Albedo

The albedo of an object is the extent to which it diffusely reflects light from the sun. It is therefore a more specific form of the term reflectivity. Albedo is defined as the ratio of diffusely reflected to incident electromagnetic radiation. It is a unitless measure indicative of a surface's or body's diffuse reflectivity. The word is derived from Latin albedo "whiteness", in turn from albus "white". The range of possible values is from 0 (dark) to 1 (bright).

The albedo is an important concept in climatology and astronomy. In climatology it is sometimes expressed as a percentage. Its value depends on the frequency of radiation considered: unqualified, it usually refers to some appropriate average across the spectrum of visible light. In general, the albedo depends on the direction and directional distribution of incoming radiation. Exceptions are Lambertian surfaces, which scatter radiation in all directions in a cosine function, so their albedo does not depend on the incoming distribution. In realistic cases, a bidirectional reflectance distribution function (BRDF) is required to characterize the scattering properties of a surface accurately, although albedos are a very useful first approximation.

Terrestrial albedo
Albedos of typical materials in visible light range from up to 90% for fresh snow, to about 4% for charcoal, one of the darkest substances. Deeply shadowed cavities can achieve an effective albedo approaching the zero of a blackbody. When seen from a distance, the ocean surface has a low albedo, as do most forests, while desert areas have some of the highest albedos among landforms. Most land areas are in an albedo range of .1 to .4. The average albedo of the Earth is about 30%. This is far higher than for the ocean primarily because of the contribution of clouds.

Human activities have changed the albedo (via forest clearance and farming, for example) of various areas around the globe. However, quantification of this effect is difficult on the global scale.

The classic example of albedo effect is the snow-temperature feedback. If a snow covered area warms and the snow melts, the albedo decreases, more sunlight is absorbed, and the temperature tends to increase. The converse is true: if snow forms, a cooling cycle happens. The intensity of the albedo effect depends on the size of the change in albedo and the amount of insolation; for this reason it can be potentially very large in the tropics.

The Earth's surface albedo is regularly estimated via Earth observation satellite sensors such as NASA's MODIS instruments onboard the Terra and Aqua satellites. As the total amount of reflected radiation cannot be directly measured by satellite, a mathematical model of the BRDF is used to translate a sample set of satellite reflectance measurements into estimates of directional-hemispherical reflectance and bi-hemispherical reflectance.

White-sky and black-sky albedo
It has been shown that for many applications involving terrestrial albedo, the albedo at a particular solar zenith angle $${\theta_i}$$ can reasonably be approximated by the proportionate sum of two terms: the directional-hemispherical reflectance at that solar zenith angle, $${\bar \alpha(\theta_i)}$$, and the bi-hemispherical reflectance, $${\bar \bar \alpha}$$ the proportion concerned being defined as the proportion of diffuse illumination $${D}$$.

Albedo $${\alpha}$$ can then be given as:

$${\alpha}= (1-D) \bar \alpha(\theta_i) + D \bar \bar \alpha.$$

Directional-hemispherical reflectance is sometimes referred to as black-sky albedo and bi-hemispherical reflectance as white sky albedo. These terms are important because they allow the albedo to be calculated for any given illumination conditions from a knowledge of the intrinsic properties of the surface.

Astronomical albedo
The albedo of planets, satellites and asteroids can be used to infer much about their properties. The study of albedos, their dependence on wavelength, lighting angle ("phase angle"), and variation in time comprises a major part of the astronomical field of photometry. For small and far objects that cannot be resolved by telescopes, much of what we know comes from the study of their albedos. For example, the absolute albedo can indicate the surface ice content of outer solar system objects, the variation of albedo with phase angle gives information about regolith properties, while unusually high radar albedo is indicative of high metallic content in asteroids.

Enceladus, a moon of Saturn, has one of the highest known albedos of any body in the solar system, with 99% of EM radiation reflected. Another notable high albedo body is Eris, with an albedo of 86%. Many objects in the outer solar system and asteroid belt have low albedos down to about 5%. Such a dark surface is thought to be indicative of a primitive and heavily space weathered surface containing some organic compounds.

The overall albedo of the Moon is around 7%, but it is strongly directional and non-Lambertian, displaying also a strong opposition effect. While such reflectance properties are different from those of any terrestrial terrains, they are typical of the regolith surfaces of airless solar system bodies.

Two common albedos that are used in astronomy are the geometric albedo (measuring brightness when illumination comes from directly behind the observer) and the Bond albedo (measuring total proportion of electromagnetic energy reflected). Their values can differ significantly, which is a common source of confusion.

In detailed studies, the directional reflectance properties of astronomical bodies are often expressed in terms of the five Hapke parameters which semi-empirically describe the variation of albedo with phase angle, including a characterization of the opposition effect of regolith surfaces.

The correlation between astronomical (geometric) albedo, absolute magnitude and diameter is $$A =\left ( \frac{1329\times10^{-H/5}}{D} \right ) ^2$$,

where $$A$$ is astronomical albedo, $$D$$ is diameter in km, and H is the absolute magnitude.

Other types of albedo
Single scattering albedo - is used to define scattering of electromagnetic waves on small particles. It depends on properties of the material (refractive index), the size of the particle(s), and the wavelength of the incoming radiation.

Fairbanks, Alaska
According to the National Climatic Data Center's GHCN 2 data, which is composed of 30-year smoothed climatic means for thousands of weather stations across the world, the college weather station at Fairbanks, Alaska, is about 3 °C (5.4 °F) warmer than the airport at Fairbanks, partly because of air drainage patterns but also largely because of the lower albedo at the college resulting from a higher concentration of spruce trees and therefore less open snowy ground to reflect the heat back into space.

