Geoscience Reference
In-Depth Information
i.e.
β
, at noon when
h
=
0? (b) When and where on Earth is the day length 12 hours, i.e.,
h
= π
/
2
when the Sun rises and sets? Show with (2.77) that there are two possible situations for this to
occur.
2.15
Prove Equation (2.78) by integration of (2.77) over one day.
Calculate the total daily solar radiation (W m
−
2
) on a horizontal plane in the absence of an
atmosphere for a latitude of 45
◦
on June 21. Compare with the value shown in Figure 2.23.
2.16
2.17
The following data are averages for a typical summer day in a temperate climate: air tem-
perature,
T
a
=
17
.
94
◦
C; relative humidity, 66%; and incoming, short-wave radiation,
R
s
=
468 cal cm
−
2
d
−
1
. Calculate the net radiation,
R
n
(inWm
−
2
), for a surface covered with vibrant,
but short vegetation. (To a first approximation, assume that the daily average of the surface tem-
perature,
T
s
, is the same as the air temperature, and that cloudiness does not affect the long-wave
radiation, when it is derived from
T
a
.)
2.18
Same as Problem 2.17 but with the following data: air temperature,
T
a
=
20
.
45
◦
C; relative humid-
ity, 64%; and incoming, short-wave radiation,
R
s
=
477 cal cm
−
2
d
−
1
.
2.19
The following data are available for a deep lake in a temperate climate (latitude 42.5
◦
N) for
typical days respectively in the months of December (not frozen) and July: mean air temperature,
T
a
=−
2.78 and 20.56
◦
C; mean water surface temperature,
T
s
=
6.12
◦
C and 19.20
◦
C; relative
humidity for the region, 76% and 64%; and fraction of sunshine hours for the region,
n
/
N
=
0.33 and 0.63. Estimate the daily incoming short-wave radiation,
Q
s
(in W m
−
2
)
,
by using cli-
matological methods with (2.74) and Figure 2.23. With this value as an estimate of
R
s
, calculate
the mean daily net radiation,
R
n
(in W m
−
2
). Assume a surface emissivity of unity, and that the
temperatures remain roughly constant through the day.
During the night, a cloud layer, whose temperature is 4
◦
C, moves over an area covered with snow,
whose temperature is
−
3
◦
C. Calculate the maximal rate of evaporation of the snow cover, which
is due to the radiation from the clouds, if the absorptivity of the cloud is 0.93 and that of snow,
0.99. Assume that the atmosphere is transparent, that the air temperature is also
−
3
◦
C and that
steady conditions prevail. The latent heat of sublimation is 2
.
8
×
10
6
2.20
Jkg
−
1
. Give the result in
Wm
−
2
and mm day
−
1
.
2.21
Give an estimate of typical values of
c
R
=
R
n
in Equation (2.86), that can be expected for (a)
cropland and (b) grassland, on the basis of (2.87).
G
/
2.22
Show why the global incoming short-wave radiation is one fourth of the solar constant, as indicated
in Figure 2.28.
