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The Ice-Ocean InterfaceMiles McPhee
McPhee Research
• Anecdotal history
• Heat and salt transfer (freezing)
• Heat and salt transfer (melting)
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Maykut, G.A., and N. Untersteiner, 1971. Some results from a time-dependent thermodynamic model of sea ice, J. Geophys. Res., 76, 1550-1575.
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Estimates of upward heat flux out of the Atlantic layer based on temperature changes and circulation, adapted from Treshnikov and Baranov (1972, Water circulation in the Arctic Basin)
Alaska
Greenland
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McPhee, M.G., and N. Untersteiner, 1982. Using sea ice to measure vertical heat flux in the ocean. J. Geophys. Res., 87, 2071-2074.
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formation ice ofheat latent theis
reference thebelowcontent heat in change total theis
level reference agh flux throuheat of integral time theis where
)(1
L
s
f
Lsfw
Q
Q
Q
QQQt
F
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Perovich, D. K., and B. Elder. Estimates of ocean heat flux at SHEBA, Geophys. Res. Lett., 29 (9), doi: 10.1029/2001GL014171, 2002.
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. Martin, S., P. Kauffman, and C. Parkinson, 1983: The movement and decay of ice edge bands in the winter Bering Sea, J. Geophys. Res.,88, 2803-2812.
Initial ice thickness, 1.2 m
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My theory for ice edge bands (McPhee, M.G.. J. Geophys. Res., 88, 2827-2835, 1983): rapidly melting ice stabilizes the OBL, reducing its effective drag. The band separates from the pack because the leading edge always encounters warm water and rapidly cools the water as it passes over.
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w=w0+wp
Latent heat source or sink
Turbulent heat flux from ocean
Thermal conduction into iceAdvection into control volume
Advection out of control volume
dzdT
Ice
water
Thermal Balance at the Ice/Ocean Interface
T0, S0
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Heat Equation at the Ice/Ocean Interface
• Heat conduction through the ice
• Sensible heat from percolation of fresh water through the ice column
• Latent exchange at the interface
• Turbulent heat flux from (or to) the ocean
Small
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Heat conduction through the ice
1-
1-1-op
p
3-
ice
1-o1-
1-1-fresh
icefresh
pice
ice
s mK unitsflux with heat ice theof form kinematic"" theis
Kkg J 4019psu) 30 C, 64.1( :salinity and
re temperatuoffunction weak seawater, ofheat specific is
m kgdensity water is
scale)salinity (practicalsalinity ice is
C m J 117.0
Km J 04.2
ice sea ofty conductivi thermal/
q
c
c
S
K
TSKK
qcTKdz
dTKH
i
zii
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Latent heat exchange at the interface
(K) units erature with tempheat,
specificby divided volumebrineby adjustedfusion ofheat latent is Q
kg kJ 333.5 ice,fresh for fusion ofheat latent theis
)03.01(
L
1-fresh
0icefresh0Lp0iceL
L
wSLwQcwLH
Turbulent ocean heat flux
field"far " theof re temperatu theis
stress turbulentofroot square elocity,friction v interface is
tcoefficien exchange essdimensionl a is
''
w
0*
H
0w0*Hp0pT
T
u
a
TTucTwcH
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w=w0+wp
Turbulent salt flux from ocean
Advection into control volume
Advection out of control volume
Ice
Salt Balance at the Ice/Ocean Interface
S0
Sice
00*0'' SSuSw wS
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“Kinematic” Interface Heat Equation
Interface Salt Conservation Equation
0'' 00pp0 wQTTwTwq L
small
0'' 0ice0 SSwSw
Interface freezing condition
000 )( mSSTT f
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ku
kz
ku
kz
zzz
SK
zz
SSku
zzz
TK
zz
TTku
ss
tt
s
t
H
H
00
00
0
00
0
,
,)/ln(
,)/ln(
Mellor, G.L., M.G. McPhee, and M. Steele. 1986. Ice-seawater turbulent boundary layer interaction with melting or freezing. J. Phys. Oceanogr., 16, 1829-1846.
