Lake Water Body in the Ice Season - Freezing of Lakes and the Evolution of their Ice Cover - page 204

Fig. 7.2 Cooling of surface
layer water in a tundra lake,
Lake Kilpisj ä rvi in years
2008 - 2010. The data are from
the data base Hertta of the
Finnish Environment Centre

brackish lakes the Tf m > T f but the difference Tf m − T f decreases with salinity and the

density maximum at T = T m weakens. In saline and hypersaline lakes, T m < T f so that
convection continues down to the halocline until freezing. In saline lakes the freezing
point is still above

− 2 ° C, but in hypersaline lakes the freezing point can become very

low, at extreme around − 50 ° C in Don Juan Pond in Victoria Land, Antarctica. In brackish

(T f , S) < 0.1 kg m − 3 , which corresponds to the in lakes, ρ (T m , S) − ρ fl uence of increase of

0.1 rst order

independent of the absolute salinity level, it is seen that quite weak halocline is able to
stop convection in cooling of cold lakes.
Heat is transferred into/out of lakes by

‰ salinity unit to density. Since the salinity in fl uence to density is to

fluxes at the boundaries and by solar radiation in
the interior. In three-dimensional analyses it is convenient to

fl

fix the zero level of the
vertical co-ordinate (z) beneath the lake bottom. The lake bottom and surface are then
b = b(x, y) and ʾ = ʾ (x, y), respectively. The heat conservation law for a lake is expressed

as

@
@ t

ð q cT Þþ u rq cT ð Þ ¼ r jr T ð Þþ exp ½ k n z ð Þ Q T ð 7 : 3 Þ

is thermal conductivity tensor. 2 We can approximate the

where c is speci c heat, and κ

ρ 0 c 0 = 4.20 MJ m − 3 C − 1 volumetric heat content as ρ cT ≈ ρ 0 c 0 T, where ° is a xed

reference heat capacity. In turbulent fl flow, the thermal conductivity is anisotropic with

κ = κ H in the horizontal plane and κ = κ V in the vertical direction, κ H ≫ κ V ; thus

κ xx = κ yy = κ H , κ zz = κ V and κ pq =0(p ≠ q).

2 It is assumed here that lakes with open water surface are turbulent. For laminar conditions, the heat
conductivity would be replaced by the isotropic molecular heat conductivity κ .