Frazil Ice Formation in an Ice Shelf Water Plume

Frazil Ice Formation in an Ice Shelf Water Plume
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, C03025, doi:10.1029/2003JC001851, 2004
Frazil ice formation in an ice shelf water plume
Lars H. Smedsrud1 and Adrian Jenkins
British Antarctic Survey, Cambridge, UK
Received 11 March 2003; revised 22 October 2003; accepted 11 December 2003; published 17 March 2004.
[1] We present a model for the growth of frazil ice crystals and their accumulation as
marine ice at the base of Antarctic ice shelves. The model describes the flow of buoyant
water upward along the ice shelf base and includes the differential growth of a range of
crystal sizes. Frazil ice formation starts when the rising plume becomes supercooled.
Initially, the majority of crystals have a radius of 0.3 mm and concentrations are below
0.1 g/L. Depending on the ice shelf slope, which controls the plume speed, frazil crystals
increase in size and number. Typically, crystals up to 1.0 mm in radius are kept in
suspension, and concentrations reach a maximum of 0.4 g/L. The frazil ice in suspension
decreases the plume density and thus increases the plume speed. Larger crystals precipitate
upward onto the ice shelf base first, with smaller crystals following as the plume slows
down. In this way, marine ice is formed at rates of up to 4 m/yr in some places, consistent
with areas of observed basal accumulation on Filchner-Ronne Ice Shelf. The plume
continues below the ice shelf as long as it is buoyant. If the plume reaches the ice front, its
rapid rise produces high supercooling and the ice crystals attain a radius of several
millimeters before reaching the surface. Similar ice crystals have been trawled at depth
north of Antarctic ice shelves, but otherwise no observations exist to verify these first
INDEX TERMS: 1827 Hydrology: Glaciology
predictions of ice crystal sizes and volumes.
(1863); 4207 Oceanography: General: Arctic and Antarctic oceanography; 4255 Oceanography: General:
Numerical modeling; 4540 Oceanography: Physical: Ice mechanics and air/sea/ice exchange processes; 4568
Oceanography: Physical: Turbulence, diffusion, and mixing processes; KEYWORDS: frazil ice crystals, ice shelf
water, marine ice
Citation: Smedsrud, L. H., and A. Jenkins (2004), Frazil ice formation in an ice shelf water plume, J. Geophys. Res., 109, C03025,
doi:10.1029/2003JC001851.
1. Introduction
[2] Approximately 60% of the ice discharge from Antarctica passes through floating ice shelves, from which it is
lost by basal melting and iceberg calving. The ice shelves
cover a total area as large as the Greenland Sea and range in
thickness from 100 to 2000 m. Because the freezing point of
seawater falls with increasing pressure, the water that flows
in beneath the ice shelves is invariably warmer than the
freezing point in situ. Melting at the ice-water interface
cools and dilutes the seawater, creating ice shelf water
(ISW), a water mass colder than the surface freezing point.
The ISW is buoyant compared with the warmer, saltier
inflow and thus tends to rise along the base of the ice shelf,
entraining the surrounding water to some degree [Nøst and
Foldvik, 1994]. This process drives an overturning circulation in the sub-ice shelf ocean.
[3] As the ISW rises, it becomes supercooled in situ, and
formation of ice starts. Observations suggest that the ice
forms as frazil ice crystals, which are initially suspended in
the water column but are subsequently deposited as a slushy
1
Now at Geophysical Institute, University of Bergen, Bergen, Norway.
Copyright 2004 by the American Geophysical Union.
0148-0227/04/2003JC001851$09.00
layer at the base of the ice shelf. Consolidation of the slush
then leads to layers of solid marine ice that have been
observed up to 350 m thick [Oerter, 1992; Thyssen et al.,
1992]. Some of the frazil crystals remain in suspension
and are transported out from underneath the ice shelf
[Dieckmann et al., 1986].
[4] Frazil ice is important to the sub-ice ocean dynamics
and overall glacial ice mass balance for two reasons:
(1) Frazil ice growth is a more effective sink for supercooling than is the growth of columnar ice directly onto the
ice shelf base, and (2) the presence of suspended ice crystals
makes the ISW more buoyant. The formation of frazil thus
modifies the forcing on the overturning circulation, which,
in combination with the process of crystal deposition,
determines the location and rate of marine ice accumulation
at the ice shelf base [Jenkins and Bombosch, 1995].
[5] Growth of frazil ice in salt water has been studied in
laboratory experiments over timescales of the order of
minutes by Tsang and Hanley [1985]. More recently, a set
of longer laboratory experiments has been conducted
[Smedsrud, 1998, 2001]. These experiments show that
supercooling reaches a maximum before efficient frazil ice
formation starts. The initial growth rate of ice is high, but
this partially quenches the supercooling, and subsequent
frazil ice formation proceeds at a lower rate with a persistent, low level of supercooling (0.02C) for up to 24 hours.
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SMEDSRUD AND JENKINS: FRAZIL ICE FORMATION IN AN ISW PLUME
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Figure 1. Sketch of the ice shelf water (ISW) plume model setup and parameters as well as the two
major frazil ice processes.
This ice formation is highly dynamic, as there is a continuous increase in both the number of crystals and the
individual sizes (from micrometers to 10 mm in radius).
[6] In this paper, dynamic growth of frazil ice is incorporated into the ISW plume model of Jenkins and Bombosch
[1995]. The following new processes are considered: (1) an
evolving distribution of ice crystal sizes ranging from the
micrometer to the millimeter scale, (2) differential growth
and rise of ice crystals based on the crystal radius, and
(3) secondary nucleation of new crystals of the smallest size.
We describe the behavior of this model and how it differs
from that of the earlier model of Jenkins and Bombosch
[1995], both for an idealized, linear ice shelf base and for
realistic ice thickness profiles taken from the Filchner-Ronne
Ice Shelf.
2. Plume Model
[7] The plume model used here was developed by
Jenkins [1991] as a model of the ocean beneath an Antarctic
ice shelf. The model treats the ocean as a two-layer system,
with the ambient water filling most of the cavity and the
plume as the upper mixed layer of ISW. Tides are assumed
to be a source of turbulence, which helps to keep the plume
well mixed. A steady state solution for the plume is found
along the (close to horizontal) ice shelf base. The plume
starts at the grounding line, follows a prescribed path across
the ice shelf, and ends at the ice front. The plume is
characterized by a thickness D and depth-averaged values
of velocity U, temperature T, and salinity S, as shown in
Figure 1. The ISW plume is initiated as a small flux
(0.01 m2/s) of water at the grounding line and flows upward
along the ice shelf base as a turbulent gravity current driven
by its positive buoyancy, entraining ambient water along
the way, as well as melting basal ice and forming new ice.
[8] Formation of frazil ice was added into the plume
model by Jenkins and Bombosch [1995] using a single
crystal size. Conservation of mass in the ISW plume takes
the following forms when looking at the water fraction, the
ice fraction, and the mixture, respectively:
@
ð DU Þ ¼ e0 þ m0 þ f 0
@s
ð1Þ
@
r
½ DUCi ðk Þ ¼ w ½ p0 ðk Þ f 0 ðk Þ
ri
@s
ð2Þ
@
ð DU Þ ¼ e0 þ m0 þ p0 ;
@s
ð3Þ
where s is a coordinate that follows the ice shelf base
(Figure 1). The rate of entrainment of the ambient water
from below is e0, and the melting and freezing at the iceocean interface is denoted m0. The mean reference seawater
density of 1028 kg/m3 is denoted rw, and ri is the constant
density of (freshwater) ice of 917 kg/m3. The frazil ice
concentration Ci(k) is calculated for every size class k on the
basis of freezing/melting of frazil ice f 0(k) (section 5.3), and
precipitation of frazil crystals from the plume is denoted
p0(k) (section 3). The terms m0, f 0, and p0 are negative when
mass leaves the water fraction (freezing) or ice fraction
(precipitation) of the plume, and where the dependency on
size class is not explicitly written, a summation over all
classes is implied. Note that a factor of 1 Ci formally
appears on the right-hand side of equation (1), but here, as
elsewhere, it has been approximated as 1. Maximum frazil
ice concentrations generated by the model are 0.2 103
by volume, so this is a good approximation.
