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Modeling the impact of glacial runoff on fjord circulation and submarine melt rate using a new subgrid-scale parameterization for glacial plumes

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The injection at depth of ice sheet runoff into fjords may be an important control on the frontal melt rate of tidewater glaciers. Here, we develop a new parameterization for ice marginal plumes within the Massachusetts Institute of Technology General Circulation Model (MITgcm), allowing three-dimensional simulation of large (500km2) glacial fjords on annual (or longer) timescales. We find that for an idealized fjord (without shelf-driven circulation), subglacial runoff produces a thin, strong and warm down-fjord current in the upper part of the water column, balanced by a thick and slow up-fjord current at greater depth. Although submarine melt rates increase with runoff due to higher melt rates where the plume is in contact with the ice front, we find that annual submarine melt rate across the ice front is relatively insensitive to variability in annual runoff. Better knowledge of the spatial distribution of runoff, controls on melt rate in those areas not directly in contact with plumes and feedback mechanisms linking submarine melting and iceberg calving are necessary to more fully understand the sensitivity of glacier mass balance to runoff-driven fjord circulation. This article is protected by copyright. All rights reserved.
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RESEARCH ARTICLE
10.1002/2014JC010324
Modeling the impact of glacial runoff on fjord circulation and
submarine melt rate using a new subgrid-scale
parameterization for glacial plumes
Tom Cowton
1
, Donald Slater
2
, Andrew Sole
1
, Dan Goldberg
2
, and Peter Nienow
2
1
Department of Geography, University of Sheffield, Sheffield, UK,
2
School of Geosciences, University of Edinburgh,
Edinburgh, UK
Abstract The injection at depth of ice sheet runoff into fjords may be an important control on the frontal
melt rate of tidewater glaciers. Here we develop a new parameterization for ice marginal plumes within the
Massachusetts Institute of Technology General Circulation Model (MITgcm), allowing three-dimensional sim-
ulation of large (500 km
2
) glacial fjords on annual (or longer) time scales. We find that for an idealized fjord
(without shelf-driven circulation), subglacial runoff produces a thin, strong, and warm down-fjord current in
the upper part of the water column, balanced by a thick and slow up-fjord current at greater depth.
Although submarine melt rates increase with runoff due to higher melt rates where the plume is in contact
with the ice front, we find that annual submarine melt rate across the ice front is relatively insensitive to var-
iability in annual runoff. Better knowledge of the spatial distribution of runoff, controls on melt rate in those
areas not directly in contact with plumes, and feedback mechanisms linking submarine melting and iceberg
calving are necessary to more fully understand the sensitivity of glacier mass balance to runoff-driven fjord
circulation.
1. Introduction
The melting of Greenland’s marine terminating glaciers by warm oceanic waters may be a significant cause
of dynamic mass loss from the Greenland ice sheet [Holland et al., 2008; Straneo and Heimbach, 2013]. Rela-
tively little is however known about this process, particularly the interaction between the glacier (and sub-
glacial runoff), fjord circulation, and terminus melt rates [Straneo et al., 2013]. For example, although very
high (>5md
21
) melt rates have been predicted in areas directly adjacent to upwelling subglacial runoff
[Jenkins, 2011; Xu et al., 2012], the importance of this process when considered across the entirety of the gla-
cier front remains unclear. The significance of glacially forced estuarine circulation within the fjords as a
means of replenishing the supply of warm water available for melting at the fjord head is also debated [e.g.,
Motyka et al., 2013; Straneo et al., 2010].
Obtaining field measurements from Greenland’s ice-choked fjords has proven extremely difficult, particu-
larly in the critical area close to glacier fronts [Straneo et al., 2013]. As such, data sets of water properties
[e.g., Chauch
eetal., 2014; Mortensen et al., 2011; Rignot et al., 2010; Straneo et al., 2011, 2010] are rare and
often limited with regard to timeframe and proximity to the glacier, making interpretation challenging. The
convection of glacial plumes was modeled by Jenkins [2011], providing a theoretical relationship between
meltwater discharge and submarine melt rate, but this approach cannot provide information on the impact
of such plumes on the wider fjord circulation. In recent years, numerical ocean models have also been used
to examine the impact of glacial runoff on fjord circulation [Salcedo-Castro et al., 2011; Sciascia et al., 2013;
Xu et al., 2013, 2012]. Such studies have however been limited by the computational expense of both resolv-
ing the fine-scale, highly nonhydrostatic dynamics of the turbulent glacial outflow plume and incorporating
the wider circulation of fjords that may be hundreds of square kilometers in area. This constraint has
resulted in simulations being limited to two-dimensional fjords [Sciascia et al., 2013; Xu et al., 2012] or small
(<0.1 km
2
) three-dimensional domains [Xu et al., 2013], and short (hours to days) simulation times.
Here we aim to overcome these constraints by parameterizing the glacial plume. Parameterization of verti-
cal motion is a technique commonly employed in ocean modeling, allowing incorporation of processes
occurring at a scale finer than the grid resolution [e.g., Campin and Goosse, 1999; Paluszkiewicz and Romea,
Key Points:
We present a method for
parameterizing subglacial runoff in
ocean models
This is used to examine fjord
circulation and glacier melt on
annual time scales
We find interannual runoff variability
to have only limited impact on melt
rate
Supporting Information:
Cowton Supporting Information
Correspondence to:
T. Cowton,
t.cowton@sheffield.ac.uk
Citation:
Cowton, T., D. Slater, A. Sole,
D. Goldberg, and P. Nienow (2015),
Modeling the impact of glacial runoff
on fjord circulation and submarine
melt rate using a new subgrid-scale
parameterization for glacial plumes, J.
Geophys. Res. Oceans,120, 796–812,
doi:10.1002/2014JC010324.
Received 18 JUL 2014
Accepted 7 JAN 2015
Accepted article online 22 JAN 2015
Published online 12 FEB 2015
This is an open access article under the
terms of the Creative Commons
Attribution-NonCommercial-NoDerivs
License, which permits use and
distribution in any medium, provided
the original work is properly cited, the
use is non-commercial and no
modifications or adaptations are
made.
COWTON ET AL. V
C2015. The Authors. 796
Journal of Geophysical Research: Oceans
PUBLICATIONS
1997; Price and Yang, 1998]. We start by developing a plume model based on an input of subglacial runoff
from a point source (i.e., a major subglacial channel), as is expected based on the observation of discrete
plumes adjacent to tidewater glacier fronts [e.g., Chauch
eetal., 2014; Sole et al., 2011]. This is then used to
calculate the vertical movement of water, heat, and salt at each time step at a specified location within an
ocean model. Doing so eliminates the need to resolve the glacial plume, thus permitting much coarser
model resolution. This has the advantage of greatly reducing the simulation time while still allowing the
plume to evolve as runoff varies or conditions in the fjord change.
This model is used to examine ice-ocean interaction on annual time scales in an idealized fjord, similar in
scale to a large Greenlandic fjord such as Sermilik or Kangerdlugssuaq. Greenland’s glacial fjords are com-
plex environments, driven by a range of highly variable terrestrial, atmospheric, and oceanic forcings [Stra-
neo and Heimbach, 2013]. We do not attempt to realistically recreate or assess the relative importance of
the multiple components of fjord circulation. Instead we single out the glacial forcing, in particular assessing
the impact of glacial melting and runoff on fjord circulation and the sensitivity of submarine melt rate to
glacial runoff. In doing so, we seek to aid the interpretation of existing oceanographic data and assess the
significance of glacially forced fjord circulation for the future stability of Greenland’s tidewater glaciers. Fur-
thermore, this idealized study provides an initial framework in which to develop and test the new plume
parameterization, which we envisage applying to complex, realistic fjord systems in future work.
2. Methods
2.1. Model
2.1.1. Ocean Model
The Massachusetts Institute of Technology General Circulation Model (MITgcm, http://mitgcm.org) [Adcroft
et al., 2004; Marshall et al., 1997a, 1997b] is a versatile general circulation model that solves the incompressi-
ble Navier-Stokes equations using finite-volume methods on an orthogonal curvilinear grid. The model has
a nonhydrostatic capability that makes it suitable for the study of areas of complex bathymetry and buoyant
upwellings and includes options to incorporate horizontal ice shelves [Losch, 2008] and vertical ice faces [Xu
et al., 2012]. To date, it has been used in several studies of glacial ice-ocean interaction both beneath Ant-
arctic ice shelves [Heimbach and Losch, 2012; Losch, 2008] and in Greenland’s fjords [Sciascia et al., 2014,
2013; Xu et al., 2013, 2012]. We use the model in nonhydrostatic mode, but the plume parameterization
(described in the following sections) is equally suitable for incorporating glacial plumes in relatively coarse
hydrostatic simulations.
2.1.2. Plume Model
Theoretical models of turbulent plumes have been developed and utilized for over 50 years [e.g., Morton
et al., 1956] and have proven highly effective at representing a wide range of oceanic and atmospheric
phenomena [Kaye, 2008]. The plume model that forms the basis of the parameterization is motivated by
that of Jenkins [2011], which coupled a buoyant plume model to equations describing heat exchange at
the ice-ocean interface. Jenkins’s [2011] model does not include plume expansion or entrainment in an
across-fjord direction, and so is only appropriate in scenarios in which the input of runoff is uniform
across the width of the glacier. At tidewater glaciers in Greenland, localized turbid plumes have been
observed at the fjord surface in summer [e.g., Chauch
eetal., 2014; Sole et al., 2011; Tedstone and Arnold,
2012], suggesting the presence of large subglacial channels providing a localized input of runoff to the
fjord at the glacier grounding line. As such, an alternative plume geometry, permitting a discrete source
of freshwater input, is required (M. O’Leary, Frontal processes on tidewater glaciers, University of Cam-
bridge, unpublished thesis, 2011). In these cases, a half-conical plume geometry, with flat side against the
glacier, is more appropriate (Figure 1). We therefore construct a model for an ice marginal plume of this
geometry utilizing well-established plume theory [Kaye, 2008]. This model is described here, with symbols
and parameter values defined in Table 1.
