Solar Radiation under Clouds
173
through the atmosphere to zenith path length. For zenith angles less than
SO0, refraction effects in the atmosphere are negligible, and m is given
by:
m =
Pa
101.3 cos + '
The ratio pa/lO1 .3 is atmospheric pressure at the observation site divided by sea level atmospheric pressure, and corrects for altitude effects.
Equation (3.7) can be used to calculate this ratio. It can be shown that
Eq. (1 1.11) is mathematically equivalent to Beer's law (Eq. (10.4)).
Liu and Jordan (1960) measured t on clear days, and found values
ranging from 0.75 to around 0.45 at two sites. When t is lower than about
0.4, one would consider the sky to be overcast. Gates (1980) suggests
values of t between 0.6 and 0.7 to be typical of clear sky conditions.
Values on the clearest days would be around 0.75.
Of the radiation that starts through the atmosphere, part reaches the
ground as beam radiation (Eq. (1 1.1 I)), part is absorbed by the atmosphere, part is scattered back to space, and part is scattered downward
toward the ground. The down scattered part is called the sky diffuse radiation. The actual amount of diffuse radiation reaching the ground is
difficult to compute because it depends, in part, on the albedo of the
ground. All else being equal, the sky is brighter when the ground is snow
covered than it is when the ground is covered with dense, dark vegetation. Without getting into these complications, approximate values can
be computed for sky diffuse radiation on clear days using an empirical
equation adapted from Liu and Jordan (1960):
The airmass factor partially compensates for the effect of the cosine factor
in Eq. (1 1.13), so that the diffuse radiation remains relatively constant
throughout clear days. In fact, Peterson and Dirmhirn (1981) found that
the ratio Sd/Sp is nearly constant on clear days. Figure 11.2 shows the
beam, diffuse, and total radiation computed using Eqs. (1 1.1 1) and (1 1.13)
for a clear atmosphere. Figure 11.3 shows these same radiation streams,
but for a turbid atmosphere. Note that as the dust and haze increase, beam
radiation is decreased and diffuse radiation increases.
11.3 Solar Radiation under Clouds
When clouds obscure the sun, Sd = St, since there is no beam radiation
component. Empirical transmission coefficients have been worked out for
various cloud types and used to determine the shortwave irradiance under
clouds. Total shortwave irradiance is shown in Fig. 11.4 as a function of
solar elevation angle for various cloud types. Clearly the presence of some
kinds of clouds can cause widely fluctuating irradiance so the curves in
Figure 1 1.4 are averages.
173
through the atmosphere to zenith path length. For zenith angles less than
SO0, refraction effects in the atmosphere are negligible, and m is given
by:
m =
Pa
101.3 cos + '
The ratio pa/lO1 .3 is atmospheric pressure at the observation site divided by sea level atmospheric pressure, and corrects for altitude effects.
Equation (3.7) can be used to calculate this ratio. It can be shown that
Eq. (1 1.11) is mathematically equivalent to Beer's law (Eq. (10.4)).
Liu and Jordan (1960) measured t on clear days, and found values
ranging from 0.75 to around 0.45 at two sites. When t is lower than about
0.4, one would consider the sky to be overcast. Gates (1980) suggests
values of t between 0.6 and 0.7 to be typical of clear sky conditions.
Values on the clearest days would be around 0.75.
Of the radiation that starts through the atmosphere, part reaches the
ground as beam radiation (Eq. (1 1.1 I)), part is absorbed by the atmosphere, part is scattered back to space, and part is scattered downward
toward the ground. The down scattered part is called the sky diffuse radiation. The actual amount of diffuse radiation reaching the ground is
difficult to compute because it depends, in part, on the albedo of the
ground. All else being equal, the sky is brighter when the ground is snow
covered than it is when the ground is covered with dense, dark vegetation. Without getting into these complications, approximate values can
be computed for sky diffuse radiation on clear days using an empirical
equation adapted from Liu and Jordan (1960):
The airmass factor partially compensates for the effect of the cosine factor
in Eq. (1 1.13), so that the diffuse radiation remains relatively constant
throughout clear days. In fact, Peterson and Dirmhirn (1981) found that
the ratio Sd/Sp is nearly constant on clear days. Figure 11.2 shows the
beam, diffuse, and total radiation computed using Eqs. (1 1.1 1) and (1 1.13)
for a clear atmosphere. Figure 11.3 shows these same radiation streams,
but for a turbid atmosphere. Note that as the dust and haze increase, beam
radiation is decreased and diffuse radiation increases.
11.3 Solar Radiation under Clouds
When clouds obscure the sun, Sd = St, since there is no beam radiation
component. Empirical transmission coefficients have been worked out for
various cloud types and used to determine the shortwave irradiance under
clouds. Total shortwave irradiance is shown in Fig. 11.4 as a function of
solar elevation angle for various cloud types. Clearly the presence of some
kinds of clouds can cause widely fluctuating irradiance so the curves in
Figure 1 1.4 are averages.