Emissivity

The emissivity of the surface of a material is its effectiveness in emitting energy as thermal radiation. Thermal radiation is electromagnetic radiation that most commonly includes both visible radiation (light) and infrared radiation, which is not visible to human eyes. A portion of the thermal radiation from very hot objects (see photograph) is easily visible to the eye.

The emissivity of a surface depends on its chemical composition and geometrical structure. Quantitatively, it is the ratio of the thermal radiation from a surface to the radiation from an ideal black surface at the same temperature as given by the Stefan–Boltzmann law. (A comparison with Planck's law is used if one is concerned with particular wavelengths of thermal radiation.) The ratio varies from 0 to 1.

The surface of a perfect black body (with an emissivity of 1) emits thermal radiation at the rate of approximately 448 watts per square metre (W/m²) at a room temperature of 25 °C (298 K; 77 °F).

Objects generally have emissivities less than 1.0, and emit radiation at correspondingly lower rates.<ref>The Stefan–Boltzmann law is that the rate of emission of thermal radiation is σT⁴, where σ = 5.67×10⁻⁸ W/m²·K⁴, and the temperature T is in kelvins. See Trefil, James S. (2003). The Nature of Science: An A-Z Guide to the Laws and Principles Governing Our Universe. Houghton Mifflin Harcourt. p. 377. ISBN 9780618319381.</ref>

However, wavelength- and subwavelength-scale particles,<ref name="Bohren"> Bohren, Craig F.; Huffman, Donald R. (1998). Absorption and scattering of light by small particles. Wiley. pp. 123–126. ISBN 978-0-471-29340-8.</ref> metamaterials,<ref> Narimanov, Evgenii E.; Smolyaninov, Igor I. (2012). "Beyond Stefan–Boltzmann Law: Thermal Hyper-Conductivity". Conference on Lasers and Electro-Optics 2012. OSA Technical Digest. Optical Society of America. pp. QM2E.1. arXiv:1109.5444. CiteSeerX 10.1.1.764.846. doi:10.1364/QELS.2012.QM2E.1. ISBN 978-1-55752-943-5. S2CID 36550833.</ref> and other nanostructures<ref name="Golyk2012">Golyk, V. A.; Krüger, M.; Kardar, M. (2012). "Heat radiation from long cylindrical objects". Phys. Rev. E. 85 (4): 046603. arXiv:1109.1769. Bibcode:2012PhRvE..85d6603G. doi:10.1103/PhysRevE.85.046603. hdl:1721.1/71630. PMID 22680594. S2CID 27489038.</ref> may have an emissivity greater than 1.

Practical applications

Emissivities are important in a variety of contexts:

Insulated windows: Warm surfaces are usually cooled directly by air, but they also cool themselves by emitting thermal radiation. This second cooling mechanism is important for simple glass windows, which have emissivities close to the maximum possible value of 1.0. "Low-E windows" with transparent low-emissivity coatings emit less thermal radiation than ordinary windows.<ref name=roadmap>"The Low-E Window R&D Success Story" (PDF). Windows and Building Envelope Research and Development: Roadmap for Emerging Technologies. U.S. Department of Energy. February 2014. p. 5.</ref> In winter, these coatings can halve the rate at which a window loses heat compared to an uncoated glass window.<ref name=Fricke>Fricke, Jochen; Borst, Walter L. (2013). Essentials of Energy Technology. Wiley-VCH. p. 37. ISBN 978-3527334162.</ref>