A vertically issuing, conical plume model has previously been described by Morton et al. [1956]. This model
was written in terms of density; we modify the equations therein to split out temperature and salinity and
to take into account the half-conical geometry. Plume density q
p
is then given as a function of plume tem-
perature T
p
and plume salinity S
p
using the modified UNESCO equation of state of Jackett and MacDougall
[1995]. Following Morton et al. [1956], entrainment of ambient water into the plume is proportional to the
Journal of Geophysical Research: Oceans 10.1002/2014JC010324
COWTON ET AL. V
C2015. The Authors. 797
plume velocity with rate a. We employ the standard Boussinesq approximation, which introduces a refer-
ence density q
0
into the equations. With plume radius band vertical velocity u, the defining equations (1–4)
state conservation of mass, momentum, heat, and salt:
d
dz b2u

52abu14
pb_
m(1)
d
dz b2u2

5gb2qa2qp
q0
24Cd
pbu2(2)
d
dz b2uTp

52abuTa14
p
_
mbTb24CTC1=2
d
pbu Tp2Tb
 (3)
d
dz b2uSp

52abuSa14
p
_
mbSb24CSC1=2
d
pbu Sp2Sb
 (4)
As in Jenkins [2011], the last term in (1) and the last two terms in (3) and (4) describe the melting of the ice, and
the last term in (2) is a reduction in momentum due to friction, with additional multipliers to take into account
the plume geometry. T
a
,S
a
,andq
a
are the ambient fjord conditions. The submarine melt rate _
mis related to the
plume variables T
p
,S
p
,anduand the ice-ocean boundary layer temperature T
b
and salinity S
b
using a three-
equation formulation which has frequently been used in this setting [e.g., Holland and Jenkins, 1999]:
_
mc
iTb2Ti
ðÞ1LðÞ5CTC1=2
ducwTp2Tb
 (5)
_
mSb5CsC1=2
duS
p2Sb
 (6)
Tb5k1Sb1k21k3z (7)
An analytical solution to the plume equations can be obtained using a number of simplifications (support-
ing information). For example, neglecting the melt and friction terms in (1)–(4) (which is a good approxima-
tion for a high initial discharge) and assuming a linear equation of state and uniform ambient conditions,
equations (1–4) have the solution described in Straneo and Cenedese [2015] for a point source plume. This
analytical solution can provide physical intuition, but for the more general cases of finite source size,
Subglacial
runoff
Plume
model
Ocean
model
Outflow from
plume at Tp, Sp
Entrainment into
plume at Ta, Sa
Buoyant
upwelling
Turbulent
entrainment
Plume spreads
out at surface
or when ρa=ρp
1
2
3
Figure 1. Schematic of the coupled plume-ocean model used in this paper. T
a
,S
a
,q
a
5ambient (fjord) temperature, salinity, and density,
T
p
,S
p
,q
p
5plume temperature, salinity, and density. (1) At each time step, ambient temperature and salinity profiles are sent from the
ocean model to the plume model. (2) These are used in conjunction with subglacial discharge to calculate the vertical fluxes of water,
heat, and salt. (3) These fluxes are then used to calculate source and sink terms in the ocean model.
Journal of Geophysical Research: Oceans 10.1002/2014JC010324
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stratified ambient conditions, a nonlinear equation of state, and inclusion of the melt and friction terms, the
equations must be solved numerically. In this study, we therefore solve the equations numerically using the
DLSODE differential equation solver [Hindmarsh, 1983].
In common with the model of Jenkins [2011], the plume emerges vertically into the domain. This is unlikely
to occur in reality, and thus it is not clear how to choose the initial plume radius b
i
and velocity u
i
for a given
discharge Q, related in our model by Q5pb2
iui=2. We find however that the model is insensitive to this
choice, in that solutions converge quickly on one another for various combinations of (b
i
u
i
) so long as Q
remains fixed. Accordingly, we maintain a constant u
i
of 1 m s
21
and vary b
i
to provide the required
discharge.
2.1.3. Integration of the Plume and Ocean Models
To allow the simulation of plumes at subgrid scale, we embed the plume model as a new module within
the MITgcm (Figure 1). In grid locations where subglacial runoff is specified, ambient conditions (T
a
,S
a
,q
a
)
are passed at each time step from the MITgcm to the plume model. These are used, in conjunction with the
specified runoff (b
i
,u
i
,T
i
,S
i
), to calculate plume radius, velocity, temperature, and salinity as described
above. The vertical extent of the plume is also calculated, with the plume terminating upon reaching neu-
tral buoyancy or the fjord surface. Water, heat, and salt are then removed from MITgcm cells at the rate pre-
dicted by the plume model in those vertical layers where the plume is entraining, and put into the cell at
the depth at which the plume is predicted to terminate. Further detail on the model implementation is pro-
vided in the supporting information.
The primary advantage of this approach over models which seek to resolve the plume is that it permits a
relatively coarse spatial and temporal resolution to be used throughout the domain, greatly increasing com-
putational efficiency. Xu et al. [2013], for example, required grid cells of 1 m
3
at the ice front to resolve the
plume, necessitating limiting their domain to a section of fjord 500 m long, 500 m deep, and 150 m wide.
Such high spatial resolution also requires a very small time step, particularly since vertical plume velocities
may exceed 2 m s
21
[Xu et al., 2013], which again increases the computational demands. Because the plume
parameterization presented here undertakes vertical transport outside of the MITgcm framework, the time
constraint imposed by high vertical velocities within the model domain is avoided. An additional benefit of
Table 1. Model Parameters
Symbol Name Value Units
c
i
Heat capacity of ice 2000 J kg
21
C
21
c
w
Heat capacity of water 3974 J kg
21
C
21
aEntrainment parameter 0.1
gGravitational acceleration 9.81 m s
21
T
i
Ice temperature 210 C
LLatent heat of melting 3.35 310
5
Jkg
21
U
T
Thermal turbulent transfer coefficient 2.20 310
22
U
S
Salt turbulent transfer coefficient 6.20 310
24
C
d
Ice-plume drag coefficient 2.50 310
23
k
1
Freezing point slope 25.73 310
22
C psu
21
k
2
Freezing point offset 8.32 310
22
C
k
3
Freezing point depth 7.61 310
24
Cm
21
q
0
Reference density 1020 kg m
23
q
a
Ambient density kg m
23
q
p
Plume density kg m
23
T
p
Plume temperature C
S
p
Plume salinity psu
T
b
Boundary temperature C
S
b
Boundary salinity psu
uPlume velocity ms
21
bPlume radius m
_
mMelt rate md
21
zDepth m
u
bg
Background velocity 0.01, 0.06, 0.10 m s
21
fCoriolis parameter 1.37 310
24
rad s
21
k
z
Vertical Laplacian diffusivity 10
25
m
2
s
21
k
h
Lateral Laplacian diffusivity 30 m
2
s
21
A
z
Vertical eddy viscosity 10
25
m
2
s
21
A
h
Lateral eddy viscosity 30 m
2
s
21
Journal of Geophysical Research: Oceans 10.1002/2014JC010324
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this method is that it may improve the prediction of plume dynamics relative to intermediate resolution
models (10–20 m horizontal resolution) which seek to resolve the plume, as such models remain highly
dependent on viscosity and diffusivity parameterization terms within the ocean model that are difficult to
constrain [Sciascia et al., 2013; Xu et al., 2012].
Along the remainder of the ice front, there is melting but no-runoff input. The melt rate in these cells is cal-
culated using the same formulation as in the plume model (equations (5–7)) using the temperature, salinity,
and velocity as determined by the ocean model. The impact of this melting is taken into account by gener-
ating a virtual salinity and heat flux out of the domain, thus cooling and freshening the cells, based on the
approach used to incorporate the melting of glacial ice in previous studies using MITgcm [e.g., Losch, 2008;
Xu et al., 2012]. In reality, this melting would likely establish convective cells against the ice front on spatial
scales too small to feasibly resolve in a fjord model [Wells and Worster, 2008]. Although these convective
cells are expected to be much weaker than those forced by subglacial runoff (with a vertical extent on the
order of 10 m in a stratified ocean environment [Huppert and Josberger, 1980; Jacobs et al., 1981]), it is
important that these currents are taken into consideration. This is because they control the melt rate on
parts of the calving front not in contact with a runoff-driven plume, which may be the majority of the ice
front. As such, in some experiments we specify a minimum velocity in equations (5–7) (similar to Xu et al.
[2013]). Experiments were undertaken using a minimum velocity of 0.01, 0.06, and 0.10 m s
21
, based on a
range of modeling and field experiments, to assess the influence of this value on the processes simulated in
this study (supporting information).
2.2. Initial Fjord Conditions
We utilize temperature and salinity profiles taken in front of Store Glacier, west Greenland, during August
2010 [Chauch
eetal., 2014] as initial and ocean-boundary conditions for all experiments presented in this
paper (Figure 2a). These records, chosen because they provide a detailed survey of temperature and salinity
within a few kilometers of the calving front of a major Greenlandic outlet glacier, were averaged to provide
representative near-glacier conditions. Although in reality conditions down-fjord may vary from those
recorded near to the calving front, we specify horizontally uniform initial conditions. This means that no
model spin-up period is required, with initial velocities throughout the domain zero and any subsequent cir-
culation resulting from the evolution of water properties over the course of the simulation.
3. Experiments
3.1. Plume Model
As a first step, we examine the plume model independently of the ocean model. Plumes are calculated
based on subglacial discharges of 1, 10, and 100 m
3
s
21
, using an initial plume temperature of 0Cand
0 1 2 3
500
400
300
200
100
0
Temperature (°C)
Depth (m)
a.
32 33 34 35
Salinity (psu)
S
T
0 100 200 300
0
100
200
300
400
500
600
Discharge (m3 s−1)
Day of experiment
b.
0.5x
1x
1.5x
2x
01Mar 01Jul 01Nov
Date
0 100 200 300
0
50
100
150
200
250
300
Discharge (m3 s−1)
Day of experiment
c.
01Mar 01Jul 01Nov
Date
Figure 2. Initial conditions and forcings used in the model experiments. (a) Temperature and salinity profiles used as initial conditions, derived by averaging Store Fjord profiles taken
during August 2010 [Chauch
eetal., 2014]. Idealized runoff used in experiments: (b) variation in runoff intensity and (c) variation in runoff duration. The thick black line, showing the
‘‘standard’’ forcing, is the same in both plots.
Journal of Geophysical Research: Oceans 10.1002/2014JC010324
COWTON ET AL. V
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salinity of 0 psu and ambient fjord conditions as described in section 2.2. We compare the results to that
of Jenkins’s [2011] model, run using the same initial plume conditions, to assess the difference in the
model solution generated by the different plume geometries. The horizontal extent of the plume is
described in terms of the plume radius in the half-conical model and the thickness of the plume perpen-
dicular to the ice front in Jenkins’s [2011] model (because of the differing geometry); however, these two
variables are directly comparable in terms of the expansion of the plume as it rises through the water
column.
The results of the half-conical plume model, along with those from the model by Jenkins [2011], are shown
in Figure 3. The two models produce similar plume behavior: the plumes expand as they rise, entraining
salty water until they become denser than the ambient waters (due to the salinity stratification), which
occurs at greater depth for a smaller initial discharge. Because the water column is warmest at depth, both
models predict the plumes to be warmer than the ambient conditions above 350 m depth. The principal
difference between the two models is that our model entrains more rapidly. This is because the half-conical
form gives the plume a greater surface area across which to entrain relative to the sheet form of Jenkins’s
[2011] model. Because the plume entrains more rapidly, it rises more slowly and reaches neutral buoyancy
at a greater depth relative to the sheet model. For example, at a discharge of 10 m
3
s
21
,Jenkins’s [2011]
model produces a plume that reaches almost to the surface of the fjord, while our modeled plume reaches
neutral buoyancy at a depth of 70 m. The geometry of Jenkins’s [2011] model requires that the input of
runoff is constant across the full width of the grounding line, a scenario that is unlikely to occur in reality at
tidewater glaciers given the presence of subglacial drainage channels and uneven bed topography. The
0 20 40 60
500
400
300
200
100
0
Plume radius (m)
Water depth (m)
a.a.a.a.a.a.a.a.a.
0 1 2 3
500
400
300
200
100
0
Vertical velocity (m s−1)
Water depth (m)
b.b.b.b.b.b.b.b.b.
0 1 2 3
500
400
300
200
100
500
Temperature (°C)
Water depth (m)
c.c.c.c.c.c.c.c.c.
0 10 20 30 40
500
400
300
200
100
0
Salinity (psu)
Water depth (m)
d.d.d.d.d.d.d.d.d.
1000 1010 1020 1030
500
400
300
200
100
0
Density (kg m−3)
Water depth (m)
e.e.e.e.e.e.e.e.e.
0 5 10
500
400
300
200
100
0
Melt rate (m d−1)
Water depth (m)
f.f.f.f.f.f.f.f.f.
