; Vallot et al., 2018).
Besides the cited physical implications, buoyant plumes also play a key role
in important fjord biogeochemical processes. They enrich the uppermost
layers of the fjord by upwelling nutrients (e.g., Fe, NO3, PO4, Si)
that come primarily from the nutrient-rich deep ocean waters but also from
the subglacial bedrock weathering and the ice meltwater
(Bhatia
et al., 2013; Cape et al., 2019; Hopwood et al., 2018; Meire et al., 2017).
If the nutrient-laden plume reaches the photic zone, the increase in
nutrient availability can enhance phytoplankton productivity during the
summer season (Hopwood et al., 2018),
favoring CO2 trapping in fjord waters
(Meire et al., 2015), sustaining
important fisheries in Greenland (Meire et al.,
2017) and supporting Arctic seabird populations
(Arimitsu et al., 2012).
Alternatively, the turbidity associated with the sediment-laden plumes can
also stress benthic ecosystems (Korsun and Hald, 2000)
and inhibit light penetration, limiting photosynthesis and therefore
phytoplankton productivity
(Arimitsu et
al., 2012; Meire et al., 2017).
The effect that a buoyant plume will have on the physics and biogeochemistry
of the fjord and glacier is sensitive to the vertical extent of the plume in
the water column. The vertical extent can influence the distribution of
melting along the glacier and therefore the glacier shape
(Slater et al., 2017) and the layers that are
nutrient enriched (Hopwood et al., 2018).
Theoretical considerations suggest that in stratified environments such as
glacial fjords, buoyant plumes have two characteristic heights
(List, 1982; Morton et
al., 1956). The first is the neutral buoyancy depth (NBD), reached at the
depth where the plume density equals the ambient density. The second is the
maximum height depth (MHD), which is situated above NBD and reached at the depth
where the plume vertical velocity decreases to zero
(Baines, 2002; Morton et
al., 1956). The relationship between these two characteristic heights and
the fjord surface determines whether the plume is visible at the
surface, is visible only adjacent to the glacier, or is visible throughout
the fjord (Slater et al., 2016). Theory
furthermore suggests that these two characteristic heights (and thus the
vertical extent of the plume) are primarily determined by two factors: the
intensity of the subglacial discharge, acting to increase the vertical
extent, and the strength of the fjord stratification, acting to decrease the
vertical extent (Morton et al., 1956).
Despite the long history of theoretical and modeling work on subglacial
discharge plumes, field observations with which to test our understanding
remain limited due to the extreme difficulty of obtaining measurements
adjacent to tidewater glaciers. To address this gap, here we present repeat
surveys from 2012 and 2013 of a major plume and associated jet at the edge
of a midsized glacier in central-western Greenland. We find that the plume did
not reach the fjord surface in summer 2012, despite this being a year of
record surface melting (Tedesco
et al., 2013), while the plume did reach the fjord surface in 2013, a year
of average melt (Mankoff et al., 2016). We combine our
field observations with a plume model to explain these counterintuitive
observations and, more generally, to investigate how plume vertical extent
is controlled by subglacial discharge and fjord stratification. We finally
discuss how the vertical extent of plumes may evolve in the future under
climate warming.
Methods
Saqqarleq Fjord (SF) is the southernmost branch of an intricate system of
fjords connected to Jakobshavn Isfjord (JI) in central-western Greenland (Fig. 1). It is a midsized fjord, being approximately 6 km wide in the vicinity
of the glacial front (Saqqarliup Sermia, SS), where the depth reaches 150 m
(Stevens et al.,
2016; Wagner et al., 2019). SF meets Tasiussaq Fjord (TF) at a sill of 70 m
depth, located 15 km from SS terminus (Fig. 1; Stevens et al., 2016). TF then connects to JI over a sill over 125 m
depth located at the junction of these fjords (Fig. 1). The glacier (SS) is
a midsized marine-terminating glacier with maximum velocities in summer of
2 m d-1 near the calving front (Wagner
et al., 2019) and an upstream subglacial catchment of 400±50 km2 (Stevens et al., 2016).
Bathymetric map of the Saqqarleq Fjord area (dark rectangle in Fig. 1). CTD cast locations (white dots) and ADCP transects (dark lines) in 2012 (a) and 2013 (b). The location of the main plume is indicated by the black
arrow.
Field data
Two field surveys were carried out in consecutive summers from 17 to 27 July 2012 and from 24 to 31 July 2013
(Mankoff
et al., 2016; Slater et al., 2018; Stevens et al., 2016; Wagner et al.,
2019). The glacier terminus was located approximately in the same position
during the summers of 2012 and 2013 (Stevens et al., 2016), so that the
geometry of the system can be considered the same in both field surveys. In
2012 (2013), a total of 90 (96) CTD (conductivity, temperature and depth)
profiles were collected using an RBR XR 620 sensor that was calibrated pre-deployment
and post-deployment. CTD stations were distributed along several
across-fjord (terminus-parallel) and along-fjord transects (Fig. 2). The CTD
profiles were collected from a small boat, and they extend from 150 m to 5 km from
the glacier terminus. Temperature and salinity profiles even closer to the
glacier front (and inside of the plume surface expression in 2013) were
collected by deploying Sippican xCTDs (expendable CTDs) from a helicopter: 2
such profiles were obtained in 2012 and 12 in 2013. All CTD and xCTD data were
depth-averaged to a resolution of 1 m. One-way ANOVA (analysis of
variance) showed no significant differences between CTD and xCTD casts taken on
different days (Mankoff et al., 2016), and thus we assume
that properties did not change considerably within either field campaign.
Temperature and conductivity values have been converted to conservative
temperature (Θ) and absolute salinity (SA), respectively
(IOC, SCOR and IAPSO, 2010), using the
thermodynamic equation of state, TEOS-10 (McDougall and Barker,
2011).
Parallel to and at a distance of ∼1.5 km from the glacier
front, water velocity surveys were performed on 20 July 2012 (DOY 202)
and 26 July 2013 (DOY 207) (Fig. 2). The observations were obtained from
an acoustic Doppler current profiler (ADCP, RDI 300 kHz) mounted on the
small boat and binned into 4 m depth bins after removing the ship motion and
corrected for local magnetic declination. ADCP data were processed using
CODAS (Common Oceanographic Data Access System) from the University of
Hawaii. Data were spatially interpolated by kriging to obtain the
cross-sectional (terminus-parallel) contour maps.
