Kirchhoff's law of thermal radiation

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https://en.wikipedia.org/wiki/Kirchhoff%27s_law_of_thermal_radiation 

Gustav Kirchhoff (1824–1887)

In heat transfer, Kirchhoff's law of thermal radiation refers to wavelength-specific radiative emission and absorption by a material body in thermodynamic equilibrium, including radiative exchange equilibrium.

A body at temperature T radiates electromagnetic energy. A perfect black body in thermodynamic equilibrium absorbs all light that strikes it, and radiates energy according to a unique law of radiative emissive power for temperature T, universal for all perfect black bodies. Kirchhoff's law states that:

For a body of any arbitrary material emitting and absorbing thermal electromagnetic radiation at every wavelength in thermodynamic equilibrium, the ratio of its emissive power to its dimensionless coefficient of absorption is equal to a universal function only of radiative wavelength and temperature. That universal function describes the perfect black-body emissive power.

Here, the dimensionless coefficient of absorption (or the absorptivity) is the fraction of incident light (power) that is absorbed by the body when it is radiating and absorbing in thermodynamic equilibrium.

In slightly different terms, the emissive power of an arbitrary opaque body of fixed size and shape at a definite temperature can be described by a dimensionless ratio, sometimes called the emissivity: the ratio of the emissive power of the body to the emissive power of a black body of the same size and shape at the same fixed temperature. With this definition, Kirchhoff's law states, in simpler language:

For an arbitrary body emitting and absorbing thermal radiation in thermodynamic equilibrium, the emissivity is equal to the absorptivity.

In some cases, emissive power and absorptivity may be defined to depend on angle, as described below. The condition of thermodynamic equilibrium is necessary in the statement, because the equality of emissivity and absorptivity often does not hold when the material of the body is not in thermodynamic equilibrium.

Kirchhoff's law has another corollary: the emissivity cannot exceed one (because the absorptivity cannot, by conservation of energy), so it is not possible to thermally radiate more energy than a black body, at equilibrium. In negative luminescence the angle and wavelength integrated absorption exceeds the material's emission, however, such systems are powered by an external source and are therefore not in thermodynamic equilibrium.

History

Before Kirchhoff's law was recognized, it had been experimentally established that a good absorber is a good emitter, and a poor absorber is a poor emitter. Naturally, a good reflector must be a poor absorber. This is why, for example, lightweight emergency thermal blankets are based on reflective metallic coatings: they lose little heat by radiation.

Kirchhoff's great insight was to recognize the universality and uniqueness of the function that describes the black body emissive power. But he did not know the precise form or character of that universal function. Attempts were made by Lord Rayleigh and Sir James Jeans 1900–1905 to describe it in classical terms, resulting in Rayleigh–Jeans law. This law turned out to be inconsistent yielding the ultraviolet catastrophe. The correct form of the law was found by Max Planck in 1900, assuming quantized emission of radiation, and is termed Planck's law. This marks the advent of quantum mechanics.

Theory

In a blackbody enclosure that contains electromagnetic radiation with a certain amount of energy at thermodynamic equilibrium, this "photon gas" will have a Planck distribution of energies.

One may suppose a second system, a cavity with walls that are opaque, rigid, and not perfectly reflective to any wavelength, to be brought into connection, through an optical filter, with the blackbody enclosure, both at the same temperature. Radiation can pass from one system to the other. For example, suppose in the second system, the density of photons at narrow frequency band around wavelength ${\displaystyle \lambda }$ were higher than that of the first system. If the optical filter passed only that frequency band, then there would be a net transfer of photons, and their energy, from the second system to the first. This is in violation of the second law of thermodynamics, which requires that there can be no net transfer of heat between two bodies at the same temperature.

In the second system, therefore, at each frequency, the walls must absorb and emit energy in such a way as to maintain the black body distribution. Hence absorptivity and emissivity must be equal. The absorptivity ${\displaystyle \alpha _{\lambda }}$ of the wall is the ratio of the energy absorbed by the wall to the energy incident on the wall, for a particular wavelength. Thus the absorbed energy is ${\displaystyle \alpha _{\lambda }E_{b\lambda }(\lambda ,T)}$ where ${\displaystyle E_{b\lambda }(\lambda ,T)}$ is the intensity of black body radiation at wavelength ${\displaystyle \lambda }$ and temperature ${\displaystyle T}$. Independent of the condition of thermal equilibrium, the emissivity of the wall is defined as the ratio of emitted energy to the amount that would be radiated if the wall were a perfect black body. The emitted energy is thus ${\displaystyle \varepsilon _{\lambda }E_{b\lambda }(\lambda ,T)}$ where ${\displaystyle \varepsilon _{\lambda }}$ is the emissivity at wavelength ${\displaystyle \lambda }$. For the maintenance of thermal equilibrium, these two quantities must be equal, or else the distribution of photon energies in the cavity will deviate from that of a black body. This yields Kirchhoff's law:

${\displaystyle \alpha _{\lambda }=\varepsilon _{\lambda }}$

By a similar, but more complicated argument, it can be shown that, since black body radiation is equal in every direction (isotropic), the emissivity and the absorptivity, if they happen to be dependent on direction, must again be equal for any given direction.

Average and overall absorptivity and emissivity data are often given for materials with values which differ from each other. For example, white paint is quoted as having an absorptivity of 0.16, while having an emissivity of 0.93. This is because the absorptivity is averaged with weighting for the solar spectrum, while the emissivity is weighted for the emission of the paint itself at normal ambient temperatures. The absorptivity quoted in such cases is being calculated by:

${\displaystyle \alpha _{\mathrm {sun} }=\displaystyle {\frac {\int _{0}^{\infty }\alpha _{\lambda }(\lambda )I_{\lambda \mathrm {sun} }(\lambda )\,d\lambda }{\int _{0}^{\infty }I_{\lambda \mathrm {sun} }(\lambda )\,d\lambda }}}$

while the average emissivity is given by:

${\displaystyle \varepsilon _{\mathrm {paint} }={\frac {\int _{0}^{\infty }\varepsilon _{\lambda }(\lambda ,T)E_{b\lambda }(\lambda ,T)\,d\lambda }{\int _{0}^{\infty }E_{b\lambda }(\lambda ,T)\,d\lambda }}}$

Where ${\displaystyle I_{\lambda \mathrm {sun} }}$ is the emission spectrum of the sun, and ${\displaystyle \varepsilon _{\lambda }E_{b\lambda }(\lambda ,T)}$ is the emission spectrum of the paint. Although, by Kirchhoff's law, ${\displaystyle \varepsilon _{\lambda }=\alpha _{\lambda }}$ in the above equations, the above averages ${\displaystyle \alpha _{\mathrm {sun} }}$ and ${\displaystyle \varepsilon _{\mathrm {paint} }}$ are not generally equal to each other. The white paint will serve as a very good insulator against solar radiation, because it is very reflective of the solar radiation, and although it therefore emits poorly in the solar band, its temperature will be around room temperature, and it will emit whatever radiation it has absorbed in the infrared, where its emission coefficient is high.

