Question 5.2: Use the simple model for solar radiation under cloudless ski...
Use the simple model for solar radiation under cloudless skies (p. 64) to estimate the direct, diffuse, and total solar irradiance on a horizontal surface at 45°N at local solar noon on 21 June for three values of aerosol optical thickness, 0.05, 0.20, 0.40. Assume that the optical thickness for molecular attenuation is 0.30.
At solar noon \psi =\phi -\delta =45.0-23.5=21.5 . Hence m = sec 21.5 = 1.075. Then S_{p} = 1366 \exp (-0.30\times 1.075) (\exp -(1.075\times \tau_{a} )) =990\exp (-1.075\times \tau_{a} ) and S_{s} = S_{p} \cos \psi .
Diffuse radiation is calculated as S_{d} = 0.3 \times 1366 \times \cos 21.5(1-\exp (-(\tau_{m} + \tau_{a} )\times 1.075)) , and S_{t} =S_{s} +S_{d} . The table shows results of the calculations in W m^{-2} for the three values of τ_{a}.
| τ_{a} | S_{p} | S_{s} | S_{d} | S_{t} |
| 0.05 | 941 | 875 | 118 | 993 |
| 0.20 | 802 | 746 | 160 | 906 |
| 0.4 | 644 | 599 | 202 | 801 |