Freezing of Lakes - Freezing of Lakes and the Evolution of their Ice Cover - page 38

Fig. 2.12 The water budget of frozen lakes is reduced as compared with open water season.
Precipitation is stored in the snow layer, and the ground over large regions is also frozen

(b) The change of the water storage can be written as

dS

dt ¼ A dH dt þ H dA

dt

ʲ

Consider a circular lake with a diameter L and a fixed shore slope around the lake. Then

dH
dt

1
A

dS

dt ¼ 1 þ H L 4

tan b

10 − 3 and H/L =10 − 3 , changes in the water storage are equally If the shoreline slope is 4 ×

re ected both in the depth and surface area. The equation can be generalized by changing

the factor 4/tan

fl

ʲ into a general form B = b/tan ʲ *, where ʲ * is the characteristic slope

around the lake and b 4 is a parameter depending on the slope statistics around the lake.

*