Black bodies

Near-black materials

It has long been known that a lamp-black coating will make a body nearly black. Some other materials are nearly black in particular wavelength bands. Such materials do not survive all the very high temperatures that are of interest.

An improvement on lamp-black is found in manufactured carbon nanotubes. Nano-porous materials can achieve refractive indices nearly that of vacuum, in one case obtaining average reflectance of 0.045%.

Opaque bodies

Bodies that are opaque to thermal radiation that falls on them are valuable in the study of heat radiation. Planck analyzed such bodies with the approximation that they be considered topologically to have an interior and to share an interface. They share the interface with their contiguous medium, which may be rarefied material such as air, or transparent material, through which observations can be made. The interface is not a material body and can neither emit nor absorb. It is a mathematical surface belonging jointly to the two media that touch it. It is the site of refraction of radiation that penetrates it and of reflection of radiation that does not. As such it obeys the Helmholtz reciprocity principle. The opaque body is considered to have a material interior that absorbs all and scatters or transmits none of the radiation that reaches it through refraction at the interface. In this sense the material of the opaque body is black to radiation that reaches it, while the whole phenomenon, including the interior and the interface, does not show perfect blackness. In Planck's model, perfectly black bodies, which he noted do not exist in nature, besides their opaque interior, have interfaces that are perfectly transmitting and non-reflective.

Cavity radiation

The walls of a cavity can be made of opaque materials that absorb significant amounts of radiation at all wavelengths. It is not necessary that every part of the interior walls be a good absorber at every wavelength. The effective range of absorbing wavelengths can be extended by the use of patches of several differently absorbing materials in parts of the interior walls of the cavity. In thermodynamic equilibrium the cavity radiation will precisely obey Planck's law. In this sense, thermodynamic equilibrium cavity radiation may be regarded as thermodynamic equilibrium black-body radiation to which Kirchhoff's law applies exactly, though no perfectly black body in Kirchhoff's sense is present.

A theoretical model considered by Planck consists of a cavity with perfectly reflecting walls, initially with no material contents, into which is then put a small piece of carbon. Without the small piece of carbon, there is no way for non-equilibrium radiation initially in the cavity to drift towards thermodynamic equilibrium. When the small piece of carbon is put in, it transduces amongst radiation frequencies so that the cavity radiation comes to thermodynamic equilibrium.

A hole in the wall of a cavity

For experimental purposes, a hole in a cavity can be devised to provide a good approximation to a black surface, but will not be perfectly Lambertian, and must be viewed from nearly right angles to get the best properties. The construction of such devices was an important step in the empirical measurements that led to the precise mathematical identification of Kirchhoff's universal function, now known as Planck's law.

Kirchhoff's perfect black bodies

Planck also noted that the perfect black bodies of Kirchhoff do not occur in physical reality. They are theoretical fictions. Kirchhoff's perfect black bodies absorb all the radiation that falls on them, right in an infinitely thin surface layer, with no reflection and no scattering. They emit radiation in perfect accord with Lambert's cosine law.

Original statements

Gustav Kirchhoff stated his law in several papers in 1859 and 1860, and then in 1862 in an appendix to his collected reprints of those and some related papers.

Prior to Kirchhoff's studies, it was known that for total heat radiation, the ratio of emissive power to absorptive ratio was the same for all bodies emitting and absorbing thermal radiation in thermodynamic equilibrium. This means that a good absorber is a good emitter. Naturally, a good reflector is a poor absorber. For wavelength specificity, prior to Kirchhoff, the ratio was shown experimentally by Balfour Stewart to be the same for all bodies, but the universal value of the ratio had not been explicitly considered in its own right as a function of wavelength and temperature.

Kirchhoff's original contribution to the physics of thermal radiation was his postulate of a perfect black body radiating and absorbing thermal radiation in an enclosure opaque to thermal radiation and with walls that absorb at all wavelengths. Kirchhoff's perfect black body absorbs all the radiation that falls upon it.

Every such black body emits from its surface with a spectral radiance that Kirchhoff labeled I (for specific intensity, the traditional name for spectral radiance).

Kirchhoff's postulated spectral radiance I was a universal function, one and the same for all black bodies, only depending on wavelength and temperature.

The precise mathematical expression for that universal function I was very much unknown to Kirchhoff, and it was just postulated to exist, until its precise mathematical expression was found in 1900 by Max Planck. It is nowadays referred to as Planck's law.

Then, at each wavelength, for thermodynamic equilibrium in an enclosure, opaque to heat rays, with walls that absorb some radiation at every wavelength:

For an arbitrary body radiating and emitting thermal radiation, the ratio E / A between the emissive spectral radiance, E, and the dimensionless absorptive ratio, A, is one and the same for all bodies at a given temperature. That ratio E / A is equal to the emissive spectral radiance I of a perfect black body, a universal function only of wavelength and temperature.

 

Albedo

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https://en.wikipedia.org/wiki/Albedo 

The percentage of diffusely reflected sunlight relative to various surface conditions

Albedo (/ælˈbiːdoʊ/) (Latin: albedo, meaning 'whiteness') is the measure of the diffuse reflection of solar radiation out of the total solar radiation and measured on a scale from 0, corresponding to a black body that absorbs all incident radiation, to 1, corresponding to a body that reflects all incident radiation.

Surface albedo is defined as the ratio of radiosity to the irradiance (flux per unit area) received by a surface. The proportion reflected is not only determined by properties of the surface itself, but also by the spectral and angular distribution of solar radiation reaching the Earth's surface. These factors vary with atmospheric composition, geographic location and time (see position of the Sun). While bi-hemispherical reflectance is calculated for a single angle of incidence (i.e., for a given position of the Sun), albedo is the directional integration of reflectance over all solar angles in a given period. The temporal resolution may range from seconds (as obtained from flux measurements) to daily, monthly, or annual averages.

Unless given for a specific wavelength (spectral albedo), albedo refers to the entire spectrum of solar radiation. Due to measurement constraints, it is often given for the spectrum in which most solar energy reaches the surface (between 0.3 and 3 μm). This spectrum includes visible light (0.4–0.7 μm), which explains why surfaces with a low albedo appear dark (e.g., trees absorb most radiation), whereas surfaces with a high albedo appear bright (e.g., snow reflects most radiation).

Albedo is an important concept in climatology, astronomy, and environmental management (e.g., as part of the Leadership in Energy and Environmental Design (LEED) program for sustainable rating of buildings). The average albedo of the Earth from the upper atmosphere, its planetary albedo, is 30–35% because of cloud cover, but widely varies locally across the surface because of different geological and environmental features.

