To compute the solar radiation flux density at the surface we need to know effects of atmosphere in filtering and depleting the beam from the top of the atmosphere to the ground Absorption and scattering by the atmosphere

Scattering Rayleigh, for molecules and tiny particles Mie for larger particles Rayleigh, blue sky Mie, with large particulate matter. Whitish sky

Absorption, especially due to O 3, H 2 O,CO 2

Combined in a simple slab approach, scattering and absorption reduce transmissivity, so for cloudless atmosphere: Depends on turbidity of the air (scattering + absorption) and path length or optical air mass (m) Z Typically varies from about 0.9 (clean) to 0.6 (dirty), typical 0.84

Physically based models Attempt to account for all physical processes in the chain Some calculate components of direct (S) and diffuse (D) radiation

Absorption Scattering Example: Davies et al Assumptions: Absorption occurs before scattering Half of dust deplection is due to absorption Scattering occurs equally in forward and backward direction Absorption by ozone neglected Cloudless sky

Cloudy sky Davies et al (continue) Cloud layers

Comparison with measurements Physical models are capable of approaching accuracy of measurements, especially in cloudless case and for daily averages

Won (1977) Absorption + Scattering It uses hourly reported meteorological parameters In the computation of the T p,w,d functions, empirical coefficients are used. It may be place specific

Beer’s Law (Monteith p ) It describes the attenuation of flux density of a parallel beam of monochromatic radiation through an homogeneous medium dx x Integrating

It has been found that the very restrictive assumption about single wave length and homogeneity of the medium can be relaxed or modified. So the Beer’s Law can be applied to: Air (Won, 1977 model), k= atmospheric extinction due to turbidity x=path length And also in water, snow, ice, soil, vegetation canopy