The tropics
Although the albedo-temperature effect is most famous in colder regions of Earth, because more snow falls there, it is actually much stronger in tropical regions because in the tropics there is consistently more sunlight. When Brazilian ranchers cut down dark, tropical rainforest trees to replace them with even darker soil in order to grow crops, the average temperature of the area increases up to 3 °C (5.4 °F) year-round, although part of the effect is due to changed evaporation (latent heat flux).

Small scale effects
Albedo works on a smaller scale, too. People who wear dark clothes in the summertime put themselves at a greater risk of heatstroke than those who wear lighter color clothes.

Albedo of various terrains
The albedo of a pine forest at 45°N in the winter in which the trees cover the land surface completely is only about 9%, among the lowest of any naturally occurring land environment. This is partly due to the color of the pines, and partly due to multiple scattering of sunlight within the trees which lowers the overall reflected light level. Due to light penetration, the ocean's albedo is even lower at about 3.5%, though this depends strongly on the angle of the incident radiation. Dense swampland averages between 9% and 14%. Deciduous trees average about 13%. A grassy field usually comes in at about 20%. A barren field will depend on the color of the soil, and can be as low as 5% or as high as 40%, with 15% being about the average for farmland. A desert or large beach usually averages around 25% but varies depending on the color of the sand.

Urban areas
Urban areas in particular have very unnatural values for albedo because of the many human-built structures which absorb light before the light can reach the surface. In the northern part of the world, cities are relatively dark, and Walker has shown that their average albedo is about 7%, with only a slight increase during the summer. In most tropical countries, cities average around 12%. This is similar to the values found in northern suburban transitional zones. Part of the reason for this is the different natural environment of cities in tropical regions, e.g., there are more very dark trees around; another reason is that portions of the tropics are very poor, and city buildings must be built with different materials. Warmer regions may also choose lighter colored building materials so the structures will remain cooler.

Trees
Because trees tend to have a low albedo, removing forests would tend to increase albedo and thereby could produce localized climate cooling. Cloud feedbacks further complicate the issue. In seasonally snow-covered zones, winter albedos of treeless areas are 10% to 50% higher than nearby forested areas because snow does not cover the trees as readily. Deciduous trees have an albedo value of about 0.15 to 0.18 while coniferous trees have a value of about 0.09 to 0.15. The difference between deciduous and coniferous is because coniferous trees are darker in general and have cone-shape seeds. The pattern of these seeds trap light energy more than deciduous trees.

Studies by the Hadley Centre have investigated the relative (generally warming) effect of albedo change and (cooling) effect of carbon sequestration on planting forests. They found that new forests in tropical and midlatitude areas tended to cool; new forests in high latitudes (e.g. Siberia) were neutral or perhaps warming.

Snow
Snow albedos can be as high as 90%; this, however, is for the ideal example: fresh deep snow over a featureless landscape. Over Antarctica they average a little more than 80%.

If a marginally snow-covered area warms, snow tends to melt, lowering the albedo, and hence leading to more snowmelt (the ice-albedo positive feedback). This is the basis for predictions of enhanced warming in the polar and seasonally snow covered regions as a result of global warming.

Water
Water reflects light very differently from typical terrestrial materials. The reflectivity of a water surface is calculated using the Fresnel equations (see graph). At the scale of the wavelength of light even wavy water is always smooth so the light is reflected in a specular manner (not diffusely). The glint of light off water is a commonplace effect of this. At small angles of incident light, waviness results in reduced reflectivity (from as high as 100%) because of the steepness of the reflectivity-vs.-incident-angle curve and a locally increased average incident angle.

Although the reflectivity of water is very low at high and medium angles of incident light, it increases tremendously at small angles of incident light such as occur on the illuminated side of the earth near the terminator (early morning, late afternoon and near the poles). However, as mentioned above, waviness causes an appreciable reduction. Since the light specularly reflected from water does not usually reach the viewer, water is usually considered to have a very low albedo in spite of its high reflectivity at low angles of incident light.

Note that white caps on waves look white (and have high albedo) because the water is foamed up (not smooth at the scale of the wavelength of light) so the Fresnel equations do not apply. Fresh ‘black’ ice exhibits Fresnel reflection.

Clouds
Clouds are another source of albedo that play into the global warming equation. Different types of clouds have different albedo values, theoretically ranging from a minimum of near 0% to a maximum in the high 70s. "On any given day, about half of Earth is covered by clouds, which reflect more sunlight than land and water. Clouds keep Earth cool by reflecting sunlight, but they can also serve as blankets to trap warmth."

Albedo and climate in some areas are already affected by artificial clouds, such as those created by the contrails of heavy commercial airliner traffic. A study following the burning of the Kuwaiti oil fields by Saddam Hussein showed that temperatures under the burning oil fires were as much as 10oC colder than temperatures several miles away under clear skies.

Aerosol effects
Aerosol (very fine particles/droplets in the atmosphere) has two effects, direct and indirect. The direct (albedo) effect is generally to cool the planet; the indirect effect (the particles act as CCNs and thereby change cloud properties) is less certain.

Black carbon
Another albedo-related effect on the climate is from black carbon particles. The size of this effect is difficult to quantify: the IPCC say that their "estimate of the global mean radiative forcing for BC aerosols from fossil fuels is ... +0.2 W m-2 (from +0.1 W m-2 in the SAR) with a range +0.1 to +0.4 W m...-2".