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

Terrestrial albedo

Any albedo in visible light falls within a range of about 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. The average albedo of Earth is about 0.3. This is far higher than for the ocean primarily because of the contribution of clouds.

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

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, and the CERES instrument on the Suomi NPP and JPSS. As the amount of reflected radiation is only measured for a single direction by satellite, not all directions, a mathematical model is used to translate a sample set of satellite reflectance measurements into estimates of directional-hemispherical reflectance and bi-hemispherical reflectance (e.g.). These calculations are based on the bidirectional reflectance distribution function (BRDF), which describes how the reflectance of a given surface depends on the view angle of the observer and the solar angle. BDRF can facilitate translations of observations of reflectance into albedo.

Earth's average surface temperature due to its albedo and the greenhouse effect is currently about 15 °C. If Earth were frozen entirely (and hence be more reflective), the average temperature of the planet would drop below −40 °C. If only the continental land masses became covered by glaciers, the mean temperature of the planet would drop to about 0 °C. In contrast, if the entire Earth was covered by water – a so-called ocean planet – the average temperature on the planet would rise to almost 27 °C.

White-sky, black-sky, and blue-sky albedo

For land surfaces, it has been shown that the albedo at a particular solar zenith angle θ_i can be approximated by the proportionate sum of two terms:

• the directional-hemispherical reflectance at that solar zenith angle, ${\displaystyle {{\bar {\alpha }}(\theta _{i})}}$, sometimes referred to as black-sky albedo, and
• the bi-hemispherical reflectance, ${\displaystyle {\bar {\bar {\alpha }}}}$, sometimes referred to as white-sky albedo.

with ${\displaystyle {1-D}}$ being the proportion of direct radiation from a given solar angle, and ${\displaystyle {D}}$ being the proportion of diffuse illumination, the actual albedo ${\displaystyle {\alpha }}$ (also called blue-sky albedo) can then be given as:

${\displaystyle {\alpha }=(1-D){\bar {\alpha }}(\theta _{i})+D{\bar {\bar {\alpha }}}.}$

This formula is important because it allows the albedo to be calculated for any given illumination conditions from a knowledge of the intrinsic properties of the surface.

Astronomical albedo

The albedos of planets, satellites and minor planets such as 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 composes 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, whereas unusually high radar albedo is indicative of high metal content in asteroids.

Enceladus, a moon of Saturn, has one of the highest known albedos of any body in the Solar System, with an albedo of 0.99. Another notable high-albedo body is Eris, with an albedo of 0.96. Many small objects in the outer Solar System and asteroid belt have low albedos down to about 0.05. A typical comet nucleus has an albedo of 0.04. 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 measured to be around 0.14, but it is strongly directional and non-Lambertian, displaying also a strong opposition effect. Although 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: ${\displaystyle A=\left({\frac {1329\times 10^{-H/5}}{D}}\right)^{2}}$,

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

Examples of terrestrial albedo effects

Illumination

Albedo is not directly dependent on illumination because changing the amount of incoming light proportionally changes the amount of reflected light, except in circumstances where a change in illumination induces a change in the Earth's surface at that location (e.g. through melting of reflective ice). That said, albedo and illumination both vary by latitude. Albedo is highest near the poles and lowest in the subtropics, with a local maximum in the tropics.

Insolation effects

The intensity of albedo temperature effects depends on the amount of albedo and the level of local insolation (solar irradiance); high albedo areas in the arctic and antarctic regions are cold due to low insolation, whereas areas such as the Sahara Desert, which also have a relatively high albedo, will be hotter due to high insolation. Tropical and sub-tropical rainforest areas have low albedo, and are much hotter than their temperate forest counterparts, which have lower insolation. Because insolation plays such a big role in the heating and cooling effects of albedo, high insolation areas like the tropics will tend to show a more pronounced fluctuation in local temperature when local albedo changes.

Arctic regions notably release more heat back into space than what they absorb, effectively cooling the Earth. This has been a concern since arctic ice and snow has been melting at higher rates due to higher temperatures, creating regions in the arctic that are notably darker (being water or ground which is darker color) and reflects less heat back into space. This feedback loop results in a reduced albedo effect.

Climate and weather

Albedo affects climate by determining how much radiation a planet absorbs. The uneven heating of Earth from albedo variations between land, ice, or ocean surfaces can drive weather.

Albedo–temperature feedback

When an area's albedo changes due to snowfall, a snow–temperature feedback results. A layer of snowfall increases local albedo, reflecting away sunlight, leading to local cooling. In principle, if no outside temperature change affects this area (e.g., a warm air mass), the raised albedo and lower temperature would maintain the current snow and invite further snowfall, deepening the snow–temperature feedback. However, because local weather is dynamic due to the change of seasons, eventually warm air masses and a more direct angle of sunlight (higher insolation) cause melting. When the melted area reveals surfaces with lower albedo, such as grass or soil, the effect is reversed: the darkening surface lowers albedo, increasing local temperatures, which induces more melting and thus reducing the albedo further, resulting in still more heating.

Snow

Snow albedo is highly variable, ranging from as high as 0.9 for freshly fallen snow, to about 0.4 for melting snow, and as low as 0.2 for dirty snow. Over Antarctica snow albedo averages 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 because more radiation is being absorbed by the snowpack (the ice–albedo positive feedback).

Just as fresh snow has a higher albedo than does dirty snow, the albedo of snow-covered sea ice is far higher than that of sea water. Sea water absorbs more solar radiation than would the same surface covered with reflective snow. When sea ice melts, either due to a rise in sea temperature or in response to increased solar radiation from above, the snow-covered surface is reduced, and more surface of sea water is exposed, so the rate of energy absorption increases. The extra absorbed energy heats the sea water, which in turn increases the rate at which sea ice melts. As with the preceding example of snowmelt, the process of melting of sea ice is thus another example of a positive feedback. Both positive feedback loops have long been recognized as important for global warming.

Cryoconite, powdery windblown dust containing soot, sometimes reduces albedo on glaciers and ice sheets.

The dynamical nature of albedo in response to positive feedback, together with the effects of small errors in the measurement of albedo, can lead to large errors in energy estimates. Because of this, in order to reduce the error of energy estimates, it is important to measure the albedo of snow-covered areas through remote sensing techniques rather than applying a single value for albedo over broad regions.

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.

Solar photovoltaic effects

Albedo can affect the electrical energy output of solar photovoltaic devices. For example, the effects of a spectrally responsive albedo are illustrated by the differences between the spectrally weighted albedo of solar photovoltaic technology based on hydrogenated amorphous silicon (a-Si:H) and crystalline silicon (c-Si)-based compared to traditional spectral-integrated albedo predictions. Research showed impacts of over 10%. More recently, the analysis was extended to the effects of spectral bias due to the specular reflectivity of 22 commonly occurring surface materials (both human-made and natural) and analyzes the albedo effects on the performance of seven photovoltaic materials covering three common photovoltaic system topologies: industrial (solar farms), commercial flat rooftops and residential pitched-roof applications.