Ambient 10 m3s−1 100 m3s−1 1 m3s−1 10 m3s−1 100 m3s−1
Figure 3. Results generated using the plume model with a freshwater input of 1, 10, and 100 m
3
s
21
(blue). Also shown for comparison are the plumes generated by the model of Jenkins
[2011] using freshwater inputs of 10 and 100 m
3
s
21
(red). The results shown are based on ambient temperature and salinity profiles taken from Store Glacier [Chauch
eetal., 2014],
shown in Figure 2a and as black lines above. Dashed lines indicate the continuation of the plume beyond the point of neutral buoyancy due to momentum.
Journal of Geophysical Research: Oceans 10.1002/2014JC010324
COWTON ET AL. V
C2015. The Authors. 801
main implication of this therefore is that plumes are likely to reach neutral buoyancy somewhat lower in
the water column than predicted by Jenkins [2011].
3.2. Coupled Plume-Ocean Model
The next step is to examine the representation of one of these plumes (subglacial discharge 5100 m
3
s
21
)
in the coupled plume-ocean model. The focus of this experiment is across-fjord variation in conditions at
the fjord-glacier boundary. To do this, we use a rectangular domain 6.7 km long, 1.8 km wide, and 500 m
deep. Grid resolution is 200 m in the cross-fjord direction (chosen such that the width of a cell is compara-
ble to the predicted maximum width of the plume) and 10 m in the vertical. In the along-fjord direction,
model resolution is 200 m for the 2 km of the domain closest to the glacier, decreasing linearly to 1500 m
at the fjord mouth. The sides of the domain are closed, while a glacier extends the full width of the domain
at the fjord head, with the plume in the center. A relaxation zone is used to restore properties to the initial
conditions at the ocean boundary. The model is run for a simulation time of 1 h, during which time currents
generated at the glacier do not reach the ocean boundary.
Initial conditions throughout the domain are set based on the temperature and salinity profiles from Store
Glacier (Figure 2a). Diffusivity and viscosity parameters are chosen to be as low as possible without generat-
ing numerical noise [Kantha and Clayson, 2000] and are constant between experiments (Table 1; see sup-
porting information for assessment of the sensitivity to these and other parameters). In order to assess the
impact of cross-fjord circulatory patterns on melt rate, we do not specify a minimum background velocity in
this experiment (section 2.1.3).
The interaction between the plume and fjord is best seen by looking at the modification of water properties
across the ice front (Figure 4). As in the plume model output (Figure 3), the plume forms a zone of relatively
fresh, warm water rising up the center of the ice front (Figures 4a and 4b). As it rises, the plume entrains
water from the fjord, generating relatively weak (0.01 m s
21
) currents flowing toward the center of the ice
front. Where the plume reaches neutral buoyancy, this pattern is reversed, with somewhat stronger currents
(up to 0.07 m s
21
) flowing away from the center of the ice front (Figure 4d). These currents are however
dwarfed by the vertical motion occurring within the plume itself, where velocities exceed 2 m s
21
. Conse-
quently, while melt rate does increase toward the center of the fjord, this variation is extremely small
Depth (m)
b.
0
100
200
300
400
500
Temperature (°C)
0.5
1
1.5
2
2.5
Depth (m)
c.
0
100
200
300
400
500
Vertical velocity (ms−1)
0
1
2
Depth (m)
d.
0
100
200
300
400
500
Cross−fjord velocity (ms−1)
−0.05
0
0.05
Width (m)
Depth (m)
e.
500 1000 1500
0
100
200
300
400
500
Melt rate (md−1)
2
4
6
Width (m)
Depth (m)
f.
500 1000 1500
0
100
200
300
400
500
Melt rate (md−1)
0
0.1
0.2
Depth (m)
a.
0
100
200
300
400
500
Salinity (psu)
30
32
34
Figure 4. Face-on profiles of the ice front, shown following a subglacial discharge of 100 m
3
s
21
for 1 h. (a) Salinity, (b) temperature, (c) vertical velocity, (d) cross-fjord velocity, (e) sub-
marine melt rate, (f) as for Figure 4e, but with a different color-scale emphasizing melting away from the plume. All values have been linearly interpolated from the original horizontal
200 m grid. The plume model output is shown to scale in the center of each plot (except Figure 4d, as the plume model does not include horizontal velocity).
Journal of Geophysical Research: Oceans 10.1002/2014JC010324
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compared to the melting taking place where the plume contacts the ice front (Figures 4e and 4f). Further-
more, these patterns are only visible because there is no specified minimum velocity used in the melt calcu-
lation in this scenario, and so melt rate is negligible except where currents are stimulated by the plume. If
in reality other processes such as melt-driven convection, tides, and wind-forced circulation generate addi-
tional currents parallel to the ice front, then it is likely that the significance of plume-induced cross-fjord cir-
culation on melt rate will be further diminished. Although the relatively coarse resolution of the model may
dampen currents in the area around the plume, we note similar findings from higher-resolution simulations,
which suggest extremely low melt rates except where the glacier is in direct contact with the plume [Xu
et al., 2013].
3.3. Impact of Runoff on Fjord Circulation
In this experiment, we seek to examine the impact of glacial melt and runoff on the circulation of a fjord
over the course of a year. For simplicity, we use a rectangular fjord of constant width and depth. Model
resolution is 200 m in the cross-fjord direction and 10 m in the vertical, with a domain width and depth of
5 km and 500 m, respectively (chosen as appropriate dimensions for a large Greenlandic tidewater glacier).
Resolution in the along-fjord direction is 200 m at the ice front, decreasing linearly to 2400 m at the fjord
mouth, with a domain length of 130 km. The fjord is considered to comprise 100 km of this length, while
the remaining 30 km represents a coastal strip. In this coastal zone, a relaxation zone restores water proper-
ties to the initial conditions—in this way, coastal properties remain constant, with all variability driven at
the ice front [e.g., Sciascia et al., 2013]. The Coriolis parameter is set to 1.37 310
24
, appropriate for a typical
Greenlandic latitude of 70N[Kantha and Clayson, 2000].
Three experiments are undertaken, running for 12 months from January to January. In the first, the head
of the fjord is simply a rock wall, with no melting and no input of runoff. In the second, there is an ice wall
at the head of the fjord, allowing melting, but there is no runoff. In the third experiment, runoff enters from
the base of the glacier in the center of the fjord. We use an idealized runoff input, interpolating linearly
between monthly values. These values are based on a normal distribution centered on a mean July value of
300 m
3
s
21
(Figures 2b and 2c). While runoff is expected to vary significantly between glaciers and years
(meaning there is no representative value for a typical Greenlandic fjord), this is chosen as an appropriate
peak runoff as predicted for outlet glaciers such as Helheim Glacier [e.g., Mernild and Liston, 2012; Sciascia
et al., 2013] and Store Glacier [e.g., Xu et al., 2012]. The effect of varying the duration and intensity of the
melt season, and hence total annual runoff, is examined in the following experiment (section 3.4).
Each of these scenarios was run using three different values of background velocity (0.01, 0.06, and 0.10 m
s
21
). The choice of background velocity affects the predicted submarine melt rate (as described in section
3.4), but has little impact on the overall circulation (supporting information). As such, only those scenarios
with the moderate background velocity (0.06 m s
21
) are described in this section (with additional details in
section 3.4). The velocity fields generated in these experiments are approximately symmetrical across the
fjord (with along-fjord velocities increasing toward the fjord center) and so presentation and discussion of
results is focused on properties along the fjord centerline (across-fjord variation in velocity is illustrated in
the supporting information).
Figure 5 shows the along-fjord velocity patterns produced in these simulations. In the absence of a glacier,
there is little movement: only weak currents near the ocean boundary generated by horizontal salinity gra-
dients forming in response to gradual vertical diffusion (Figure 5ai). The addition of an ice front, but no runoff,
generates a series of vertical circulation cells, driven by melting at the fjord head (Figure 5bi). These currents
remain very weak, however, with maximum predicted velocities of the order of 10
23
ms
21
. The addition of
runoff stimulates a much stronger circulation, with a clear seasonality (Figures 5ci–fi). As runoff increases dur-
ing the spring, a down-fjord current forms at the depth at which the plume reaches neutral buoyancy, com-
pensated by a weaker but thicker up-fjord current below (Figure 5ci). The depth of the down-fjord current
decreases and its strength increases as runoff increases, until by peak runoff it occupies the upper 100 m of
the water column with a maximum velocity of the order of 0.1 m s
21
(Figure 5di). At this stage, the fjord
resembles a single-cell estuarine circulation. The reverse of this process happens during autumn, with the
down-fjord current increasing in depth and decreasing in strength as runoff decreases (Figure 5ei).
In the no-glacier scenario, temperature change is limited to the vertical smoothing of the tempera-
ture profile by diffusion (Figure 5aii). The addition of the ice front generates cooling near the fjord
Journal of Geophysical Research: Oceans 10.1002/2014JC010324
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head, most notably in the lower part of the water column where the warmer waters are cooled by
0.1 to 0.2C (Figure 5bii). A similar cooling occurs in the runoff scenario, but greater change to the
temperature structure occurs due to the vertical movement of water within the plume (Figures 5cii–
5fii). In keeping with the results of the plume model experiment (Figure 3), the waters exiting the
plume at the depth of neutral buoyancy tend to be warmer than the ambient conditions at that
depth, particularly when the plume terminates in the cold band between approximately 80 and
180 m depth. This generates a general warming of the upper part of the water column, with the
warmest layer in the upper part of the water column often coinciding with the depth of the down-
fjord current at that time (Figure 5).
Changes to the salinity distribution in the fjord are less notable (Figures 5aii–5fii). Outflow from the plume
inputs a large quantity of water of constant salinity at some depth in the water column. This water may
pileup near the ice front, generating a slight along-fjord salinity gradient. As runoff increases and the depth
of the plume outflow decreases, the up-fjord currents generated by plume entrainment serve to restore the
original salinity distribution.
Figure 5. Fjord centerline sections showing (i) along-fjord velocity (m s
21
) and (ii) temperature anomaly (C) with isohalines (psu). The gla-
cier is located at the left of the figures, and positive velocities show currents flowing in an up-fjord direction. The color scales and isohaline
labels shown in (a) are valid for plots a and b, while those shown in (c) are valid for plots c–f. Scenarios shown are: (a) control run with no
runoff or ice melt, shown after 12 months; (b) experiment with ice melt but no runoff, shown after 12 months; Experiment with standard
runoff forcing (Figure 2), shown after (c) 5, (d) 7, (e) 9, and (f) 11 months. The temperature anomaly in Figure 5aii (control run) is shown rel-
ative to the initial conditions, while in the temperature anomaly in Figures 5bii–fii is shown relative to the control run following an equal
period of model time.
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3.4. Impact of Runoff on Submarine Melt Rate
Theoretical and numerical modeling experiments have shown that submarine melt rate increases with the
discharge of subglacial runoff from a single channel [e.g., Jenkins, 2011; Sciascia et al., 2013; Xu et al., 2013,
2012]. However, the significance of this relationship when considered across the entire ice front and on
annual and interannual time scales is not well understood. To investigate this, we conducted a series of 1
year experiments in which the magnitude of the summer melt season was varied. Taking the seasonal run-
off distribution used in section 3.3 (7 months long, peaking at 300 m
3
s
21
in July) as a base case ‘‘standard’’
year, we conducted a series of experiments with total annual runoff scaled to 0.5, 1.5, and 2 times this value,
representing a generous allowance for interannual variability. (For comparison, Mernild et al. [2010] estimate
interannual variability in total annual runoff from Helheim Glacier to reach a maximum of approximately
625% of the mean over the period 1999–2008.) In the first set of experiments, we achieve this by varying
the intensity of melt season, such that its duration remains constant but the magnitude of runoff is scaled
accordingly. In the second set of experiments, we keep the peak July runoff at 300 m
3
s
21
, and instead vary
the duration of the melt season, maintaining a normal distribution. The resulting runoff time series are
shown in Figures 2b and 2c.
