Thermodynamics of Seasonal Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 111

providing weight to submerge the ice. The maximum snow-ice thickness is then 2/3 h s .

The insulation effect can be strong so that semi-permanent slush layers form inside the ice
sheet. Furthermore, a new

*

flooding event produces slush on top of the existing snow-ice,
and thus it is possible that alternating slush and snow-ice layers exist. However, published
data indicate only the existence of a single slush layer inside the ice sheet.
In melt

fl

freeze metamorphosis, liquid water is provided by the snow layer itself.
Meltwater may be convected down before freezing and will form snow-ice thereafter. The
maximum thickness of snow-ice produced by this mechanism is h s /3. When the volume of
meltwater is small, hard crust layers or ice lenses may result from freeze-melt meta-
morphosis. In case liquid precipitation is the source of the water, in principle the maxi-
mum snow-ice thickness is

-

2/3 h s . Data from the coastal landfast ice of Sakhalin has
shown that the springtime snow-ice formation (melt

*

freeze cycles and liquid precipita-
tion) may add up to 20 cm to the total ice thickness of about 100 cm (Shirasawa et al.
2005).

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4.2.4 Frazil Ice Growth

Frazil ice forms in turbulent, supercooled open water (e.g., Michel 1978; Martin 1981).
Ice crystals flow free in turbulent eddies and are transported by the mean current. They
have buoyancy, which overcomes the turbulence when the frazil mass is large enough,
and then a

floating surface frazil ice layer forms. In lakes frazil ice may form the primary
ice. In large lakes, there may be quasi-persistent open water areas to serve as frazil ice
source areas. Because the surface water temperature is kept at 0

fl

C during frazil ice
formation, the heat losses from the water body and consequently rate of frazil accumu-
lation can be large.
Formulation of the physical law of frazil ice formation is straightforward, since the
surface temperature must be at the freezing point and the surface heat loss changes the
volume of frazil and compensates for the heat

°

fl flux coming from the deeper water:

q L f dh

dt þ Q w ¼ Q 0 þ Q T

ð Þ ð 4 : 31 Þ

where h represents the volume of frazil per unit area or the equivalent thickness of the
frazil ice mass. The frazil may form a local ice cover or drift away, depending on the
turbulence and circulation characteristics.
When the surface water has reached the freezing point, Eq. ( 4.31 ) shows that the water
surface remains open as long as Q w + Q T + Q 0 ≥ 0. When this is no more true, the surface

layer cools, and after minor supercooling, frazil accumulation is commenced. Assuming
that the heat

flux from deeper waters is small, the volume of frazil can be directly
integrated from Eq. ( 4.31 ), since the solar and atmospheric

fl

fluxes are independent of the
frazil volume. Thus there is no self-insulating mechanism as in the case of congelation ice,

fl