Fjord bathymetry was obtained from the shipboard single-beam depth sounder,
the shipboard ADCP and the REMUS-100 (remote environmental measuring units)
autonomous underwater vehicle (AUV), as described in
Stevens et al. (2016) and Wagner et al. (2019). We also make use of aerial photographs
taken from the helicopter in May–June and July of 2012 and 2013 to provide a
snapshot of the surface expression of the sediment-laden buoyant plumes.
Runoff estimates
Estimates for subglacial runoff from SS were determined as in
Mankoff et al. (2016) and
Stevens et al. (2016). Briefly, the SS catchment area was determined based
on hydropotential flow routing, which is governed by SS surface and bed topography
(Cuffey and Paterson, 2010; Stevens
et al., 2016). Stevens et al. (2016)
determined that SS has three subcatchments each draining through the
terminus; in this study, we consider both the SS total catchment (Ctot)
and the largest subcatchment (C1). Once these catchments have been
defined, subglacial runoff for both 2012 and 2013 was estimated by summing
RACMO2.3 surface melting over the catchments
(van den Broeke et al., 2009). We make
the common assumption that meltwater generated at the glacier surface
emerges instantaneously from the glacier grounding line.
Buoyant plume model
Buoyant plume theory is a common tool for developing insight into plume
dynamics and the dominant controls on their variability
(e.g.,
Carroll et al., 2015, 2016; Cowton et al., 2016; Jenkins, 2011). The limited
information we have on plume geometry suggests a truncated line plume model
is the most appropriate for plumes driven by subglacial discharge at
tidewater glaciers
(Fried et
al., 2015; Jackson et al., 2017). Therefore, in this study, we use the line
plume model of Jenkins (2011) to reproduce the observed plume features and
to elucidate the mechanism that suppressed the buoyant plume extent during
the record 2012 melt season. We generalize the relative importance of
environmental forcings by obtaining a scaling for plume vertical extent in
terms of subglacial discharge flux and stratification.
Model description
In the plume model, the evolution of the buoyant plume properties (width,
vertical velocity, temperature and salinity) along the vertical glacier face
is described by four ordinary differential equations that conserve the
fluxes of mass, momentum, heat and salt (the reader is directed to Jenkins, 2011, for details of the equations solved). The model is steady in time and
integrated over the plume cross section, leaving the along-flow direction
(i.e., z) as the only independent variable. The entrainment of ambient waters
into the plume is assumed to be proportional to the vertical velocity along
the plume with a constant of proportionality α. We assume a constant
value of the entrainment coefficient, α=0.09, which falls within the
range obtained empirically for geophysical fluid processes
(Carazzo et al., 2008) and within the values
used in previous studies in SF (Mankoff et al., 2016; Stevens et al., 2016).
The model is closed using constant drag (9.7×10-3)
coefficient, the thermodynamic equation of seawater (TEOS-10,
McDougall and Barker, 2011) and three equations representing the
thermodynamic equilibrium at the ice–ocean interface
(Holland and Jenkins, 1999), which allows estimation
of the submarine melt rate of the calving front. As boundary conditions the
plume model requires profiles of the ambient fjord conditions, which are
obtained from observations as described further below. Given an initial flux
of subglacial discharge, assumed to have zero salinity and to be at the
pressure melting point, the solution is then obtained by numerical
integration.
Model experiments
While immersed in stratified environments, vertical plume development is
finite and the plume has two characteristic plume heights (Fig. 3;
List, 1982; Morton et
al., 1956). The first, NBD, is reached when the plume density equals the
ambient density. From this point, the plume continues upwards due to
vertical momentum but slows due to the reversed buoyancy experienced above
the NBD. The plume reaches MHD where the vertical velocity reaches zero
(Baines,
2002; Morton et al., 1956; Slater et al., 2016). Buoyant plume theory does
not capture the dynamics of waters in the plume beyond this point; however,
the waters are negatively buoyant and will therefore sink as they flow away
from the glacier, eventually equilibrating somewhere near the NBD (Fig. 3;
e.g., Carroll et al., 2015). Thereafter, waters in
the plume flow horizontally and can be treated as a jet
(Bleninger and Jirka, 2004;
Caufield and Woods, 1998; Jirka, 2004).
Schematic of plume characteristic heights, i.e., neutral buoyancy depth
(NBD) and maximum height depth (MHD), and the associated jet pathway. Note
that the plume model does not represent plume dynamics after the maximum
height is reached (red line), but it is expected that the jet will sink to a
depth similar to the NBD.
To analyze the sensitivity of plume vertical extent to subglacial discharge
and fjord stratification, we run the plume model for each year using ambient
fjord conditions constructed from averaging all CTD casts from the given
year, excluding casts from within the plume as the ambient fjord conditions
are intended to represent the ambient waters through which the plume is
rising. We consider a wide range of subglacial discharge fluxes (Qsg,
from 10 to 400 m3 s-1, every 10 m3 s-1) and subglacial
channel widths (W, from 50 to 200 m, every 10 m), though ultimately it is
only the combined quantity Qsg/W that affects the line plume model
solution (Slater et al., 2016). We evaluate the model on three principal
aspects. First, the fact that, according to our field observations, the plume
should surface in 2013 but not in 2012. Second, we compare the modeled plume
NBD with the observed depth of the jet in the water velocity measurements.
Third, we compare modeled and observed plume temperature and salinity
properties at the fjord surface.
Scalings
After evaluating the model at SF with realistic 2012 and 2013 conditions, we
seek to generalize our results by investigating the scaling of plume
vertical extent with subglacial discharge flux and stratification.
Stratification may be quantified through the squared
Brunt–Väisälä buoyancy frequency, N2, defined as follows:
N2=-gρrefdρdz,
where ρ is water density determined from Θ and
SA at depth, ρref is the reference density, which, for our
purposes, will be that at the fjord bottom, and g is the gravitational
acceleration (with no geographical dependency). To find a scaling, we fit a
suite of plume model results, using nonlinear least squares, to a simple
curve that takes the following form:
Z=AN2N02aQsgQ0bZ0,
where Z accounts for the characteristic plume height (either of NBD or
MHD) in meters, A is a dimensionless constant of proportionality and a
and b are the (dimensionless) powers of the scaling. N0 and Q0
are constant values of stratification and subglacial discharge, respectively, here taken to be N02=4×10-4 s-2 and Q0=100 m3 s-1, and
Z0 is a constant height defined in Appendix A. According to the
bathymetry and CTD data (see Sect. 3), the fjord depth is set to 150 m and divided into two layers: the unstratified bottom layer (from the
bottom to 100 m depth) and the linearly stratified top layer (100 m depth to
the sea surface), so that N2 in the scaling (Eq. 2) is taken to be the
stratification on the top layer. Given the weak impact of temperature on
density, in this exercise we assume a constant temperature profile
Θz=1∘C (which is in fact
close to the real conditions at Saqqarleq, except close to the surface), so
that the stratification is determined solely by salinity gradient. SA
of the bottom layer is held constant at 33.6 g kg-1, while the top layer
is linearly stratified in salinity with a sea surface SA ranging from
33 to 24 g kg-1, which allows us to analyze stratification strengths
(N2) from 2 to 8×10-4 s-2. Runoff (Qsg) varies
from 60 to 180 m3 s-1 every 20 m3 s-1. An identical
procedure is used to find a scaling for the submarine melt flux, in m3 s-1, defined by the following equation:
M=W∫z=-150z=-NBDm˙(z)dz,
where m˙z is the submarine melt rate, in m s-1,
as calculated by the plume model. In this case the scaling takes the following form:
M=AN2N02aQsgQ0bM0,
where N0 and Q0 are the same as for the height scaling and M0 is a
constant melt rate factor defined in Appendix A.