Trees

Because forests generally have a low albedo, (the majority of the ultraviolet and visible spectrum is absorbed through photosynthesis), some scientists have suggested that greater heat absorption by trees could offset some of the carbon benefits of afforestation (or offset the negative climate impacts of deforestation). In the case of evergreen forests with seasonal snow cover albedo reduction may be great enough for deforestation to cause a net cooling effect. Trees also impact climate in extremely complicated ways through evapotranspiration. The water vapor causes cooling on the land surface, causes heating where it condenses, acts a strong greenhouse gas, and can increase albedo when it condenses into clouds. Scientists generally treat evapotranspiration as a net cooling impact, and the net climate impact of albedo and evapotranspiration changes from deforestation depends greatly on local climate.

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. Variation in summer albedo across both forest types is correlated with maximum rates of photosynthesis because plants with high growth capacity display a greater fraction of their foliage for direct interception of incoming radiation in the upper canopy. The result is that wavelengths of light not used in photosynthesis are more likely to be reflected back to space rather than being absorbed by other surfaces lower in the canopy.

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.

Water

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

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 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.

Although the reflectivity of water is very low at low and medium angles of incident light, it becomes very high at high angles of incident light such as those that occur on the illuminated side of Earth near the terminator (early morning, late afternoon, and near the poles). However, as mentioned above, waviness causes an appreciable reduction. Because 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. Snow on top of this sea ice increases the albedo to 0.9.

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."

Albedo and climate in some areas are 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 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.

Aerosol effects

Aerosols (very fine particles/droplets in the atmosphere) have both direct and indirect effects on 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. As per Spracklen et al. 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. Black carbon is a bigger cause of the melting of the polar ice cap in the Arctic than carbon dioxide due to its effect on the albedo.

Human activities

Human activities (e.g., deforestation, farming, and urbanization) change the albedo of various areas around the globe. However, quantification of this effect on the global scale is difficult, further study is required to determine anthropogenic effects.

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.

 

Future of Earth

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https://en.wikipedia.org/wiki/Future_of_Earth 

 

Conjectured illustration of the scorched Earth after the Sun has entered the red giant phase, about 5 billion years from now

The biological and geological future of Earth can be extrapolated based upon the estimated effects of several long-term influences. These include the chemistry at Earth's surface, the rate of cooling of the planet's interior, the gravitational interactions with other objects in the Solar System, and a steady increase in the Sun's luminosity. An uncertain factor in this extrapolation is the continuous influence of technology introduced by humans, such as climate engineering, which could cause significant changes to the planet. The current Holocene extinction is being caused by technology and the effects may last for up to five million years. In turn, technology may result in the extinction of humanity, leaving the planet to gradually return to a slower evolutionary pace resulting solely from long-term natural processes.

Over time intervals of hundreds of millions of years, random celestial events pose a global risk to the biosphere, which can result in mass extinctions. These include impacts by comets or asteroids, and the possibility of a massive stellar explosion, called a supernova, within a 100-light-year radius of the Sun. Other large-scale geological events are more predictable. Milankovitch theory predicts that the planet will continue to undergo glacial periods at least until the Quaternary glaciation comes to an end. These periods are caused by the variations in eccentricity, axial tilt, and precession of the Earth's orbit. As part of the ongoing supercontinent cycle, plate tectonics will probably result in a supercontinent in 250–350 million years. Some time in the next 1.5–4.5 billion years, the axial tilt of the Earth may begin to undergo chaotic variations, with changes in the axial tilt of up to 90°.

The luminosity of the Sun will steadily increase, resulting in a rise in the solar radiation reaching the Earth. This will result in a higher rate of weathering of silicate minerals, which will cause a decrease in the level of carbon dioxide in the atmosphere. In about 600 million years from now, the level of carbon dioxide will fall below the level needed to sustain C₃ carbon fixation photosynthesis used by trees. Some plants use the C₄ carbon fixation method, allowing them to persist at carbon dioxide concentrations as low as 10 parts per million. However, the long-term trend is for plant life to die off altogether. The extinction of plants will be the demise of almost all animal life, since plants are the base of the food chain on Earth.

In about one billion years, the solar luminosity will be 10% higher than at present. This will cause the atmosphere to become a "moist greenhouse", resulting in a runaway evaporation of the oceans. As a likely consequence, plate tectonics will come to an end, and with them the entire carbon cycle.

Following this event, in about 2–3 billion years, the planet's magnetic dynamo may cease, causing the magnetosphere to decay and leading to an accelerated loss of volatiles from the outer atmosphere. Four billion years from now, the increase in the Earth's surface temperature will cause a runaway greenhouse effect, heating the surface enough to melt it. By that point, all life on the Earth will be extinct. The most probable fate of the planet is absorption by the Sun in about 7.5 billion years, after the star has entered the red giant phase and expanded beyond the planet's current orbit.

Human influence

Anti-nuclear weapons protest march in Oxford, 1980

Humans play a key role in the biosphere, with the large human population dominating many of Earth's ecosystems. This has resulted in a widespread, ongoing mass extinction of other species during the present geological epoch, now known as the Holocene extinction. The large-scale loss of species caused by human influence since the 1950s has been called a biotic crisis, with an estimated 10% of the total species lost as of 2007. At current rates, about 30% of species are at risk of extinction in the next hundred years. The Holocene extinction event is the result of habitat destruction, the widespread distribution of invasive species, hunting, and climate change. In the present day, human activity has had a significant impact on the surface of the planet. More than a third of the land surface has been modified by human actions, and humans use about 20% of global primary production. The concentration of carbon dioxide in the atmosphere has increased by close to 30% since the start of the Industrial Revolution.

The consequences of a persistent biotic crisis have been predicted to last for at least five million years. It could result in a decline in biodiversity and homogenization of biotas, accompanied by a proliferation of species that are opportunistic, such as pests and weeds. Novel species may also emerge; in particular taxa that prosper in human-dominated ecosystems may rapidly diversify into many new species. Microbes are likely to benefit from the increase in nutrient-enriched environmental niches. No new species of existing large vertebrates are likely to arise and food chains will probably be shortened.

There are multiple scenarios for known risks that can have a global impact on the planet. From the perspective of humanity, these can be subdivided into survivable risks and terminal risks. Risks that humanity pose to itself include climate change, the misuse of nanotechnology, a nuclear holocaust, warfare with a programmed superintelligence, a genetically engineered disease, or a disaster caused by a physics experiment. Similarly, several natural events may pose a doomsday threat, including a highly virulent disease, the impact of an asteroid or comet, runaway greenhouse effect, and resource depletion. There may also be the possibility of an infestation by an extraterrestrial lifeform. The actual odds of these scenarios occurring are difficult if not impossible to deduce.

