Ice-Covered Lakes Environment - Freezing of Lakes and the Evolution of their Ice Cover - page 265

For the first factor, a linear model T a = ʺ t + ʔ T a can be taken resulting with ʔ R = ½

ʺ − 1 ( T a ) 2 +

T a t. It is plausible that the second factor is somewhere between zero and the
shift in the zero upcrossing time of air temperature, 0

ʔ ʔ

t m ≤ ʺ − 1 ≤ ʔ ʔ T a . Then we have

s

l c ½ q L ð h 0 þ Dh Þ k 1 ð R þ DR Þ 3

t ð t m þ Dt m Þ ¼ ð 8 : 13 Þ

ʔ

t m is the strongest, since ice thickness change and positive degree-days
change appear under the cube root. The cube root was obtained from a simple model for
the increase of solar radiation and decrease of albedo during the melting period, and it
could be changed into a general power law

The role of

ʽ ,0< ʽ <1.

8.4.3 Numerical Modelling

A numerical model can be used to produce projections for the future ice seasons. If air
temperature change only is considered, the first order analytic model is usually quite good,

but to examine the in fl uence of snow accumulation and qualitative changes, numerical

models provide a more ranta 2009a; Yang et al. 2012).

An example is shown in Fig. 8.15 for southern Finland, where model simulations for a

firm basis (e.g., Lepp ä

' normal ' winter are compared with those for winters where the mean air temperatures are

1 and 5 ° C higher or lower than the present (1980 2010) baseline. In the numerical model,

-

the lake freezes during the first strong cold spell. The observed, present average maximum

annual ice thickness of 45 cm decreases by 5 cm for the

rst 1 ° C warming, 20 cm for the

next 3 ° C warming, and 10 cm for the final 2 ° C increase. The ice break-up date also shifts

Fig. 8.15 Model sensitivity to

the air temperature. The black
solid line is the reference of
present climate. The grey solid
lines show the modelled ice
thickness based on air
temperature decrease by 5 and
1 ° C, and the grey dashed line
show modelled ice thickness
based on air temperature
increase by 5 and 1 ° C (Yang
et al. 2012)

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

Oct Nov Dec Jan Feb Mar Apr May Jun

Time of year