[9] The governing equations for momentum, heat, and
salt then become
2 of 15
@ DU 2 ¼ DDrg sin q Cd U
@s
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
UT2 þ U 2
ð4Þ
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SMEDSRUD AND JENKINS: FRAZIL ICE FORMATION IN AN ISW PLUME
@
L
Tf f 0
ð DUT Þ ¼ e0 Ta þ m0 Tb gT ðT Tb Þ @s
Cw
@
ð DUS Þ ¼ e0 Sa :
@s
ð5Þ
p0 ¼
3. Entrainment and Precipitation
[11] Tidal currents below Antarctic ice shelves depend to a
large degree on water column thickness. Makinson and
Nicholls [1999] found average tidal RMS speeds up to
40 cm/s below the Filchner-Ronne Ice Shelf in a barotropic
model. Away from the ice front, speeds are usually in the
range 2 – 15 cm/s, which will lead to varying current shear at
the base of the ice shelf, influencing both the frictional drag
and the precipitation of frazil crystals. The increased friction
due to the tides is incorporated in a simple way in equation (4)
by adding the tidal RMS speeds UT.
[12] The entrainment of ambient water into the plume is
parameterized as by Jenkins [1991] using
e0 ¼ E0 U sin q:
[14] Precipitation of frazil crystals is modified in the same
way as frictional drag by adding UT2 to U2 in the approach
used by Jenkins and Bombosch [1995]. In addition, each
frazil size class has its own precipitation rate, so
ð6Þ
Equation (4) describes the water and ice mixture, while for
the flux of heat and salt, equations (5) and (6) describe
properties of the water phase only. The density difference
Dr between the plume and the ambient water is expressed
by Dr = bS(Sa S) bT(Ta T) Ci[(ri rw)/rw], where
bS and bT are haline contraction and thermal expansion
coefficients, respectively. Ta and Sa are the temperature and
salinity of the ambient water below the ISW plume, while
Ta and Sa are vertical averages of the ambient water over the
plume depth. A dimensionless, constant drag coefficient Cd
is set to 2.5 103. The parameter g is gravity, q is the
slope of the ice shelf, and UT is an RMS tidal current speed
specified for every location along the prescribed plume
track.
[10] The ice-ocean boundary temperature Tb and salinity
Sb are constrained by a linear pressure freezing point relationship Tb = aSb + b + czb, where zb is the elevation of the ice
shelf base. The coefficients a, b, and c are the slope of the
liquidus (0.0573C per practical salinity unit (psu)), offset
of the liquidus (0.0832C), and depression of the freezing
point with depth (0.761C/km), respectively, all for seawater.
The symbol gT denotes a heat transfer coefficient, specified
in ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
equation (10) of Jenkins [1991], but with U replaced by
p
U 2 þ UT2 , to incorporate the increased heat transfer from
tidally induced turbulence at the ice-ocean interface. L is the
latent heat of ice fusion, 3.35 105 J/kg, and Cw is the
specific heat capacity of seawater, 3974 J/kg C. The symbol
Tf is the pressure freezing point at mid-depth in the plume,
calculated using the plume salinity S.
ð7Þ
[13] Here E0 is a dimensionless constant of 0.036. Simulations with a tidal model beneath the ice shelf indicate an
upper mixed layer of 13-m thickness using a tidal RMS
velocity of 7 cm/s [Makinson, 2002; K. Makinson, personal
communication, 2001]. This finding supports the simple
parameterization of the entrainment process of equation (7)
in that the tides do not increase mixing significantly beyond
this depth.
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Nice
X
p0 ðk Þ
"
#
ri
U 2 þ UT2
p ðk Þ ¼ Ci ðk Þwi ðk Þ cos q 1 :
rw
UC ðk Þ2
k¼1
ð8Þ
0
Precipitation starts as soon as the velocity at the base
becomes lower than the critical velocity U C (k) =
{[0.1grie(k)(rw ri)]/rwCd}1/2. The model can handle an
arbitrary number of frazil ice size classes Nice, but 10 sizes
were used as the standard, and the sensitivity to the sizes
used is discussed in section 7. Here rie(k) is the equivalent
radius of a sphere with the same volume as the frazil disk,
and wi(k) is the rise velocity of the respective frazil crystal
size [Gosink and Osterkamp, 1983]. Precipitation occurs in
only one direction, so no erosion of crystals is permitted,
and p0(k) = 0 if U2 + UT2 > UC(k)2.
4. Frazil Ice Nucleation
[15] When the ISW plume reaches its pressure freezing
point, melting at the ice shelf base will cease. Shortly
thereafter, the plume will become supercooled, and the heat
flux will now be reversed, that is, from the ice-ocean
interface downward into the plume.
[16] This situation resembles that in which platelet ice
(disoriented, bladed, dendrite-like crystals) grows below
thick (>1.7 m) sea ice during late winter in the Ross Sea
[Gow et al., 1998]. The platelet crystals can be up to
100 mm long and 50 mm wide but are more commonly
around 10– 20 mm, and their growth is probably due to
ISW flowing beneath the sea ice cover [Smith et al., 2001].
These platelet ice crystals appear to be very similar to the
‘‘large vertical crystals’’ observed in a core from the Ross
Ice Shelf [Zotikov et al., 1980]. The latter were found all the
way through a 6-m-thick marine ice layer below 410 m of
meteoric ice and were reported to be about 5 mm thick and
20 mm long. Platelet ice has also been observed in the
lower parts of thick multiyear sea ice in the central Weddell
Sea [Gow et al., 1987].
[17] In the plume model it is assumed that the first growth
of ice will be downward growing platelet ice as well as
‘‘normal’’ congelation ice. Some of the platelet ice crystals
are then assumed to be broken off by turbulent eddies and
will subsequently be suspended in the plume.
5. Frazil Ice Population Dynamics
[18] The frazil ice crystals are assumed to be circular
disks characterized by their radius ri(k) and thickness ti(k).
The size range used (ri is between 0.01 and 4.0 mm) is
similar to the range used in other numerical studies and
experiments, and the approach used by Smedsrud [2002] is
generally followed. Smedsrud [2002] used equations developed by Hammar and Shen [1995] and Svensson and
Omstedt [1998], calibrated against experimental data on
the evolution of water temperature, mean crystal diameter,
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SMEDSRUD AND JENKINS: FRAZIL ICE FORMATION IN AN ISW PLUME
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and total number of crystals. On timescales of up to 24 hours
the presence of many nearby crystals effectively limits the
maximum crystal size [Forest, 1986] and explains the
maximum crystal radius of 10 mm observed by Smedsrud
[2001]. Smedsrud [2002] evaluated frazil growth over a
24-hour period, but in the ISW plume, frazil growth lasts for
a number of days.
[19] The frazil disk is assumed to increase in thickness
following ti(k) = 1/50 2ri, i.e., having a constant aspect ratio
ar = 1/50. This value is in the middle of the range proposed
by laboratory [Gosink and Osterkamp, 1983] and numerical
[Jenkins and Bombosch, 1995] experiments.
5.1. Differential Growth
[20] The heat flux from a growing ice crystal of the class
k to the surrounding plume water, given in watts, is
described by
qi ðk Þ ¼ rw Cw NuKT
Tf T
2pri ðk Þti ðk Þ ½W:
ri ðk Þ
ð9Þ
Here Nu is a Nusselt number, describing the ratio between
the actual (turbulent) heat flux and the heat conduction. Nu
may vary with the flow conditions and has earlier either
been set of the order of 1 [Svensson and Omstedt, 1994] or
been made a function of the turbulent dissipation rate and
the Kolmogorov length scale, giving generally higher
values [Hammar and Shen, 1995]. The molecular thermal
diffusivity of seawater, KT, is 1.4 107 m2/s.
[21] In equation (9), no account has been made for the
slower diffusivity of the salt expelled from the growing
crystals. Holland and Jenkins [1999] show that under
typical conditions the melt rate is an approximately linear
function of Tf T even with this effect included. It is
therefore possible to simulate the impact of salt rejection at
the interface simply by reducing the effective heat transfer
coefficient by a factor that varies between 1/1.6 and 1/5.7
depending on the value assumed for the haline transfer
coefficient. We allow Nu to become as low as 0.2 to account
for this effect here, and as discussed in section 7, this has a
minor effect on the volumes of frazil formed in the plume.
The radius ri is chosen as the characteristic length scale over
which the thermal gradient is estimated following Hammar
and Shen [1995]. Our assumption that the crystals maintain
a constant aspect ratio implies that two thirds of the ice
growth occurs at the disk edges. We therefore use the edge
area, 2pri(k)ti(k), in equation (9) to estimate the rate of heat
transfer between water and a growing frazil ice crystal.
