The Ice-Ocean Interface Miles McPhee McPhee Research Anecdotal history Heat and salt transfer (freezing) Heat and salt transfer (melting)

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

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, Using sea ice to measure vertical heat flux in the ocean. J. Geophys. Res., 87,

Perovich, D. K., and B. Elder. Estimates of ocean heat flux at SHEBA, Geophys. Res. Lett., 29 (9), doi: /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, Initial ice thickness, 1.2 m

My theory for ice edge bands (McPhee, M.G.. J. Geophys. Res., 88, , 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=w 0 +w p Latent heat source or sink Turbulent heat flux from ocean Thermal conduction into ice Advection into control volume Advection out of control volume Ice water Thermal Balance at the Ice/Ocean Interface T 0, S 0

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

Latent heat exchange at the interface Turbulent ocean heat flux

w=w 0 +w p Turbulent salt flux from ocean Advection into control volume Advection out of control volume Ice Salt Balance at the Ice/Ocean Interface S 0 S ice

“Kinematic” Interface Heat Equation Interface Salt Conservation Equation small Interface freezing condition

Mellor, G.L., M.G. McPhee, and M. Steele Ice-seawater turbulent boundary layer interaction with melting or freezing. J. Phys. Oceanogr., 16,  T=1 K  T=2 K Inertial periods w 0 ~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, z 0t and z 0S, 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.

measured model w/laminar sublayers ablation rates

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, SHEBA

“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

Collaborative Study of Ice-Ocean Interaction in Svalbard Turbulence Mast Ice Temperature & Solid Fraction Supercoolometer

SonTek ADVOcean (5 MHz) SBE 03 thermometer SBE 07 micro- conductivity meter SBE 04 conductivity meter SonTek Instrument Cluster Ice T-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

Impact of exchange coefficient ratio on melting with

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h/s h/sh/s

No Boundary Layer Supercooling at Van Mijen Fjord

Simulations for  =1 agree with observed profiles of T-T f Simulations for  =40 disagree with observed profiles of T-T f

How could C s = C h ? 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 Hanson maintained an array of depth gauges at the main station Big Bear. Here are 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 cm by the end of melt season. “False bottom” 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.

Assuming a linear temperature gradient in the thin false bottom: If the upper layer is fresh, at temperature presumably near freezing:

This modifies the heat equation slightly, but leads to a similar quadratic for S 0

Estimated friction velocity for different values of bottom surface roughness, z 0 = 0.6 and 6 cm respectively Changes in ice bottom elevation relative to a reference level on day 190, at the “false bottom” sites. Note that false bottoms appear to form at all sites during the relative calm starting about day 205, and start migrating upward on or near day 210, when the wind picks up

false bottom “true” bottom upward heat flux down “water table”

Winter ARctic Polynya Study Special thanks to Anders Sirevaag, Ilker Fer and Ursula Schauer

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