ResultsObservationsPlume observations
Aerial images show that the main plume at SS was observed at the fjord
surface on 1 June 2012 (Fig. 4a) but that it was not at the fjord surface
once the field campaign began on 17 July 2012 (Fig. 4b, c). The plume
was furthermore not seen at the fjord surface at any point during the 11 d of the 2012 field campaign. Conversely, the plume was clearly visible
at the fjord surface on 23 July 2013 (Fig. 4d, e), and it was
continuously at the fjord surface for the 8 d of the 2013 field campaign.
The surface expression of the plume observed in 2013 extended approximately
200 m along the glacier front and 300 m into the fjord (Fig. 4d, e; Mankoff
et al., 2016). Water inside the plume appeared brown due to the high
sediment concentration of subglacial discharge. Despite the differing
surface expression of the plume in 2012 and 2013, as described further
below, we know from hydrographic and velocity measurements that the plume
and the associated jet were indeed present at the same location in both
years (Mankoff et al., 2016; Stevens
et al., 2016).
Aerial images of the main plume at Saqqarliup–Saqqarleq front
visible at the fjord surface on (a) 1 June 2012, (d) and (e) 23 July 2013 but absent on (b) 17 July 2012. Also absent was the
plume on 23 July 2012, as shown in (c), a photograph taken from the boat,
which covers the black rectangle in (b). The yellow arrows approximately
indicate the ice flow direction in that corner of the glacier and point at
the plume origin. The brown plume surface expression in (d) extends
approximately 200 m along the glacier front and around 300 m into the fjord.
Fjord structure
CTD profiles from SF show that, in general, the fjord properties were similar
in both years with a strongly stratified, warm and fresh upper 20 m layer
and a more weakly stratified deeper layer (Fig. 5). The water column was
substantially more stratified in 2012 than in 2013, due largely to fresher
conditions in the upper 20 m but also a more moderate freshening extending
to ∼100 m depth. Fjord waters in the upper 20 m were also
substantially warmer in 2012 than 2013. The waters found at depth in SF are
cooler than the relatively warm Atlantic Waters (AW) often found at depth in
Greenlandic fjords (Straneo et al.,
2012; Straneo and Cenedese, 2015). SF is relatively shallow, having a
maximum depth of 230 m, and is separated from the open ocean by sills at 70 m to Tasiusaq Fjord and 125 m to Ilulissat Icefjord (Fig. 1). As such we do
not see AW in Saqqarleq Fjord, instead we see cooler Ilulissat Icefjord
waters (IIW, Fig. 5, Stevens et al., 2016).
(a) Conservative temperature, (b) absolute salinity, (c) sigma–theta
(potential density – 1000 kg m-3) and (d) squared
Brunt–Väisälä frequency profiles (Eq. 1) derived from CTD casts
in Saqqarleq fjord during field surveys in July 2012 (red) and 2013
(grey). Averaged profiles are shown as darker lines and are used as ambient
boundary conditions for the line plume model. Casts from inside the plume
are not included here. Note that the water column is characterized in three
layers separated by dashed horizontal lines.
To characterize differences between the years, we first divide the profiles
into three layers, according to common characteristics (Fig. 5). The bottom
layer, defined from the fjord bottom to -100 m, was well mixed in the
vertical and had a conservative temperature around 1 ∘C and absolute
salinity of ∼34.6 g kg-1. Differences observed in this
layer between the 2 years are negligible. The intermediate layer, from
∼20 to 100 m depth, was also characterized by a temperature
of approximately 1 ∘C and a weak salinity stratification.
The salinity gradient within this layer in 2012 was double that of 2013
(-0.04 g kg-1 m-1 compared to -0.02 g kg-1 m-1). The
top layer comprises the uppermost 20 m of the water column and has a strong
gradient in both temperature and salinity in both years. The conditions of
maximum temperature and minimum salinity occurred at the surface. In 2012,
surface conditions were warmer (up to 10 ∘C) and fresher
(as low as 17 g kg-1) than in 2013, and the upper layer was more
strongly stratified in 2012 compared to 2013, reaching maximum values of
N2>0.011 s-2 in 2012 compared to N2<0.006 s-2 in 2013
when we average over all profiles in the year (Fig. 5d).
A comparison of Θ-SA properties of the water masses (Fig. 6)
again shows that the decreased salinity in 2012 relative to 2013 was
distributed from the intermediate layer (σΘ of
∼24–26 kg m-3) towards the surface. The near-vertical
isopycnals in Fig. 6 result from the dominant effect of salinity on water
density within the ranges considered in this study. Thus, the freshening of
the fjord in 2012 relative to 2013 means that middle and upper layers in
2012 were much lighter than in 2013.
Conservative temperature vs. absolute salinity diagram, showing
the different water properties in Saqqarleq Fjord during fieldwork in July 2012 (red) and 2013 (grey). Isopycnals of sigma–theta are plotted as
dotted near-vertical lines.
To quantify the additional freshwater in the inner part of the fjord (up to
the SF–TF sill; see Fig. 1) in 2012 relative to 2013, we consider the depth
range from z= m (sea surface) to z=-10 m depth (bottom–middle layer
interface). We assume the area of the inner part of the fjord to be constant
in the vertical, Afz=Af≈35 km2,
and, following Rabe et al. (2011), we
calculate the volume of additional freshwater as follows:
V0=Af∫-1000S2013-S2012S2013dz,
where S2013,2012(z) are the averaged salinity profiles for the
respective years (see Fig. 5). We obtain a freshwater excess of 0.16 km3 (i.e., ∼0.16 Gt) in 2012 relative to 2013, equivalent
to 4.5 m of additional freshwater per unit area of the inner fjord.
