Freezing of Lakes - Freezing of Lakes and the Evolution of their Ice Cover - page 33

Air temperature, humidity and wind speed determine the turbulent transfer of
momentum, heat and moisture between the atmosphere and lakes. The bulk formulae to
estimate these fl fluxes are, respectively,

s a ¼ q a C a U a U a ð 2 : 13a Þ

Q c ¼ q a c p C H T a T 0 ð Þ U a ð 2 : 13b Þ

Q e ¼ q a L C e q a q 0 ð Þ U a ð 2 : 13c Þ

where cients for

momentum, heat and moisture, and L* is the latent heat of evaporation (L*=L e ) or latent
heat of sublimation (L*=L f + L e ) depending on the quality of the moisture transfer, and
U a is the wind speed. We can assume that the humidity is at the saturation level at the
surface, q 0 = q s (T 0 ). The magnitude of the turbulent exchange coef

ˁ a is the air density, C a , C H and C E are the bulk exchange coef

cients is 10 − 3 , and in

general they depend on the surface roughness and strati cation of the atmospheric surface

boundary layer (see Sect. 4.1.4 for more details). In the neutral case, 1.2 10 − 3 is a good

reference value (Andreas 1998). Example for the wind speed of 5 m s − 1 , the momentum
transfer is 0.039 Pa, the sensible heat exchange is 7.8 W m − 2 /1

×

C temperature difference
between air and the surface, and the latent heat exchange is 12.1 W m − 2 (evaporation/
condensation) or 13.7 W m − 2 (sublimation/deposition) per 1 mbar difference in the water
vapour pressure.
The characteristics of the atmospheric surface boundary layer have a clear seasonal
dependence. In autumn, lakes are usually warmer than the air, and the boundary layer is
unstable. Then the turbulent

°

fluxes are strong. In spring and early summer the air is
warmer than lake surface, the boundary layer is stable and winds usually remain weak,
and, consequently, turbulent transfer is weak. Routine weather station observations pro-
vide the atmospheric information needed to evaluate the air

fl

lake interaction except for the

-

surface temperature.

2.2.5 Radiation Balance

The radiation balance consists of solar and terrestrial radiation, and the net radiation
provides the governing forcing to the annual course of the freezing lakes. The physical
basis is the Planck is law of black body radiation, which provides the distribution of

thermal radiation as a function of temperature and wavelength. When this law is integrated
over the wavelengths, we have the Stefan-Boltzmann law, which tells that the radiative
heat

'

flux is proportional to the fourth power of the absolute temperature. Natural objects
radiate a little less than a black body; if the spectral distribution of radiation is similar to
the black body law, the object is called a grey body. The radiative flux of a grey body

fl