S SH ¼ r t  S dt
ð7:8Þ
Equations (7.3) and (7.8) are applied to radiation data collected over a period of
4 days. The data was measured over daily periods as well as half-hour periods. The
results are shown in Fig. 7.1 and give a comparison between the radiation values
measured over successive half-hour periods with the corresponding values, calculated using Eqs. (7.3) and (7.8) applied to daily measured values. On days that were
slightly cloudy or with clear skies (August 8 and September 7), the values obtained
from the equations show good agreement with the measured data. However, on
cloudier days (August 17 and September 17) the modeled data does not accurately
reflect the experimental data.
7.4 Example 3: Estimation of Atmospheric Transmissivity
from Solar Radiation Values Measured at the Surface
From known values of measured total solar radiation (direct + diffuse) incident on
the Earth's surface, the transmissivity of the atmosphere to solar radiation s can be
calculated using the inverse of Eq. (6.88) from Sect. 6.3.3.3, as
S t ¼ S 0 s
m cos w þ S 0 0:271 À 0:294s
m
ð
Þ cos w
ð6:88Þ
Fig. 7.1 Experimental and theoretical radiation calculated using Eq. (7.9) for October 8
(a) August 17 (b), September 7 (c), and September 17, 2000 (d)
7.3 Example 2: Estimation of Solar Hourly Radiation
241