Plume-driven jets
Velocity data from across-fjord transects approximately ∼1.5 km from the glacier (Fig. 2) reveal the presence of a jet both in 2012 and
2013 (Fig. 7). The jet is a subsurface-intensified localized region of water
flowing away from the glacier, located in the same spot in the along-front
transect, oceanward of the main plume location (Figs. 2, 4 and 7). In 2012,
the jet was more diffuse in the vertical, extending to 35 m depth, while in
2013 the jet was confined to the upper 20 m. Although the fjord was overall
more stratified in 2012, the vertical spreading of the jet observed in 2012
could be associated with the reduced stratification surrounding the jet in
2012, N20122z=-25=5×10-4 s-1,
compared to that of 2013, N20132z=-13=1.3×10-3 s-1. Maximum velocities of 0.35–0.4 m s-1 were found at
a depth of 25 m in 2012 and 13 m in 2013. A numerical simulation of the
circulation in this fjord (Slater et al.,
2018) shows that these jets are the horizontal outflow from the main plume
(e.g., Fig. 3). Outside of the jets, flow was generally directed towards the
glacier (Fig. 7; Slater et al., 2018).
(a, b) Fjord water velocity transects and (c, d) velocity
profiles from ADCP measurements taken in 2012 (a, c) and 2013 (b, d) parallel to and at a distance of 1.5 km from the glacier front (see
Fig. 2). Darker profiles in (a, b) correspond to the vertical
straight lines shown in (c, d) that span the jet. The contour
lines in (a) and (b) are isopycnals of sigma–theta.
The amplitude of the barotropic and baroclinic tidal currents, derived from
an ADCP deployed in the middle of the fjord in summer 2012, were
approximately 0.01 and 0.06 m s-1, respectively (Robert M.
Sanchez, personal communication, 2020). These currents are much smaller than those
observed in the jet (∼0.3 m s-1) and shown in Fig. 7,
thus we do not expect that removal of the tidal velocities would
significantly change the structure of the jet. The jet structure, in turn,
is here used mostly to identify the water masses that are carried away from
the glacier in the jet.
No local wind observations are available for the duration of the 2012 and
2013 surveys. During both surveys, however, wind conditions and sea state
were largely calm and permitted surveys to be conducted from small boats and
autonomous vehicles. This observation, together with the highly localized
nature of the jet, support the conclusion that the jet is associated with
subglacial discharge plume and is not a wind-driven feature. The numerical
simulations of Slater et al. (2018), who were able to reproduce the jet with
no wind forcing, also support this conclusion.
Subglacial runoff
One of the main sources of fjord freshwater is surface meltwater from the
glacier's hydrological catchment basin, which enters the fjord from beneath
the glacier as subglacial runoff (Fig. 8). Glacier surface melting that
resulted in substantial runoff began around 1 June (DOY 150) in 2013 and
around 10 d earlier in 2012. Runoff is highly variable on daily
timescales but was generally greater during summer 2012 (average 122 m3 s-1) than in summer 2013 (average 92 m3 s-1), with a
peak runoff in 2012 of ∼350 m3 s-1, far exceeding
any value in 2013. During the time period of the fieldwork, mean daily
runoff for the total catchment (major subcatchment) was 144
and 132 m3 s-1 (113 and 105 m3 s-1) in 2012 and 2013, respectively. Considering cumulative
summer runoff (Fig. 8), we obtain a total of 0.98 Gt in 2012 and 0.72 Gt in
2013. That is, in 2012 there was additional freshwater runoff input of 0.26 Gt. These differences are consistent with the observation that 2012 was a
record melt year in Greenland
(Nghiem
et al., 2012; Smith et al., 2015; Tedesco et al., 2013).
SS runoff for the total catchment (Ctot, darker lines) and
the major subcatchment (C1, lighter lines). Daily runoff estimates are
shown from June to August of (a) 2012 and (b) 2013. The shaded regions
comprise the field survey period (17–27 July, DOY 199-209 in 2012; 24–31 July, DOY 205-212 in 2013). The average runoff over the field survey period
for C1 is shown inside the shading by a dotted line. (c) Cumulative
runoff volume throughout both years, 2012 (red) and 2013 (dark grey),
expressed in Gt.
Plume modeling
Analysis of the oceanographic data (Sect. 3.1) shows that a plume and the
resulting jet were present during both surveys but that their
characteristics were different. Specifically, (i) the plume did not reach
the fjord surface in July of 2012, while it did in July 2013; (ii) fjord
conditions were considerably fresher within the intermediate and top layers
in 2012 than in 2013; and (iii) the plume-driven jet was found deeper in
2012 than 2013. Here, we use the line–plume model constrained by the
averaged year's bulk oceanographic profiles (Fig. 5) and forced by different
subglacial discharge scenarios to investigate plume behavior. The resulting
modeled NBD and MHD for the main plume at SF are shown as a function of the
subglacial runoff in Fig. 9. Results are shown for both 2012 and 2013, which
differ in their fjord stratification as described above. For a line plume
the runoff is prescribed as a runoff per unit width of grounding line
(Qsg/W); however, we also include an axis in Fig. 9 showing the absolute
runoff (Qsg) assuming a line plume width of W=90 m, which was
suggested by Jackson et al. (2017) to
be the most appropriate for the main plume at SS.
Characteristic plume heights obtained from the line–plume model.
NBD (solid lines) and MHD (dotted lines) are obtained for 2012 (red) and
2013 (grey). Dashed horizontal lines mark the depth of the jet core observed
from water velocity observations in 2012 and 2013 (Fig. 7). The top x axis represents the subglacial discharge flux applied through a channel
width (W) of 90 m. The blue vertical line shows the subglacial
runoff estimate (from RACMO2.3) averaged over the 5 d prior to the
velocity measurements in the fjord each year (which were approximately the
same: 101.7±5.7 m3 s-1 in 2012 and 101.9±13.4 m3 s-1 in 2013). The standard deviation
of subglacial discharge during these 5 d is represented by the red (grey)
shaded region for 2012 (2013).
We obtained deeper NBD and MHD in 2012 than 2013 for any given Qsg/W
ratio (Fig. 9), indicating that the increased stratification and freshwater
content of the fjord in 2012 suppressed the vertical extent of the plume.
The NBD remains subsurface for all of the Qsg/W ratios considered here,
indicating that the runoff is insufficient to generate a plume that would
remain at the surface as it flowed down-fjord. The plume reaches the surface
(MHD =0 m) in 2013 for Qsg/W ratios higher than ∼0.4 m2 s-1, while the ratio has to be above ∼1.3 m2 s-1 for surfacing in 2012 (Fig. 9). Assuming a subglacial
channel width of W=90 m, runoff must exceed ∼40 or ∼120 m3 s-1 for it to surface in 2013
or 2012, respectively.
