Environmental Engineering Reference
In-Depth Information
Table 2.10
Constants for Estimating
F
1
and
F
2
as a Function of
ε
ε
class
1
2
3
4
5
6
7
8
ε
1.000-
1.065-
1.230-
1.500-
1.950-
2.800-
4.500-
6.200-
1.065
1.230
1.500
1.950
2.800
4.500
6.200
F
11
-0.008
0.130
0.330
0.568
0.873
1.132
1.060
0.678
F
12
0.588
0.683
0.487
0.187
-0.392
-1.237
-1.600
-0.327
F
13
-0.062
-0.151
-0.221
-0.295
-0.362
-0.412
-0.359
-0.250
F
21
-0.060
-0.019
0.055
0.109
0.226
0.288
0.264
0.156
F
22
0.072
0.066
-0.064
-0.152
-0.462
-0.823
-1.127
-1.377
F
23
-0.022
-0.029
-0.026
-0.014
0.001
0.056
0.131
0.251
Source:
Perez et al, 1990
E
diff,hor
∆
=
AM
•
(2.31)
E
0
With these parameters, the circumsolar brightening coefficient
F
1
and the
horizon brightening coefficient F
2
can be calculated:
F
1
=
F
11
(
ε
) +
F
12
(
ε
)
•
∆
+
F
13
(
ε
)
•
θ
hor
(2.32)
F
2
=
F
21
(
ε
) +
F
22
(
ε
)
•
∆
+
F
23
(
ε
)
•
θ
hor
(2.33)
The constants
F
11
to
F
23
are estimated from Table 2.10. They vary according
to the eight different atmospheric clearness classes (
class
= 1-8) that
correspond to the equivalent atmospheric clearness index values
ε
ε
.
With
F
1
and
F
2
as well as
a
= max (0; cos
θ
gen
) and
b
= max (0.087;
sin
γ
S
), the diffuse irradiance
E
diff,tilt
on a tilted plane using the diffuse irradiance
E
diff,hor
on a horizontal plane becomes:
E
diff,tilt
=
E
dir,hor
•
[
•
(1 +
cos
t
)
•
1 -
F
1
) +
•
F
1
+
F
2
•
sin
t
]
1
2
a
b
(2.34)
γ
γ
Ground reflection
For calculating the ground reflection
E
refl,tilt
an isotropic approach is sufficient.
Anisotropic approaches have shown only insignificant improvements. With
the global irradiance
E
G,hor
on a horizontal surface and the albedo
A
, the
ground reflected irradiance
E
refl,tilt
on a surface with tilt angle
γ
t
becomes:
1
2
E
refl,tilt
=
E
G,hor
•
A
•
(1 -
cos
γ
t
)
(2.35)
