The Ice-Ocean InterfaceMiles McPhee

McPhee Research

• Anecdotal history

• Heat and salt transfer (freezing)

• Heat and salt transfer (melting)

Maykut, G.A., and N. Untersteiner, 1971. Some results from a time-dependent thermodynamic model of sea ice, J. Geophys. Res., 76, 1550-1575.

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

McPhee, M.G., and N. Untersteiner, 1982. Using sea ice to measure vertical heat flux in the ocean. J. Geophys. Res., 87, 2071-2074.

formation ice ofheat latent theis

reference thebelowcontent heat in change total theis

level reference agh flux throuheat of integral time theis where

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L

s

f

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F

Perovich, D. K., and B. Elder. Estimates of ocean heat flux at SHEBA, Geophys. Res. Lett., 29 (9), doi: 10.1029/2001GL014171, 2002.

. 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

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.

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

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

Heat conduction through the ice

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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

“Kinematic” Interface Heat Equation

Interface Salt Conservation Equation

0'' 00pp0 wQTTwTwq L

small

0'' 0ice0 SSwSw

Interface freezing condition

000 )( mSSTT f

ku

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kz

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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

“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.”

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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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

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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!

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

Freezing

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

Collaborative Study of Ice-Ocean Interaction in Svalbard

Turbulence Mast

Ice Temperature& Solid Fraction

Supercoolometer

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

Supercoolometer:

Seamore ROV

SBE 39 T Probe

Heater

SBE-19+Temperature & Conductivity

Optical Backscatter

Water In

Heat and Salt Fluxes at 1 m Below Ice

Temperature Profiles in Ice:Range of Possible Heat Fluxes, q

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

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ROV23/7/20011153Z

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-0.08 -0.06 -0.04 -0.02 0 0.02 0.04

0

2

4

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8

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Boundary Layer T - Tfreezing(S,p)

T-Tfreeze (°C)

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m)

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No Boundary Layer Supercooling at Van Mijen Fjord

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Boundary Layer T - Tfreezing(S,p)

T-Tfreeze (°C)

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Day 1

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= 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

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

Melting

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.

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.

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.

.

Fresh W a ter Layer

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Sea water ~ slightly abo ve freezing

Multiyear Ice

False Bottom

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Assuming a linear temperature gradient in the thin false bottom:

If the upper layer is fresh, at temperature presumably near freezing:

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This modifies the heat equation slightly,but leads to a similar quadratic for S0

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

false bottom “true” bottomupward heat flux

down

“water table”

Winter ARctic Polynya Study -- 2003

Special thanks to Anders Sirevaag, Ilker Fer and Ursula Schauer

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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