As seen in Figure 4, the average ice front melt rate can be broken into two components: ‘‘plume melting,’’
where the plume comes into contact with the glacier, and ‘‘background melting’’ where it does not. The for-
mer component scales with discharge, causing average melt rate to rise toward the middle of the melt sea-
son then fall again (Figures 6a and 6b). If only the central 200 m of the ice front are considered, plume
melting dominates and we find a similar power law relation between melt and discharge to that identified
in previous studies [Jenkins, 2011; Sciascia et al., 2013; Xu et al., 2012], with _
m/Q2=5(Figure 6c). However,
0 100 200 300
0.18
0.2
0.22
0.24
0.26
0.28
Day of experiment
Melt rate (md−1)
a.
0 100 200 300
0.18
0.2
0.22
0.24
0.26
0.28
Day of experiment
Melt rate (md−1)
b.
0 1 2 3
x 109
15
20
25
d.
Runoff (m3)
Melt (m)
00.5 11.5 2
0.6
0.8
1
1.2
1.4
Normalized runoff
Normalized melt
ubg = 0.01 ms−1
0 1 2 3
x 109
60
80
100
Runoff (m3)
Melt (m)
e.
Intensity Duration 0x 0.5x 1x 1.5x 2x
00.5 11.5 2
0.6
0.8
1
1.2
1.4
Normalized runoff
Normalized melt
ubg = 0.06 ms−1
0 1 2 3
x 109
80
100
120
140
160 f.
Runoff (m3)
Melt (m)
00.5 11.5 2
0.6
0.8
1
1.2
1.4
Normalized runoff
Normalized melt
ubg = 0.10 ms−1
0200 400 600
0
1
2
3
Discharge (m3 s−1)
Melt rate (m d−1)
c.
Model output
Q2/5
Figure 6. Relationships between runoff and submarine melt rate. Seasonal variation in mean melt rate across the ice front with varying (a) runoff intensity and (b) runoff duration, using
a background velocity of 0.06 m s
21
. Results calculated with alternative background velocities are shown in the supporting information. (c) Seasonal relationship between runoff and
melt rate for the central 200 m of the ice front (containing the plume), throughout the 23runoff intensity experiment. Dots show the value every 4 days, while the red line shows the
trendline with _
m/Q2=5. Relationship between total annual runoff and total annual melt (m water equivalent, averaged across the ice front), using a background velocity of (d) 0.01 m
s
21
, (e) 0.06 m s
21
, and (f) 0.10 m s
21
. Shown on the top and right axes are values normalized relative to the standard forcing scenario. All plots follow the same color scheme used in
Figures 2b and 2c, with colors denoting the runoff forcing used. In Figures 6d–6f, the gray line joins those scenarios in which the runoff intensity is varied, while the black line joins sce-
narios in which the runoff duration is varied.
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when the entire width of the ice front is considered, the background melt rate becomes much more signifi-
cant. As in Figure 4, we do not find that the plume generates sufficient cross-fjord circulation to strongly
influence this background melt rate, although the existence of relatively warm glacially modified waters
leads to a slightly higher melt rate in the autumn relative to spring (Figures 6a and 6b). Instead, we find that
the background melt rate is strongly dependent on the minimum velocity value prescribed in equation (6)
(see also supporting information). This is problematic, as this value remains somewhat artificial and is diffi-
cult to constrain.
Increasing the intensity of runoff results in higher peak summer melt rates (Figures 6a and 6b). However, as
identified here (Figure 6c) and in previous studies [Jenkins, 2011; Sciascia et al., 2013; Xu et al., 2012], the sen-
sitivity of plume melt rate to discharge decreases as discharge rises (Figure 6c), meaning the difference
between scenarios is somewhat subdued. For example, doubling peak runoff from 300 to 600 m
3
s
21
results
in a 25% increase in peak melt rate relative to the background melt rate (Figure 6a). Increasing the dura-
tion of the melt season has a greater effect for the same increase in annual runoff, because plume melt rate
is more sensitive to variation in discharge at lower discharge values (Figure 6c). This effect can be seen
most clearly when the duration of the melt season is altered while the total annual runoff is kept constant
(Figure 7). Although the more intense melt seasons generate higher peak melt rates, this is more than com-
pensated by the greater duration of enhanced melt rates in the longer melt seasons (Figure 7).
The significance of annual and interannual variability in runoff on total melt rate depends on the back-
ground melt rate, which in turn depends on the prescribed background velocity (Figures 6d–6f). In the sce-
nario with the smallest background melt rate (Figure 6d), doubling total runoff from the standard scenario
results in a 15–45% increase in total annual melting. In the moderate background melt rate scenario, this
drops to a 3–12% increase (Figure 6e), while in the highest background melt rate scenario, this falls further
to 2–8% (Figure 6f). This behavior is discussed further in section 4.
Following this, the model was run for 10 consecutive years to examine whether there was a cumulative
impact on melt rate over this time (for example, due to a sustained cooling near the ice front). Two scenar-
ios were run—in the first, there was no runoff; in the second, the standard runoff forcing was repeated for
10 cycles. In order to reduce the computational time required, the horizontal model resolution was
increased to a uniform 1000 m in along and across-fjord directions. The effect of this coarser resolution is
assessed in Figure 8a, which shows the submarine melt rate over the course of 1 year, as predicted using
the original horizontal model resolution and the coarser grid. During the first part of the year, the predicted
melt rates in the two simulations are almost identical, while in the second part of the year, the predicted
melt rate is slightly reduced in the coarser domain. The overall similarity of results demonstrates the impor-
tance of the plume melting (which is independent of the model resolution) on the total melt rate and justi-
fies the use of the coarser-resolution domain for these experiments (see also supporting information). The
0 100 200 300
0
100
200
300
400
500
600
Day of experiment
Runoff (m3s−1)
a.
0 100 200 300
0.18
0.2
0.22
0.24
0.26
0.28
0.3
Day of experiment
Melt rate (m d−1)
b.
15 30 45 60
74
76
78
80
Melt (m)
Standard deviation (days)
c.
0.96
0.98
1
1.02
1.04
1.06
Normalized melt
Figure 7. Effect on melt rate of modifying the duration of seasonal runoff while keeping total seasonal runoff constant. (a) Runoff forcing used in each experiment. The thick black line
corresponds to the standard runoff forcing (Figure 2). (b) Submarine melt rate averaged across the ice front. (c) Increase in total annual melt with the duration of the seasonal runoff,
with this duration expressed as the standard deviation of the idealized, Gaussian seasonal runoff distribution. The right-hand axis shows melt normalized relative to the standard runoff
scenario. The color of the lines in Figure 7b and circles in Figure 7c reflects the runoff scenario in Figure 7a.
Journal of Geophysical Research: Oceans 10.1002/2014JC010324
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results of the 10 year simulations are shown in Figure 8b. There is a small increase in melt rate following the
first year in the standard runoff scenario due to the displacement of cold water from adjacent to the glacier
by warmer glacially modified water. With the exception of this, there is however little change in melt rate in
either scenario over the 10 years. This suggests that, with or without runoff, there is no significant cumula-
tive cooling or warming of the fjord waters surrounding the glacier front on this time scale (assuming no
other external change in properties of the fjord water entering the fjord mouth).
4. Discussion
4.1. Glacial Modification of Fjord Oceanography
Oceanographic survey data from Greenland’s fjords are sparse and frequently limited to late summer when
ice cover in the fjords is at its annual minimum. The area close to the ice front, often choked with icebergs
and sea ice and at risk from calving events, is extremely difficult to survey, making data from this crucial
location in which glacially modified water masses are formed particularly rare [Straneo et al., 2013]. This
makes interpretation of existing data sets and model results challenging, limiting our understanding of the
impact of glaciers on fjord oceanography.
Nevertheless, several authors have used temperature and salinity characteristics to argue for the existence
of glacially modified layers in fjord survey data. At Sermilik Fjord, east Greenland, Straneo et al. [2011] identi-
fied a relatively warm layer extending over 50 km from the ice front at a depth of between 100 and 200 m.
They argued that this layer was formed by subglacial runoff and entrained warm Atlantic waters, rising
upward until it reached neutral buoyancy at the steep halocline between the Atlantic waters and the overly-
ing cooler, fresher Polar waters. Similarly at Store Glacier, Chauch
eetal. [2014] reported the presence of
warm, glacially modified layers in the upper part of the water column. In August 2010, this layer occurred at
the surface, above the coldest water, while during the cooler August of 2009 the glacially modified waters
were found both at the surface and lower in the water column. This occurred, they argued, because
reduced runoff meant that the plume reached neutral buoyancy lower in the water column during the
cooler year.
Our findings support and add further detail to these hypotheses. We find that as runoff increases through
the spring, the plume grows in strength and rises higher in the water column. As it does so, the waters near
the ice front are replaced with a mixture of entrained fjord waters, glacial runoff, and the products of sub-
marine melt. Of these, the fjord waters are dominant and the submarine meltwater is negligible. For exam-
ple, by the point of neutral buoyancy in the highest discharge scenario in Figure 3, the plume is
transporting >6000 m
3
s
21
of entrained fjord water, 100 m
3
s
21
of glacial runoff, and 1.5 m
3
s
21
of fresh-
water from submarine melting. If the fjord was vertically uniform in temperature, this mixture would be
slightly cooler than the ambient waters. However, because deep silled Greenlandic fjords are characterized
by a warmer, saltier layer of Atlantic waters underlying a cooler, fresher layer of Polar waters [Straneo and
0 100 200 300
0.18
0.2
0.22
0.24
0.26
0.28
0.3
Day
Melt rate (m d−1)
a.
2 4 6 8 10
0.17
0.18
0.19
0.2
0.21
0.22
0.23
Year
Melt rate (m d−1)
b.
1000m
200m
No runoff
Runoff
Figure 8. (a) Mean ice front melt rate over a 1 year experiment with standard runoff forcing, conducted using the original horizontal reso-
lution (200 m at the ice front) and a coarser grid with 1000 m horizontal resolution throughout. (b) Annual average melt rate over the
course of 10 years using the 1000 m resolution domain and standard runoff forcing, compared to an identical setup with no-runoff
forcing.
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Heimbach, 2013], this glacially modified water is typically warmer than the ambient waters at the depth at
which it reaches neutral buoyancy.
The plume outflow sets up a circulatory cell, with a thinner, stronger down-fjord current overlying a thicker,
weaker, up-fjord current. Maximum modeled along-fjord velocities are on the order of 0.01–0.1 m s
21
,in
agreement with the residual runoff-driven circulation identified by Sutherland and Straneo [2012] in Sermilik
Fjord, east Greenland. Glacially modified waters are reentrained by this cell as the outlet point of the plume
rises during the spring, and so in summer there may be little evidence of this modification below the depth
of the main plume outflow (e.g., Figure 5d). This is likely to be the scenario observed by Chauch
eetal.
