# The paths of the sun rays in the atmosphere

Scattering can modify the trajectory of incident solar rays, unlike absorption. Strictly speaking, the description of photon paths in the atmosphere must be done using probabilities. I voluntarily simplify the speech here and I adopt a geometric description, certainly less rigorous but easier to explain and make understood. This simplification has no impact on the rest.

Figures 4.11 and 4.12 are schematic representations of the different paths of the solar rays as they pass through the atmosphere from top to bottom. As with the following

Figure 4.11 Schematic view of different paths of the downwelling solar rays, (a) Solar rays do not reach the ground, (b) Solar rays reaching the flat collector are parallel and seem to come from the direction of the sun.

Figure 4.12 Schematic view of the different paths of the downwelling solar rays received by a flat collector at ground, showing various contributions to the diffuse component of the radiation at ground.

diagrams, these are valid for a particular wavelength as well as for integrals on all or part of the solar spectrum.

In the diagram on the left in Figure 4.11, the solar rays incident at the top of the atmosphere are deviated from their original direction by multiple scattering due to the constituents of the atmosphere (molecules, aerosols, water droplets, ice crystals). Their routes are such that they do not reach the collector plane on the ground; they therefore do not contribute to the irradiance received by the plane and are a net loss from this point of view.

In the diagram on the right in Figure 4.11, the solar rays incident at the top of the atmosphere are not deviated from their original direction, that of the sun, by the multiple scattering. I remind you that in the atmosphere, the probability of having a forward scattering, i.e., in the same direction as the incident, is generally greater than for the other directions. There can also be multiple scattering that deviates rays from the original direction, before bringing them back into the original beam. The incident rays on the collector plane are parallel, and all seem to come from the direction of the sun, the latter appearing at a solid angle with an apparent diameter of about 32'±0.5'ofarc.

This is called the direct component of irradiance, or irradiation. 1 will show in the next chapter, however, that this definition is not as clear.

Figure 4.12 show's three different paths, for w'hich the collector plane receives rays that do not seem to come from the direction of the sun. These are contributions to the diffuse component of solar radiation at ground.

In the diagram on the left in Figure 4.12, the solar rays incident at the top of the atmosphere are deflected from the direction of the sun by multiple scatterers such as molecules, aerosols, water droplets, or ice crystals, but end up on the flat collector with various angles of incidence. In the central diagram, some rays are not deviated from the original direction; they are reflected upward by the ground surrounding the collector and then scattered by the atmospheric constituents downward and reach the flat collector. Other rays follow the same kind of path but after deviating from the original direction. Finally, the diagram on the right in Figure 4.12 is a kind of continuation of the diagram on the right in Figure 4.11 show'ing the direct component. The “direct” rays are reflected by the flat collector itself; some of them are backscattered by the various atmospheric constituents and return to the collector with various angles of incidence.

The irradiance received by the horizontal collector is the sum of its direct and diffuse components. This sum is sometimes called global irradiance when it comes to making a distinction w'ith its components. Be careful not to confuse the terms global irradiance and total irradiance. The first term is the sum of the direct and diffuse components while the last term means the integral over the entire solar spectrum. You can therefore deal with global total irradiance, or global spectral irradiance, or direct total component, or diffuse spectral component, etc.

The direct component is the sum of all the photons that are received on the plane with an angle of incidence equal to the solar zenithal angle in the solid angle under which the sun appears regardless of the effective path of the photons in the atmosphere. The diffuse component is the sum of all the other photons received by the horizontal collector.

# Summary of contributions of atmospheric constituents to attenuation of radiation

All the constituents of the atmosphere contribute in varying degrees to the attenuation of solar radiation. In the stratosphere, the main phenomena are the absorption of X-rays and ultraviolet rays and the scattering of short wavelengths in purple and blue. Radiation with wavelengths less than 300 nm is absorbed by ozone. The wavelengths of the radiation reaching the ground are mainly between 300 and 4000 nm. As the solar rays enter the atmosphere, the longer wavelengths are more and more attenuated. Variations in the concentrations of gases and aerosols, as well as in their optical properties, cause the attenuation of the atmosphere to vary over time and in geographic space with sometimes very short time and space scales. It is therefore difficult to estimate very accurately the effects of the atmosphere on solar radiation.

Table 4.2 schematically summarizes the contributions of the various constituents of the atmosphere to the attenuation of the solar radiation incident at the top of the atmosphere, during its downward path toward the ground. The latter plays an important role; it contributes to the diffuse component w'ith generally a strong spectral dependence. This is the subject of the following chapter.

Table 4.2 Summary of the contributions of the various constituents of the

atmosphere to the attenuation of solar radiation during its downward path to the ground

 Constituent Scattering Absorption Ozone Can be neglected Strong for A less than 300 nm, otherwise negligible Gases (other than ozone and water vapor) Strong (in Я-4). Increases as the wavelength decreases. Negligible for Я greater than 700 nm Weak Water vapor Can be neglected Significant to very strong when Я is greater than 650 nm Aerosols Can be strong, dependence on Га with -1 <«<4 Weak Clouds Strong, weak dependence on Я Weak

Я is the wavelength.

Chapter S