When frazil crystals are melting, we assume that the heat
transfer takes place all over the surface, so the area of both
sides of the frazil disk is added in equation (9) to yield
rw Cw NuKT
i
Tf T h
2pri ðk Þti ðk Þ þ 2pri ðk Þ2 :
ri ðk Þ
[22] The frazil ice concentration in equation (2) is defined
as being a volume of frazil ice suspended in a unit volume
of water DV:
Ci ¼
k¼N
Xice
Ci ðk Þ
k¼1
Ci ðk Þ ¼
N ðk Þ
1 X
vi ðk Þ
DV n¼1
ð10Þ
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in m3/m3. Here N(k) is the number of crystals in each class
k, and vi(k) is the (uniform) volume of the ice crystals in that
specific class, vi(k) = pri(k)2ti(k). The growth rate of a frazil
size class per unit volume is then
2
DCi ðk Þ Cw NuKT Tf T
Ci ðk Þ:
¼
Lw
Dt
ri ðk Þ2
ð11Þ
The growth rate DCi(k)/Dt is calculated for each size class
(k = 1, Nice 1) and represents the growth of a constant
number of ice crystals. Notice that the largest crystals (k =
Nice) are not permitted to grow because they have already
reached the maximum size. For melting conditions the melt
rate of a frazil size class was computed in the same manner
as in equation (11) with the extra surface area included, and
all crystal sizes melted.
5.2. Secondary Nucleation
[23] Secondary nucleation is the term used for the production of new small crystals by removal of nuclei from the
surface of parent crystals. The main processes thought to
occur are collision between crystals (collision breeding) and
detachment of surface irregularities by fluid shear [Daly,
1984]. During melting conditions the small crystals produced by secondary nucleation will soon melt away, so the
process is activated in the model only during frazil ice
growth. The simplified approach of Svensson and Omstedt
[1994] is followed here.
[24] A crystal moving relative to the fluid will sweep a
volume DVi during a time interval Dt:
DVi ðk Þ ¼ Ur ðk Þprie ðk Þ2 Dt;
ð12Þ
where
Ur ðk Þ ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
½2rie ðk Þ2 þ wi ðk Þ2 ;
15n
ð13Þ
incorporating both the rise velocity and the turbulence
intensity. The dissipation rate is 7.4 106 W/kg unless
otherwise stated, and the kinematic viscosity n is 1.95 106 m2/s. The equivalent crystal radius rie(k) must be used
here because the crystal can twist and turn in all directions
and no method for modeling a disk in a turbulent flow has
yet been formulated. The growth rate for the smallest size
class resulting from collision between all the different size
classes is then calculated as
Nice
DCi ðk ¼ 1Þ X
Ur ðk Þ
pni
rie ðk ¼ 1Þ3 Ci ðk Þ;
¼
ð
k
Þ
Dt
r
ie
k¼1
ð14Þ
where ni is the average number of all the different ice
crystals per unit volume in the plume. The DCi(k = 1) in
equation (14) is always positive (i.e., gain in ice volume),
and there is a corresponding loss of (exactly the same)
volume for the other classes for each part of the summation
in equation (14). Several processes may limit the efficiency
of the secondary nucleation process [Smedsrud, 2002], and
ni = 1.0 103 was found to be an empirical upper limit.
5.3. Total ‘‘Melt’’ Rate for Frazil Ice
[25] The ISW plume is treated as being a well-mixed
upper layer, and consequently, Ci is the mean frazil ice
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SMEDSRUD AND JENKINS: FRAZIL ICE FORMATION IN AN ISW PLUME
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concentration over the plume depth D. The total rate of
change of the frazil ice volume in the ISW plume in
equation (5) is therefore
f0 ¼
Xk¼Nice
k¼1
f 0 ðk Þ ¼ D
Xk¼Nice
k¼1
w0 ðk Þ:
[26] Here w0(k) is comparable with w0, the rate of loss of
frazil ice due to melting per unit volume of plume defined
by Jenkins and Bombosch [1995]. Both f 0 and w0 are
negative for freezing conditions when water is lost from
the plume.
[27] Because of the constant mean radius in the size
classes ri(k), the actual rate of change of ice volume in
one size class, w0(k), depends on the melting/freezing rate
DCi(k)/Dt from equation (11) in the size below k 1 and
above k + 1. In addition, w0(k) has to be consistent with a
certain number of crystals being transferred to, or from, the
size class. In this way the melting/freezing of all crystals in
a class results in a transfer of a specific number of them to
the class below/above:
w0 ðk Þ ¼
1 DCi ðk þ 1Þ
DCi ðk Þ
vi ð k Þ
Dt
Dvi ðk Þ
Dvi ðk 1Þ
ð15Þ
1 DCi ðk 1Þ DCi ðk Þ
vi ðk Þ
Dt Dvi ðk 1Þ Dvi ðk Þ
ð16Þ
for melting and
w0 ðk Þ ¼ for freezing. Here Dvi(k) = vi(k + 1) vi(k), and equation
(16) is the same as equation (18) of Hammar and Shen
[1995]. With this formulation a class increases in volume
due to melting in the class above and decreases in volume
due to melting of its own crystals. In the same way a class
increases in volume because of growth in the class below
and decreases in volume because of growth of its own
crystals. The smallest crystals (k = 1) have a pure loss to the
class above due to growth but increase in volume because of
the secondary nucleation process (equation (14)).
6. Model Behavior for a Linear Ice Shelf Base
[28] Changes in the basal slope of the ice shelf have a
large impact on the behavior of a model ISW plume
[Jenkins, 1991; Jenkins and Bombosch, 1995]. Therefore,
in order to demonstrate more clearly the impact that the
frazil ice processes described in section 5 have on the
behavior of a plume, we first apply the model to an
idealized ice shelf base having a constant basal slope. The
early stages of the plume evolution, up to the point where
the ISW becomes supercooled, are unaffected, as frazil only
grows from that point onward. Following Jenkins and
Bombosch [1995], the plume is initiated at a depth of
1400 m and ascends below a 600-km-long ice shelf, which
ends at a depth of 285 m. The ambient water has linear
profiles of both temperature, Ta = 1.9 to 2.18C, and
salinity, Sa = 34.5 to 34.71 psu, from the surface to 1400 m
depth. No tidal velocities are added below the linear shelf
(UT = 0), and the results are identical up to 420 km and
650 m depth in all cases. Freezing processes taking place in
the plume after this point will be described for the ‘‘standard
Figure 2. Supercooling (T Tf) and plume speed (U )
from 400 to 540 km for the linear ice shelf. The solid lines
indicate standard run values. The other lines show model
sensitivity.
run’’ in this section, and the sensitivity of the results to
some of the key frazil ice parameters will be described in
section 7. The only significant change of frazil ice parameters from Jenkins and Bombosch [1995] is that the crystals
are assumed to be twice as thick, ti = ar2ri, where ar = 1/50
and not 1/100.
[29] Frazil ice formation in the ISW plume takes place
0.05 m/s between 420 and 500 km. With a mean speed U
4 km/d, this distance corresponds to a time interval of about
3 weeks. Formation is initiated with a small volume of
crystals (F0 = 40.0 109 m3/m3) divided equally over the
crystal spectrum. Levels of supercooling typically reach
0.2 103 C, as shown by the solid line in Figure 2,
but show no indication of oscillations like those discussed
by Jenkins and Bombosch [1995]. The plume reaches
maximum supercooling shortly after it has become supercooled, before much growth of frazil ice has taken place.
[30] The plume speed U gets a kick from the frazil ice
formation, starting at 420 km (Figure 2, solid line), due to
the increase in plume buoyancy caused by a positive Ci. The
maximum density deficit created by frazil ice is 21.8 103 kg/m3 when the frazil ice concentration of the plume is
at its maximum, 0.18 g/L.
[31] The size spectrum for the suspended frazil ice
crystals is shown in Figure 3 as a function of distance along
the plume path. The radius of the frazil ice class having the
largest concentration will hereinafter be called the significant frazil ice radius ris. This is the radius of the class
constituting the peak in the frazil ice spectrum at any given
position along the plume path shown in Figure 3. At the
start of the formation process, ris = 0.3 mm. Between 460
and 490 km, ris has reached 0.5 mm, and the concentration
for this class is 0.07 g/L. Toward the end, ris decreases again
as precipitation outweighs growth for the larger classes and
ends up at ris = 0.4 mm.
[32] The supercooling in the ISW plume drives an almost
constant production of frazil crystals, as shown in Figure 4.