Should the human species become extinct, then the various features assembled by humanity will begin to decay. The largest structures have an estimated decay half-life of about 1,000 years. The last surviving structures would most likely be open pit mines, large landfills, major highways, wide canal cuts, and earth-fill flank dams. A few massive stone monuments like the pyramids at the Giza Necropolis or the sculptures at Mount Rushmore may still survive in some form after a million years.

Potential events

The Barringer Meteorite Crater in Flagstaff, Arizona, showing evidence of the impact of celestial objects upon the Earth

As the Sun orbits the Milky Way, wandering stars may approach close enough to have a disruptive influence on the Solar System. A close stellar encounter may cause a significant reduction in the perihelion distances of comets in the Oort cloud—a spherical region of icy bodies orbiting within half a light year of the Sun. Such an encounter can trigger a 40-fold increase in the number of comets reaching the inner Solar System. Impacts from these comets can trigger a mass extinction of life on Earth. These disruptive encounters occur at an average of once every 45 million years. The mean time for the Sun to collide with another star in the solar neighborhood is approximately 3 × 10¹³ years, which is much longer than the estimated age of the Universe, at ~1.38 × 10¹⁰ years. This can be taken as an indication of the low likelihood of such an event occurring during the lifetime of the Earth.

The energy release from the impact of an asteroid or comet with a diameter of 5–10 km (3–6 mi) or larger is sufficient to create a global environmental disaster and cause a statistically significant increase in the number of species extinctions. Among the deleterious effects resulting from a major impact event is a cloud of fine dust ejecta blanketing the planet, blocking some direct sunlight from reaching the Earth's surface thus lowering land temperatures by about 15 °C (27 °F) within a week and halting photosynthesis for several months (similar to a nuclear winter). The mean time between major impacts is estimated to be at least 100 million years. During the last 540 million years, simulations demonstrated that such an impact rate is sufficient to cause 5–6 mass extinctions and 20–30 lower severity events. This matches the geologic record of significant extinctions during the Phanerozoic Eon. Such events can be expected to continue into the future.

A supernova is a cataclysmic explosion of a star. Within the Milky Way galaxy, supernova explosions occur on average once every 40 years. During the history of the Earth, multiple such events have likely occurred within a distance of 100 light years; known as a near-Earth supernova. Explosions inside this distance can contaminate the planet with radioisotopes and possibly impact the biosphere. Gamma rays emitted by a supernova react with nitrogen in the atmosphere, producing nitrous oxides. These molecules cause a depletion of the ozone layer that protects the surface from ultraviolet (UV) radiation from the Sun. An increase in UV-B radiation of only 10–30% is sufficient to cause a significant impact to life; particularly to the phytoplankton that form the base of the oceanic food chain. A supernova explosion at a distance of 26 light years will reduce the ozone column density by half. On average, a supernova explosion occurs within 32 light years once every few hundred million years, resulting in a depletion of the ozone layer lasting several centuries. Over the next two billion years, there will be about 20 supernova explosions and one gamma ray burst that will have a significant impact on the planet's biosphere.

The incremental effect of gravitational perturbations between the planets causes the inner Solar System as a whole to behave chaotically over long time periods. This does not significantly affect the stability of the Solar System over intervals of a few million years or less, but over billions of years the orbits of the planets become unpredictable. Computer simulations of the Solar System's evolution over the next five billion years suggest that there is a small (less than 1%) chance that a collision could occur between Earth and either Mercury, Venus, or Mars. During the same interval, the odds that the Earth will be scattered out of the Solar System by a passing star are on the order of one part in 10⁵. In such a scenario, the oceans would freeze solid within several million years, leaving only a few pockets of liquid water about 14 km (8.7 mi) underground. There is a remote chance that the Earth will instead be captured by a passing binary star system, allowing the planet's biosphere to remain intact. The odds of this happening are about one chance in three million.

Orbit and rotation

The gravitational perturbations of the other planets in the Solar System combine to modify the orbit of the Earth and the orientation of its rotation axis. These changes can influence the planetary climate. Despite such interactions, highly accurate simulations show that overall, Earth's orbit is likely to remain dynamically stable for billions of years into the future. In all 1,600 simulations, the planet's semimajor axis, eccentricity, and inclination remained nearly constant.

Glaciation

Historically, there have been cyclical ice ages in which glacial sheets periodically covered the higher latitudes of the continents. Ice ages may occur because of changes in ocean circulation and continentality induced by plate tectonics. The Milankovitch theory predicts that glacial periods occur during ice ages because of astronomical factors in combination with climate feedback mechanisms. The primary astronomical drivers are a higher than normal orbital eccentricity, a low axial tilt (or obliquity), and the alignment of summer solstice with the aphelion. Each of these effects occur cyclically. For example, the eccentricity changes over time cycles of about 100,000 and 400,000 years, with the value ranging from less than 0.01 up to 0.05. This is equivalent to a change of the semiminor axis of the planet's orbit from 99.95% of the semimajor axis to 99.88%, respectively.

The Earth is passing through an ice age known as the quaternary glaciation, and is presently in the Holocene interglacial period. This period would normally be expected to end in about 25,000 years. However, the increased rate of carbon dioxide release into the atmosphere by humans may delay the onset of the next glacial period until at least 50,000–130,000 years from now. On the other hand, a global warming period of finite duration (based on the assumption that fossil fuel use will cease by the year 2200) will probably only impact the glacial period for about 5,000 years. Thus, a brief period of global warming induced through a few centuries' worth of greenhouse gas emission would only have a limited impact in the long term.

Obliquity

The rotational offset of the tidal bulge exerts a net torque on the Moon, boosting it while slowing the Earth's rotation (not to scale).

The tidal acceleration of the Moon slows the rotation rate of the Earth and increases the Earth-Moon distance. Friction effects—between the core and mantle and between the atmosphere and surface—can dissipate the Earth's rotational energy. These combined effects are expected to increase the length of the day by more than 1.5 hours over the next 250 million years, and to increase the obliquity by about a half degree. The distance to the Moon will increase by about 1.5 Earth radii during the same period.

Based on computer models, the presence of the Moon appears to stabilize the obliquity of the Earth, which may help the planet to avoid dramatic climate changes. This stability is achieved because the Moon increases the precession rate of the Earth's rotation axis, thereby avoiding resonances between the precession of the rotation and precession of the planet's orbital plane (that is, the precession motion of the ecliptic). However, as the semimajor axis of the Moon's orbit continues to increase, this stabilizing effect will diminish. At some point, perturbation effects will probably cause chaotic variations in the obliquity of the Earth, and the axial tilt may change by angles as high as 90° from the plane of the orbit. This is expected to occur between 1.5 and 4.5 billion years from now.

A high obliquity would probably result in dramatic changes in the climate and may destroy the planet's habitability. When the axial tilt of the Earth exceeds 54°, the yearly insolation at the equator is less than that at the poles. The planet could remain at an obliquity of 60° to 90° for periods as long as 10 million years.

