Structure and Properties of Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 89

Fig. 3.20 Ice-covered lake in the Beiluhe Basin, Qinghai - Tibet Plateau at 4,000 m altitude.
Photograph Zhijun Li

dS 2
dt ¼ q w dh i

q i

dt þ f

A þ I O ð 3 : 26 Þ

An important dimensionless measure is the ratio of ice thickness to lake depth,

˅ = h/(H + h). Normally ˅ ≪ 1 and the ice cover has a minor in fl uence on the lake volume,

but as ˅ → 1, a signi cant portion of the water body freezes and at ˅ = 1 the lake has

frozen to the bottom.
In the system ( 3.25 , 3.26 ) it is implicitly assumed that the whole lake is covered by ice.
If this is not true, a quantity ice coverage needs to be introduced. Ice coverage,

ˇ ,is

de ned as the relative area of ice in the lake, 0 ≤ ˇ ≤ 1. Then S 1 = ˇ hA, and the

conservation laws are

!

h i [ 0 þ f þ P E h i ¼0

dS 1

dt ¼ v dh i

Þ A dh i
dt

A þ 1 v ð ð 3 : 27a Þ

dt