Toward the end both supercooling and crystal growth
decrease. This is caused by the thickening of the plume,
which tends to lower the depth-averaged freezing point used
5 of 15
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SMEDSRUD AND JENKINS: FRAZIL ICE FORMATION IN AN ISW PLUME
Figure 3. Frazil ice size spectrum from 420 to 509 km for
the linear ice shelf.
to calculate f 0, as it slows down. The slightly positive values
of f 0(4) and f 0(5) between 460 and 500 km are indications
not of melting but of a net loss of mass to larger classes.
This is caused by an ice growth in the class itself that is
larger than in the class with the smaller radius that feeds it.
[33] The decrease in Ci toward the end is caused by the
precipitation of the larger crystals upward onto the ice shelf
base, as shown in Figure 4. Up to 470 km the precipitation
comprises the 0.6- and 0.8-mm crystals, but as the plume
slows down, the smaller crystals also add to the total
precipitation.
[34] The plume speed and ice precipitation rate presented
here are similar to the results obtained by Jenkins and
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Bombosch [1995] for crystals of 1.5 mm diameter, i.e., a
frazil radius of 0.75 mm, because of the different ar and the
resulting rise velocities. The thinner 0.75-mm crystals of
Jenkins and Bombosch [1995] have a rise velocity similar to
the crystals having the significant radius of 0.5 mm found
here. The evolution of T and p0 differs from all the presented
cases of Jenkins and Bombosch [1995]. In particular, there
is no sign of oscillations of any kind in these parameters
with the frazil spectrum included. Instead, we see a smooth
return to the pressure freezing point following the initial
peak in supercooling and an even distribution of p0, with the
largest crystals deposited before the smaller ones.
[35] The d18O values of the plume water and precipitating
frazil ice have also been computed. Assuming a constant
d18O in the ambient water of 0.5%, the plume water value
decreases to 0.78% over the first 10 km of the plume
path. This decrease is due to input of meltwater from the ice
shelf with d18O = 40%. Along the track, d18O increases
steadily in the plume until the point of neutral buoyancy.
The increase is due to entrainment of the ambient water,
which dominates over further melting. When melting ends
and frazil ice starts forming at 420 km, d18O = 0.623%.
The supercooling of 0.2 103 C drives an individual
frazil crystal growth rate of up to 0.2 mm/h, highest for the
smallest crystals. This results in d18O values for the growing
frazil ice between 2.03% and 2.08%, and for the larger
classes, which dominate precipitation, the values are between 2.07% and 2.08%. Alternatively, the fractionation
for the precipitating ice is 2.695, very close to the equilibrium fractionation for sea ice of 2.7 [Eicken, 1998]. The
frazil formation process therefore leads to d18O values
similar to those produced by the growth of ‘‘normal’’
congelation ice directly to the ice shelf base. In both cases,
equilibrium fractionation results in d18O values close to
Figure 4. (top) Frazil ice growth and (bottom) precipitation for the linear ice shelf.
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Table 1. Model Sensitivity to Frazil Parameters for the Linear Ice Shelfa
Parameter
, cm/s
U
m
D,
Maximum
Ci, g/L
ris, mm
Maximum
(T Tf), C
Standard run
Nu = 0.2
Nu = 8.0
ar = 0.01
ar = 0.05
Low ni
High ni
Small seed
Large seed
Low F0
Low F0/High ni
Nice = 3
Nice = 25
4.8
5.1
6.0
5.2
4.7
4.8
5.5
6.3
4.6
4.6
4.6
5.0
5.5
9.5
8.5
16.8
11.0
22.2
9.4
15.5
16.6
46.3
46.3
10.0
9.5
16.7
0.18
0.17
0.18
0.31
0.06
0.18
0.29
0.62
0.03
0.03
0.04
0.03
0.1
0.5
0.5
0.5
0.6
0.3
0.5
0.5
0.6
0.6
0.6
0.5
0.5
0.5
0.35 103
1.15 103
0.07 103
0.38 103
11.69 103
0.35 103
0.35 103
0.25 103
27.03 103
27.02 103
0.98 103
0.6 103
0.4 103
R end
0
m0ds, m3/yr
197
197
198
193
196
198
193
183
190
189
198
198
198
103
103
103
103
103
103
103
103
103
103
103
103
103
R end 0
3
0 f ds, m /yr
R end 0
3
0 p ds, m /yr
End,
km
33 103
32 103
33 103
55 103
21 103
33 103
59 103
112 103
8 103
8 103
31 103
30 103
31 103
30 103
30 103
31 103
42 103
21 103
30 103
44 103
75 103
8 103
8 103
30 103
29 103
29 103
502
502
502
533
509
502
537
598
512
512
497
496
499
a
The details for the different runs are given in the text, and averages and integrals are from a grounding line at 1400 m depth to the point where the plume
leaves the ice shelf, given as ‘‘end.’’ The significant frazil radius ris is given at the point of maximum Ci.
2.0% as found in a core from the Ronne Ice Shelf [Oerter,
1992]. The ice formation in the plume slows the rate of
increase in d18O, and at 500 km d18O = 0.605%.
7. Sensitivity of Model Results to Frazil
Ice Parameters
[36] Table 1 summarizes how some key model outputs
change in response to varying the input parameters that
define the frazil ice growth. In general, we find that the
model is less sensitive to changes in the parameterization of
frazil processes than was the earlier version of Jenkins and
Bombosch [1995]. This is a result of the addition of an
evolving spectrum of crystal sizes, which means that the
size classes favored for growth (smaller) and precipitation
(larger) either are present or can be developed.
[37] The stability of the model is well illustrated by its
response to changing the Nusselt number, Nu, as given in
Table 1. Although Nu analytically has a lower bound of 1.0,
we use lower values here to mimic the effect of the slower
(molecular) diffusion of salt, compared with heat, for the
case when turbulent conditions in the plume are not fully
developed. Changing Nu alters the supercooling of the
plume as shown in Figure 2, but the crystal spectrum and
the total growth and precipitation of frazil ice are nearly the
same in the Nu = 0.2 and Nu = 8.0 cases. The differences in
and D
are caused by the quicker start of the frazil
U
formation process with higher Nu, giving a slightly higher
and thus a higher entrainment, increasing D.
U
[38] The ease with which the ice can be retained in
suspension has an important influence on model behavior.
If a significant volume of frazil is suspended, then U
increases and the plume stays fairly thin. The more rapid
ascent of the plume increases the rate at which its pressure
freezing point falls, and thus more frazil ice is produced in a
feedback loop. This is illustrated by varying the crystal
thickness ti, which controls the rise velocity wi and thus the
critical velocity Uc, at which a frazil class starts to precipitate (given by equation (8)). As shown in Figure 2 and
given in Table 1, a smaller ti (ar = 1/100) leads to higher U
and Ci and more frazil growth. This makes the plume more
buoyant, and it continues to 533 km, only depositing a
portion of its suspended frazil crystals. On the other hand,
thicker crystals (ar = 1/20) have a larger buoyancy for any
given radius and precipitate more easily. This leads to lower
and a thicker plume. The frazil spectrum is also
Ci and U
altered, with ris = 0.3 mm; all the crystals precipitate out at
480 km; and the total precipitation is half of that in the ar =
1/100 case. The supercooling grows toward the end and
reaches a high value, as there is no frazil growth after
480 km.
[39] The efficiency of the secondary nucleation process is
controlled by the upper limit on ni , the average number of
crystals per unit volume. In the low ni case (Table 1) the
maximum is set to one crystal, the absolute lower limit, thus
effectively not permitting any secondary nucleation of new
crystals. This makes hardly any difference to the results,
indicating that there are enough small crystals available in
the initial flux without this process and that subsequent
addition of more small crystals does not alter results
significantly. The high ni case has the maximum set at ni =
100 103 m3. This increases frazil ice production
significantly and keeps the plume buoyant to 537 km.
[40] The first frazil crystals that appear in the plume are
assumed to be crystals breaking off from the base, as
discussed in section 5. As there are no observations to
guide us toward the size of these crystals, the initial flux of
frazil has been set equally between the 10 sizes used. The
effect of partitioning this flux unevenly in favor of the small
side of the frazil spectrum is shown in the small seed case in
Table 1. The five smallest sizes have 19% of the initial flux
each, while the five largest sizes have 1% each. This leads
to the highest levels of frazil ice and precipitation, the
, and a plume that stays buoyant to 598 km.
highest U
The supercooling is low, as there are initially so many small
crystals that can grow rapidly, and ris reaches 0.6 mm as Ci
keeps increasing until 580 km, when most of the crystals
have attained this size.
