Ground reflection

At a glance

The solar radiation reaching the ground is reflected by the ground. The reflected radiation can contribute after multiple scattering to the irradiance received by a horizontal plane.

The reflection of the ground strongly depends on the material, its shape, its surface properties, including its roughness, the wavelength of the incident radiation, and the angle of incidence. It is rarely known with great accuracy. It can be characterized by the reflection factor or the bidirectional reflectance distribution function. These two quantities are related and describe how a beam of parallel rays is reflected according to the directions of illumination and observation.

The reflection factor or reflectance quantifies the effectiveness of a body in reflecting solar radiation. The greater the reflection factor, the greater the reflected radiation. The bidirectional reflectance distribution function is an intrinsic property of the reflecting body. It is often approximated by an isotropic part, which is the main contributor under most conditions, and an anisotropic part.

Albedo is a quantity that synthesizes the combined effects of the attenuation of the solar radiation by the atmosphere and the reflection of the ground. Black- sky albedo and white-sky albedo are other quantities to describe the reflection of natural surfaces. The black-sky albedo is that which would be obtained if the downwelling irradiance were composed only of its direct component. The white-sky albedo is that which would be obtained with isotropic illumination of the surface.

The reflection of the ground presents significant spectral variations. The spectral distributions are various depending on the surfaces and weather conditions. The reflection properties and the associated quantities can be defined for a particular wavelength or over spectral intervals or over the entire spectrum.

Part of the radiation reaching the ground is reflected, part of which is backscattered toward the ground. The central and right diagrams of Figure 4.12 of Chapter 4 highlighted the importance of the reflection by the ground and the collector in the diffuse component of the irradiance. This chapter addresses the reflection of the solar radiation by the ground. Several quantities, namely the reflection factor, the reflectance,

Figure 5.1 Schematic view of the reflection on the Thartar Lake and surroundings and the contribution of the ground to the diffuse component.

the bidirectional reflectance distribution function, and the albedo, are defined that describe how the sun rays are reflected by the ground. Several examples of the spectral distribution of the reflectance are given.

First of all, to better enlighten you, allow me, reader, to illustrate the importance of the phenomenon with the example of Thartar Lake, in Iraq, which is not at all an exceptional case. Figure 5.1 is a schematic view of this lake that is surrounded by a large desert area of erg type. Let me assume a spatially homogeneous atmosphere, without cloud, as well as a weak reflection of water (except for specular reflection). The direct component of the irradiance received by a plane at the surface of the water is large: It typically represents 70 % of the global irradiance. About 10 km inland, reflection of the solar radiation by rocky and sandy soil is more important than on the lake and contributes more to the diffuse component. As the direct component is the same, the irradiance received on a flat collector located in the erg is greater than on the lake. The reality is more complex, notably due to the presence of clouds, but this rapid calculation may explain a relative difference in irradiance observed in the order of 5 %.

Reflection factor – its spectral variations

Generally, when the rays arrive on the collecting plane, a part is absorbed, a part is possibly transmitted if the plane is not opaque, and the rest is reflected. The reflection strongly depends on the material, its shape, its surface properties, including its roughness, the wavelength of the incident radiation, and the angle of incidence. The reflection properties and the associated quantities can be defined for a particular wavelength or over spectral intervals or over the entire spectrum.

Reflection factor

Consider an incident flux in the direction of incidence or illumination (в, у/) received by a collector plane, where в is the angle of incidence and у/ is the corresponding azimuth. Figure 5.2 depicts the reflection in the direction of observation (O', y/'), where в' is the angle of reflection and y/' is the corresponding azimuth.

Figure 5.2 Diagram illustrating the reflection. The incident flux arrives from the direction of illumination (в, yj). It can be reflected in several directions, including the direction (в «//'), called here observation direction.

The reflection factor г(в, у/, в', у/') is defined as the ratio of the radiance L(6 y/') reflected in the direction of observation to the incident radiance L(d, y/)

The reflection factor is also called directional reflectance and is dimensionless. A perfectly reflecting material has a reflection factor equal to 1 in all directions.

Specular reflection is a special case of reflection. It occurs when the energy reflected is only in the opposite direction to the direction of illumination:

Specular reflection occurs on a very smooth surface that reflects like a mirror. A common case is that of calm, fairly clear waters more than a few meters deep, such as oceans and lakes. Solar radiation is reflected in the direction opposite to the illumination direction. When the sea state gets rougher due to the wind for example, the reflective small facets are more numerous and more randomly orientated, increasing the roughness of the water surface. Under these conditions, the reflection of water departs from the specular case, and diffuse reflection, that is, reflection in several directions, if not in all directions, becomes more important.