We now consider whether the plume model can reproduce our observations of
plume surfacing (Fig. 4 in the observations, MHD in the model) and jet depth
(Fig. 7 in the observations, NBD in the model). Following
Mankoff et al. (2016), we assume a subglacial runoff for
each year that is averaged over the 5 d prior to the water velocity
measurements that identify the jet, giving Qsg=101.7±5.7 m3 s-1 in 2012 and Qsg=101.9±13.4 m3 s-1
in 2013 (Figs. 8 and 9), and we assume a subglacial channel width of W=90 m in both years (Jackson et al., 2017).
With these choices, as illustrated in Fig. 9 (see also Fig. 3), we find
that (i) the model predicts plume surfacing in 2013 but not 2012
(consistent with observations) and that (ii) the model predicts neutral buoyancy
depth that is in reasonable agreement with the observed jet depth. Given
that this simple plume model is able to capture characteristics of the plume
and jet in 2012 and 2013 and that the imposed subglacial runoff is
almost identical between the 2 years, this confirms that differences in
the plumes and jet between the 2 years are driven by differences in the
stratification of the fjord.
We next consider the modeled plume temperature and salinity at NBD and MHD
and compare these with observed properties within the jets flowing down
fjord. Plume model properties at NBD in 2012 are characterized by SA and
Θ of 30.4 g kg-1 and 0.8 ∘C,
respectively, while they are 31.0 g kg-1 and 0.9 ∘C in
2013 (Fig. 10). The fresher value in 2012 is due to the greater volume of
freshwater present in the fjord in 2012 (Figs. 5 and 6), which is entrained
into the plume. The properties at MHD (Fig. 10) are warmer and fresher than
at NBD, since the plume has by then mixed in some of the warmer and fresher
waters from the upper water column (Figs. 3 and 5). The waters in the jets
(∼1.5 km from the calving front) were in both years
considerably warmer, fresher and lighter than at MHD in the plume (Fig. 10).
The outflowing jet was also significantly fresher in 2012 than in 2013.
Conservative temperature (Θ) and absolute salinity
(SA) of Saqqarleq Fjord waters in (a) July 2012 and (b) July 2013. Light
points show CTD measurements, while dark dots are xCTD measurements (closest
to the plume). Conservative temperature and absolute salinity at the NBD and
MHD as predicted by the plume model are shown as a yellow star and triangle,
respectively. The solid blue circles represent the water properties in the
core of the observed jets in Fig. 7.
Lastly, we seek to quantify the relative contribution of runoff and fjord
stratification on the vertical extent of the plume in SF through a suite of
plume simulations in which we systematically vary runoff and stratification.
Given the very good match with observations (Fig. 9), we use the line plume
model and consider a glacier front submerged in water of 150 m depth. To
have better control of the stratification parameters, we approximate the
observed stratification (Fig. 5), by assuming an unstratified bottom layer
of 50 m and a linearly stratified upper layer with fixed thickness of 100 m
representing both the middle and top layers in SF (see also Sect. 2.3.3). For
simplicity, we do not separately account for the highly stratified top layer.
Figure 11 and Table 1 show the results of fitting curves of the form in Eqs. (2) and (4) to the results from the plume model. Included are both the
plume extents and the vertically integrated submarine melt
rate. The power law captures plume vertical extent very well (Fig. 11a),
with both neutral buoyancy depth and maximum height scaling with N2
raised to the power -0.4 and runoff raised to the power 0.24. These
scalings are similar to those considered in
the Supplement to Slater et al. (2016), in which the
equivalent exponents were -0.5 and 0.3, respectively.
Slater et al. (2016), however, considered a
linear stratification while here we have considered a two-layer
stratification that is more representative of SF. Our results therefore show
that power law scalings of the form in Eqs. (2) and (4) continue to hold in
the two-layer case, provided small modifications are made to the exponents.
It is also notable that the power law scalings for characteristic plume
heights (Fig. 11a) perform well even in the absence of the “point source
correction”; an additional term that is often added to the scaling to
account for the finite size of the source of subglacial runoff
(Slater et al., 2016; Straneo and
Cenedese, 2015).
Results of fitting plume outputs to Eqs. (2) and (4). The plume
outputs presented here are the characteristic plume heights at neutral
buoyancy (Znb) and maximum extent
(Zmh) and the vertically integrated submarine melt
rates from the source to the neutral buoyancy height (M).
Scaling for (a) characteristic plume heights from the source and
(b) total submarine melt rates from the source to the neutral buoyancy
height. Plume model results are plotted by black dots. Straight and dotted
black lines represent fitting curves according to Eqs. (2) and (4) and
95 % confidence bounds, respectively. The fjord surface level has been included in
panel (a) as a dashed horizontal line.
Vertically integrated submarine melt rates (i.e., the total flux of meltwater
resulting from the plume) may also be expressed as a simple function of
N2 and Qsg (Fig. 11b and Table 1). The stratification exponent is
similar to that for the characteristic plume heights. The runoff exponent is,
however, twice that of NBD and MHD, indicating that total melt rate is twice
as sensitive to runoff as NBD and MHD. This reflects the fact that submarine
melt rate depends on plume velocity, which also scales positively with
subglacial runoff.
DiscussionImpact of fjord stratification on plume dynamics in Saqqarleq Fjord
We have combined a simple plume model with oceanographic data to explain the
observation of a discharge plume at SF reaching the fjord surface in 2013
but not in 2012 (Fig. 4), despite 2012 being a record surface melt year at
the ice sheet scale. This is consistent with the increased stratification of
the fjord in 2012 (Fig. 5), which meant that the characteristic plume heights
(Fig. 3) were significantly deeper in 2012 than in 2013 (Fig. 9). The plume
model also suggests that for the plume to reach the surface in 2012, the
rate of subglacial discharge would have had to be 3 times that what was needed in
2013. The fact that the estimated neutral buoyancy depth is deeper in 2012
(∼25 m, Fig. 9) than the very fresh layer at the fjord
surface (∼15 m, Fig. 5) suggests that it was not just the
fresh surface waters that influenced plume dynamics but that the differences
were also due to the stratification of the intermediate layer.
Given the observed fjord stratification and estimated subglacial discharge,
the plume model shows good agreement with our plume and jet observations.
