Geoscience Reference
In-Depth Information
Example 2.7.
In the tropical zone, in the coldest month T
a
= 300 K. Taking the adiabatic
= 6.5 K km
−
1
, the air temperature reaches the freezing point at the altitude
of 4.1 km. For the scaling magnitude, we can take Q
s
∝
lapse rate as
ʓ
t
day
, where Z
0
is the solar
zenith angle at noon and t
day
is the length of the day. In the northern hemisphere mid-
winter, we have approximately
cos Z
0
×
ð/ dÞ; / d
90
, where Q
s0
is the
Q
s
¼ Q
s0
cos
scale of radiation in the tropics,
is declination. Assuming
T
0
= T
a
, the surface temperature is obtained from the radiation balance as
˕
is latitude, and
ʴ
* -
15
°
T
0
ð/Þ
¼
ð
1
a
Þ
Q
s0
cos
ð/ dÞ
e
0
ð
1
e
a
Þr
The temperature decreases with altitude and latitude as
T
0
ð
z
; /Þ
¼T
0
ð
0
; /ÞC
z
. We can
then solve for z = z(
˕
) where T
0
(z,
˕
)=T
f
as:
s
ð
1
aÞ
Q
s0
e
0
ð
1
e
a
Þr
cos
"
#
z
¼
1
C
4
ð/ dÞ
T
f
The altitude increases towards lower latitudes from zero at
˕
*
40
°
-
50
°
.
2.3
Water Budget of Lakes
2.3.1 General Form
Lakes are associated with a water budget. The lake water storage S changes by precipi-
tation (P), evaporation/sublimation (E), in
fl
ow (I) and out
fl
ow (O):
dS
dt
¼
ð
P
E
Þ
A
þ
I
O
ð
2
:
16
Þ
where A is the area of the lake. In
ow consist of surface and groundwater
components. The term E is normally positive but occasionally, in case of condensation or
solid deposition of water vapour, it may appear negative. Sometimes it is desirable to
express the storage as S = AH, where H is the mean depth. The relative magnitudes of
in
fl
ow and out
fl
ow and precipitation are related to the size of the drainage basin of the lake.
The water storage is easy to monitor from the water level elevation, which changes due
to the external
fl
fluxes. Precipitation is directly measured (Sect.
2.2.3
), while evaporation/
sublimation can be obtained directly only in special campaigns, and normally it is esti-
mated indirectly from weather station data (Sect.
2.2.4
). The most dif
fl
cult parts are
usually the groundwater
fluxes and the surface runoff. Figure
2.11
shows an example of
the annual course of the water budget in Lake Vanajanselk
fl
, southern Finland. The area of
the lake is 103 km
2
, the mean depth is 7.7 m, and the area of the drainage basin is
ä
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