[41] With mostly large crystals in the initial frazil flux, the
large seed case in Table 1, the opposite effect is seen: less
frazil ice and precipitation, a larger supercooling, and a
This has approximately the same effect as a lower
lower U.
initial flux, the low F0 case, where F0 = 4.0 109, one
tenth of the standard run. The similarity is caused by the
lower initial concentration of the smaller crystals in both
cases.
[42] The low frazil production caused by the low F0 can
be compensated by setting the maximum ni = 100 103,
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Figure 5. Map of the Filchner-Ronne Ice Shelf. The proposed plume paths illustrate results for different
regions but are not predictions of ISW flow. Along the Foundation Ice Stream, there are two paths: the
standard run and one farther to the east that is based on a data set from the Alfred Wegener Institute
(AWI). Calculated freezing rates are indicated along the different plume paths: 0 – 0.5 m/yr (open circles),
0.5– 1 m/yr (plus signs), 1 – 2 m/yr (asterisks), and >2 m/yr (solid circles). Drill sites mentioned in the text
are also marked (circled crosses).
the low F0/high ni case. This increases frazil ice growth and
precipitation back to the level of the standard run despite an
overall lower ice concentration. The lower concentration
promotes growth in all size classes because of the higher
level of supercooling, and with a very efficient secondary
nucleation process a supply of the precipitating size classes
can be maintained.
[43] With equations (9) – (16) describing the frazil growth,
the minimum value for Nice = 3. Using ri = (0.01, 0.5, 0.8) mm
leads to a maximum Ci of 0.03 g/L, much lower than the
standard run value of 0.18 g/L (Table 1). Despite this, the
total volume of frazil grown and precipitated remains almost
unchanged. Once again, the higher supercooling promotes
crystal growth, and with fewer size classes, frazil reaches
the greatest volume (0.8 mm) faster. Precipitation therefore
parallels growth and maintains the low concentration.
This leads to a more evenly distributed precipitation around
0.4 m/yr between 420 and 500 km, very similar in pattern to
the total f 0 shown in Figure 4, divided equally between the
0.5- and 0.8-mm crystals. There is a small sign of an
oscillation in the temperature of the plume: first, the usual
return to the (now lower) equilibrium temperature, then an
increase in supercooling, resulting from the low frazil
concentrations, before entrainment raises T again around
480 km. This is very similar to the form of T in the case of
Nu = 0.2, shown in Figure 2.
[44] Increasing the number of crystal classes (Nice) to 25
allows a 0.1-mm resolution in the ri spectrum but does not
alter the results significantly (Table 1). There is a slight
broadening of the peak in the frazil spectrum shown in
Figure 3, and the maximum Ci reaches 0.1 g/L at 454 km.
[45] Overall, we find that the most robust result is the size
spectrum of suspended crystals, as characterized by ris. This
is a key finding, which lends us some confidence in our
predictions of the crystal sizes precipitated to form marine
ice. The total amount of precipitation is also a fairly robust
result, although it is sensitive to the availability of small
seed crystals. Unfortunately, this is the parameter we
probably know least about. The result which shows most
sensitivity to the choice of model parameters is the level of
supercooling. However, its impact on model results is
relatively small, since changes in the level of supercooling
are often compensated by variations in ice concentration or
plume volume flux, such that the total growth of frazil ice
remains relatively stable. There is also an advantage in the
high sensitivity of this variable. Salinity, temperature, and
pressure are the easiest properties of all to observe beneath
an ice shelf and turn out to be the most useful in helping us
to narrow down the appropriate choices for our unknown
model parameters.
8. Foundation Ice Stream Results
[46] The Foundation Ice Stream flows into the central
area of the Filchner-Ronne Ice Shelf as shown in Figure 5.
The largest body of marine ice on the ice shelf is thought
to originate from water flowing approximately along the
proposed standard run path [Bombosch and Jenkins, 1995].
We use the plume paths to represent a region of ISW flow.
The plume paths in Figure 5 are not predictions of ISW
flow, as there is only one horizontal coordinate in the model
and no account is taken of cross-flow forces (i.e., Coriolis).
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Figure 6. Along-track ice shelf and seabed topography for the Foundation Ice Stream, with (top) plume
thickness and (bottom) speed of the plume U and prescribed tidal speed UT.
We will use this section to describe model results in a
natural setting, and the model’s response to different
forcing will be discussed in section 9. The ambient water
properties are the same as for the linear ice shelf, and they
have been used throughout unless otherwise stated. The
properties are Ta = 1.9C and Sa = 34.5 psu at the surface,
decreasing/increasing to Ta = 2.18C and Sa = 34.71 psu
at 1400 m depth.
[47] The depth of the Filchner-Ronne Ice Shelf along the
proposed standard run path is shown in Figure 6 together
with the calculated plume depth D and a rough bottom
bathymetry. The value of D increases almost linearly from
0 to 20 m over the first 250 km, then stays fairly constant
around 30 m for the next 100 km before increasing to 100 m
over the final 100 km. The ISW plume becomes neutrally
buoyant here and leaves the ice shelf at approximately 500 m
depth, with 300 m of ambient water below.
[48] The plume speed U shown in Figure 6 is controlled
largely by the slope of the ice shelf base. The variability in
U between 250 and 400 km is caused by increased
resolution in the ice shelf profile in this region. Up to
250 km the data on ice shelf thickness are more sparse, so
basal elevation and velocity profiles appear smoother
[Lythe et al., 2001]. The effect of suspended frazil ice in
the plume is shown by plotting U from a model run without
frazil ice, where U is 3 cm/s lower between 320 and
400 km. Prescribed UT is also shown and has been added in
both cases to the ice-ocean drag in equation (4). The main
impact of this is to reduce U by 2 cm/s in the region
between 50 and 250 km, where tidal currents are high
and the plume remains thin. At 370 km, Ci is at its
maximum, 0.38 g/L, and this makes the plume density
45.8 103 kg/m3 less than it would be without frazil ice.
This increases U from 5.5 cm/s with no frazil to the 9 cm/s
shown in Figure 6.
[49] Frazil ice starts to form when the plume becomes
supercooled at 315 km, as shown in Figure 7. The rise of the
plume increases Tf, and this is the source of supercooling
driving the growth of frazil ice. As all the frazil crystals in
the plume model experience the same supercooling, it is the
smallest crystals that grow most efficiently because of the
Figure 7. Frazil ice size spectrum for the Foundation Ice
Stream. Size classes Ci(1), C i(2), and C i(10) have
concentrations too small to show on the plot.
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Figure 8. Freezing (negative) and melting (positive) of (top) frazil ice f 0(k) and (bottom) precipitation
of frazil ice p0(k) for the Foundation Ice Stream.
[T Tf]/[ri(k)] term in equation (9). This also means that
they leave their size class quickly, and only Ci(3) to Ci(9)
hold enough mass to show in Figure 7. The delay before the
rise in mass of each of the different classes shows clearly in
Figure 7, and Ci(9) is the last class to gain any significant
mass around 340 km.
[50] Significant precipitation starts at 350 km, then occurs
again at 370 km, with the 0.8-mm crystals, p0(8), as shown
in Figure 8. Thus the decreases in Ci(8) in Figure 7 are
caused by precipitation out of the plume. Shortly thereafter,
the 0.6-mm crystals, p0(7), also start to precipitate. While Ci
is at its maximum, Ci(7) is the class with the major ice
volume; that is, ris = 0.6 mm. Between 370 and 410 km, U
decreases steadily, causing successive peaks for p0(8) and
p0(7) and just a small contribution from p0(6) at 405 km.
There is an increase in the slope of the ice shelf around
420 km, causing a rise in U and lower p0(7) and thereby an
increase and second peak in Ci(7) at 430 km, shown in
Figure 7. After this the smaller sizes (Ci(6) and Ci(5)) take
over as the ones with the major volumes. In this way the
frazil spectrum resembles the one for the linear shelf in
Figure 3 with a buildup from the smaller to larger classes,
precipitation, and then a shift toward smaller crystals
thereafter.
[51] Melting of frazil ice (Figure 8) starts at 430 km,
caused by the thickening of the plume as it slows down.
This is at least partially an artifact caused by the mixed layer
approach. The frazil crystals in the upper half of the plume
will still be in supercooled water, and growing, while the
ones in the lower part will be surrounded by water that is
above the local freezing point. Because we assume that Ci is
well mixed, melting dominates once supercooling is confined to less than half the plume depth. When the plume
leaves the shelf at 448 km, Ci = 0.08 g/L. That is, the plume
holds a total of 7.7 kg/m2 of frazil ice in suspension.