The model reproduces the surfacing of the plume in 2013 but not in 2012. The
simulated NBD is deeper in 2012 than in 2013 and shows reasonable
agreements with the depths at which we observe jets ∼1.5 km
away from the glacier (Fig. 9). Lastly, the temperature and salinity
properties of the plume at the fjord surface in 2012 and 2013 lie close to
those observed by expendable probes dropped close to the glacier (Fig. 10),
indicating that the mixing of the plume and ambient water is reasonably
captured by the model. The agreement between the model and observations is
improved with respect to previous studies of Saqqarleq
(Mankoff et al., 2016; Stevens et
al., 2016). In our study, the modeled plume properties at NBD fall within
the range of the observed water properties (Fig. 10), whereas in Stevens et
al. (2016) and Mankoff et al. (2016) the modeled plume properties were
consistently too light and fresh. We attribute our improved model to
observation agreement to our use of a line plume model of appropriate width
(Jackson et al., 2017), which, due to a
larger plume surface area at depth, allows greater entrainment of denser
deep waters compared with the half-conical plume model employed by Stevens
et al. (2016) and Mankoff et al. (2016).
Our results also show that the observed (or modeled) plume properties, i.e.,
the properties observed within 150 m of the glacier face which the plume
model can reproduce given the observed stratification and estimated
discharge, are very different from those of the waters exported as a jet
observed 1.5 km away from the glacier (Fig. 10). The fact that the
properties of the jet, in both years, were considerably warmer, fresher and
lighter than the observed and modeled plume properties is indicative of
significant mixing with the surface waters that must occur as waters from
the plume sink and flow away from the glacier. We stress that the plume
model does not include this dilution, something that must be taken into
account both in interpreting observations taken farther than a few 100 m away from any glacier face and/or in extrapolating plume
observations and properties away from the glacier. More complex models are
needed to capture this mixing and export (e.g.,
Slater et al., 2018).
Despite good agreement between model and observations in the plume
characteristics, a number of key assumptions are worth commenting on. Our
results are relatively insensitive to the assumed value of the entrainment
coefficient (α). For example, allowing α to vary between
0.07 and 0.12 (which brackets the values to be found in the literature)
leads to a range in NBD of 21 to 29 m in 2012 and 13 to 17 m in 2013. NBD is
deeper for larger values of α because the plume entrains greater
volumes of deep ambient water and is therefore denser. NBD and MHD are
deeper in 2012 than in 2013 for any given value of α, confirming
that stratification played a crucial role in determining plume vertical
extent, and therefore our conclusions do not depend on the value of the
entrainment coefficient used.
Sensitivity analyses also showed that our plume model results are
insensitive to how we define the ambient fjord conditions. In principle,
fjord conditions close to the glacier through which the plume is rising
could differ from those a few kilometers away, meaning that the modeled
characteristic plume heights (NBD and MHD) could vary depending on which CTD
casts were used to define the ambient conditions for the plume model. We
find, however, that in 2012 NBD only varies from 20 to 26 m when CTD casts
within 150 m of the glacier or 1.5 km from the glacier are used to define
the ambient fjord conditions. In 2013, the equivalent values are 13 to 15 m.
MHD is similarly insensitive. Therefore, although we see substantial
differences in plume dynamics between 2012 and 2013 due to differing fjord
stratification, spatial variability in fjord stratification in a given year
does not lead to significant differences in plume dynamics, and hence our
results are not sensitive to how we define the ambient conditions in a given
year.
We have assumed that meltwater from the glacier surface emerges from the
grounding line instantaneously, so that estimated daily surface melting can
be equated to daily subglacial discharge. Although this is a widespread
assumption in glacier–fjord studies
(Mankoff
et al., 2016; Slater et al., 2018; Stevens et al., 2016), it is a
simplification because a number of hydrological processes will act to delay
this meltwater, including storage of water in supra-glacial and subglacial lakes
and the finite transit time of meltwater along the ice sheet surface and bed
(Fountain and Walder, 1998). This delay is
likely to be significantly longer, perhaps even weeks, at the beginning of
the melt season when there is still a significant snowpack and the
subglacial drainage system may be inefficient
(De
Andrés et al., 2018; Campbell et al., 2006; Cowton et al., 2013; Schild
et al., 2016). As the melt season progresses, drainage becomes more
efficient, with subglacial transit velocities exceeding 1 m s-1
(Cowton et al., 2013), so that by late July when our
field seasons took place, surface meltwater likely emerges from the
grounding line as subglacial discharge rather rapidly, supporting our
assumption. Nevertheless, uncertainty in meltwater transit time results in
uncertainty in the magnitude of subglacial discharge; however, we do not
believe this is sufficient to modify our conclusions.
Another source of uncertainty is the width of the subglacial channel
delivering discharge into the fjord. Following
Jackson et al. (2017), we have
considered a channel of fixed width equal to 90 m. It is, however, expected
that channel width growths with subglacial discharge due to increased
melting of the channel's walls
(Greenwood et al., 2016;
Lliboutry, 1983). It is therefore plausible that due to the overall higher
subglacial discharge in 2012 (Fig. 8), the main discharging channel at SF
was larger in 2012 than 2013. A larger channel could contribute to the plume
not surfacing in 2012. If the discharge was more laterally spread, the
resulting plume would be less intense and would not attain the same vertical
extent. The plume model nevertheless shows that the channel width would have
to change by a factor of ∼3 to assume equal importance to the
differing fjord stratification. Since channel theory suggests this is
unlikely (e.g., Slater et al., 2015), here we have
focused on the impact of fjord stratification.
Lastly, we generalized our results by using the plume model to fit a scaling
between stratification (N2), subglacial discharge (Qsg), and
characteristic plume heights NBD and MHD. We found that both characteristic
plume heights scaled with N2 raised to the power -0.4 and Qsg
raised to the power 0.24 (Fig. 11a), which are similar to those obtained by
Slater et al. (2016). This means that a
doubling of subglacial runoff would increase plume vertical extent (NBD and
MHD) by 18 %, while a doubling of stratification would decrease plume
vertical extent by 25 %. While the net impact on plume vertical extent
depends on the intrinsic variability of runoff and stratification, this
scaling taken together with our observations shows that stratification plays
a dominant role in setting plume vertical extent. In contrast, a doubling of
runoff increases total submarine melting by 40 %, while a doubling of
stratification decreases total submarine melting by 26 % (Fig. 11b). For
submarine melting, stratification is not dominant but still plays
an important role that is worth considering in bulk submarine melt rate
parameterizations.