[2014] during August 2010, when the only runoff-modified waters are in the surface layer. As runoff
decreases in the autumn, the plume loses strength and drops down through the water column again (Fig-
ure 5e). Glacially modified waters become trapped in the relatively slow flowing zone above the level of the
main circulatory cell as the depth of the down-fjord current increases during this phase. These glacially
modified waters may form a warm zone around the glacier front, as observed by Chauch
eetal. [2014] dur-
ing August 2009.
Not all fjord survey data fit this picture. In Kangerdlugssuaq Fjord, east Greenland, Inall et al. [2014] report
cold glacially modified waters, while warm surface waters originate on the shelf, the opposite of the sce-
nario reported at Store Glacier [Chauch
eetal., 2014]. This may be because an extensive ice m
elange exists
in front of Kangerdlugssuaq Glacier, acting as a substantial additional heat sink [Enderlin and Hamilton,
2014]. This demonstrates the complexity of the glacial fjord system, with multiple freshwater inputs (includ-
ing subglacial and surface runoff, as well as meltwater from icebergs and glaciers) interacting with complex
and evolving water masses originating beyond the fjord mouth. In this study, we are focusing on a simpli-
fied system, in which only subglacial runoff and melting from a single glacier act upon the fjord. As such,
the features that we identify here will in reality be but one component of more complex and variable circu-
lation [Sutherland and Straneo, 2012].
A further level of complexity that may be present in real-world scenarios is across-fjord variability in circula-
tion and fjord water properties, introduced by both topographic complexity and the effects of rotation. The
Rossby radius of deformation of our idealized fjord is 9 km, which is large compared to the fjord width of
5 km (Kelvin number 50.55) [Garvine, 1995]. As such, the modeled fjord is dynamically narrow and rotation
is not important. Large Greenlandic fjords such as Sermilik Fjord and Kangerdlugssuaq Fjord are typically
slightly wider than the 5 km width used here, and the Kelvin number can equal or exceed unity in places
[Sutherland et al., 2014]. Sutherland et al. [2014] find geostrophic currents to be of importance offshore of
the fjord mouths, but report only limited evidence of lateral gradients within the fjords themselves. Con-
trastingly, Inall et al. [2014] report significant across-fjord gradients midway along Kangerdlugssuaq Fjord,
arguing that circulation within the fjord is in geostrophic balance. It is therefore possible that in Greenland’s
largest (and in particular broadest) fjords, rotation may become significant, generating greater across-fjord
variation in circulation patterns than is apparent in the experiments undertaken here (supporting
information).
4.2. Interaction of Runoff, Fjord Circulation, and Submarine Melt Rate
There are several ways in which variability in runoff could influence glacier melt rate. The first, as investi-
gated in previous studies [e.g., Jenkins, 2011; Xu et al., 2012], is that increased runoff generates a more vigor-
ous upwelling, and as such generates higher melt rates where this plume comes into contact with the ice
front. The second mechanism would be if this plume generated stronger currents across a wider part of the
ice front, causing an increase in melt rate extending beyond the area in contact with the plume. The third
mechanism is that the along-fjord circulation driven by the runoff could help to supply warm water to the
fjord head.
In keeping with previous studies [Jenkins, 2011; Sciascia et al., 2013; Xu et al., 2013, 2012], we find that melt
rate is strongly dependent on runoff, when measured across the region immediately surrounding the plume
(Figure 6c). A single plume covers only a small proportion of the ice front however, and when averaged
across the remainder of the glacier, the effect is reduced accordingly. We do not find that runoff generates
significant cross-fjord circulation away from the plume (Figure 4). We also do not observe a strong differ-
ence in along-fjord temperature gradient between the runoff and no-runoff scenarios, with melt-driven cir-
culation sufficient to prevent sustained cooling of waters adjacent to the ice front even in the no-runoff
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scenario (Figure 5). A similar cooling at depth close to the ice front is observed in the runoff and no-runoff
scenarios even after 10 years, although there is a modest (<3%) increase in melt rate in the runoff scenario
due to the displacement of cold water masses in the upper part of the water column by glacially modified
waters (Figure 8). This situation may be different if the temperature of the water mass at the fjord mouth
changed over time, as the glacially forced circulation could serve to accelerate the rate at which these
changes affected the properties of the water in contact with the glacier. Further work is required to address
this uncertainty, in particular examining the relative importance of glacially and coastally forced fjord shelf
exchange in a range of geographical settings [e.g., Jackson et al., 2014; Sciascia et al., 2014; Sutherland et al.,
2014].
The cumulative effect of these processes is that average melt rate increases in the summer due to more
rapid melting where the ice is in contact with the plume and remains slightly elevated the following winter
due to the displacement of cold water masses (Figure 6). Whether or not these processes result in a signifi-
cant increase in the total mass loss through submarine melting depends on the background melt rate,
which remains comparatively steady across large sections of the ice front over the course of the year. Melt
rate is strongly dependent on the velocity at the ice-ocean interface [Jenkins et al., 2010], and so cannot be
properly predicted without knowledge of these currents (supporting information). However, resolving buoy-
ant convection due to melting on this boundary would require an extremely fine mesh in this zone, which
is computationally impractical. It may be possible to include this process through the use of an additional
coupled model similar to our parameterization of the main runoff-forced plume, but this would require the
development of an appropriate melt-driven convection model, which lies beyond the scope of this paper.
Alternatively, a simple parameterization based on observation of submarine melt rates at tidewater glaciers
would be invaluable, but obtaining the data required to formulate such a parameterization remains
extremely challenging in this hostile environment [Straneo et al., 2013].
If the background melt rate is in reality very low, then variability in runoff may be responsible for large rela-
tive changes in melt rate (Figure 6d). However, it is difficult to reconcile low overall melt rates with those
derived from field-based heat flux estimates which place typical submarine melt rates at Greenland’s gla-
ciers in the range of 1–10 m d
21
[Inall et al., 2014; Rignot et al., 2010; Sutherland and Straneo, 2012], which
would imply melt rate away from the main plume is high and contributes significantly to the total melt rate.
If this is the case, then runoff variability, particularly on the scale of interannual variability, may not result in
substantial variability in submarine melt rate. There are however large uncertainties in the melt calculations
used in both modeling and observational studies. The melt parameterizations used here and in other mod-
els of submarine melting [Sciascia et al., 2013; Xu et al., 2013, 2012] remain poorly validated for the vertical
faces and strong currents of tidewater glacier fronts, having been developed and tested based on heat
transfers beneath ice shelves and sea ice [Holland and Jenkins, 1999]. Field-based melt rate estimations [Inall
et al., 2014; Rignot et al., 2010; Sutherland and Straneo, 2012] on the other hand, are often based on heat
flux estimates from relatively sparse observations acquired at some distance from the ice front, and do not
account for the potentially considerable loss of heat through melting of the ice m
elange [Enderlin and Ham-
ilton, 2014]. As such, comparing field and model-based melt rate estimates remains problematic.
A further consideration is that runoff may not be concentrated into a single large channel when it enters
the fjord. Although field observations seldom report more than one large plume [e.g., Chauch
eetal., 2014;
Sole et al., 2011], there may be numerous smaller plumes that never reach the fjord surface and so remain
undetected. If runoff is shared between several smaller channels rather than (or in addition to) emerging
from a single main source, the individual plumes will be weaker, and so the melting associated with each
individual plume smaller. Nevertheless, average melt rate across the entire ice front may be increased as a
greater proportion of the ice is affected by plumes [Kimura et al., 2014]. The basis of this result lies in the
sublinear relationship between freshwater discharge and average plume melt rate, with melting scaling
with discharge raised to the power of 1/3 to 1/2 [Jenkins, 2011; Sciascia et al., 2013; Xu et al., 2012]. This
means that for a given total runoff, concentrating this runoff leads to a decrease in total melting. This rea-
soning also applies with respect to time, with a longer melt season generating greater total melting for a
given total runoff (Figure 7).
The distribution of runoff has the potential to influence the seasonal variability in melt rate. A greater num-
ber of channels would result in a greater proportion of the ice front being influenced by seasonal runoff
input, potentially increasing the submarine melt rate in summer relative to winter. Conversely, a distributed
Journal of Geophysical Research: Oceans 10.1002/2014JC010324
COWTON ET AL. V
C2015. The Authors. 809
drainage system may persist during the winter months (fed by basal frictional melting), reducing seasonal
variability in submarine melt rate. It is clear that a more complete understanding of tidewater glacier hydrol-
ogy is required to better constrain submarine melt rate, and how this varies in space and time [Straneo
et al., 2013].
A further factor that is likely to be important in this respect is the feedback between submarine melting and
calving as the morphology of the calving front is modified by spatially uneven melting [O’Leary and Christof-
fersen, 2013]. If submarine melt is concentrated around a large channel then this may cut back into the gla-
cier, causing enhanced calving in the surrounding region that spreads out across the ice front [Chauch
e
et al., 2014]. Alternatively, if runoff is more widely distributed across the grounding line, greater melting at
depth may undercut the ice front [O’Leary and Christoffersen, 2013]. Better understanding of the links
between submarine melting and calving mechanics is therefore necessary in order to assess whether the
average ice front melt rate, or the spatial distribution of submarine melting, is more important in controlling
tidewater glacier mass balance.
4.3. Comparison With Previous Numerical Modeling Studies
This paper represents a first attempt to model the impact of glacial runoff on fjord oceanography by cou-
pling a theoretical plume routine to an ocean circulation model. In recent years however, several studies
have used MITgcm to model the formation of plumes arising from subglacial discharge by using a high-
resolution set up in which the plume turbulence is partially resolved [Sciascia et al., 2013; Xu et al., 2013,
2012]. Several key elements are consistent between this study, previous numerical modeling studies and
field surveys: subglacial runoff generates a plume that rises adjacent to the glacier, producing a glacially
modified down-fjord current underlain by an up-fjord current. One feature of field surveys that modeling
studies have sought to reproduce is the observation that glacially modified currents may form at an inter-
mediate depth between the surface and bed [Chauch
eetal., 2014; Straneo et al., 2011], in contrast to a clas-
sic estuarine circulation in which the outflow occurs at the surface [e.g., Motyka et al., 2013]. While previous
modeling studies have succeeded in generating glacial plumes which reach neutral buoyancy and flow
down-fjord at some intermediate depth, this has only occurred at discharges less than 5m
3
s
21
[Sciascia
et al., 2013; Xu et al., 2012] to 30 m
3
s
21
[Xu et al., 2013]. These values are very low compared to the
expected summer runoff from these glaciers (hundreds of cubic meters per second), indicating that runoff-
modified waters should be present at the surface throughout much of the year.
In the case of Xu et al. [2012] and Sciascia et al. [2013], this discrepancy occurs principally because the
domains used in these earlier studies were two dimensional. This means that the surface area across which
fjord water can be entrained into the plume is greatly reduced (i.e., there is no entrainment in an across-
fjord direction), allowing the plume to remain buoyant higher into the water column. This case is similar to
the plume model of Jenkins [2011], in which entrainment is only permitted on the down-fjord face of the
plume, allowing the plume to rise higher into the water column relative to the half-conical plume geometry
that we employ in this study (Figure 3).
In the three-dimensional domain of Xu et al. [2013] (which uses a similar Store Glacier temperature and
salinity stratigraphy to this paper), the plume reaches the surface at a discharge of less than 30 m
3
s
21
.