9. Sensitivity of Foundation Ice Stream Results to
Variations in Forcing
[52] Temperature and salinity data from below the Filchner-Ronne Ice Shelf have been obtained, using hot waterdrilled access holes, at five sites during the 1990s [Nicholls
and Makinson, 1998; Nicholls et al., 2001]. Sites 4 and 5
were drilled at the southern tip of Berkner Island 200 km
north of the grounding line of Foundation Ice Stream
(Figure 5). Properties close to the seabed at the two sites
were quite similar, with a temperature close to 2.25C and
a salinity of around 34.65 psu for the bottom 200– 300 m.
The S4 case in Table 2 is forced with the observed temperature and salinity from site 4 as Ta and Sa between 700 m and
the depth of the grounding line (1400 m). Because of the low
Ta, melting is modest (up to 1.1 m/yr), and the plume reaches
Tf after 190 km. Frazil ice starts to precipitate at 200 km and
reaches a peak of 1 m/yr at 240 km, before the plume
becomes neutrally buoyant at 246 km (800 m depth).
[53] The conductivity-temperature-depth data indicate
that no water below the Filchner-Ronne Ice Shelf is warmer
or saltier than Western Shelf Water (WSW) with properties
Tw 1.9C and Sw 34.8 psu [Nicholls and Makinson,
1998; Nicholls et al., 2001]. This means that WSW acts as an
upper boundary on the heat content and salinity of the
ambient water. Tidal stirring is, in general, strong enough
to promote basal melting along the Ronne ice front, cooling
the inflowing WSW toward the temperatures quoted above
[Makinson, 2002]. The WSW case in Table 2 is forced by a
homogeneous ambient water column with Ta = 1.9C and
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Table 2. Model Response for Foundation Ice Stream
Parameter
, cm/s
U
, m
D
Maximum
Ci, g/L
ris, mm
Standard run
S4
WSW
UT = 0
0.5 UT
2.0 UT
Cd = 0.25 103
Cd = 15.0 103
AWIa, UT = 0
AWI
7.7
6.5
11.3
8.8
6.3
6.7
18.4
2.5
12.6
11.8
23.8
12.2
29.1
20.6
96.3
24.6
19.6
49.0
51.5
58.4
0.35
0.16
1.01
0.32
0.33
0.46
0.09
0.11
1.62
2.32
0.6
0.5
1.0
0.6
0.6
0.6
0.5
0.4
1.0
1.3
Maximum
(T Tf), C
0.53
0.33
59.2
0.51
0.55
0.55
1.23
0.27
0.80
58.6
103
103
103
103
103
103
103
103
103
103
R end
0
m0ds, m3/y
216 103
120 103
419 103
236 103
186 103
166 103
470 103
59 103
747 103
581 103
R end
0
f 0ds, m3/yr
43 103
23 103
236 103
31 103
30 103
4 103
71 103
0
421 103
1071 103
R end 0
3
0 p ds, m /yr
End,
km
35 103
21 103
0.4 103
31 103
30 103
0.5 103
54 103
0
271 103
109 103
446
246
716
423
589
474
430
416
605
736
a
AWI is Alfred Wegener Institute.
Sa = 34.8 psu, representing the maximum possible heat
transport to the grounding line. The warm WSW nearly
doubles the total melting of the plume, and the high salinity
of the upper water column means that the plume remains
buoyant until it reaches the surface at the ice front. The
melting peak increases from 1.65 m/yr in the standard run to
2.85 m/yr, and freezing starts at 415 km instead of 313 km.
[54] The impact of the added tidal speeds UT in the
standard run is demonstrated by comparison with a run
using UT = 0 throughout. In the latter case the precipitation
takes place in one major event at 380 km, with a peak of
1.9 m/yr, and the plume ends at 423 km when all frazil has
precipitated out. The frazil ice production is a lot higher in
the standard run because of continued growth up to the end
of the integration at 446 km. However, much frazil ice
remains
R end 0 in suspension at the end point, so the difference in
0 p ds between the two runs is only minor (Table 2).
[55] A lower tidal speed will occur during neap tides, and
the effect is illustrated by setting UT to half its value in
the standard run. This leads to one precipitation event, as
in the UT = 0 case, but the peak is broader and reaches only
1.5 m/yr. The lower mean speed and the higher mean
thickness of the plume are caused by deceleration and
thickening between 400 km and the end point at 589 km.
Higher tidal speeds will occur during spring tides, and with
UT set to twice its standard run value, there
R is hardly any
precipitation at all. The total frazil growth 0endf 0ds, shown
in Table 2, is only 10% of that in the standard run because
the net frazil ice production (melting subtracted from
freezing) is very low. Although frazil concentrations reach
higher values than in the standard run, nearly all of the frazil
ice stays in suspension and melts before the plume becomes
neutrally buoyant at 474 km.
[56] The roughness of the basal ice interface is not
known. Variations in the drag coefficient Cd alter the model
results, most directly by slowing down or speeding up the
plume. Decreasing Cd to 10% of the standard run value of
Cd = 2.5 103 more than doubles the speed and leads to a
thinner plume (Table 2). The high speed increases entrainment through equation (7) and leads to more melting of
basal ice. The high speed also leads to higher supercooling
as the plume ascends faster. Even though the plume
becomes supercooled as late as 363 km and ends as early
as 430 km in this case, more frazil has grown and precipitated because of the persistent high level of supercooling.
Another effect serving to increase precipitation is the
increase in the critical velocity for precipitation to occur
(equation (8)); that is, decreased turbulent mixing leads to
easier precipitation.
[57] Increasing Cd to 15.0 103 has the opposite effect
in all respects. The plume slows down and thickens, and
there is a large decrease in basal melting. Even though there
is frazil growth, nothing precipitates, and all frazil melts
within the plume.
[58] A new set of seabed bathymetry and ice shelf
thickness data suggests that the grounding line of the
Foundation Ice Stream is as deep as 2000 m [Lambrecht
et al., 1999]. This data set was obtained along the path
labeled AWI (Alfred Wegener Institute) in Figure 5. The
deeper grounding line increases melt rates significantly as
the in situ freezing point falls to 3.42C, as opposed to
2.95C in the standard run, and the ambient water is
effectively 0.5C warmer (AWI cases in Table 2). Without
tides the basal melting peaks at 17.5 m/yr; with tides it
peaks at 20 m/yr. The total melted volume is very similar
between the two AWI cases. The frazil ice growth is also
similar between the two AWI cases, at least up to 600 km,
but without tides most of it precipitates, and with tides most
of it stays in suspension.
[59] The AWI plume with tides is buoyant enough to keep
going all the way to the ice front, and the frazil volumes
increase to an overall maximum for all the runs on the
Foundation Ice Stream. With the vertical rise at the ice front
the ris reaches 1.3 mm, and the largest crystals are 2 mm in
radius. The total frazil growth exceeds the total melt in this
case, caused mainly by Ta being set below the surface
freezing point at depth. This implies that the ambient water
has already been cooled by melting basal ice elsewhere on
its way south before it is entrained into the plume [Nicholls
et al., 2001]. This south flowing current along Berkner
Island may also force the proposed AWI plume path farther
toward the west. An additional reason for the frazil growth
to exceed total melting is the heat lost by the plume in
warming the glacial ice that is melted from the ice shelf base
to Tf. This is a relatively small part of the total heat budget.
With the far-field temperature in the ice shelf, Tice, set to
3.5C, almost no heat goes into warming the ice, and the
total melt increases by 10% from that in the standard run.
With Ti = 27C, there is a decrease of 8% from the
standard run value.
[60] Overall, we find that the model results are most
sensitive to the specification of the ambient water properties. Lane-Serff [1995] demonstrated that the behavior of a
simple plume model was determined primarily by the
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Table 3. Model Results for Freezing in the Proposed Plume Paths From West to East on the Filchner-Ronne Ice Shelfa
Path
Region of
p0, km
Minimum
p0, m/yr
Minimum
m0, m/yr
ris, mm
End Depth, m
End
Ci, g/L
End
ris, mm
Evans Ice Stream
Carlson Inlet
Rutford Ice Stream
Institute Ice Stream
Foundation Ice Stream
AWI
Support Force Glacier
Recovery Glacier
Slessor Glacier
Bailey Ice Stream
164 – 245
225 – 308
321 – 415
308 – 396
343 – 448
543 – 652
276 – 440
303 – 330
297 – 330
243 – 260
0.67
1.05
1.46
0.41
0.82
2.73
0.70
1.16
0.16
0.11
0.13
0.27
0.16
0.11
0.28
0.57
0.26
0.08
0.08
0.10
0.4
0.6
0.6
0.4
0.6
1.0
1.0
0.6
0.4
0.3
319
511
466
392
420
0
0
0
0
0
0.0
0.0
0.02
0.0
0.08
2.32
1.91
1.12
1.22
1.38
0.4
0.5
1.3
1.6
1.3
1.3
1.3
a
Region of precipitation (p0) is given for values below 0.01 m/yr. The largest precipitation rate of frazil ice (minimum p0) may be
compared to the largest rates of basal freezing (minimum m0). The first significant frazil radius (ris) is for the largest precipitation event. The
draft of the ice shelf at the end of the integration is given (end depth), with the accompanying frazil concentration (end Ci) and significant
frazil radius (end ris).
temperature of the ambient water. In the model equations
both mixing and heat transfer at the ice shelf base are linear
functions of the plume velocity, and this simple proportionality lies behind the stability of the zones of melting and
freezing. The relationship between plume speed and precipitation rate is nonlinear, so precipitation shows a higher
sensitivity to the parameters that determine the plume
velocity than is shown by either melting or direct freezing
at the ice shelf base. We find that a sufficiently turbulent
plume can retain all its frazil crystals in suspension, eliminating precipitation altogether.