Solar heat collectors: Similarly, solar heat collectors lose heat by emitting thermal radiation. Advanced solar collectors incorporate selective surfaces that have very low emissivities. These collectors waste very little of the solar energy through emission of thermal radiation.<ref name=Fricke1>Fricke, Jochen; Borst, Walter L. (2013). "9. Solar Space and Hot Water Heating". Essentials of Energy Technology. Wiley-VCH. p. 249. ISBN 978-3527334162.</ref>
Thermal shielding: For the protection of structures from high surface temperatures, such as reusable spacecraft or hypersonic aircraft, high-emissivity coatings (HECs), with emissivity values near 0.9, are applied on the surface of insulating ceramics.<ref name="rtps">Shao, Gaofeng; et al. (2019). "Improved oxidation resistance of high emissivity coatings on fibrous ceramic for reusable space systems". Corrosion Science. 146: 233–246. arXiv:1902.03943. doi:10.1016/j.corsci.2018.11.006. S2CID 118927116.</ref> This facilitates radiative cooling and protection of the underlying structure and is an alternative to ablative coatings, used in single-use reentry capsules.
Passive daytime radiative cooling: Daytime passive radiative coolers use the extremely cold temperature of outer space (~2.7 K) to emit heat and lower ambient temperatures while requiring zero energy input.<ref name=":212">Aili, Ablimit; Yin, Xiaobo; Yang, Ronggui (October 2021). "Global Radiative Sky Cooling Potential Adjusted for Population Density and Cooling Demand". Atmosphere. 12 (11): 1379. doi:10.3390/atmos12111379.</ref> These surfaces minimize the absorption of solar radiation to lessen heat gain in order to maximize the emission of LWIR thermal radiation.<ref name=":213">Aili, Ablimit; Yin, Xiaobo; Yang, Ronggui (October 2021). "Global Radiative Sky Cooling Potential Adjusted for Population Density and Cooling Demand". Atmosphere. 12 (11): 1379. doi:10.3390/atmos12111379.</ref> It has been proposed as a solution to global warming.<ref name=":5">Chen, Meijie; Pang, Dan; Chen, Xingyu; Yan, Hongjie; Yang, Yuan (2022). "Passive daytime radiative cooling: Fundamentals, material designs, and applications". EcoMat. 4. doi:10.1002/eom2.12153. S2CID 240331557. Passive daytime radiative cooling (PDRC) dissipates terrestrial heat to the extremely cold outer space without using any energy input or producing pollution. It has the potential to simultaneously alleviate the two major problems of energy crisis and global warming.</ref>
Planetary temperatures: The planets are solar thermal collectors on a large scale. The temperature of a planet's surface is determined by the balance between the heat absorbed by the planet from sunlight, heat emitted from its core, and thermal radiation emitted back into space. Emissivity of a planet is determined by the nature of its surface and atmosphere.<ref name="ACS">"Climate Sensitivity". American Chemical Society. Retrieved 2014-07-21.</ref>

Temperature measurements: Pyrometers and infrared cameras are instruments used to measure the temperature of an object by using its thermal radiation; no actual contact with the object is needed. The calibration of these instruments involves the emissivity of the surface that's being measured.<ref name="Siegel" />

Mathematical definitions

In its most general form, emissivity can specified for a particular wavelength, direction, and polarization.

However, the most commonly used form of emissivity is the hemispherical total emissivity, which considers emissions as totaled over all wavelengths, directions, and polarizations, given a particular temperature.<ref name="SH92">Siegel, Robert; Howell, John R. (1992). Thermal Radiation Heat Transfer (3 ed.). Taylor & Francis. ISBN 0-89116-271-2.</ref>^: 60

Some specific forms of emissivity are detailed below.

Hemispherical emissivity

Hemispherical emissivity of a surface, denoted ε, is defined as<ref name="ISO_9288-1989">"Thermal insulation — Heat transfer by radiation — Physical quantities and definitions". ISO 9288:2022. ISO catalogue. 1989. Retrieved 2015-03-15.</ref>

<math>\varepsilon = \frac{M_\mathrm{e}}{M_\mathrm{e}^\circ},</math>

where

M_e is the radiant exitance of that surface;
M_e° is the radiant exitance of a black body at the same temperature as that surface.

Spectral hemispherical emissivity

Spectral hemispherical emissivity in frequency and spectral hemispherical emissivity in wavelength of a surface, denoted ε_ν and ε_λ, respectively, are defined as<ref name="ISO_9288-1989"/>

<math>\begin{align}

     \varepsilon_\nu &= \frac{M_{\mathrm{e},\nu}}{M_{\mathrm{e},\nu}^\circ}, \\
 \varepsilon_\lambda &= \frac{M_{\mathrm{e},\lambda}}{M_{\mathrm{e},\lambda}^\circ},

\end{align}</math>

where

M_e,ν is the spectral radiant exitance in frequency of that surface;
M_e,ν° is the spectral radiant exitance in frequency of a black body at the same temperature as that surface;
M_e,λ is the spectral radiant exitance in wavelength of that surface;
M_e,λ° is the spectral radiant exitance in wavelength of a black body at the same temperature as that surface.

