Geoscience Reference
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where
c
is the fractional cloud cover and
a
s
and
b
s
empirical constants here assumed
equal to their typical all-day average values, i.e.,
a
s
= 0.25 and
b
s
= 0.5.
Develop a spreadsheet to make the calculations in sections 2(a) to 2(e) below
and sections (g) and (h) then reduce to applying this spreadsheet in different
conditions. The spreadsheet should set the value of
S
top
to zero for hours when
Equation (26.1) gives a negative value and the Sun is below the horizon. Set up the
spreadsheet to also calculate the daily average values of solar, net solar, net
longwave and net radiation.
On July 13 at an arid site 32.5°N of the equator the measured all-day average
values of air temperature and relative humidity are 71.6 °F and 50 %, respectively.
(a) What are the equivalent all-day average values of air temperature in K, the
saturated vapor pressure in kPa, and the vapor pressure in kPa on this day.
(b) Assuming the cloud factor
c
= 0.7 all day, estimate the all-day average net
longwave radiation in W m
−2
(giving results of intermediate calculations) at
this
arid
site and recalling that the Stefan-Boltzmann constant is 5.67 × 10
−8
W m
−2
K
−4
.
(c) Still assuming the cloud factor
c
= 0.7 all day, now estimate the all-day
average net longwave radiation in W m
−2
(giving results of intermediate
calculations) had this been assumed to be a
humid
site.
(d) Still assuming the cloud factor
c
= 0.7 all day and also that the albedo at this
site is equal to 0.23 and is constant through the day and that the net
longwave radiation flux is also constant all day. At hourly intervals between
05:00 and 23.30 hours, calculate and plot the incoming solar radiation, net
solar radiation, and the net radiation fluxes assuming first that this is an
arid site, and second, a humid site.
(e) Calculate the all-day average values of the incoming solar radiation, net
solar radiation and net radiation assuming first that this is an arid site, and
second, a humid site.
You have now created a spreadsheet which you can use to make estimates of solar,
net solar, longwave and net radiation at any latitude, for any day of the year, in dif-
ferent cloud cover conditions and for different types of land cover, as characterized
by their albedo. Using this spreadsheet make the following investigations. You will
need to make appropriate selections for albedo from Table 5.1.
(f ) Explore the effect of seasonality by making calculations and plotting graphs
for a humid grassland site near Saskatoon, Canada at 55°N on January 15
when the air temperature is 33°F, and on July 15 when the air temperature
is 90°F. For simplicity, assume
c
= 0.6 all day and the relative humidity is
80% on both days.
(g) Explore the effect of deforestation on the surface radiation balance by
making calculations and plotting graphs for a humid site near Manaus,
Brazil on March 23 with forest cover and pasture cover. Assume a
temperature of 90
°
F, a relative humidity of 85%, and a cloud cover of 70%.
