Heat and mass transfer Processes - Focus on Polar Regions during Winter
Processes cooling surface water during the polar winter are longwave emission, sensible heat transfer and latent heat transfer
Wintertime cooling rates over the East Greenland Sea during winter:
Q = cooling rate = 200 W m -2 = 200 J s -1 m -2

Heat and mass transfer Processes - Focus on Polar Regions during Winter
Important Simplification: The cooling only effects the surface mixed layer, depth =

Z~100 m
1) The cooling can chill the seawater: Q =

C

Z (dT/dt)
Or, if the seawater temperature is at the freezing point,
2) The cooling forms sea ice: Q =
 i
L f
(dZ/dt)

Heat and mass transfer Processes - Focus on Polar Regions during Winter
Estimate the water cooling rate and the ice thickening rate assuming:

=1028 kg/m 3 ; C=4000 J kg -1 o C -1 ;

Z=100 m; L f
=0.33x10
6 J kg -1 ;
 i
= 500 kg/m 3 and
Q = 200 J s -1 m -2
Water cooling rate = (dT/dt) ~ 1 o C/month
Ice thickening rate = (dZ/dt) ~ 3 meter/month

Heat and mass transfer – Focus on Polar Regions during Winter
There are complications:
1) Once sea ice forms it decreases the magnitude of the Q. Calculations shown previously overestimate the ice thickening rate for wintertime conditions in the East Greenland Sea (dZ/dt ~ 1 meter/month is more reasonable)
2) Constitutional Supercooling - before we discuss this we need to talk about the chemical thermodynamics of a solution/ice system

SEA ICE FORMATION – CURRY AND WEBSTER, pp. 119-126, pp. 151-156, pp. 255-257
Chemical thermodynamics of sea ice formation –
Seawater (one phase; liquid) is composed of two components (water and salt), so the Gibb’s phase rule indicates three degrees of freedom
We measure pressure, salinity and temperature. It follows that the thermodynamic state of seawater is "fixed" by measurement (at least where we make measurements)
Freezing occurs at the ocean surface, pressure is constant at a known value (1 bar), hence only two of three degrees of freedom are actually "free"
When chilled to the freezing point an additional phase (solid ice) is formed. Now the system has only one degree of freedom. Thus prescribing, or measuring, the water temperature implies that the salinity of the water is constrained and vice versa
This relationship is called the liquidus curve or liquidus function:
T fp
= T o
– K S
Where: T fp
=freezing point, T o
=273, K=positive constant and S is the salinity

CURRY AND WEBSTER -
FIGURE 4.8
-The liquidus describes the temperature/salinity relationship
-For typical salinities (35 psu) the freezing point is ~ -2 o C
-Imagine a mixed layer containing seawater at point “B”
-Cooling results in freezing of a fraction of the water
-Freezing results in a rejection of salt into the remaining liquid
-The ice is purified (we will see an important caveat to this)
-Salt rejected from the ice enhances the salinity of the water immediately below the ice/water interface

Constitutional Supercooling
Sea Ice
Environmental Temp
Seawater
Environmental Temp and Freezing Point
Temp
Heat
Salinity
Note: Ice growth rates are largest where the difference between the freezing point temperature curve and the environmental temp curve is largest. In this region a phenomenon called constitutional supercooling can develop
Salinity

Constitutional Supercooling:
At the ice/water interface, the fluxes of heat and salt are carried by molecular diffusion (Fick’s Law type formulation)
F
Q
  
Q

C
   dT dz
F
S
  
S
   dS dz
The thermal diffusivity (

Q
) of seawater is one hundred times larger than salt diffusivity (

S
) in seawater
The heat and salt fluxes are coupled, i.e. the heat flux "drives" ice formation and thus increases in salinity (note: salt is excluded from the growing ice)
The salinity gradient must be appreciable to transport the salt
It follows that the difference between the blue and red curves is a maximum close to, but not right at, the ice/water interface
The ice growth rate is proportional to the “distance” between the blue and red curves
Perturbations at a flat ice/water interface become unstable, the perturbations amplify, "ice fingers propagate" away from the interface
Brine occlusions forming between the ice fingers, can seal off, contaminating the ice with salty brine (bad news if you melt sea ice for a drink)

Constitutional Supercooling at the ice/solution interface:
Ice Solution

Freshly formed sea ice, when melted, has appreciable salt in it (~ 10 psu)
This salinity is not trapped in the crystals but within brine channels formed during freezing
Constitutional supercooling , including the processes of ice growth and brine occlusion results in brine entrapment within sea ice
With aging, particularly over a complete season, ice becomes less saline as brine drains from the brine pockets.
I.e., the sea ice becomes less salty with age