Geodynamics

Pangaea was the last supercontinent to form before the present.

Tectonics-based events will continue to occur well into the future and the surface will be steadily reshaped by tectonic uplift, extrusions, and erosion. Mount Vesuvius can be expected to erupt about 40 times over the next 1,000 years. During the same period, about five to seven earthquakes of magnitude 8 or greater should occur along the San Andreas Fault, while about 50 magnitude 9 events may be expected worldwide. Mauna Loa should experience about 200 eruptions over the next 1,000 years, and the Old Faithful Geyser will likely cease to operate. The Niagara Falls will continue to retreat upstream, reaching Buffalo in about 30,000–50,000 years.

In 10,000 years, the post-glacial rebound of the Baltic Sea will have reduced the depth by about 90 m (300 ft). The Hudson Bay will decrease in depth by 100 m over the same period. After 100,000 years, the island of Hawaii will have shifted about 9 km (5.6 mi) to the northwest. The planet may be entering another glacial period by this time.

Continental drift

The theory of plate tectonics demonstrates that the continents of the Earth are moving across the surface at the rate of a few centimeters per year. This is expected to continue, causing the plates to relocate and collide. Continental drift is facilitated by two factors: the energy generation within the planet and the presence of a hydrosphere. With the loss of either of these, continental drift will come to a halt. The production of heat through radiogenic processes is sufficient to maintain mantle convection and plate subduction for at least the next 1.1 billion years.

At present, the continents of North and South America are moving westward from Africa and Europe. Researchers have produced several scenarios about how this will continue in the future. These geodynamic models can be distinguished by the subduction flux, whereby the oceanic crust moves under a continent. In the introversion model, the younger, interior, Atlantic Ocean becomes preferentially subducted and the current migration of North and South America is reversed. In the extroversion model, the older, exterior, Pacific Ocean remains preferentially subducted and North and South America migrate toward eastern Asia.

As the understanding of geodynamics improves, these models will be subject to revision. In 2008, for example, a computer simulation was used to predict that a reorganization of the mantle convection will occur over the next 100 million years, creating a new supercontinent composed of Africa, Eurasia, Australia, Antarctica and South America to form around Antarctica.

Regardless of the outcome of the continental migration, the continued subduction process causes water to be transported to the mantle. After a billion years from the present, a geophysical model gives an estimate that 27% of the current ocean mass will have been subducted. If this process were to continue unmodified into the future, the subduction and release would reach an equilibrium after 65% of the current ocean mass has been subducted.

Introversion

A rough approximation of Pangaea Ultima, one of the three models for a future supercontinent

Christopher Scotese and his colleagues have mapped out the predicted motions several hundred million years into the future as part of the Paleomap Project. In their scenario, 50 million years from now the Mediterranean Sea may vanish, and the collision between Europe and Africa will create a long mountain range extending to the current location of the Persian Gulf. Australia will merge with Indonesia, and Baja California will slide northward along the coast. New subduction zones may appear off the eastern coast of North and South America, and mountain chains will form along those coastlines. The migration of Antarctica to the north will cause all of its ice sheets to melt. This, along with the melting of the Greenland ice sheets, will raise the average ocean level by 90 m (300 ft). The inland flooding of the continents will result in climate changes.

As this scenario continues, by 100 million years from the present, the continental spreading will have reached its maximum extent and the continents will then begin to coalesce. In 250 million years, North America will collide with Africa. South America will wrap around the southern tip of Africa. The result will be the formation of a new supercontinent (sometimes called Pangaea Ultima), with the Pacific Ocean stretching across half the planet. Antarctica will reverse direction and return to the South Pole, building up a new ice cap.

Extroversion

The first scientist to extrapolate the current motions of the continents was Canadian geologist Paul F. Hoffman of Harvard University. In 1992, Hoffman predicted that the continents of North and South America would continue to advance across the Pacific Ocean, pivoting about Siberia until they begin to merge with Asia. He dubbed the resulting supercontinent, Amasia. Later, in the 1990s, Roy Livermore calculated a similar scenario. He predicted that Antarctica would start to migrate northward, and east Africa and Madagascar would move across the Indian Ocean to collide with Asia.

In an extroversion model, the closure of the Pacific Ocean would be complete in about 350 million years. This marks the completion of the current supercontinent cycle, wherein the continents split apart and then rejoin each other about every 400–500 million years. Once the supercontinent is built, plate tectonics may enter a period of inactivity as the rate of subduction drops by an order of magnitude. This period of stability could cause an increase in the mantle temperature at the rate of 30–100 °C (54–180 °F) every 100 million years, which is the minimum lifetime of past supercontinents. As a consequence, volcanic activity may increase.

Supercontinent

The formation of a supercontinent can dramatically affect the environment. The collision of plates will result in mountain building, thereby shifting weather patterns. Sea levels may fall because of increased glaciation. The rate of surface weathering can rise, resulting in an increase in the rate that organic material is buried. Supercontinents can cause a drop in global temperatures and an increase in atmospheric oxygen. This, in turn, can affect the climate, further lowering temperatures. All of these changes can result in more rapid biological evolution as new niches emerge.

The formation of a supercontinent insulates the mantle. The flow of heat will be concentrated, resulting in volcanism and the flooding of large areas with basalt. Rifts will form and the supercontinent will split up once more. The planet may then experience a warming period as occurred during the Cretaceous period, which marked the split-up of the previous Pangaea supercontinent.

Solidification of the outer core

The iron-rich core region of the Earth is divided into a 1,220 km (760 mi) radius solid inner core and a 3,480 km (2,160 mi) radius liquid outer core. The rotation of the Earth creates convective eddies in the outer core region that cause it to function as a dynamo. This generates a magnetosphere about the Earth that deflects particles from the solar wind, which prevents significant erosion of the atmosphere from sputtering. As heat from the core is transferred outward toward the mantle, the net trend is for the inner boundary of the liquid outer core region to freeze, thereby releasing thermal energy and causing the solid inner core to grow. This iron crystallization process has been ongoing for about a billion years. In the modern era, the radius of the inner core is expanding at an average rate of roughly 0.5 mm (0.02 in) per year, at the expense of the outer core. Nearly all of the energy needed to power the dynamo is being supplied by this process of inner core formation.

The growth of the inner core may be expected to consume most of the outer core by some 3–4 billion years from now, resulting in a nearly solid core composed of iron and other heavy elements. The surviving liquid envelope will mainly consist of lighter elements that will undergo less mixing. Alternatively, if at some point plate tectonics comes to an end, the interior will cool less efficiently, which may end the growth of the inner core. In either case, this can result in the loss of the magnetic dynamo. Without a functioning dynamo, the magnetic field of the Earth will decay in a geologically short time period of roughly 10,000 years. The loss of the magnetosphere will cause an increase in erosion of light elements, particularly hydrogen, from the Earth's outer atmosphere into space, resulting in less favorable conditions for life.

