Available Energy: Net Radiation and Soil Heat Flux - Transport in the Atmosphere-Vegetation-Soil Continuum - page 28

denoted by T L,2 . Typical values for the Linke turbidity factor range from 2 (clear, cold
air), through 4 (moist, warm air) to 8-10 (polluted air) (Scharmer and Greif, 2000 ).
Various empirical models for T L exist, which usually link the turbidity to the amount
of water vapour, ozone and aerosols (e.g., Jacovides, 1997 ; Gueymard, 1998 ).
The transmissivity that can be derived based on the Linke turbidity is a beam trans-
missivity (Eq. ( 2.18 )): it can be used to obtain the direct radiation. To obtain the
global radiation (direct plus diffuse) using the Linke turbidity, a model is needed (see
Ineichen, 2006, for an overview). One example is the model of Ineichen and Perez
( 2002 ):

↓

K
K

− 0 0387 . mT

r

== τ b 0 868 . e

L , 2

(2.19) ↓

0

where T L,2 is the Linke turbidity at relative optical mass 2.

Question 2.8: See Figure 2.6 . On May 22 and 23, at 12 UTC, the solar zenith angle is

2


 


 

d
d

Sun

about 32 degrees. The ratio is about 0.974 for these dates and the solar constant

Sun

can be taken as 1365 W m -2 .
Estimate T L,2 at 12 UTC for both days. Are these reasonable values?

2.2.3 Relected Shortwave Radiation
Because terrestrial surfaces, under natural conditions, are never so hot that they can
emit signiicant amounts of shortwave radiation, the sole source of upwelling short-
wave radiation is relected solar radiation. Thus the speciication of the upwelling
shortwave radiation boils down to the speciication of the relectivity of the surface.
But, similar to the case of atmospheric extinction, the relection both has spectral and
directional dependencies. The spectral dependence is easily illustrated by the fact that
some natural surfaces are green (relatively high relectivity at a wavelength around
0.53 μm) and others are red (high relectivity around 0.68 μm). Thus the relectivity
of surfaces is wavelength dependent.
Regarding the directional dependence of relected radiation three cases can be dis-
tinguished (for the geometry, see Figure 2.8 ):

• Specular relection: The incoming and relected light make the same angle with respect

to the surface normal ( θ out = θ in ) and the direction of relection is opposite to the direction
of the incident beam ( ϕ out = ϕ in +180º). Specular relection appears if the irregularities of
the surface are small as compared to the wavelength (e.g., a lake under low-wind condi-
tions). The relectivity for specular relection strongly depends on the zenith angle (see,
e.g., Hecht, 1987 ): high relectivity at large zenith angles (low incidence angles) and low
relectivity at normal incidence.