T=1 K T=2 K
Inertial periods
w0~1/2 to 1 m/day
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“Throughout the mixed layer the [MY2-1/2 model] calculations produced a small amount of supercooling, implying the creation of frazil ice. The process may be understood as follows. Over the domain of the model the average change in salinity is the time integral of the surface salinity flux, since there is no flux at the bottom. Similarly, the average change in temperature is the time integral of kinematic heat flux. If the entire water column started at its (surface) freezing point, it will remain on the freezing line if the ratio of surface fluxes … is equal to m. This will be true only if the eddy diffusivities and surface roughnesses for heat and salt, z0t and z0S, are equal. In the model, the temperature surface roughness is larger than the salinity roughness, which means that across the surface layer heat is transported faster than salt, supercooling the water column. The effect is small. In these calculations, if the supercooled water were restored to equilibrium, the amount of frazil production amounts to only a half percent of the total.”
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The first direct measurements of turbulent heat flux in the ocean were made from drifting ice north of Fram Strait during the 1984 MIZEX project.
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00*0'' TTuTw wT
rh
pTms
z hturbTsm
khu
K
dzu
uTw
TzT
)/()/(1
'
/''
)(
0*
00*
0*0
0
8.0
///
/1
32
r
kk rShTmsSmsST
TslT
70/35 ST
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measured
model w/laminar sublayers
ablation rates
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)('' 0*0 wfwH STTucTw
A simpler approach is just to assume that a bulk heat exchange coefficient describes the exchange:
From: McPhee, Kottmeier, Morison, 1999, J. Phys. Oceanogr., 29, 1166-1179.
SHEBA
/Re 00** zu
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“Throughout the mixed layer the [MY2-1/2 model] calculations produced a small amount of supercooling, implying the creation of frazil ice. The process may be understood as follows… The effect is small…” No longer true! Now it amounts to about a third!
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Straight congelation growth Growth with frazil accretion
Holland, M. M., J. A. Curry, and J. L. Schramm, 1997: Modeling the thermodynamics of a sea ice
thickness distribution 2. Sea ice/ocean interactions, J. Geophys. Res., 102, 23,093-23,107
Holland et al. found in their coupled model that frazil accretion under different ice types resulted in increased equilibrium thickness
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Freezing
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Impact of exchange coefficient ratio on freezing with 01.00* u
1Sh cc
30Sh cc
30Sh cc
1/ Sh
30/ Sh
1/ Sh
30/ Sh
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Collaborative Study of Ice-Ocean Interaction in Svalbard
Turbulence Mast
Ice Temperature& Solid Fraction
Supercoolometer
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SonTekADVOcean (5 MHz)
SBE 03 thermometer
SBE 07 micro-conductivity meter
SBE 04 conductivitymeter
SonTek Instrument Cluster
.
8
8
IceT-string
ROV-CTD
0.6 m
1 m
Van Mijen Fjord Instruments
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Supercoolometer:
Seamore ROV
SBE 39 T Probe
Heater
SBE-19+Temperature & Conductivity
Optical Backscatter
Water In
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Heat and Salt Fluxes at 1 m Below Ice
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Temperature Profiles in Ice:Range of Possible Heat Fluxes, q
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VanMijenFjord conditions: u*=0.003 m s-1, S=34.2 psu, T at freezing
Ice Balance:Only matches ocean fluxes for near 1
h/s
h/s
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ROV23/7/20011153Z
.
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04
0
2
4
6
8
10
12
Boundary Layer T - Tfreezing(S,p)
T-Tfreeze (°C)
Dis
tan
ce
Be
low
Ic
e-O
ce
an
In
terf
ac
e (
m)
Supercooled
No Boundary Layer Supercooling at Van Mijen Fjord
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.