However, the glacially modified waters discharged by the plume remain saline relative to the surface waters
and quickly sink back to a depth in excess of 100 m [Xu et al., 2013, Figure 2c]. Similarly, we find that if
momentum is allowed to carry the plume past the point of neutral buoyancy in our model, then the plume
will reach the surface at a subglacial discharge of 50 m
3
s
21
(supporting information). As found by Xu
et al. [2013], this water would however be denser than its surroundings and sink back to the depth of neu-
tral buoyancy (below 100 m) as it moves away from the upwelling. To avoid this density inversion, we termi-
nate the plume at the depth of neutral buoyancy. This means that while in reality the plume may break the
surface before sinking back to a depth of neutral buoyancy (a process observed at Store Glacier by Chauch
e
et al. [2014]), our simulated plume is not visible at the surface until the glacially modified waters discharged
by the plume are of density equal to or less than the surface waters. This requires a subglacial discharge of
several hundred cubic meters per second (Figure 5 and supporting information). A wider implication of this
mechanism is that while plumes may become visible at the surface at relatively low discharges (tens of
cubic meters per second), much greater discharges (hundreds of cubic meters per second) may be required
to generate runoff-modified waters that flow down-fjord at the fjord surface.
Journal of Geophysical Research: Oceans 10.1002/2014JC010324
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C2015. The Authors. 810
5. Conclusions
In this paper, we have used a plume model to parameterize the buoyant upwelling of subglacial runoff in
an ocean circulation model. This greatly improves the computational efficiency of modeling glacial fjords,
permitting simulation of larger domains (hundreds of square kilometers in area) over longer time periods
(years to decades) than has previously been possible. This model has been used to examine the effect of
runoff on fjord circulation and submarine melt rate independent of coastal forcing. In these simulations,
runoff generates a relatively thin, strong, down-fjord current overlying a relatively thick, slow up-fjord cur-
rent. The strength and depth of the down-fjord current varies with runoff on annual time scales, being
strongest, and forming highest in the water column, when runoff is greatest. Because this current contains
entrained Atlantic waters from the lower part of the water column, it is typically warmer than the ambient
conditions at the depth at which it forms. This finding supports the identification of anomalously warm, gla-
cially modified waters in some Greenlandic fjords [Chauch
eetal., 2014; Straneo et al., 2011].
Submarine melt rate increases strongly with runoff in areas where ice is in contact with a buoyant runoff-
driven plume. This contact area may be small however relative to the width of the tidewater glacier margin,
and the impact is greatly reduced when averaged across the entire ice front. We find the submarine melt
rate to be only weakly sensitive to runoff when considered on the scale of interannual variability and across
the full width of the glacier. The significance of the relationship between runoff and submarine melt rate is
however dependent on the distribution of runoff across the grounding line and the strength of the back-
ground melt rate in those areas not in contact with the plume, both of which remain poorly constrained. In
recent years, there has been much interest in the relationship between melt rate and discharge in the vicin-
ity of ice marginal plumes [e.g., Jenkins, 2011; Sciascia et al., 2013; Xu et al., 2013]; further work is needed to
better constrain both the proportion of the ice front directly affected by runoff-driven plumes and the sub-
marine melt rate across the remainder in order to improve the prediction of melt rate across the full width
of the glacier front. Furthermore, this must be combined with a better knowledge of how the rate and distri-
bution of melting influences calving mechanics before the significance of submarine melting for the mass
balance of tidewater glaciers can be accurately assessed.
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Acknowledgments
This work was funded by NERC grant
NE/K014609/1 to Peter Nienow and
Andrew Sole. We thank Nolwenn
Chauch
e, Alun Hubbard, and the crew
of SV Gambo for the Store Glacier CTD
data, and two anonymous reviewers
whose comments substantially
improved the manuscript. Please
contact the corresponding author at
t.cowton@sheffield.ac.uk to obtain the
data or numerical model described in
this paper.
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... On the western boundary, the model is forced by a subglacial discharge plume pa-117 rameterization at the fjord midpoint (x = 0, y = W/2) and a face-wide melt plume 118 parameterization across the glacial face. Both types of plumes are parameterized using 119 the ICEPLUME package Cowton et al. (2015) with the subglacial discharge plume mod-120 eled as a point/cone plume (see Cowton et al. (2015)) and a face-wide ambient melt plume/sheet 121 plume (based on Jenkins (2011)). The slightly modified version of ICEPLUME used in 122 this study differs only from Cowton et al. (2015) by how the plume is injected into the 123 model domain, which permits higher horizontal resolution simulations. ...
... On the western boundary, the model is forced by a subglacial discharge plume pa-117 rameterization at the fjord midpoint (x = 0, y = W/2) and a face-wide melt plume 118 parameterization across the glacial face. Both types of plumes are parameterized using 119 the ICEPLUME package Cowton et al. (2015) with the subglacial discharge plume mod-120 eled as a point/cone plume (see Cowton et al. (2015)) and a face-wide ambient melt plume/sheet 121 plume (based on Jenkins (2011)). The slightly modified version of ICEPLUME used in 122 this study differs only from Cowton et al. (2015) by how the plume is injected into the 123 model domain, which permits higher horizontal resolution simulations. ...
... Both types of plumes are parameterized using 119 the ICEPLUME package Cowton et al. (2015) with the subglacial discharge plume mod-120 eled as a point/cone plume (see Cowton et al. (2015)) and a face-wide ambient melt plume/sheet 121 plume (based on Jenkins (2011)). The slightly modified version of ICEPLUME used in 122 this study differs only from Cowton et al. (2015) by how the plume is injected into the 123 model domain, which permits higher horizontal resolution simulations. The melt plume 124 is driven by face-wide melting, which in turn is driven primarily by the horizontal ve- Table S1. ...
Article
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Plain Language Summary Glacial fjords are long, narrow, and deep inlets that connect glaciers to the open ocean. These glacial fjords exist around the margins of Greenland, West Antarctica, Alaska, and other regions, and collectively contribute a significant source of ice discharge into the ocean. Over the past two decades, tidewater glaciers in Greenland have accelerated, which can lead to sea level rise, and there is growing evidence that this acceleration is caused by deep warm water currents that flow into the fjords from the open ocean. These warm water currents have the potential to melt the submarine sides of glaciers, causing them to retreat over time. The dynamics of warm water delivery to the glacier face, particularly its interaction with fjord circulation, are presently poorly understood. In this study, we use high‐resolution, process‐oriented simulations to understand fjord currents and how they vary with different fjord characteristics and lead to different rates of submarine melting of the glacier face. We find that submarine glacial melt can cause feedbacks by amplifying the strength of the ocean currents, which further increase glacial melt. These results are an important step toward understanding a critical process that may help us improve sea level rise predictions.
... During the process, the buoyant meltwater plume may entrain and transport nutrients and zooplankton to the surface, increasing their accessibility for surface-feeding predators, such as seabirds (Lydersen et al. 2014, Carroll et al. 2015, Nishizawa et al. 2020. Most importantly, the upwelling of the subglacial plume accelerates the along-fjord circulation of water masses and entrains seawater, from intermediate depths, of 10 to 30 times the original meltwater volume (Mortensen et al. 2013, Cowton et al. 2015, Meire et al. 2017, Halbach et al. 2019. Through its contribution to the plume's velocity and entrainment capacity, the subglacial discharge appears an important factor regulating the use of glacier fronts by marine wildlife (Lydersen et al. 2014, Everett et al. 2018). ...
... Two direct mechanisms may explain this unexpected result: (1) the direct negative effect of surface current on kittiwake foraging at the front, and (2) the negative effect of turbidity on prey detection. Greater discharge level can lead to stronger down-fjord surface currents (Cowton et al. 2015), which can push kittiwakes off the protruding site and therefore increase the energetic costs of foraging at the front (i.e. as birds would rely to a greater extent on short flights to return to the foraging patch). However, flight costs are low in kittiwakes relative to other foraging behaviors (Jodice et al. 2003), and the cost of flying back to the protruding site should be negligible. ...
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Tidewater glacier fronts can represent important foraging areas for Arctic predators. Their ecological importance is likely to change in a warmer Arctic. Their profitability and use by consumers are expected to vary in time, but the underlying mechanisms driving such variation remain poorly known. The subglacial plume, originating from meltwater discharge, is responsible for the entrainment and transport of zooplankton to the surface, making them more readily available for surface-feeding seabirds. Both discharge and zooplankton abundance are known to fluctuate in time and are thus expected to modulate the foraging profitability of glacier fronts. This study tested the predictions that annual use of glacier fronts by black-legged kittiwakes Rissa tridactyla is positively related to the average glacier discharge and prey biomass in the fjord. To do this, we combined a multiyear dataset of environmental drivers and GPS tracks of birds in Kongsfjorden, Svalbard. Our results confirmed the interannual variation in the use of glacier fronts by kittiwakes; however, contrary to our predictions, these variations were negatively correlated to both glacier discharge and zooplankton abundance. These apparent negative relationships likely reflect non-linear effects and complex interactions between local and regional environmental factors that affect the relative profitability of glacier fronts as foraging areas. Despite their high spatial predictability, glacier fronts may not offer consistent foraging opportunities for marine predators over time.
... This is often coupled with a well-established buoyant plume theory (Morton et al, 1956;MacAyeal, 1985), which calculates near-terminus temperature and salinity based on the far-field properties. This parameterization was used either as a stand-alone tool to quantify melt rate (Jenkins, 2011;Slater et al, 2016) or within a numerical ocean model to prescribe a boundary condition in an ocean simulation (Xu et al, 2012;Sciascia et al, 2013;Kimura et al, 2014;Cowton et al, 2015;Carroll et al, 2017). This approach, however, was shown to underestimate the observed melt rates (Jackson et al, 2017). ...
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The Non-hydrostatic Unified Model of the Ocean (NUMO) has been developed to advance model capability to realistically represent the dynamics and ice/ocean interactions in Greenland fjords, including an accurate representation of complex fjord geometries. To that end, NUMO uses high-order spectral element methods on unstructured grids to solve the incompressible Navier-Stokes equations complemented with heat and salinity transport equations. This paper presents the model's description and discusses the formulation of ice/ocean Neu-mann boundary conditions based on the three-equation model. We validate the model on a range of test cases. The convergence study on the classical Kovasznay flow shows exponential convergence with 1 2 NUMO model with application to ice/ocean interaction modeling. arbitrary basis function polynomial order. The lock-exchange and density current cases show that the model results of buoyancy-driven flows solved with 2D and 3D unstructured meshes agree well with previously published findings. Finally, we show that a high-order simulation of an ice block immersed in saline water produces results that match both direct numerical simulation and laboratory experiments.
... For the modeling of basal melting under the ice shelves, different models have adopted written as a module in the ice sheet model PISM: at each timestep, PICO provides melt rates and temperatures to PISM and PISM provides evolving geometry to PICO. For Greenland, IcePlume package (Cowton et al. 2015) is built within MITgcm (Marshall et al. 1997a, b) and it is utilized to analyze how glaciers respond under warming ocean. This package can simulate the process of a half-conical shape plume, which is initiated from a point-source freshwater runoff at the grounding line, rising along the glacier face and melting the ice in the meantime until it reaches either the ocean surface or the neutral buoyancy level. ...
