Geoscience Reference
In-Depth Information
and daily average humidity were given in Chapter 5. An overview of the steps
required to make the calculation is as follows:
1.
Use the day of the year,
D
y
, to calculate: (a) the eccentricity factor,
d
r
, from
Equation (5.5); and (b) the solar declination,
d
, from Equation (5.8).
2.
Use the calculated value of
d
and the latitude of the site,
f
(in radians)
to calculate the sunset hour angle,
w
s
(also in radians), from
Equation (5.12).
3.
From the calculated values of
d
r
, d
, and
w
s
, calculate the solar radiation
incident at the top of the atmosphere at the site,
S
o
d
in mm of evaporated
water per day, from Equation (5.15).
4.
If estimated fractional cloud cover,
c
, and locally derived values of the con-
stants
a
s
and
b
s
are available, use these values in Equation (5.16) to calculate
the daily total solar radiation,
S
d
, reaching the ground. If local values of
a
s
and
b
s
are not available, assume
a
s
=
0.25 and
b
s
=
0.5.
5.
Alternatively, if a measure of bright sunshine hours,
n
, is available (rather
than cloud cover), first calculate the day length,
N
, in hours from
w
s
using
Equation (5.13), then calculate
S
d
from Equation (5.17) using locally
derived values of
a
s
and
b
s
if available, but assume
a
s
=
0.25 and
b
s
=
0.5
otherwise.
6.
Select a value for the albedo,
a
, (see Table 5.1, for example) then use this
with the calculated value of
S
d
to calculate the net daily solar radiation,
S
n
d
,
from Equation (5.18).
7.
From a measurement or estimate of
e
d
, the daily average vapor pressure in
kPa, calculate an estimate of the effective emissivity,
e'
, from Equation
(5.23).
8.
Calculate the daily total solar radiation that would have reached the ground
had the sky been clear,
S
d
clear
, from Equation (5.16) with
c
=
0, using the
same values of
a
s
and
b
s
as were used in step 4 (or step 5).
9.
On the basis of available measurements or otherwise, categorize the site as
being either 'humid' or 'arid, and on this basis select either Equation (5.24)
or (5.25) to calculate empirical cloud factor,
f
, using
S
d
from step 4 (or step 5)
and
S
d
clear
from step 8.
10.
Use the value of the Stefan-Boltzmann constant re-expressed in units of
mm of evaporated water per day (i.e.,
10
−9
mm d
−1
m
−2
K
−4
), with
e'
from step 7, and
f
from step 9, and
T
air
, the measured daily average air tem-
perature (in
σ
=
2
×
K), to calculate the daily average net longwave radiation,
L
n
d
,
in mm of evaporated water per day using Equation (5.22).
°
11.
Finally, use the values of
S
n
d
from step 5 and
L
n
d
from step 10 to calculate
the daily average net radiation flux,
R
n
d
, in mm of evaporated water per day
from Equation (5.26).
Table 23.2 demonstrates examples of the steps in calculation of net radiation for
three example sites A, B, C specified earlier with cloud cover measured at A and C
and the number of bright sunshine hours measured at B.
