Environmental Engineering Reference
In-Depth Information
isotropic approach assumes that the diffuse radiance is constant across the
whole sky. An important conclusion from this approximation is that the
isotropic diffuse irradiance on a tilted surface is always lower than the diffuse
irradiance on a horizontal surface because a receiver does not see the diffuse
irradiance from behind the tilted surface. The diffuse sky irradiance
E
diff,tilt
on
a tilted surface with the surface tilt angle
γ
t
can be estimated directly from the
diffuse irradiance
E
diff,hor
on the horizontal surface:
1
2
γ
(1 + cos
t
)
E
dir,tilt
=
E
dir,hor
•
(2.28)
•
However, the isotropic assumption is only applicable for rough estimations or
very overcast skies. An anisotropic approach should be chosen for more precise
calculations of the irradiance on tilted surfaces because diffuse irradiance is
directional. It can be seen with the naked eye that the brightness increases at
the horizon and near the sun. Two models, which consider these effects, are
described here.
Klucher's model
(Klucher, 1979) calculates the diffuse irradiance
E
diff,tilt
on
a tilted surface in a relatively simple way:
2
E
dir,hor
E
G,hor
F
= 1 -
With
, the diffuse irradiance is given by:
t
2
γ
1
2
E
dir,tilt
=
E
dir,hor
•
(1 +
cos
γ
t
)
•
1 +
F
+ sin
3
•
•
(1 +
F
cos
2
θ
tilt
•
cos
3
γ
S
)
•
(2.29)
This model gives a relatively good estimation of the diffuse irradiance. A more
precise model for the calculation of the diffuse irradiation on a tilted surface is
the so-called
Perez model
(Perez and Stewart, 1986; Perez et al, 1987; Perez
et al, 1990). However, this model is also more complex.
The Perez model defines an atmospheric clearness index
ε
and an
atmospheric brightness parameter
θ
hor
of
the sunlight on the horizontal surface (measured in rad), the constant
∆
that uses the angle of incidence
=
1.041, the solar constant
E
0
, the direct and diffuse irradiance on the horizontal
surface as well as the air mass Air Mass (
AM
= 1/sin
κ
γ
S
):
E
diff,hor
+
E
dir,hor
•
sin
-1
γ
t
•
3
κ
+
θ
hor
E
dir,hor
(2.30)
ε
=
3
1 +
κ
•
θ
hor
