Thermodynamics of Seasonal Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 104

Internal melting is re fl ected in the porosity of the ice, de ned as the relative volume of

pores in the ice.

m ¼ 1 V i
V

ð 4 : 23 Þ

where V i is the volume of ice in a volume element V. In growing ice the porosity equals
the gas content and is very small, but in the melting season it can reach the limiting
strength needed to keep the ice sheet together.
Lake ice may become thinner also by sublimation. In a dry environment, the ice is often
snow-free, and if strong winds occur frequently, sublimation can become signi

cant, to an
order of 10 cm during one winter. There are such dry areas, e.g. northern China, Tibet and
dry valleys in Antarctica, where snow cover is absent all winter (e.g., Priscu 1998; Huang
et al. 2012). Then sublimation needs to be included into the ice thickness evolution models.
In 24 h, heat loss by 30 Wm − 2 can sublimate a 1-mm layer of ice. Sublimation of snow also
takes place but that is normally hidden behind snowdrift and the low accuracy of snow
thickness data. Deposition of water vapour on ice and snow is a small and transient feature
but appears as beautiful formations such as frost fl flowers on lake ice.

rvi, Finland was examined based on
field data by Wang et al. (2005). The heat fluxes were derived from high-resolution
measurements by Automatic Ice Station Lotus (Fig. 2.9 ). The radiation balance (solar plus
terrestrial radiation) dominates the total heat

The surface heat budget of ice cover of Lake P ää j ä

fl flux (Fig. 4.5 ). In January the total heat loss

70 W m − 2 due to the strong outgoing terrestrial radiation, and at about mid-March
the daytime solar radiation was high enough to turn the balance into a gain reaching
200 W m − 2 at daily maximum. The level of the turbulent

was 50

-

fl fluxes was high only for short

periods and typically ranged between 20 and 30 W m − 2

10 to
10 W m − 2 in March. In another study in the same lake, Jakkila et al. (2009) estimated the
monthly average heat budgets. The surface balance was always negative, and in March
internal melting of the ice was signi

in January and from

-

flux from the water body also increased
due to penetration of solar radiation through the ice (Table 4.2 ). The residual of the heat
budget is due to errors in the estimation of the heat budget terms.
Thermodynamics of saline (or brackish) ice differs qualitatively from the fresh water
ice case. The thermal properties change signi

cant and heat fl

cantly as a function of temperature and
salinity (Schwerdtfeger 1963; Yen 1981). Along with temperature evolution, the brine
volume changes with associated phase changes at brine pocket boundaries. This brings an
interesting viewpoint: saline ice has no de nite melting point but always there is melting

involved when ice warms in order to dilute the brine and vice versa (Assur 1958;
Schwerdtfeger 1963). Thus brine pocket dynamics has a strong in

uence on the heat
connected to temperature changes of saline ice, especially when the temperature is high. 4

fl

4 High temperature refers here to vicinity of the freezing point of meltwater of the saline ice; in sea
ice, with the freezing point of - 1.8 ° C, high temperatures are above - 5 ° C.