Directional emissivity

Directional emissivity of a surface, denoted ε_Ω, is defined as<ref name="ISO_9288-1989"/>

<math>\varepsilon_\Omega = \frac{L_{\mathrm{e},\Omega}}{L_{\mathrm{e},\Omega}^\circ},</math>

where

L_e,Ω is the radiance of that surface;
L_e,Ω° is the radiance of a black body at the same temperature as that surface.

Spectral directional emissivity

Spectral directional emissivity in frequency and spectral directional emissivity in wavelength of a surface, denoted ε_ν,Ω and ε_λ,Ω, respectively, are defined as<ref name="ISO_9288-1989"/>

<math>\begin{align}

     \varepsilon_{\nu,\Omega} &= \frac{L_{\mathrm{e},\Omega,\nu}}{L_{\mathrm{e},\Omega,\nu}^\circ}, \\
 \varepsilon_{\lambda,\Omega} &= \frac{L_{\mathrm{e},\Omega,\lambda}}{L_{\mathrm{e},\Omega,\lambda}^\circ},

\end{align}</math>

where

L_e,Ω,ν is the spectral radiance in frequency of that surface;
L_e,Ω,ν° is the spectral radiance in frequency of a black body at the same temperature as that surface;
L_e,Ω,λ is the spectral radiance in wavelength of that surface;
L_e,Ω,λ° is the spectral radiance in wavelength of a black body at the same temperature as that surface.

Hemispherical emissivity can also be expressed as a weighted average of the directional spectral emissivities as described in textbooks on "radiative heat transfer".<ref name=Siegel/>

Emissivities of common surfaces

Emissivities ε can be measured using simple devices such as Leslie's cube in conjunction with a thermal radiation detector such as a thermopile or a bolometer. The apparatus compares the thermal radiation from a surface to be tested with the thermal radiation from a nearly ideal, black sample. The detectors are essentially black absorbers with very sensitive thermometers that record the detector's temperature rise when exposed to thermal radiation. For measuring room temperature emissivities, the detectors must absorb thermal radiation completely at infrared wavelengths near 10×10⁻⁶ metre.<ref>For a truly black object, the spectrum of its thermal radiation peaks at the wavelength given by Wien's Law: λ_max = b/T, where the temperature T is in kelvins and the constant b ≈ 2.90×10⁻³ metre-kelvins. Room temperature is about 293 kelvins. Sunlight itself is thermal radiation originating from the hot surface of the Sun. The Sun's surface temperature of about 5800 kelvins corresponds well to the peak wavelength of sunlight, which is at the green wavelength of about 0.5×10⁻⁶ metres. See Saha, Kshudiram (2008). The Earth's Atmosphere: Its Physics and Dynamics. Springer Science & Business Media. p. 84. ISBN 9783540784272.</ref> Visible light has a wavelength range of about 0.4–0.7×10⁻⁶ metre from violet to deep red.

Emissivity measurements for many surfaces are compiled in many handbooks and texts. Some of these are listed in the following table.<ref>Brewster, M. Quinn (1992). Thermal Radiative Transfer and Properties. John Wiley & Sons. p. 56. ISBN 9780471539827.</ref><ref>2009 ASHRAE Handbook: Fundamentals - IP Edition. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers. 2009. ISBN 978-1-933742-56-4. "IP" refers to inch and pound units; a version of the handbook with metric units is also available. Emissivity is a simple number, and doesn't depend on the system of units.</ref>

Photographs of an aluminium Leslie's cube. The color photographs are taken using an infrared camera; the black and white photographs underneath are taken with an ordinary camera. All faces of the cube are at the same temperature of about 55 °C (131 °F). The face of the cube that has been painted (black or white paint has negligible impact) has a large emissivity, which is indicated by the reddish color in the infrared photograph. The polished face of the cube has a low emissivity indicated by the blue color, and the reflected image of the warm hand is clear.

