Introduction - Freezing of Lakes and the Evolution of their Ice Cover - page 7

Fig. 1.4 Fish kill in Lake Ä im ä j ä rvi, southern Finland, March 2003. Ice season 2002 - 2003 began
exceptionally early (late October), and the oxygen storage was not sufficient for the whole ice
season. Photograph by Mr. Jouni Tulonen, printed with permission

content depends on the strength of the autumn mixing. In windy autumn conditions the
whole water body may cool down to 1

2 ° C, and the cold water will then contain a large

-

amount of oxygen. Strati cation conditions can be favourable for primary production

beneath the ice cover, and an under-ice bloom may form if the bare ice period lasts long
enough in spring.
Mathematical modelling applications in lake ice research have concerned ice growth
and decay, radiation transfer, ice forces, and ice drift or ice displacements (Fig. 1.5 ). The
models are used in basic science, forecasting, ice engineering, and environmental and
climate research. Two classical, analytical models, which are still applicable as

rst
approximations, are the ice growth model by Stefan (1891) and the bearing capacity
model by Hertz (1884). The former model predicts ice thickness proportional to the square
root of the freezing-degree-days, and the latter model predicts bearing capacity of a point
load to be proportional to square of the ice thickness.
Until 1990s, thermodynamic lake ice models were mostly semi-analytical, based on the
freezing-degree-days for ice growth and positive degree-days for melting (e.g., Ashton
1986; Lepp

ä

ranta 2009a). Thereafter also numerical models have been employed (e.g.,