Controls on fjord stratification
By analogy with other fjords around Greenland, water properties in SF are
expected to experience strong seasonal variability as a consequence of
increased glacial freshwater inputs and solar radiation during summer
(Jackson
et al., 2014; Schild et al., 2016; Sciascia et al., 2013; Straneo et al.,
2011). We have focused largely on interannual variability by contrasting
plume dynamics between July 2012 and July 2013, but in fact we also observed
the plume at the fjord surface in early June 2012, when runoff is low (Figs. 4 and 8). We do not have any records of fjord properties in early June 2012,
but we suspect the plume was able to surface due to a relatively
unstratified water column at the beginning of the melt season. The strong
stratification and the subsurface-trapped plume in late July 2012 suggests
seasonal variability in fjord stratification with the fjord becoming more
stratified as the melt season progresses.
The additional freshwater in the fjord in July 2012 relative to July 2013
amounts to 0.16 Gt when summed over the inner part of SF (i.e., the region
shown in Fig. 2). This could be accounted for by the high subglacial
discharge in 2012 which, by the end of the melt season, exceeded that from
2013 by 0.26 Gt. We do not attempt a rigorous freshwater budget here, which
would account for additional freshwater sources and sinks such as the
formation and melting of sea ice, melting of the calving front and icebergs,
land runoff, and freshwater import and export from the fjord. Rather we
suggest that due to the strong zones of recirculation observed and modeled
in SF during summer (Slater et al.,
2018), it is plausible that a significant fraction of the additional
freshwater in 2012 remained in the inner fjord long enough to freshen the
water column, leading to a stronger stratification and inhibiting the
vertical extent of the plume in July 2012 compared to June 2012 and July 2013. The implication is that the glacier itself impacts the stratification
of the fjord which, in turn, will have an impact on glacier–ocean exchanges
and on where and how the meltwater is exported
(Curry
et al., 2014; Gladish et al., 2015a, b; Oliver et al., 2018; Straneo et
al., 2011).
The increased freshwater content of the fjord in 2012 is not limited to the
surface layer, instead extending to 100 m depth (Fig. 5). Precipitation, sea
ice melting and land runoff would most strongly affect the near-surface and
would have to be mixed downwards to significantly impact properties at
depth. Therefore, the increased freshwater content at depth is more likely to
have a glacial origin: either the melting of large deep-keeled icebergs
(Enderlin
et al., 2016; Moon et al., 2018), melting of the calving front itself
(Slater et al.,
2018; Wagner et al., 2019) or the trapping of subglacial discharge plumes
below the surface (Fig. 4; Stevens et al.,
2016). Considering the last point, secondary discharge channels with weaker
plumes that find neutral buoyancy at greater depths
(Slater et al., 2018) may play an
important role in setting the seasonal fjord stratification. Equally,
temporal variability in subglacial discharge of the main plume, resulting in
periods where the plume reaches neutral buoyancy at depth, may drive
freshening of the fjord and feedback on the dynamics of the plume. Overall
we are suggesting that high surface melting through the melt season in 2012
may have freshened the fjord, driving increased fjord stratification and
leading to the suppression of the plume later in the melt season.
Wider impacts of glacier–fjord coupling
In line with previous studies, our observations and supporting plume model
results suggest that both subglacial discharge and fjord stratification
exert a strong control on the dynamics of subglacial discharge plumes (e.g.,
Slater et al., 2016) with implications for melting of the glacier face and
export of meltwater (Jackson et al., 2017; Mankoff et al., 2016; Stevens et
al., 2016). We have also speculated that part of the differences between
2012 and 2013 in SF are due to the impact of the extreme surface melt of
2012 on the fjord raising the possibility of feedbacks between surface melt,
submarine melt and export. Considering that under a high greenhouse gas
emissions scenario (RCP8.5) subglacial runoff may increase by as much as a
factor of 6 by the end of the century (Slater et
al., 2019), it is possible that fjords will become increasingly stratified.
Since stratification has proven such an important determinant of plume
dynamics in this study, it is possible that despite the increased buoyancy
provided by increased subglacial discharge, plumes may reach the fjord
surface less often over the coming century. This may decrease our ability to
observe and monitor plumes based on their surface expression, which has
served as a basic but important observation for studies of fjord processes
and subglacial hydrology
(Schild et al., 2016; Slater
et al., 2017).
From a biogeochemical perspective, a suppression of the vertical extent of
plumes driven by increased fjord stratification could limit the upwelling
into the photic zone of nutrients in deep water masses and from subglacial
bed weathering
(Cape
et al., 2019; Hopwood et al., 2018; Meire et al., 2017). We acknowledge that
the impact in SF in July 2012 may have been limited because, although the
plume did not surface, our model suggests it was very close to the surface.
Nevertheless, many of these nutrients act as a limiting factor for the
primary productivity (phytoplankton) within the photic zone
(Cape et al., 2019). Therefore, in contrast to some
expectations (Bhatia et al., 2013), an
increase in ice sheet surface melting could have a negative impact on the
productivity of fjords in general. Considering that primary producers are
the base of the pelagic ecosystem, a decrease in the productivity of fjord
waters could negatively impact fisheries and bird populations
(Arimitsu et
al., 2012; Meire et al., 2017). Nevertheless, our model experiments suggest
that the maximum plume height in July 2012 was only a few meters below the
surface, so reduced impacts on nutrient limitations are expected to happen
during July 2012. It has also been observed that the surface layer of the
fjord waters (in contact with the atmosphere) is undersaturated in CO2
during the summer. Around 28 % of the uptake is attributed to the input of
glacial waters and ∼72 % to primary producers
(Meire et al., 2015). Therefore, a
reduction of these organisms together with the subsurfacing of glacial
waters could decrease the ability of the fjords to act as atmospheric
CO2 sinks.
Regarding the potential implications on melting of the submerged calving
front, our scalings show that stratification does indeed suppress melting of
the calving front within the plume through dampening of its vertical
velocity and extent. However, increased subglacial discharge has a stronger
influence on melting through increasing the vertical velocity, and therefore
submarine melt rates are likely to increase in response to increased ice
sheet surface melting, though their vertical reach may be diminished,
potentially leading to undercutting.
Lastly, stratification likely impacts on circulation more widely in the
fjord, though this is beyond what we can quantify with a simple plume model.
Our oceanographic observations of the jet show that due to increased
stratification in 2012 compared to 2013, the jet that carries plume waters
away from the glacier is deeper (Fig. 7) and fresher (Fig. 10) in 2012 than
in 2013. These waters are subsequently exported from the fjord to the
continental shelf where they may impact shelf properties
(Luo et al., 2016), primary productivity
(Arrigo et
al., 2017; Oliver et al., 2018) and potentially the larger-scale ocean
circulation (Böning
et al., 2016; Saenko et al., 2017). Our observations suggest that in the
future, increased ice sheet surface melting may stratify Greenland's fjords
and modify the depth and properties of waters that are exported to the
shelf. Further observations and modeling would be needed to better
understand how these processes will evolve in the future.