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04
0
2
4
6
8
10
12
ROV
Boundary Layer T - Tfreezing(S,p)
T-Tfreeze (°C)
Dis
tan
ce
Be
low
Ic
e-O
ce
an
In
terf
ac
e (
m)
Day 1
Supercooled
= 40
= 1
Day 1
Day 4
= 40Day 4
ROV 4
ROV 16
Simulations for =1 agree with observed profiles of T-Tf
Simulations for =40 disagree with observed profiles of T-Tf
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How could Cs= Ch?
Implies fluxes are not dependent on diffusion across molecular sublayers, w’, T’, S’ = 0 at interface.
Answer: The growing ice is a mushy layer with active convection.
Mushy layers can be viewed as the consequence of morphological instabilities of would-be planar solid-liquid phase boundaries (Mullins & Sereka, 1964), and serve to reduce or eliminate regions of constitutional supercooling in the system (Worster, 1986; Fowler, 1987) that arise due to the slow diffusion of chemical species relative to heat. Worster, 1992
Worster, M.G., 1992, The Dynamics of Mushy Layers, in Interactive Dynamics of Convection and Solidification, Davis, Huppert, Muller and Worster eds., Kluwer Academic Publishers, London
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Melting
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Serendipity: Dirk’s Problem
After the UNIS 2000 AGF211 course, a student Dirk Notz contacted me asking if I could recommend a suitable air/sea/ice interaction problem for a Master’s thesis at the U. Hamburg. I tentatively suggested he look at the “false bottom” question. He did: Notz et al., 2003, J. Geophys. Res.
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During the 1975 AIDJEX Project in the Beaufort Gyre, Arne Hansonmaintained an array of depth gauges at the main station Big Bear. Hereare examples showing a decrease in ice thickness for thick ice, but an increase at several gauges in initially thin ice.
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Thick ice (BB-4 – BB-6) ablated 30-40 cm by the end of melt season. “Falsebottom” gauges showed very little overall ablation during the summer. The box indicates a 10-day period beginning in late July, when false bottoms apparently formed at several sites.
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.
Fresh W a ter Layer
Tu p =0 o C
Tw = -1.7 o C
h
Sea water ~ slightly abo ve freezing
Multiyear Ice
False Bottom
T 0 S 0 w T 0 w S 0 u *0
h
TT
c
K
c
H up
p
i
p
ice 0
Assuming a linear temperature gradient in the thin false bottom:
If the upper layer is fresh, at temperature presumably near freezing:
h
mST
c
K
c
H up
p
i
p
ice 0
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ice2up1wH
21
hLL
h0*p1
iceL2wLHice0iceL2LH
2
0
)1(
/
thicknessice is where
provided
0)()(
SmTTT
mA
QT
h
hucK
SQSTTSSASQTTAS
S
i
This modifies the heat equation slightly,but leads to a similar quadratic for S0
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Estimated frictionvelocity for differentvalues of bottom surface roughness,z0 = 0.6 and 6 cm respectively
Changes in icebottom elevationrelative to a referencelevel on day 190, atthe “false bottom” sites.
Note that false bottoms appear to form at all sites during the relative calmstarting about day 205, and start migrating upward on or near day 210, whenthe wind picks up
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false bottom “true” bottomupward heat flux
down
“water table”
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Winter ARctic Polynya Study -- 2003
Special thanks to Anders Sirevaag, Ilker Fer and Ursula Schauer
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psu 4
mK 7.21/
s mK 1054.6''
s mpsu 1073.1''
psu 34.430 C -0.962
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Conclusions
• During melting, double diffusion effects are paramount, and ice dissolves as much as it melts
• False bottoms (a) may protect thin ice from the impact of ocean heat flux during summer; (b) provide a means of determining the ratio of diffusivities appropriate for melting ice.
• WARPS provided the first actual direct estimates of the molecular sublayer exchange coefficients during rapid melting.
• During freezing, it appears that double diffusive tendencies are relieved near the interface by differential ice growth, so that supercooling and frazil production are limited during congelation growth