Available Energy: Net Radiation and Soil Heat Flux - Transport in the Atmosphere-Vegetation-Soil Continuum - page 18

the actual distance between Sun and Earth (depending on the date) and θ z is the solar
zenith angle (angle between solar beam and the normal to Earth's surface), which
depends on the location, date and time. In some applications the solar elevation angle
(angle between solar beam and horizontal) is used, which is the complementary angle
of the solar zenith angle.

Question 2.2: The distance between the Sun and Earth varies through the year and
hence the amount of solar radiation that falls on a plane perpendicular to the solar beam.

2

 

d
d

Sun

The ratio can be approximated by 10033 where n day is the

 

+ . cos[ 2 πn day / 365 ]

 

Sun

day number. The solar constant can be taken as 1365 W m -2 .
How large (in W m -2 ) is the variation through the year of the solar radiation arriving
at the top of the atmosphere (on a plane perpendicular to the solar beam)?

For a given amount of solar radiation at the top of the atmosphere, the solar radiation
at the ground level is determined by the properties of the atmosphere in-between.
Cloud cover and the type of clouds are the most important causes of variation. Apart
from the day-to-day variability, this variation can also have a latitudinal and seasonal
component depending on the local climate (e.g., northern Europe has a low fraction of
sunshine hours in winter, as compared to southern Europe; see Figure 2.3 ).
Besides the presence or absence of clouds, the composition of the atmosphere can
vary as well, both on a seasonal time scale and on shorter time scales. This encom-
passes variations in contents of water vapour (e.g., related to variations in temperature
or air mass origin) that lead to variations in absorption (see Figure 2.2b ). Further-
more, the aerosols content of air may vary (e.g., due to the presence of sea spray, soot
due to biomass-burning, desert dust).
The solar radiation that reaches Earth's surface is affected by the overlying atmo-
sphere in three respects:

1. Total lux density: absorption and backward scattering diminishes the amount of radiation.
2. Directional composition: at the top of the atmosphere all solar radiation comes from the
direction of the Sun (a disc with a diameter of about 32 arcminutes); due to scattering,
the radiation at Earth's surface comes both from the direction of the Sun, and from the
rest of the hemisphere.
3. Spectral composition: radiation is absorbed by atmospheric gases at speciic wavelengths
and scattering varies with wavelength as well.

In view of point (2), the amount of solar radiation at the surface is therefore decom-
posed into direct radiation ( S ) and diffuse radiation ( D ) (see Figure 2.4 ):

↓ =+=

(2.4)

KSDI cos( θ z ) + D

where I is the radiative lux density through a plane perpendicular to the solar beam. Because
of point (3), the discussion that follows deals with radiation of one wavelength at a time.