Conclusions
This study began with the counterintuitive observation of a surfacing
subglacial discharge plume in Saqqarleq Fjord in late July 2013 (an average
melt year) but a subsurface trapped plume during late July 2012 (a record
melt year). Increased subglacial discharge acts to drive a stronger plume
that, in the absence of other factors, will have a greater vertical extent
and probability of reaching the fjord surface. By combining oceanographic
observations together with support from a plume model we have shown that the
difference between the 2 years can be explained by the increased
freshwater content of the fjord in 2012 relative to 2013, resulting in
stronger fjord stratification and a suppression of the vertical extent of
the plume. As such, seasonal and interannual variability in fjord
stratification has a strong impact on the vertical extent of subglacial
discharge plumes at tidewater glaciers. We suggest that the increased
stratification and freshwater content of the fjord in 2012 compared to 2013
is driven by the glacier itself. In particular, strong ice sheet surface
melting throughout summer 2012, delivered to the fjord as subglacial
discharge, may have gradually accumulated freshwater in the fjord and
increased stratification, providing a negative feedback on plume vertical
extent.
Observations of the horizontal jet emanating from the plume in 2012 and 2013
show that the jet was deeper and more diffuse in 2012 and that it carried
fresher and lighter water. This interannual difference is consistent with
results from the plume model, in which the simulated neutral buoyancy depth
of the plume proves a good estimator of the depth of the jet, and suggests
once more that the driver of the observed differences is the increased
stratification of the fjord in 2012. Since waters in the jet are those which
will be exported from the fjord, variability in fjord stratification will
impart variability on the depth and properties of waters exported from the
fjord to the open ocean. We also showed, however, that the properties of
waters exported from the glacier–ocean boundary in the jet approximately 1.5
km from the ice front cannot be described fully by a plume model. Instead,
the jet is carrying strongly diluted plume waters through mixing with
surface waters. This means that plume models or near-ice front properties
are not fully representative of properties of the meltwater and ambient water
mixture.
We then used the plume model to fit a scaling for plume vertical development
and total submarine melting in terms of fjord stratification (N2) and
subglacial discharge (Qsg). We found that plume vertical extent is
proportional to N2N02-0.4QsgQ00.24, while total submarine melting is
proportional to N2N02-0.43QsgQ00.49. These highlight the important
role played by fjord stratification and the subglacial discharge flux in
the dynamics and impacts of subglacial discharge plumes. It should be noted,
however, that these scalings are based on the plume model and, as such, the
quantitative details are sensitive to applied model parameters, which are
poorly constrained.
Looking to the future, we are likely to see increased surface melting of the
ice sheet in response to climate warming. Our results suggest that through
increasing the stratification of glacial fjords, it is possible that this
melting may suppress rather than promote the vertical extent of plumes and
their presence at the fjord surface. This may limit our ability to monitor
plumes remotely, reduce the delivery of nutrients to the photic zone, and
modify the depth and properties of waters exported from the ice sheet to the
ocean. Further observations and modeling are needed to better understand how
the stratification of fjords and impacts on physical and biological systems
may evolve in the future.
In Sects. 2.3.3 and 3.3 we define and fit scalings for plume
characteristic heights and induced submarine melt rate in terms of the fjord
stratification and subglacial discharge. The scaling for subglacial
discharge includes a constant height Z0 defined by the following equation (see also Slater et
al., 2016):
Z0=(N02)-1/2Q0g0′αW1/3,
where N0 and Q0 are a constant stratification and subglacial
runoff, with values given in Sect. 2.3.3, α=0.09 is the
entrainment coefficient, g0′=0.26 m s-2 is the plume reduced
gravity at the glacier grounding line (Slater et al., 2016), and W is the
plume width, taken to be 90 m in Sect. 3.3. For the chosen parameters, Z0 takes a value 74 m in our study.
The scaling for submarine melting includes a melt rate factor M0 given
by the following equation:
M0=cwCd1/2ΓTTF0LQ0g0′αW1/3Z0W,
where cw=3974 J kg-1∘C-1 is the heat
capacity of water, Cd=9.7×10-3 is the plume–ice drag
coefficient, ΓT=1.1×10-2 is the heat
transfer coefficient, L=3.34×105 J kg-1 is the latent heat
of melting and TF0=2.9∘C is the temperature of fjord
waters (1 ∘C) above the in situ freezing point (-1.9∘C). All other variables have been previously defined. For the chosen
parameters, M0 takes the value 0.37 m3 s-1 in our study.
Data availability
All data used in this study are publicly available. CTD data may be found on
the NSF Arctic Data Center at
10.18739/A2B853H78 (Straneo, 2019) and at https://data.nodc.noaa.gov/cgi-bin/iso?id=gov.noaa.nodc:0210572 (Straneo, 2020), while ADCP data may be
found on NOAA-NCEI at
http://data.nodc.noaa.gov/cgi-bin/iso?id=gov.noaa.nodc:0177127 (Straneo et al., 2018).
Author contributions
EDA, DS and FS designed the research. FS and SD collected field
observations. EDA processed field and runoff data. DS provided the original
model code and EDA adjusted the code to this work. EDA performed the
analysis, and all the authors contributed to the discussion. EDA wrote the
original text of the paper with input from all other authors.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
Eva De Andrés is supported by the
Spanish Ministry of Education with the PhD studentship no. FPU14/04109. Fiamma
Straneo and Donald Slater would like to acknowledge WHOI's Ocean and Climate
Change Institute for funding the fieldwork and the NSF (grant no. 1418256) for funding the
analysis. We would also like to thank Dan Torres, James Holte, Jeff Pietro,
Clark Richards, Laura Stevens, Rebecca Jackson, Ken Mankoff, Amy Kukulya,
Hanumant Singh, Robin Littlefield, Al Plueddemann, Ove Villadsen, and our
colleagues from Illimanaq for their instrumental role in collecting the
data and in follow-up discussions and Till Wagner for discussions about the
paper.
Financial support
This research has been supported by the Ministerio de Educación, Cultura y Deporte (grant no. FPU14/04109), the National Science Foundation (grant no. 1418256), the Ministerio de Economía, Industria y Competitividad, Gobierno de España (grant no. CTM2017-84441-R), and the Horizon 2020 Research and Innovation Programme (grant no. 727890).
Review statement
This paper was edited by Jan De Rydt and reviewed by two anonymous referees.
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