The case of water is symptomatic of the influence on the reflection of the roughness of the surface of the reflecting material with respect to the incident wavelength. The rougher the surface, i.e., the more it offers asperities whose size is greater than the wavelength of the incident radiation, the more diffuse the reflection. If the sizes are smaller, the reflection is closer to the specular reflection. The vast majority of natural surfaces have a predominantly diffuse reflection. A perfectly diffusing material reflects the flux received in all directions, but not necessarily equally. Lambertian reflection is a special case of diffuse reflection, for which the reflected radiance L(6 y/') is orthotropic, that is to say, that it is the same angularly in all directions of the hemisphere above the horizontal collector plane.

The reflection of natural surfaces is not easy to know with accuracy because the reflection depends on their exact composition, their optical properties, and their roughness, which can vary over time. For example, snow is less reflective if it is very wet or soiled. It offers mainly diffuse reflection, but there are cases where it can be specular. The same applies to the vast salt lakes often dried up like the sebkhas, also called playas, which are very shallow floodable depressions where the soils are salty and the vegetation thin and sparse, or the salted remains of great lakes like Lake Bonneville in the United States, or the Aral Sea in Asia. When a thunderstorm occurs, the sebkha is flooded. It reflects less and the reflection is mainly diffuse. Then gradually, the water evaporates leaving the salt crust that reflects much more and anisotropically. Another example is given by the deciduous forests that reflect less in winter when the trees are leafless than in summer when they bear new foliage. But this can be different if in winter the ground is covered with thick, well-reflecting snow. Let me give a last example taken from cultivated soils. When sowing after plowing, a field looks like bare soil with a high reflection factor and offers diffuse reflection. As plants grow, the reflection factor changes in value and angular distribution.

When the reflective body has a certain volume and is not opaque, like a tree, for example, the reflection takes place on several levels, for example, at the level of the leaves, the trunk, and the ground. This is called volume reflection.

Examples of spectra of reflection factor

I mentioned above that the reflection depends on the roughness of the reflecting surface with respect to the wavelength of the incident radiation. Consequently, the reflection factor or directional reflectance r presents spectral variations. It can be defined for a particular wavelength Я or over spectral intervals [А/, A^] or over the entire spectrum. Be careful, the reflection factor is a ratio of radiances that depend on Я. Consequently, the reflection factor г(Я/, I2) is not the integral of r(A) between Я у and Я> The definitions of spectral reflection factor are as follows:

The spectral reflection factor is dimensionless.

The two following graphs exhibit spectra of reflectance between 350 and 2500 nm for certain natural bodies, chosen at random and only for illustration purposes. The graphs were made from spectra available in digital form from the USGS agency in the USA.^[1]

Figure 5.3 Examples of reflectance spectra between 350 and 2500 nm for concrete, limestone, wet beach sand and dry playa mud. Graphs made from spectra kindly provided by the federal agency USGS of the United States.

Figure 5.3 shows examples of reflectance spectra for concrete, limestone, wet beach sand, and dried mud in a sebkha or playa. The spectral curve for concrete is fairly flat, around 0.3, with lower values, down to 0.15 at wavelengths less than 600 nm. The reflectance also decreases beyond 2100 nm. The curve for limestone increases fairly regularly with the wavelength, from 0.10 to about 0.30 for 2200 nm, then presents some indentations. The reflectance for wet beach sand is fairly small and less than 0.15. The spectral curve increases fairly regularly with the wavelength, up to around 1300nm, then exhibits a succession of hollows and bumps. The dried mud of sebkha exhibits a minimum in reflectance of 0.15 at 350nm and increases rapidly with the wavelength, reaching a high plateau of 0.55 around 700nm. The reflectance decreases when the wavelength is greater than 1800 nm.

Figure 5.4 exhibits the spectral distributions for some plants: grass, poplar, and conifer. First of all, note that whatever the plant, the reflectance is weak and less than 0.04 at 350nm. The reflectance then grows, more or less quickly and regularly.

The spectral curves for the grass are fairly close to each other, although the reflectances are different. They have roughly the same hollows and bumps. The reflectance slowly decreases irregularly from 1300nm. The curve for poplar shows a sharp increase in reflectance around 700 nm to 0.48, then a plateau and an irregular decrease from BOOnrn with the same hollows and bumps as the grasses. The reflectance for the conifer is very low and less than 0.02 up to 700 nm and then shows a strong increase up to 0.2 and less up to 0.25 at llOOnm, then a very irregular decrease that only follows approximately the hollows and bumps of the other plants discussed here.

• [1] Spectral Library Version 7 - Base Spectra (splib07a), available at crustal.usgs.gov/speclab/Query-A1107a.php. [Original measurements made using lab, field and imaging spectrometers. Kokaly R. F.,Clark R. N.. Swayze G. A., Livo К. E., Hoefen T. M., Pearson N. C., Wise R. A., Benzel W. M., LowersH. A., Driscoll R. L„ Klein A. J., 2017. USGS Spectral Library Version 7: U.S. Geological Survey DataSeries 1035, 61 p. doi:10.3133/ds!035.