Solar evolution

The energy generation of the Sun is based upon thermonuclear fusion of hydrogen into helium. This occurs in the core region of the star using the proton–proton chain reaction process. Because there is no convection in the solar core, the helium concentration builds up in that region without being distributed throughout the star. The temperature at the core of the Sun is too low for nuclear fusion of helium atoms through the triple-alpha process, so these atoms do not contribute to the net energy generation that is needed to maintain hydrostatic equilibrium of the Sun.

At present, nearly half the hydrogen at the core has been consumed, with the remainder of the atoms consisting primarily of helium. As the number of hydrogen atoms per unit mass decreases, so too does their energy output provided through nuclear fusion. This results in a decrease in pressure support, which causes the core to contract until the increased density and temperature bring the core pressure into equilibrium with the layers above. The higher temperature causes the remaining hydrogen to undergo fusion at a more rapid rate, thereby generating the energy needed to maintain the equilibrium.

Evolution of the Sun's luminosity, radius and effective temperature compared to the present Sun. After Ribas (2010).

The result of this process has been a steady increase in the energy output of the Sun. When the Sun first became a main sequence star, it radiated only 70% of the current luminosity. The luminosity has increased in a nearly linear fashion to the present, rising by 1% every 110 million years. Likewise, in three billion years the Sun is expected to be 33% more luminous. The hydrogen fuel at the core will finally be exhausted in five billion years, when the Sun will be 67% more luminous than at present. Thereafter the Sun will continue to burn hydrogen in a shell surrounding its core, until the luminosity reaches 121% above the present value. This marks the end of the Sun's main sequence lifetime, and thereafter it will pass through the subgiant stage and evolve into a red giant.

By this time, the collision of the Milky Way and Andromeda galaxies should be underway. Although this could result in the Solar System being ejected from the newly combined galaxy, it is considered unlikely to have any adverse effect on the Sun or its planets.

Climate impact

The rate of weathering of silicate minerals will increase as rising temperatures speed up chemical processes. This in turn will decrease the level of carbon dioxide in the atmosphere, as these weathering processes convert carbon dioxide gas into solid carbonates. Within the next 600 million years from the present, the concentration of carbon dioxide will fall below the critical threshold needed to sustain C₃ photosynthesis: about 50 parts per million. At this point, trees and forests in their current forms will no longer be able to survive. the last living trees being evergreen conifers. This decline in plant life is likely to be a long term decline rather than a sharp drop. It is likely that plant groups will die one by one well before the 50 parts per million level is reached. The first plants to disappear will be C3 herbaceous plants, followed by deciduous forests, evergreen broad-leaf forests and finally evergreen conifers.

However, C₄ carbon fixation can continue at much lower concentrations, down to above 10 parts per million. Thus plants using C₄ photosynthesis may be able to survive for at least 0.8 billion years and possibly as long as 1.2 billion years from now, after which rising temperatures will make the biosphere unsustainable. Currently, C₄ plants represent about 5% of Earth's plant biomass and 1% of its known plant species. For example, about 50% of all grass species (Poaceae) use the C₄ photosynthetic pathway, as do many species in the herbaceous family Amaranthaceae.

When the levels of carbon dioxide fall to the limit where photosynthesis is barely sustainable, the proportion of carbon dioxide in the atmosphere is expected to oscillate up and down. This will allow land vegetation to flourish each time the level of carbon dioxide rises due to tectonic activity and respiration from animal life. However, the long-term trend is for the plant life on land to die off altogether as most of the remaining carbon in the atmosphere becomes sequestered in the Earth. Some microbes are capable of photosynthesis at concentrations of carbon dioxide as low as 1 part per million, so these life forms would probably disappear only because of rising temperatures and the loss of the biosphere.

Plants—and, by extension, animals—could survive longer by evolving other strategies such as requiring less carbon dioxide for photosynthetic processes, becoming carnivorous, adapting to desiccation, or associating with fungi. These adaptations are likely to appear near the beginning of the moist greenhouse.

The loss of higher plant life will also result in the eventual loss of oxygen as well as ozone due to the respiration of animals, chemical reactions in the atmosphere, and volcanic eruptions. This will result in less attenuation of DNA-damaging UV, as well as the death of animals; the first animals to disappear would be large mammals, followed by small mammals, birds, amphibians and large fish, reptiles and small fish, and finally invertebrates. Before this happens, it's expected that life would concentrate at refugia of lower temperature such as high elevations where less land surface area is available, thus restricting population sizes. Smaller animals would survive better than larger ones because of lesser oxygen requirements, while birds would fare better than mammals thanks to their ability to travel large distances looking for colder temperatures. Based on oxygen half-life in the atmosphere, animal life would last at most 100 million years after the loss of higher plants. However, animal life may last much longer since more than 50% of oxygen is currently produced by phytoplankton.

In their work The Life and Death of Planet Earth, authors Peter D. Ward and Donald Brownlee have argued that some form of animal life may continue even after most of the Earth's plant life has disappeared. Ward and Brownlee use fossil evidence from the Burgess Shale in British Columbia, Canada, to determine the climate of the Cambrian Explosion, and use it to predict the climate of the future when rising global temperatures caused by a warming Sun and declining oxygen levels result in the final extinction of animal life. Initially, they expect that some insects, lizards, birds and small mammals may persist, along with sea life. However, without oxygen replenishment by plant life, they believe that animals would probably die off from asphyxiation within a few million years. Even if sufficient oxygen were to remain in the atmosphere through the persistence of some form of photosynthesis, the steady rise in global temperature would result in a gradual loss of biodiversity.

As temperatures continue to rise, the last of animal life will be driven toward the poles, and possibly underground. They would become primarily active during the polar night, aestivating during the polar day due to the intense heat. Much of the surface would become a barren desert and life would primarily be found in the oceans. However, due to a decrease in the amount of organic matter entering the oceans from land as well as a decrease in dissolved oxygen, sea life would disappear too following a similar path to that on Earth's surface. This process would start with the loss of freshwater species and conclude with invertebrates, particularly those that do not depend on living plants such as termites or those near hydrothermal vents such as worms of the genus Riftia. As a result of these processes, multicellular life forms may be extinct in about 800 million years, and eukaryotes in 1.3 billion years, leaving only the prokaryotes.

Loss of oceans

The atmosphere of Venus is in a "super-greenhouse" state

One billion years from now, about 27% of the modern ocean will have been subducted into the mantle. If this process were allowed to continue uninterrupted, it would reach an equilibrium state where 65% of the current surface reservoir would remain at the surface. Once the solar luminosity is 10% higher than its current value, the average global surface temperature will rise to 320 K (47 °C; 116 °F). The atmosphere will become a "moist greenhouse" leading to a runaway evaporation of the oceans. At this point, models of the Earth's future environment demonstrate that the stratosphere would contain increasing levels of water. These water molecules will be broken down through photodissociation by solar UV, allowing hydrogen to escape the atmosphere. The net result would be a loss of the world's seawater by about 1.1 billion years from the present.

