Geoscience Reference
In-Depth Information
where
w
is the
hour angle
, i.e., the angle representing time of day, which is given by:
(
)
12
−
h
w
=π
(in radians)
(5.10)
12
where
h
is time of day in hours in local time. Thus, if there were no atmosphere, on a
particular day the daily total incoming solar energy received at the ground integrated
over daylight hours between
t
1
and
t
2
, i.e., the daily insolation
I
o
, is given by:
t
2
∫
I
S d
dt
=
(sin
fd fdw
sin
+
cos
cos
cos
)
(5.11)
or
o
t
1
The values of
t
1
and
t
2
are best expressed in terms of the equivalent hour angle that
defines both the beginning and end of the day. This angle is called the
sunset hour
angle,
w
s
, which can be calculated from;
w
=
arccos (
−
tan
f
tan
d
)
[radians]
(5.12)
s
with the
day length, N
, in hours then following immediately from:
24
N
=
w
[hours]
(5.13)
p
s
The total solar energy which would be received per unit area between sunrise and
sunset on a horizontal surface at latitude
f
if there were no intervening atmos-
phere is then obtained by integrating Equation (5.11) between
-w
s
and
+w
s
as:
d
−−
2
1
S
=
37.7
d
(
sin
fd fd
sin
+
cos
cos
sin
) [ MJ m
d
]
(5.14)
w
w
0
r
s
s
where
d
r
,
d
, and
w
s
are given by Equations (5.5), (5.8), and (5.12), respectively. When
estimating evaporation rates, it is sometimes convenient to write Equation (5.14)
in terms of an equivalent depth of evaporated water, thus:
d
S
=
15.39
d
(
w
sin
φδ
sin
+
cos
φ δω
cos
sin
) [ mm d
−
1
]
(5.15)
0
r
s
s
It is important when estimating daily average evaporation rates (see Chapter 23)
that this absolute upper limit on evaporation rate (from which estimates of actual
evaporation rates can be made) can always be calculated solely on the basis of
knowledge of the latitude of the site and the day of the year.