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Ocean warming has been accelerating both tidewater glaciers submarine melting and ice shelves basal melting. However, sufficient physical representations of key processes within the ice shelf cavities or the glacier-fjord systems require high resolution simulations, thus substantial computational costs. Current semi-empirical methods or parameterizations can reduce the simulation complexity, yet they are based on simplifications and are poorly constrained due to sparse observational data and short time coverage. Here, we propose a semi-empirical framework to obtain the melting projections of both Greenland and Antarctica under oceanic forcing. The major glaciers and ice shelves are modeled and studied. The melting processes are simulated with IcePlume package (Cowton et al. 2015) for Greenland glaciers and Potsdam Ice-shelf Cavity mOdel (PICO) (Reese et al. 2018) for Antarctica ice shelves. This study identifies the responses of glaciers and ice shelves under ocean warming and generates the melting projections from the present-day to 2100, providing a novel and alternative perspective to simulate the sea level rise contribution from the ice sheets induced by ocean warming more efficiently without loss of accuracy. Historical simulations suggest agreement with the past basal melting under the Ross and Filchner-Ronne ice shelf (FRIS) in Antarctica. The framework can be beneficial to sample uncertainties from a larger ensemble of projections, given that the input from newer climate models is available in future, without having to re-simulate the whole process.
... Subglacial discharge and submarine melt were parameterized using the IcePlume Package (Cowton et al., 2015) using a straight glacier terminus on the eastern extent of our domain ( Figure 1d). We forced the model with a subglacial discharge plume at 200 m depth on the south side of the terminus, which is consistent with multibeam sonar surveys (Sutherland et al., 2019a) and time-lapse photography (Kienholz et al., 2019) conducted during our study period. ...
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Fjords are conduits for heat and mass exchange between tidewater glaciers and the coastal ocean, and thus regulate near‐glacier water properties and submarine melting of glaciers. Entrainment into subglacial discharge plumes is a primary driver of seasonal glacial fjord circulation; however, outflowing plumes may continue to influence circulation after reaching neutral buoyancy through the sill‐driven mixing and recycling, or reflux, of glacial freshwater. Despite its importance in non‐glacial fjords, no framework exists for how freshwater reflux may affect circulation in glacial fjords, where strong buoyancy forcing is also present. Here, we pair a suite of hydrographic observations measured throughout 2016–2017 in LeConte Bay, Alaska, with a three‐dimensional numerical model of the fjord to quantify sill‐driven reflux of glacial freshwater, and determine its influence on glacial fjord circulation. When paired with subglacial discharge plume‐driven buoyancy forcing, sill‐generated mixing drives distinct seasonal circulation regimes that differ greatly in their ability to transport heat to the glacier terminus. During the summer, 53%–72% of the surface outflow is refluxed at the fjord's shallow entrance sill and is subsequently re‐entrained into the subglacial discharge plume at the fjord head. As a result, near‐terminus water properties are heavily influenced by mixing at the entrance sill, and circulation is altered to draw warm, modified external surface water to the glacier grounding line at 200 m depth. This circulatory cell does not exist in the winter when freshwater reflux is minimal. Similar seasonal behavior may exist at other glacial fjords throughout Southeast Alaska, Patagonia, Greenland, and elsewhere.
... Glacier meltwater exits from the bottom of the terminus through subglacial channels forming a buoyant turbulent plume (How et al., 2017). Subglacial runoff and consequent upwelling of meltwater plumes in front of the tidewater glacier front generate a strong surface outflow and consequent sub-surface inflow of warm and saline AW that promotes submarine melting at the glacier front (Cowton et al., 2015;Sundfjord et al., 2017). It was indeed observed that frontal ablation of tidewater glaciers is primarily controlled by warm sub-surface waters (Luckman et al., 2015;Holmes et al., 2019). ...
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Kongsfjorden (Svalbard archipelago) is subjected to strong environmental gradients creating high physical and geochemical stress on benthic faunas. The present study aims at understanding the environmental drivers governing benthic foraminifera in the innermost part of the fjord. Surface sediments from 9 stations were sampled during August 2018 along a transect starting at ca. 2 km from the tidewater glacier Kronebreen and ending 12 km seaward. Three biozones were identified in response to disturbances linked to the proximity of the Kronebreen front (i.e., high water turbidity, freshwater, and sediment inputs, reduced organic fluxes). Close to the terminus (proximal biozone), few stress-tolerant and glacier proximal species were present (i.e., Capsammina bowmanni and Cassidulina reniforme). At about 6–8 km from the front (medial biozone), reduced turbidity, and increased organic fluxes, resulted in a higher diversity, and a high abundance of the phytodetritus-indicator Nonionellina labradorica. Relatively high diversity persisted until 12 km from the front due to higher organic inputs and reduced stressful conditions. The distal biozone was dominated by the Atlantic Water (AW) indicator Adercotryma glomeratum, in coherence with the presence of warm and salty AW detected far inside the fjord. Physical stress related to the glacier dynamics appears to favour the establishment of opportunistic species close to the terminus, whereas reduced disturbance away from the glacier induces the establishment of diverse assemblages. Our results show that benthic foraminifera may be effective bioindicators to monitor the long-term retreat of tidewater glaciers induced by climate change in Kongsfjorden.
... The model formulation represents a half-conical plume forced by a point source of subglacial discharge (Eqs 1-3). Initial plume temperature and salinity are set to the pressure-salinity-dependent melting point and 0, respectively; all model parameters are as described previously (Cowton et al., 2015;Carroll et al., 2016). To simulate the flux of meltwater into the subglacial discharge plume from glacier terminus melt, a three-equation model is solved Holland and Jenkins (1999) describing conservation of heat and salt at the ocean-ice boundary, combined with a liquidus constraint at the interface: ...
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Around the Greenlandic and Antarctic coastlines, sediment plumes associated with glaciers are significant sources of lithogenic material to the ocean. These plumes contain elevated concentrations of a range of trace metals, especially in particle bound phases, but it is not clear how these particles affect dissolved (<0.2 µm) metal distributions in the ocean. Here we show, using transects in 8 glacier fjords, trends in the distribution of dissolved iron, cobalt, nickel and copper (dFe, dCo, dNi, dCu). Following rapid dFe loss close to glacier outflows, dFe concentrations in particular showed strong similarities between different fjords. Similar dFe concentrations were also observed between seasons/years when Nuup Kangerlua (SW Greenland) was revisited in spring, mid-and late-summer. Dissolved Cu, dCo and dNi concentrations were more variable and showed different gradients with salinity depending on the fjord, season and year. The lack of consistent trends for dCu and dNi largely reflects less pronounced differences contrasting the concentration of inflowing shelf waters with fresher glacially-modified waters. Particles also made only small contributions to total dissolvable Cu (dCu constituted 83 ± 28% of total dissolvable Cu) and Ni (dNi constituted 86 ± 28% of total dissolvable Ni) within glacier plumes. For comparison, dFe was a lower fraction of total dissolvable Fe; 3.5 ± 4.8%. High concentrations of total dissolvable Fe in some inner-fjord environments, up to 77 µM in Ameralik (SW Greenland), may drive enhanced removal of scavenged type elements, such as Co. Further variability may have been driven by local bedrock mineralogy, which could explain high concentrations of dNi (25-29 nM) and dCo (6-7 nM) in one coastal region of west Greenland (Kangaatsiaq). Our results suggest that dissolved trace element distributions in glacier fjords are influenced by a range of factors including: freshwater concentrations, local geology, drawdown by scavenging and primary production, saline inflow, and sediment dynamics. Considering the lack of apparent seasonality in dFe concentrations, we suggest that fluxes of some trace elements may scale proportionately to fjord overturning rather than directly to freshwater discharge flux.
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Mass loss at the Greenland Ice Sheet is influenced by atmospheric processes controlling its surface mass balance, and by submarine melt and calving where glaciers terminate in fjords. There, an ice mélange – a composite matrix of calved ice bergs and sea ice – may provide a buttressing force on a glacier terminus and control terminus dynamics. Kangerlussuaq Glacier is a major outlet of the Greenland Ice Sheet, for which recent major retreat events in 2004/2005 and 2016–2018 coincided with the absence of an ice mélange in Kangerlussuaq Fjord. To better understand the response of Kangerlussuaq Glacier to climatic and oceanic drivers, a 2D flowline model is employed. Results indicate that an ice mélange buttressing force exerts a major control on calving frequency and rapid retreat. When an ice mélange forms in Kangerlussuaq Fjord, it provides stabilising forces and conditions favourable for winter terminus re-advance. When it fails to form during consecutive years, model results indicate that Kangerlussuaq Glacier is primed to retreat into the large overdeepenings in Kangerlussuaq Fjord, and to terminus positions more than 30 km farther inland, implying that excessive mass loss from Kangerlussuaq Glacier by the year 2065 cannot be excluded.
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An effective sponge city construction evaluation system plays a crucial role in evaluating sponge city construction schemes. The construction of a sponge city evaluation system still faces challenges related to incomplete index selection and unscientific weight division. Limited studies have focused on the comprehensive assessment of sponge city construction in the early stages. This study constructed a scientific assessment indicator system and a quantitative indicator weight at all levels by literature review and statistical analysis methods from an objective perspective. To demonstrate how to utilize our evaluation methods, three construction schemes randomly generated by MATLAB were evaluated under evaluation states of constant weight and variable weight, respectively. Scheme 3 had the highest score of 0.638 under the constant weight assessment, but it cannot practically be the final construction scheme due to the imbalance between indicators. Compared to the constant weight assessment, a variable weight assessment can effectively balance the states of the evaluation index with changes in the decision variable. Among the three schemes, Scheme 2 is the best choice with a value of 0.0355 under variable weight evaluation due to punishment and incentives in the variable weight method. The concept of “punishing” a disadvantageous indicator and “motivating” an advantageous indicator increases the relative advantages of the indices, ultimately affecting the assessment results of schemes and leading to a more balanced state. This study provides reasonable analysis and decision-making mechanisms to support decision-making and guide the scientific selection of a construction scheme.
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The rate of ocean-driven retreat of Greenland's tidewater glaciers remains highly uncertain in predictions of future sea level rise, in part due to poorly constrained glacier-adjacent water properties. Icebergs and their meltwater contributions are likely important modifiers of fjord water properties, yet their effect is poorly understood. Here, we use a 3-D ocean circulation model, coupled to a submarine iceberg melt module, to investigate the effect of submarine iceberg melting on glacier-adjacent water properties in a range of idealised settings. Submarine iceberg melting can modify glacier-adjacent water properties in three principal ways: (1) substantial cooling and modest freshening in the upper ∼50 m of the water column; (2) warming of Polar Water at intermediate depths due to iceberg melt-induced upwelling of warm Atlantic Water and; (3) warming of the deeper Atlantic Water layer when vertical temperature gradients through this layer are steep (due to vertical mixing of warm water at depth) but cooling of the Atlantic Water layer when vertical temperature gradients are shallow. The overall effect of iceberg melt is to make glacier-adjacent water properties more uniform with depth. When icebergs extend to, or below, the depth of a sill at the fjord mouth, they can cause cooling throughout the entire water column. All of these effects are more pronounced in fjords with higher iceberg concentrations and deeper iceberg keel depths. These iceberg melt-induced changes to glacier-adjacent water properties will reduce rates of glacier submarine melting near the surface, increase them in the Polar Water layer, and cause typically modest impacts in the Atlantic Water layer. These results characterise the important role of submarine iceberg melting in modifying ice sheet-ocean interaction and highlight the need to improve representations of fjord processes in ice sheet scale models.
