Geoscience Reference
In-Depth Information
equals the radiative
fl
flux of a black body, at the same temperature, multiplied by its
emissivity
ʵ
(0
≤ ʵ ≤
1):
Q ¼
er
T
0
ð
2
:
14
Þ
where
r
¼
5
:
6704
10
8
Wm
2
K
4
is the Stefan-Boltzmann constant, and T
0
is the
surface temperature. The black body case comes with
= 1 in Eq. (
2.14
). Sun and lake
surface (whether liquid water, ice or snow) radiate almost as black bodies (
ʵ
> 0.95). For a
grey body, the radiative temperature T
R
is de
ʵ
ned from
r
T
R
¼
er
T
4
.
ned as the annual average of solar radiation incident on a
plane perpendicular to the solar rays on the top of the atmosphere. Its value is equal to
1367 W m
−
2
(e.g., Iqbal 1983). On the way through the atmosphere, this radiation is
reduced by 30
The solar constant is de
80 % due to absorption and scattering. Solar radiation makes a strong
seasonal cycle over freezing lakes (Table
2.7
). Part of the incoming solar radiation is
re
-
ected and scattered back at the lake surface, called as the outgoing solar radiation. The
ratio of outgoing to incoming radiation is the albedo (
fl
1), which has a very
important role during the lake ice season, in particular in the melting period.
Incoming and outgoing solar radiation are in exact terms downwelling and upwelling,
respectively, planar irradiances at the surface (see, e.g., Arst 2003). These irradiances
integrate the radiance coming from a hemisphere onto a horizontal plane element.
Downwelling and upwelling solar irradiances
8
are measured directly by using a pyra-
nometer. Only few weather stations provide direct measurements of solar radiation on a
routine basis but simple formulae are available to estimate it using routine weather data
(see Sect.
3.4.1
).
In terrestrial radiation, lake surface acts as a grey body with emissivity
ʱ
,0
≤ ʱ ≤
ʵ
0
in the range
ʵ
0
= 0.97, the emitted thermal radiation is 306 W m
−
2
at 0
0.96
-
0.98. For
°
C (the range is
309 W m
−
2
for
ʵ
0
= 0.96
°
303
-
-
0.98), and for the temperature range from
-
20 to 20
C the
406 W m
−
2
. Thermal radiation from the atmosphere
is more complicated since it comes from atmospheric gas molecules, aerosols, water
vapour, water droplets and ice crystals, from different altitudes with different tempera-
tures. An analogous formula to grey body radiation, for parameterization from normal
weather data, is used with
emitted radiation varies through 226
-
and the surface air temperature (altitude
2 m) as the representative temperature. This effective emissivity is
'
effective emissivity
'
ʵ
a
= 0.7
0.9, giving the
-
284 W m
−
2
, and, consequently, the net terrestrial
radiation at 0
°
C in the range of 221
-
radiation is then negative.
Terrestrial radiation can be measured with pyrgeometers, but such data are not avail-
able in routine weather records. To estimate the atmospheric thermal radiation is a key
problem in the heat balance evaluation since indirect estimates based on the routine
weather data are not so accurate. Cloudiness is the key factor, which is available at some
weather stations but good data are coming less and less as they are produced only by
8
The total downwelling solar irradiance on a horizontal plane is also called global radiation.
Search WWH ::
Custom Search