Thermodynamics of Seasonal Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 106

(c)

40

20

0

-20

-40

-60

1 5 10 15 20 25 30

a. Jan. 2003

40

20

0

-20

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1 5 10 15 20 25 30

b. Mar. 2003

Fig. 4.5

(continued)

In addition, the thermal conductivity of brine is a little less than that of ice, and therefore
the thermal conductivity of saline ice is slightly smaller than that of fresh water ice.

4.2.2 Congelation Ice Growth

In the growth of congelation ice, the latent heat of freezing released at the bottom of the
ice sheet needs to be conducted through the ice to the atmosphere. This conduction is
predominantly vertical. The growth of the ice sheet continues as long as the conductive
heat

flux from the water body to the ice. The
thicker the ice, the greater is the conduction distance and the slower is the subsequent rate
of ice growth. We may say that congelation ice growth is

fl flux through the ice is greater than the heat fl

' self-isolative ' (Stefan 1891;

Barnes 1928).
The temperature of ice interior changes by conduction and solar heating. The equation
of vertical heat transfer is written as:

@
@ t

Þ ¼ @
@ z

k @ T

@ z Q T e Kz

ð q cT ; T T f ð 4 : 24 Þ

where c is the specific heat of ice, and k is the thermal conductivity of ice, and the vertical
co-ordinate z is positive downward with zero at the ice surface. The thermal properties of