10. Discussion
[61] As our results are predictions of the unobserved
frazil crystal dimensions and concentrations that occur
beneath the Filchner-Ronne Ice Shelf, results may be
compared only with indirect observations. The location
and rate of frazil precipitation from the modeled ISW
plumes may be roughly compared with the occurrence of
marine ice layers from radar sounding data [Bombosch and
Jenkins, 1995] or freezing rates estimated from remote
sensing data [Joughin and Padman, 2003]. Apart from this,
grain sizes observed in cores of marine ice taken from the
Ronne Ice Shelf can provide an absolute upper bound to the
modeled frazil crystal sizes. Since grain growth will have
occurred since deposition, the frazil crystals that initially
settled onto the ice shelf base must have been smaller.
[62] Thin crystal plates have also been trawled from north
of the Filchner Ice Shelf [Dieckmann et al., 1986]. These
crystals were probably flowing northward from beneath the
ice shelf within a neutrally buoyant ISW plume [Foldvik
and Kvinge, 1974] and provide the only in situ data on
crystal sizes available to validate model results.
[63] The model as set up for the standard run described
above has been applied to the paths shown in Figure 5.
Results from these paths will be discussed in comparison
with the available data.
10.1. Ronne Ice Shelf
[64] A core drilled at site B13 (Figure 5), 30 km south of
the ice front, revealed evidence for a 90-m-thick layer of
marine ice [Eicken et al., 1994]. The presence of ice formed
from seawater was clearly seen in the measured isotopic
ratios and bulk salinities as well as in other observed
properties. The grain size in the marine ice layer was found
to increase with depth (and thus to decrease with age). This
counterintuitive result is probably caused by sediment
inclusions in the top layer that inhibit grain growth and
recrystallization, and here the mean cross-sectional area of
the grains was found to be 10 mm2. This mean crosssectional area corresponds to a frazil crystal radius of
1.8 mm. This is about twice the size of the largest crystals
that precipitate out of the model ISW plumes. Farther down
in the core the crystals have probably been able to grow
freely, and the mean cross-sectional area increases to
30 mm2, consistent with the estimated thermal history
of the ice [Eicken et al., 1994].
[65] A hot water-drilled borehole near B15 (Figure 5),
about 200 km from the ice front on a flow line from the
Foundation Ice Stream [Nixdorf et al., 1995], showed an
accumulation of unconsolidated frazil crystals, i.e., slush
ice, at the ice shelf base. This confirms the presence of loose
frazil ice crystals 80 km ‘‘downstream’’ of where the
Foundation plume becomes neutrally buoyant in the standard run. Even though this observation is qualitative, it
increases confidence in the model results.
[66] Model results for the flow of ISW beneath the Ronne
Ice Shelf along the other paths shown in Figure 5 are
qualitatively similar to those described in the standard
run. The inclusion of a frazil spectrum tends to widen
the peaks in precipitation compared with the results of
Bombosch and Jenkins [1995], but otherwise the areas of
precipitation are roughly the same, and values for the
different paths are tabulated in Table 3. Tides were included
for the Foundation and AWI paths. Results are similar to the
freezing rates estimated from remote sensing data [Joughin
and Padman, 2003], the only notable difference being more
compact areas toward the western coasts. This difference is
likely a result of the prescribed plume paths (which follow
tracks along which basal elevation data are available) of the
present model.
[67] The marine ice found along the Orville coast is thus
fed by frazil formation in the Evans plume, and the next
three plumes contribute to the marine ice west of Korff Ice
Rise. Along the plume paths between Korff and Henry Ice
Rises, no frazil growth is predicted, only basal freezing of
0.1 m/yr north of the rises. This suggests that the marine ice
north of the rises is fed mainly by frazil formation in the
Foundation plume. This is also indicated by the results of
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SMEDSRUD AND JENKINS: FRAZIL ICE FORMATION IN AN ISW PLUME
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Joughin and Padman [2003] in which the area of intense
freezing to the north and west of Henry Ice Rise appears to
be connected with ISW flow from the Foundation Ice
Stream rather than through the gaps between Doake Ice
Rumples.
[68] When tides are included for the Evans to Institute
paths, overall ice concentrations increase but precipitation
decreases, and the suspended frazil crystals eventually
melt. This is at least partially a model artifact, as water
near the ice-water interface stays supercooled, while the
plume mid-depth is slightly above its pressure freezing
point. Thus frazil then melts in the lower half but grows
in the upper half. In reality, the frazil would tend to be more
concentrated in the upper half of the plume, leading to net
growth, but our simple depth-averaged equations cannot
resolve such a structure.
10.2. Filchner Ice Shelf
[69] The ice crystals observed north of Filchner Ice Shelf
were found at 250 m depth [Dieckmann et al., 1986].
When the ice crystals where trawled, they turned out to be
thin plates (0.5 mm thick) with rough outer edges and
radii of 10 mm. It is worth noting that the trawl net had a
mesh size of 10 mm, so any crystals smaller than 5 mm in
radius may have escaped the trawl.
[70] Model runs for the Filchner Ice Shelf (Figure 5) all
produce a buoyant plume that reaches the ice front with
frazil in suspension. The plume then rises near vertically up
the ice front, the ascent from a depth of 280 m to the surface
taking 9 hours. The frazil crystal size spectrum for the
Support Force Glacier plume is shown in Figure 9 and
indicates that the frazil crystals grow to above 2 mm in
radius, i.e., still well below the 10 mm observed by
Dieckmann et al. [1986]. For this particular model run,
Ta from Dieckmann et al. [1986] was used with an upper
200-m-thick layer of water 0.1C above Tf. Suspended
frazil ice volumes increase from 1 g/L at the ice front to
1.7 g/L at the surface. Using the standard Ta, i.e., water at Tf,
further increases the frazil volume at the surface (Table 3).
[71] Using a frazil ice model including a single, evolving
crystal size, Bombosch [1998] indicated that 2.5-mm crystals could grow to a radius of 14 mm when rising 100 m at
1 cm/s in water 0.05C below Tf. This rapid growth might
be overestimated, as smaller crystals in the spectrum would
tend to use most of the supercooling, inhibiting the growth
rate of larger crystals. However, it is interesting to note
that the high level of supercooling was actually measured
at the time the crystals were trawled. The model of
Bombosch [1998] also indicates that the crystals observed
by Dieckmann et al. [1986] at 350-m depth melt before
reaching the surface. This result follows from the assumption that the crystals rise through a passive water column. In
the plume model presented here, the frazil crystals and
water are assumed to move together as a bulk volume, and
the crystals thus ‘‘lift’’ the ISW upward to the surface as in
the ‘‘conditional instability’’ described by Foldvik and
Kvinge [1974]. What happens in reality must be somewhere
between these two extremes.
[72] Once the ISW plume has reached the surface, the
integration stops, but in reality the suspended frazil crystals
and plume water would separate. With the ISW losing its
frazil ice, it would be 0.23 kg/m3 denser than the surround-
Figure 9. Frazil ice size spectrum for the Support Force
Glacier ISW plume, which rises vertically at the ice front at
430 km. Ambient temperature Ta from in situ observations
is used.
ing water and would sink. The water remains 0.02C
supercooled, so the crystals could continue to grow while
at the surface.
