Geoscience Reference
In-Depth Information
s
1
þ
DT
a
T
a
;
min
t
c2
¼ t
c
ð
8
:
10
Þ
where T
Ta,min
< Tf
if
≤
C is the winter minimum of air temperature. The change is not
symmetric: warming reduces the length more than corresponding cooling increases. As
shown in Sect.
7.1
, the length of the cold season must be approximately more than twice
the memory length, which is proportional to the depth of the mixed layer.
The case with the freezing date is straightforward. With linear atmospheric cooling, the
temperature scenario is
0
°
T
a
¼ T
a
t
þ
DT
a
, where
T
a
\
0
is the rate of temperature decrease.
It is directly seen that the freezing date would be shifted by
Dt
F
¼
DT
a
T
a
ð
8
:
11
Þ
Thus the freezing day shift not only depends on the air temperature change but also on
the rate of atmospheric cooling. The predicted change is symmetric to the air temperature
scenario. In continental tundra the cooling is faster than in maritime climate, and the
climate change impact on the freezing date is consequently weaker. Example, in Finland
the fall cooling rate is
C month
−
1
, and consequently the freezing day would shift by
5
°
*
C
−
1
).
For a change in the air temperature, the freezing-degree-days and consequently the
maximum annual ice thickness would change. Using again the parabolic approximation
for winter air temperature, the reduced ice thickness is
6 days
×
(
ʔ
T
a
°
4
h
1
¼
a
2
h
2
1
þ
DT
a
T
a
;
min
ð
8
:
12
Þ
a
1
where the lower indexes 1 and 2 refer to the present and future climate, respectively. If the
parameter a* is constant, typically in the range of 2
-
3cm(
°
C
·
day)
-
½
, Eq. (
8.12
) gives
about 10 cm for a change of 1
C in air temperature. But since a* may change due to
changing snow conditions, snow may strengthen or even compensate for the change due
to the air temperature. Evolution of ice coverage is obtained from the analytic models in
Sect.
4.3
, with the difference that the initial time has shifted as given by Eq. (
8.11
).
Melting of ice is tied to the radiation balance, and therefore the climate change impact
is not directly clear. In fact three factors need to be considered. Firstly, as many statistical
models assume, the length of the melting season is proportional to the positive degree-
days. Secondly, the start of the melting depends on the atmospheric conditions and state of
the surface, and therefore the start may become earlier if air temperature increases. So the
shift in the breakup date must contain the shift in the zero upcrossing time of the radiation
balance. Thirdly, if the ice thickness has decreased there is less ice to melt.
°
Search WWH ::
Custom Search