There will be two variations of this future warming feedback: the "moist greenhouse" where water vapor dominates the troposphere while water vapor starts to accumulate in the stratosphere (if the oceans evaporate very quickly), and the "runaway greenhouse" where water vapor becomes a dominant component of the atmosphere (if the oceans evaporate too slowly). In this ocean-free era, there will continue to be surface reservoirs as water is steadily released from the deep crust and mantle, where it is estimated that there is an amount of water equivalent to several times that currently present in the Earth's oceans. Some water may be retained at the poles and there may be occasional rainstorms, but for the most part the planet would be a dry desert with large dunefields covering its equator, and a few salt flats on what was once the ocean floor, similar to the ones in the Atacama Desert in Chile.

With no water to serve as a lubricant, plate tectonics would very likely stop and the most visible signs of geological activity would be shield volcanoes located above mantle hotspots. In these arid conditions the planet may retain some microbial and possibly even multicellular life. Most of these microbes will be halophiles and life could find refuge in the atmosphere as has been proposed to have happened on Venus. However, the increasingly extreme conditions will likely lead to the extinction of the prokaryotes between 1.6 billion years and 2.8 billion years from now, with the last of them living in residual ponds of water at high latitudes and heights or in caverns with trapped ice. However, underground life could last longer. What proceeds after this depends on the level of tectonic activity. A steady release of carbon dioxide by volcanic eruption could cause the atmosphere to enter a "super-greenhouse" state like that of the planet Venus. But, as stated above, without surface water, plate tectonics would probably come to a halt and most of the carbonates would remain securely buried until the Sun becomes a red giant and its increased luminosity heats the rock to the point of releasing the carbon dioxide.

The loss of the oceans could be delayed until 2 billion years in the future if the atmospheric pressure were to decline. A lower atmospheric pressure would reduce the greenhouse effect, thereby lowering the surface temperature. This could occur if natural processes were to remove the nitrogen from the atmosphere. Studies of organic sediments has shown that at least 100 kilopascals (0.99 atm) of nitrogen has been removed from the atmosphere over the past four billion years; enough to effectively double the current atmospheric pressure if it were to be released. This rate of removal would be sufficient to counter the effects of increasing solar luminosity for the next two billion years.

By 2.8 billion years from now, the surface temperature of the Earth will have reached 422 K (149 °C; 300 °F), even at the poles. At this point, any remaining life will be extinguished due to the extreme conditions. If all of the water on Earth has evaporated by this point, the planet will stay in the same conditions with a steady increase in the surface temperature until the Sun becomes a red giant. If not, then in about 3–4 billion years the amount of water vapour in the lower atmosphere will rise to 40% and a "moist greenhouse" effect will commence once the luminosity from the Sun reaches 35–40% more than its present-day value. A "runaway greenhouse" effect will ensue, causing the atmosphere to heat up and raising the surface temperature to around 1,600 K (1,330 °C; 2,420 °F). This is sufficient to melt the surface of the planet. However, most of the atmosphere will be retained until the Sun has entered the red giant stage.

With the extinction of life, 2.8 billion years from now it is also expected that Earth biosignatures will disappear, to be replaced by signatures caused by non-biological processes.

Red giant stage

The size of the current Sun (now in the main sequence) compared to its estimated size during its red giant phase

Once the Sun changes from burning hydrogen within its core to burning hydrogen in a shell around its core, the core will start to contract and the outer envelope will expand. The total luminosity will steadily increase over the following billion years until it reaches 2,730 times the Sun's current luminosity at the age of 12.167 billion years. Most of Earth's atmosphere will be lost to space and its surface will consist of a lava ocean with floating continents of metals and metal oxides as well as icebergs of refractory materials, with its surface temperature reaching more than 2,400 K (2,130 °C; 3,860 °F). The Sun will experience more rapid mass loss, with about 33% of its total mass shed with the solar wind. The loss of mass will mean that the orbits of the planets will expand. The orbital distance of the Earth will increase to at most 150% of its current value.

The most rapid part of the Sun's expansion into a red giant will occur during the final stages, when the Sun will be about 12 billion years old. It is likely to expand to swallow both Mercury and Venus, reaching a maximum radius of 1.2 AU (180,000,000 km). The Earth will interact tidally with the Sun's outer atmosphere, which would serve to decrease Earth's orbital radius. Drag from the chromosphere of the Sun would also reduce the Earth's orbit. These effects will act to counterbalance the effect of mass loss by the Sun, and the Earth will probably be engulfed by the Sun.

The drag from the solar atmosphere may cause the orbit of the Moon to decay. Once the orbit of the Moon closes to a distance of 18,470 km (11,480 mi), it will cross the Earth's Roche limit. This means that tidal interaction with the Earth would break apart the Moon, turning it into a ring system. Most of the orbiting ring will then begin to decay, and the debris will impact the Earth. Hence, even if the Earth is not swallowed up by the Sun, the planet may be left moonless. The ablation and vaporization caused by its fall on a decaying trajectory towards the Sun may remove Earth's mantle, leaving just its core, which will finally be destroyed after at most 200 years. Following this event, Earth's sole legacy will be a very slight increase (0.01%) of the solar metallicity.

Post-red giant stage

The Helix nebula, a planetary nebula similar to what the Sun will produce in 8 billion years

After fusing helium in its core to carbon, the Sun will begin to collapse again, evolving into a compact white dwarf star after ejecting its outer atmosphere as a planetary nebula. The predicted final mass is 54.1% of the present value, most likely consisting primarily of carbon and oxygen.

Currently, the Moon is moving away from Earth at a rate of 4 cm (1.5 inches) per year. In 50 billion years, if the Earth and Moon are not engulfed by the Sun, they will become tidelocked into a larger, stable orbit, with each showing only one face to the other. Thereafter, the tidal action of the Sun will extract angular momentum from the system, causing the orbit of the Moon to decay and the Earth's rotation to accelerate. In about 65 billion years, it is estimated that the Moon may end up colliding with the Earth, due to the remaining energy of the Earth–Moon system being sapped by the remnant Sun, causing the Moon to slowly move inwards toward the Earth.

On a time scale of 10¹⁹ (10 quintillion) years the remaining planets in the Solar System will be ejected from the system by violent relaxation. If Earth is not destroyed by the expanding red giant Sun and the Earth is not ejected from the Solar System by violent relaxation, the ultimate fate of the planet will be that it collides with the black dwarf Sun due to the decay of its orbit via gravitational radiation, in 10²⁰ (Short Scale: 100 quintillion, Long Scale: 100 trillion) years.