[73] Precipitation in the Support Force Glacier plume
(Figure 5 and Table 3) corresponds closely with the location
of the 120-m-thick marine ice described by Sandhäger
[1995]. Freezing rates estimated by Joughin and Padman
[2003] over the same area are slightly higher. For the other
plume paths on the Filchner Ice Shelf the ISW plume
becomes supercooled close to the ice front, leading to small
areas of precipitation as given in Table 3. All plumes reach
the ice front, and the frazil-laden water rises vertically to the
surface, creating high supercooling, efficient ice growth,
and ice concentrations above 1 g/L (Table 3).
[74] If the vertical rise of the ISW takes place during a
time when the tide is flowing south, the tidal current should
prolong the rise and allow the crystal size to increase further.
We cannot simulate this effect since we only add an RMS
tidal current, which increases mixing but otherwise does
not affect the plume evolution. Adding RMS tidal currents of
7 cm/s to the Support Force plume only decreases precipitation to close to zero during the last 100 km.
[ 75 ] A measurement similar to the one made by
Dieckmann et al. [1986] was made north of the Amery
Ice Shelf, but in the latter case the overall mass of ice was
measured [Penrose et al., 1994]. The trawl had a finer mesh
size of 1.5 mm, and crystals were reported to have radii in
the range 5 –12 mm. The mass of frazil ice divided by the
trawled water volume implies concentrations between 34
and 129 106 g/L for the two trawls made. This is a lower
estimate of the in situ frazil concentration, as no account
was taken of melting as the trawl was lifted up through the
50 m of surface waters that were roughly 0.5C above Tf.
[76] As the plume model only calculates Ci in the upper
mixed layer beneath the ice shelf, it is hard to compare the
measured concentrations with model results. As with the
observations of Dieckmann et al. [1986], extremely high
supercooling, in this case 0.5C, was recorded at the time
of the trawl. Such temperatures are consistent with low
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SMEDSRUD AND JENKINS: FRAZIL ICE FORMATION IN AN ISW PLUME
concentrations of exclusively large crystals (ri 5.0 mm)
and suggest that conditions might be different in a lowerturbulence environment away from solid boundaries. Certainly, secondary nucleation is likely to be ineffective with
crystal number concentrations of 1 m3 or lower [Penrose
et al., 1994]. There is evidence that upwelling events such
as those simulated by the model and postulated by Foldvik
and Kvinge [1974] do indeed occur [e.g., Fahrbach and
El Naggar, 2001], but in these cases, there are no contemporaneous measurements of ice crystal sizes.
11. Summary
[77] Our results are the first predictions of the frazil
crystal dimensions and concentrations that occur beneath
ice shelves. Below the Filchner-Ronne Ice Shelf, crystal
radii up to 1.0 mm are suggested, although the largest
proportion (by volume) of the crystals in suspension are
around 0.5 mm in radius. Maximum concentrations produced in the model runs range from 0.03 to 2.3 g/L. The
suspended frazil ice adds buoyancy to the ISW because the
bulk density of the ice-water mixture is up to 0.1 kg/m3
lower than the density of the water fraction alone. This
added buoyancy helps drive the sub-ice shelf circulation,
increasing the speed of the outflowing ISW.
[78] The addition of the frazil crystal population dynamics
has enabled us to clarify some important aspects of the
behavior of a simpler model [Jenkins and Bombosch, 1995].
In particular, the oscillations in supercooling and ice concentration that were apparent when the earlier model was
applied to an ice shelf with constant basal slope are no longer
present. These oscillations were clearly artifacts of the
restriction to a single crystal size. Simulated zones of
accumulation are only slightly modified by the new version
of the model. The reason is that the location at which the
ISW plume becomes supercooled, allowing frazil growth to
commence, is determined by the depth of origin of the plume
and the ambient water temperature. Once frazil growth has
started, the new model tends to produce broader, slightly
lower peaks of precipitation than the earlier model did.
[79] In the model runs for the Filchner-Ronne Ice Shelf,
significant precipitation occurs for crystals of radius 0.5–
1.0 mm. After the first precipitation event, smaller crystals
follow as the plume speed decreases because of the loss of
buoyancy. In this way, larger crystals are deposited first, and
smaller ones are deposited farther downstream. We have no
observational evidence with which to verify these results.
All we can say is that the minimum grain size of 1.8 mm,
found in a core of marine ice extracted from Filchner-Ronne
Ice Shelf [Eicken et al., 1994], is consistent with crystals of
these dimensions or smaller making up the initial accumulation of ice.
[80] The focusing of frazil precipitation by the dynamics
of the plume is an important feature in the model. A fast
flowing, highly turbulent plume can retain its entire crystal
load in suspension, while a decelerating plume produces
rapid precipitation as the loss of buoyancy further slows the
plume in a positive feedback loop. An increase in plume
speed both decreases precipitation and increases the effective cooling rate (i.e., the rate at which the pressure freezing
point rises with the falling pressure), producing yet more
crystals.
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[81] It is not the case that crystals of sufficient size to
precipitate will always develop, whatever the speed of the
plume. The reason is that the secondary nucleation process
ensures a continuous supply of very small seed crystals,
which grow rapidly and quench the supercooling. With the
level of supercooling thus limited, the growth of the largest
crystals is very slow, and in a sufficiently turbulent plume,
crystals that are large enough to precipitate never grow in
significant numbers.
[82] Tides increase the frictional drag felt by the plume,
so there is a general deceleration along the plume path.
However, tides also act to keep crystals in suspension by
restricting precipitation. This effect overrides the increased
frictional drag in freezing areas and increases the plume
buoyancy and speed. The plume then stays buoyant longer,
but entrainment of warmer water eventually supplies
enough heat to overcome the effective cooling caused by
the plume’s rise, and the frazil crystals end up melting while
still in suspension.
[83] The locations and rates at which ice crystal precipitation is simulated by the model along our chosen plume
paths are in reasonable agreement with the pattern of basal
freezing derived by Joughin and Padman [2003] from
remote sensing of Filchner-Ronne Ice Shelf (Table 3).
However, the net melting rates produced by the individual
plume models cannot be directly compared with the net
melting calculated by Joughin and Padman [2003] for the
entire ice shelf. Our plume paths all originate at the deep
grounding lines of the major ice streams, where the highest
melt rates are found. Between the proposed paths the ice
base is shallower and the melt rates are correspondingly
lower, so no simple extrapolation of our results into these
regions is possible.
12. Conclusions
[84] Accumulation of marine ice beneath Antarctic ice
shelves may be simulated with a relatively simple model of
frazil ice growth within an ice shelf water plume. The model
shows how the processes of crystal growth and deposition
influence both the spectrum of crystal sizes that are held in
suspension and the buoyancy and flow of the ISW. Model
results of frazil crystal size and concentrations are comparable with measurements at depths north of the ice shelves.
[85] The model, with an evolving population of frazil
crystal sizes, is able to reproduce the zones of basal
accumulation observed on Filchner-Ronne Ice Shelf. When
the frazil ice crystals reach a critical size, usually a radius of
0.8 mm, they tend to leave the ISW by precipitating upward
onto the ice shelf base, thus forming marine ice. Precipitation is generally in the range 0.5– 2 m/yr but can reach up to
6 m/yr under specific conditions.
[86] In general, the ISW flow is controlled by the basal
slope of the ice shelf. Frazil ice formation acts as a positive
feedback mechanism on the plume speed, as more crystals
in suspension increase the buoyancy and hence the speed of
the plume.
[87] If the ISW plume reaches the ice front, a rapid rise of
the water and crystals toward the sea surface is predicted.
The pressure release is then much faster than when the
plume is beneath the ice shelf, and the crystals can grow to
2.5 mm in radius. When the ice-water mixture reaches the
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surface, the water fraction is 0.1 kg/m3 denser than the
surrounding water. The ISW would therefore tend to sink,
leaving the crystals to form a surface ice cover.
[88] The primary limitation of the current model is the
greatly simplified representation of the ocean dynamics. To
remove the depth averaging and the assumption of a wellmixed layer would require the inclusion of a vertical
dimension in the model, while to include the effects of
Earth’s rotation would require an extension to two horizontal dimensions. Thus further progress in the modeling of
frazil ice beneath ice shelves will require the processes
described in this paper to be incorporated into more sophisticated, two- or three-dimensional ocean circulation models.
[89] Acknowledgments. This research has been supported through a
Marie Curie Fellowship of the European Community program ‘‘Improving
Human Research Potential and the Socio-economic Knowledge Base’’
under contract HPMF-CT-2000-01085. We are grateful to Astrid Lambrecht
(Alfred Wegener Institute) for sharing the ice shelf thickness data from the
Foundation Ice Stream and Keith Makinson (BAS) for suggestions and
model results on the tidal velocities.
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