Proglacial Lakes - Freezing of Lakes and the Evolution of their Ice Cover - page 193

z max ¼ 1
j

Q T
Q T þ

log ð 6 : 14 Þ

Q 0

).
Lower conductivity gives higher temperature, since the heat does not escape easily out of
the ice. Example, if QT T *

The temperature increase from the surface to the depth z max scales with (Q 0 + Q T )/(k ʺ

50 W m − 2 , Q 0 * - 25 W m − 2 1m − 1 , we have and ʺ ¼

z max * C. Thus, when the melting stage is achieved inside

the surface layer, the surface temperature is still quite low. According to observations in
Lake Suvivesi, the surface temperature was less than

0.69 m and T(z max ) T 0 * 20 °

-

C in this instant.
When the surface heat balance is negative (Q 0 < 0), the lake has an ice cover. This is
clear in the early stages of lake development, since ice formation starts well beneath the
surface. Heat

- 10 °

fl flux through the ice cover equals kT 0 /h, and at equilibrium it equals the heat

fl flux from the lake body to the bottom of the ice cover. The surface ice layer also becomes

thinner by sublimation, which is signi

cant in dry climate regions. Convective mixing
keeps the water temperature at the freezing point. In case conditions become favourable
for the cold skin development (z max > 0), a thin ice sheet will form at the surface.
Recurrent supraglacial lakes close up in winter. They start to freeze down from the
upper surface, as lakes usually do (see Chap. 4 ) , but also up from the bottom. The surface
heat losses are of the order of

50 W m − 2 , while the bottom loss is much smaller

*-

2Wm − 2 . These losses correspond to ice growth rates of 14 or 0.6 mm d − 1 ,
respectively.
In the closure season, the net solar plus atmospheric heat

*-

flux is negative, and the air
temperature is below the freezing point. Then the ice growth is obtained from Zubov

fl

' s

formula (see Eq. 4.41 ):

p

a 2 S h ¼ þ b 2 b ð 6 : 15 Þ

The parameter a depends on the physical properties of ice and varies very little, and in
snow-free conditions, as here, also b can be

fixed to represent typical atmospheric con-

C day) − 1/2

ditions (see Sect. 4.3 ): we can take a ≈ 3.3 cm ( ° and b ≈ 10 cm. If air

temperature is continuously below 0 ° C and the average is 15 ° C, the freezing-degree-

-

days sum to S ¼ 2,250 ° C day in 5 months, then we have h ¼ 1.48 m; in 10 months, the

2.13 m. In addition, the lake also loses heat to
the deeper ice sheet. The bottom heat loss adds a little to the growth of ice. If the
temperature decreases downward by 1

figures would be S ¼ 4,500 ° C day and h ¼

Cm − 1 , the resulting heat loss is 2 W m − 2 and in
5 months this gives 9 cm ice growth. The thickness of ice is not very sensitive to air
temperature variations. In the present case,

°

C overall change in the air temperature
would change the ice thickness from 1.48 m by less than 20 cm, to 1.31 m or 1.63 m. The
exchange of heat with the underlying ice sheet is quite stable.
The summer and winter evolution of the lake would change in a changing climate,
toward a pure blue ice layer or a perennial lake. The lake growth and closing scales are
shown by Eqs. ( 6.11 ) and ( 6.15 ), respectively. For no lake formation, the summer heat

± 3 °