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In the World Ocean, densest waters found on the continental shelves induce density driven downsloping currents that can influence the deep ocean water masses properties. This process is poorly represented in z-coordinate ocean models, especially in Ocean General Circulation Model (OGCM) with coarse resolution in both horizontal and vertical directions. Consequently, continental shelves appear to be too isolated from the open ocean, whereas the density remains too low in the deep ocean. This study presents a simple parameterization of downsloping flow designed for z-coordinate, coarse resolution ocean model. At the shelf break, when the density on the shelf is higher than that in the neighbouring deep water column, a downsloping current is set up. This current is linearly related to the horizontal density gradient between the two adjacent boxes, using a prescribed coefficient. For simplicity, a uniform value of the coefficient is used here, although it should ideally vary in space. From the shelf, the downsloping flow is assumed to go downward along the slope until it reaches a level of equal density. An upward return flow of equal magnitude maintains the conservation of mass. This parameterization has been implemented in an OGCM and two experiments, with and without this scheme, have been integrated until equilibrium using restoring boundary conditions. The impact of the downsloping parameterization on the global ocean is dominated by the improvement of the Antarctic bottom water circulation and water mass properties. The parameterization increases the density of the deep ocean and tends to reduce the intensity and depth of the North Atlantic deep water circulation, which is in better agreement with observations. As a result of a higher exchange with the open ocean, the properties of continental shelf waters are also improved, with a marked reduction of the Antarctic shelves salinities. Therefore, this simple parameterization leads to a significant improvement of the model results, at little computational cost.
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While it has been shown repeatedly that ocean conditions exhibit an important control on the behaviour of grounded tidewater glaciers, modelling studies have focused largely on the effects of basal and surface melting. Here, a finite-element model of stresses near the front of a tidewater glacier is used to investigate the effects of frontal melting on calving, independently of the calving criterion used. Applications of the stress model to idealized scenarios reveal that undercutting of the ice front due to frontal melting can drive calving at up to ten times the mean melt rate. Factors which cause increased frontal melt-driven calving include a strong thermal gradient in the ice, and a concentration of frontal melt at the base of the glacier. These properties are typical of both Arctic and Antarctic tidewater glaciers. The finding that frontal melt near the base is a strong driver of calving leads to the conclusion that water temperatures near the bed of the glacier are critically important to the glacier front, and thus the flow of the glacier. These conclusions are robust against changes in the basal boundary condition and the choice of calving criterion, as well as variations in the glacier size or level of crevassing.
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Freshwater produced by the surface melting of ice sheets is commonly discharged into ocean fjords from the bottom of deep fjord-terminating glaciers. The discharge of the freshwater forms upwelling plumes in front of the glacier calving face. This study simulates the meltwater plumes emanated into an unstratified environment using a nonhydrostatic ocean model with an unstructured mesh and subgrid-scale mixing calibrated by comparison to established plume theory. The presence of an ice face reduces the entrainment of seawater into the meltwater plumes, so the plumes remain attached to the ice front, in contrast to previous simple models. Ice melting increases with height above the discharge, also in contrast to some simple models, and the authors speculate that this "overcutting"may contribute to the tendency of icebergs to topple inwards toward the ice face upon calving. The overall melt rate is found to increase with discharge flux only up to a critical value, which depends on the channel size. Themelt rate is not a simple function of the subglacial discharge flux, as assumed by many previous studies. For a given discharge flux, the geometry of the plume source also significantly affects the melting, with higher melt rates obtained for a thinner, wider source. In a wider channel, two plumes are emanated near the source and these plumes eventually coalesce. Such merged meltwater plumes ascend faster and increase themaximummelt rate near the center of the channel. Themelt rate per unit discharge decreases as the subglacial system becomes more channelized.
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Warm, subtropical-originating Atlantic water (AW) has been identified as a primary driver of mass loss across the marine sectors of the Greenland Ice Sheet (GrIS), yet the specific processes by which this water mass interacts with and erodes the calving front of tidewater glaciers is frequently modelled and much speculated upon but remains largely unobserved. We present a suite of fjord salinity, temperature, turbidity versus depth casts along with glacial runoff estimation from Rink and Store glaciers, two major marine outlets draining the western sector of the GrIS during 2009 and 2010. We characterise the main water bodies present and interpret their interaction with their respective calving fronts. We identify two distinct processes of ice-ocean interaction which have distinct spatial and temporal footprints: (1) homogenous free convective melting which occurs across the calving front where AW is in direct contact with the ice mass, and (2) localised upwelling-driven melt by turbulent subglacial runoff mixing with fjord water which occurs at distinct injection points across the calving front. Throughout the study, AW at 2.8 +/- 0.2 degrees C was consistently observed in contact with both glaciers below 450 m depth, yielding homogenous, free convective submarine melting up to similar to 200 m depth. Above this bottom layer, multiple interactions are identified, primarily controlled by the rate of subglacial fresh-water discharge which results in localised and discrete upwelling plumes. In the record melt year of 2010, the Store Glacier calving face was dominated by these runoff-driven plumes which led to a highly crenulated frontal geometry characterised by large embayments at the subglacial portals separated by headlands which are dominated by calving. Rink Glacier, which is significantly deeper than Store has a larger proportion of its submerged calving face exposed to AW, which results in a uniform, relatively flat overall frontal geometry.
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Observed increases in iceberg discharge from Greenland's marine-terminating glaciers over the past two decades have altered the freshwater flux from glacial fjords into surrounding ocean basins. Although variations in freshwater flux due to ice-sheet discharge change have been investigated on a broad scale, the distribution of the freshwater flux due to melting of calved glacier ice (i.e. icebergs) has not been examined. Logistical challenges to collecting in situ data in glacial fjords have so far prevented a detailed examination of freshwater fluxes arising from melting beneath the waterline (i.e. submarine melting). Here we demonstrate that submarine melting of icebergs can be quantified using repeat digital elevation models derived from very high-resolution stereo satellite images. Analysis of volume changes for icebergs in Sermilik Fjord, East Greenland, yield area-averaged submarine melt rates of ∼0.39 m d–1. These rates are in relatively good agreement with simulated winter melt rates along the submerged portion of the Helheim Glacier terminus, providing independent validation of the applied technique. Further, the volume flux of fresh water from iceberg melting scales with surface and submerged iceberg areas, which suggests that iceberg meltwater may be an important freshwater component in fjords with high iceberg concentrations and/or expansive ice melange.
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Enhanced submarine melting of outlet glaciers has been identified as a plausible trigger for part of the accelerated mass loss from the Greenland ice sheet(1-3), which at present accounts for a quarter of global sea level rise(4). However, our understanding of what controls the submarine melt rate is limited and largely informed by brief summer surveys in the fjords where glaciers terminate. Here, we present continuous records of water properties and velocity from September to May in Sermilik Fjord (2011-2012) and Kangerdlugssuaq Fjord (2009-2010), the fjords into which the Helheim and Kangerdlugssuaq glaciers drain. We show that water properties, including heat content, vary significantly over timescales of three to ten days in both fjords. This variability results from frequent velocity pulses that originate on the shelf outside the fjord. The pulses drive rapid water exchange with the shelf and renew warm water in the fjord more effectively than any glacial freshwater-driven circulation. Our observations suggest that, during non-summer months, the glacier melt rate varies substantially and depends on externally forced ocean flows that rapidly transport changes on the shelf towards the glaciers' margins.
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The submarine melting of a vertical glacier front, induced by an intermediary circulation forced by periodic density variations at the mouth of a fjord, is investigated using a non–hydrostatic ocean general circulation model and idealized laboratory experiments. The idealized configurations broadly match that of Sermilik Fjord, southeast Greenland, a largely two-layers system characterized by strong seasonal variability of subglacial discharge. Consistent with observations, the numerical results suggest that the intermediary circulation is an effective mechanism for the advection of shelf anomalies inside the fjord. In the numerical simulations, the advection mechanism is a density intrusion with a velocity which is an order of magnitude larger than the velocities associated with a glacier–driven circulation. In summer, submarine melting is mostly influenced by the discharge of surface runoff at the base of the glacier and the intermediary circulation induces small changes in submarine melting. In winter, on the other hand, submarine melting depends only on the water properties and velocity distribution at the glacier front. Hence, the properties of the waters advected by the intermediary circulation to the glacier front are found to be the primary control of the submarine melting. When the density of the intrusion is intermediate between those found in the fjord's two layers there is a significant reduction in submarine melting. On the other hand, when the density is close to that of the bottom layer, only a slight reduction in submarine melting is observed. The numerical results compare favorably to idealized laboratory experiments with a similar setup.
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Rapid mass loss from the Greenland Ice Sheet has sparked interest in its glacial fjords for two main reasons: Increased submarine melting of glaciers terminating in fjords is a plausible trigger for glacier retreat, and the anomalous freshwater discharged from Greenland is transformed by fjord processes before being released into the large-scale ocean. Knowledge of the fjords' dynamics is thus key to understanding ice sheet variability and its impact on climate. Although Greenland's fjords share some commonalities with other fjords, their deep sills and deeply grounded glaciers, the presence of Atlantic and Polar Waters on the continental shelves outside the fjords' mouths, and the seasonal discharge at depth of large amounts of surface melt make them unique systems that do not fit existing paradigms. Major gaps in understanding include the interaction of the buoyancy-driven circulation (forced by the glacier) and shelf-driven circulation, and the dynamics in the near-ice zone. These must be addressed before appropriate forcing conditions can be supplied to ice sheet and ocean/climate models. Expected final online publication date for the Annual Review of Marine Science Volume 7 is January 03, 2015. Please see http://www.annualreviews.org/catalog/pubdates.aspx for revised estimates.
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[1] The circulation in a glacial fjord driven by a large tidewater glacier is investigated using a nonhydrostatic ocean general circulation model with a melt rate parameterization at the vertical glacier front. The model configuration and water properties are based on data collected in Sermilik Fjord near Helheim Glacier, a major Greenland outlet glacier. The approximately two-layer stratification of the fjord's ambient waters causes the meltwater plume at the glacier front to drive a “double cell” circulation with two distinct outflows, one at the free surface and one at the layers' interface. In summer, the discharge of surface runoff at the base of the glacier (subglacial discharge) causes the circulation to be much more vigorous and associated with a larger melt rate than in winter. The simulated “double cell” circulation is consistent, in both seasons, with observations from Sermilik Fjord. Seasonal differences are also present in the vertical structure of the melt rate, which is maximum at the base of the glacier in summer and at the layers' interface in winter. Simulated submarine melt rates are strongly sensitive to the amount of subglacial discharge, to changes in water temperature, and to the height of the layers. They are also consistent with those inferred from simplified one-dimensional models based on the theory of buoyant plumes. Our results also indicate that to correctly represent the dynamics of the meltwater plume, care must be taken in the choice of viscosity and diffusivity values in the model.
Article
The circulation regimes of two major outlet glacial fjords in southeastern Greenland, Sermilik Fjord (SF) and Kangerdlugssuaq Fjord (KF), are investigated using data collected in summer 2009. The two fjords show similar flow patterns, with a time-dependent, vertically sheared flow structure dominating over the background estuarine flow driven by buoyancy input. We show that this time-dependent flow is consistent with circulation induced by density interface fluctuations at the fjord mouth, often referred to as intermediary circulation. One difference between the fjords is that the hydrographic and velocity structure below a surface modified layer is found to be three-layer in KF in summer, compared to two-layer in SF. Outside each fjord, large-scale geostrophic currents dictate the stratification at the mouth, although the way in which these large-scale flows impinge on each fjord is distinct. Combining the observations with estimates from existing theories, we find the magnitudes of the estuarine (Qe) and intermediary (Qi) circulation and show that Qi >> Qe, although along-fjord winds can also be significant. We expect that the critical parameter determining Qi/ Qe is the sill depth compared to the fjord depth, with shallower sills corresponding to weaker intermediary circulation. Finally, we discuss the implications of strong intermediary circulation on calculating heat transport to the glacier face and its potential feedbacks on the background circulation in these highly stratified estuaries.