# Albedo

Percentage of diffusely reflected sunlight in relation to various surface conditions

Albedo, or reflection coefficient, derived from Latin albedo "whiteness" (or reflected sunlight), in turn from albus "white", is the diffuse reflectivity or reflecting power of a surface. It is defined as the ratio of reflected radiation from the surface to incident radiation upon it. Being a dimensionless fraction, it may also be expressed as a percentage, and is measured on a scale from zero for no reflecting power of a perfectly black surface, to 1 for perfect reflection of a white surface.

Albedo depends on the frequency of the radiation. When quoted unqualified, it usually refers to some appropriate average across the spectrum of visible light. In general, the albedo depends on the directional distribution of incoming radiation. Exceptions are Lambertian surfaces, which scatter radiation in all directions according to a cosine function, so their albedo does not depend on the incident distribution. In practice, a bidirectional reflectance distribution function (BRDF) may be required to characterize the scattering properties of a surface accurately, although the albedo is a very useful first approximation.

The albedo is an important concept in climatology and astronomy, as well as in calculating reflectivity of surfaces in LEED sustainable rating systems for buildings. The average overall albedo of Earth, its planetary albedo, is 30 to 35%, because of the covering by clouds, but varies widely locally across the surface, depending on the geological and environmental features.[1]

The term was introduced into optics by Johann Heinrich Lambert in his 1760 work Photometria.

## Terrestrial albedo

Sample albedos
Surface Typical
albedo
Fresh asphalt 0.04[2]
Worn asphalt 0.12[2]
Conifer forest
(Summer)
0.08,[3] 0.09 to 0.15[4]
Deciduous trees 0.15 to 0.18[4]
Bare soil 0.17[5]
Green grass 0.25[5]
Desert sand 0.40[6]
New concrete 0.55[5]
Ocean ice 0.5–0.7[5]
Fresh snow 0.80–0.90[5]

Albedos of typical materials in visible light range from up to 0.9 for fresh snow, to about 0.04 for charcoal, one of the darkest substances. Deeply shadowed cavities can achieve an effective albedo approaching the zero of a black body. When seen from a distance, the ocean surface has a low albedo, as do most forests, whereas desert areas have some of the highest albedos among landforms. Most land areas are in an albedo range of 0.1 to 0.4.[7] The average albedo of the Earth is about 0.3.[8] 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 on the global scale is difficult.

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 also 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.

2003–2004 mean annual clear-sky and total-sky albedo

The Earth's surface albedo is regularly estimated via Earth observation satellite sensors such as NASA's MODIS instruments on board 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 (e.g.[9]).

The Earth's average surface temperature due to its albedo and the greenhouse effect is currently about 15 °C. If the Earth was frozen entirely (and hence be more reflective) the average temperature of the planet would drop below −40 °C[10] If only the continental land masses became covered by glaciers, the mean temperature of the planet would drop to about 0 °C.[11] In contrast, if all the ice on Earth were to melt—a so-called aquaplanet—the average temperature on the planet would rise to just under 27 °C.[12]

### 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 θi 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.[13]

## Astronomical albedo

The albedos 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 0.96 .[14] Many small objects in the outer solar system[15] and asteroid belt have low albedos down to about 0.05.[16] A typical comet nucleus has an albedo of 0.04.[17] 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 0.12, but it is strongly directional and non-Lambertian, displaying also a strong opposition effect.[18] 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 (V-band) 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:[19] $A =\left ( \frac{1329\times10^{-H/5}}{D} \right ) ^2$,

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

## Examples of terrestrial albedo effects

### Illumination

Although the albedo–temperature effect is best known in colder, whiter regions on Earth, the maximum albedo is actually found in the tropics where year-round illumination is greater. The maximum is additionally in the northern hemisphere, varying between 3 and 12 degrees north.[20] The minima are found in the subtropical regions of the northern and southern hemispheres, beyond which albedo increases without respect to illumination.[20]

### Small-scale effects

Albedo works on a smaller scale, too. In sunlight, dark clothes absorb more heat and light-coloured clothes reflect it better, thus allowing some control over body temperature by exploiting the albedo effect of the colour of external clothing.[21]

### Trees

Because forests are generally attributed a low albedo, (as the majority of the ultraviolet and visible spectrum is absorbed through photosynthesis), it has been erroneously assumed that removing forests would lead to cooling on the grounds of increased albedo. Through the evapotranspiration of water, trees discharge excess heat from the forest canopy. This water vapour rises resulting in cloud cover which also has a high albedo, thereby further increasing the net global cooling effect attributable to forests.

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 whereas coniferous trees have a value of about 0.09 to 0.15.[4]

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.[22]

### Snow

Snow albedos can be as high as 0.9; this, however, is for the ideal example: fresh deep snow over a featureless landscape. Over Antarctica they average a little more than 0.8. 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). Cryoconite, powdery windblown dust containing soot, sometimes reduces albedo on glaciers and ice sheets.[23]

### Water

Water reflects light very differently from typical terrestrial materials. The reflectivity of a water surface is calculated using the Fresnel equations (see graph).

Reflectivity of smooth water at 20 °C (refractive index=1.333)

At the scale of the wavelength of light even wavy water is always smooth so the light is reflected in a locally 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 because of the steepness of the reflectivity-vs.-incident-angle curve and a locally increased average incident angle.[24]

Although the reflectivity of water is very low at low and medium angles of incident light, it increases tremendously at high 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 high angles of incident light.

Note that white caps on waves look white (and have high albedo) because the water is foamed up, so there are many superimposed bubble surfaces which reflect, adding up their reflectivities. Fresh ‘black’ ice exhibits Fresnel reflection.

### Clouds

Cloud albedo has substantial influence over atmospheric temperatures. Different types of clouds exhibit different reflectivity, theoretically ranging in albedo from a minimum of near 0 to a maximum approaching 0.8. "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."[25]

Albedo and climate in some areas are affected by artificial clouds, such as those created by the contrails of heavy commercial airliner traffic.[26] A study following the burning of the Kuwaiti oil fields during Iraqi occupation showed that temperatures under the burning oil fires were as much as 10 °C colder than temperatures several miles away under clear skies.[27]

### Aerosol effects

Aerosols (very fine particles/droplets in the atmosphere) have both direct and indirect effects on the Earth’s radiative balance. The direct (albedo) effect is generally to cool the planet; the indirect effect (the particles act as cloud condensation nuclei and thereby change cloud properties) is less certain.[28] As per [29] the effects are:

• Aerosol direct effect. Aerosols directly scatter and absorb radiation. The scattering of radiation causes atmospheric cooling, whereas absorption can cause atmospheric warming.
• Aerosol indirect effect. Aerosols modify the properties of clouds through a subset of the aerosol population called cloud condensation nuclei. Increased nuclei concentrations lead to increased cloud droplet number concentrations, which in turn leads to increased cloud albedo, increased light scattering and radiative cooling (first indirect effect), but also leads to reduced precipitation efficiency and increased lifetime of the cloud (second indirect effect).

### Black carbon

Another albedo-related effect on the climate is from black carbon particles. The size of this effect is difficult to quantify: the Intergovernmental Panel on Climate Change estimates that the global mean radiative forcing for black carbon aerosols from fossil fuels is +0.2 W m−2, with a range +0.1 to +0.4 W m−2.[30]

## 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 or particles; and the wavelength of the incoming radiation.

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