Material	Emissivity
Aluminium foil	0.03
Aluminium, anodized	0.9<ref>The visible color of an anodized aluminum surface does not strongly affect its emissivity. See "Emissivity of Materials". Electro Optical Industries, Inc. Archived from the original on 2012-09-19.</ref>
Aluminium, smooth, polished	0.04
Aluminium, rough, oxidized	0.2
Asphalt	0.88
Brick	0.90
Concrete, rough	0.91
Copper, polished	0.04
Copper, oxidized	0.87
Glass, smooth uncoated	0.95
Ice	0.97-0.99
Iron, polished	0.06
Limestone	0.92
Marble, polished	0.89–0.92
Nitrogen or Oxygen gas layer, pure	~0<ref name="togler95">Trogler, William C. (1995). "The Environmental Chemistry of Trace Atmospheric Gases". Journal of Chemical Education. 72 (11): 973. Bibcode:1995JChEd..72..973T. doi:10.1021/ed072p973.</ref><ref name="hopfner"/>
Paint, including white	0.9
Paper, roofing or white	0.88–0.86
Plaster, rough	0.89
Silver, polished	0.02
Silver, oxidized	0.04
Skin, human	0.97–0.999
Snow	0.8–0.9
Polytetrafluoroethylene (Teflon)	0.85
Transition metal disilicides (e.g. MoSi₂ or WSi₂)	0.86–0.93<ref name="rtps"/>
Vegetation	0.92-0.96
Water, pure	0.96

Notes:

These emissivities are the total hemispherical emissivities from the surfaces.
The values of the emissivities apply to materials that are optically thick. This means that the absorptivity at the wavelengths typical of thermal radiation doesn't depend on the thickness of the material. Very thin materials emit less thermal radiation than thicker materials.
Most emissitivies in the chart above were recorded at room temperature, 300 K (27 °C; 80 °F).

Closely related properties

Absorptance

There is a fundamental relationship (Gustav Kirchhoff's 1859 law of thermal radiation) that equates the emissivity of a surface with its absorption of incident radiation (the "absorptivity" of a surface). Kirchhoff's law is rigorously applicable with regard to the spectral directional definitions of emissivity and absorptivity. The relationship explains why emissivities cannot exceed 1, since the largest absorptivity—corresponding to complete absorption of all incident light by a truly black object—is also 1.<ref name=Siegel>Siegel, Robert (2001). Thermal Radiation Heat Transfer, Fourth Edition. CRC Press. p. 41. ISBN 9781560328391.</ref> Mirror-like, metallic surfaces that reflect light will thus have low emissivities, since the reflected light isn't absorbed. A polished silver surface has an emissivity of about 0.02 near room temperature. Black soot absorbs thermal radiation very well; it has an emissivity as large as 0.97, and hence soot is a fair approximation to an ideal black body.<ref name=table>"Table of Total Emissivity" (PDF). Archived from the original (PDF) on 2009-07-11. Table of emissivities provided by a company; no source for these data is provided.</ref><ref>"Influencing factors". evitherm Society - Virtual Institute for Thermal Metrology. Archived from the original on 2014-01-12. Retrieved 2014-07-19.</ref>

With the exception of bare, polished metals, the appearance of a surface to the eye is not a good guide to emissivities near room temperature. For example, white paint absorbs very little visible light. However, at an infrared wavelength of 10×10⁻⁶ metre, paint absorbs light very well, and has a high emissivity. Similarly, pure water absorbs very little visible light, but water is nonetheless a strong infrared absorber and has a correspondingly high emissivity.

Emittance

Emittance (or emissive power) is the total amount of thermal energy emitted per unit area per unit time for all possible wavelengths. Emissivity of a body at a given temperature is the ratio of the total emissive power of a body to the total emissive power of a perfectly black body at that temperature. Following Planck's law, the total energy radiated increases with temperature while the peak of the emission spectrum shifts to shorter wavelengths. The energy emitted at shorter wavelengths increases more rapidly with temperature. For example, an ideal blackbody in thermal equilibrium at 1,273 K (1,000 °C; 1,832 °F), will emit 97% of its energy at wavelengths below 14 μm.<ref name="rtps"/>

The term emissivity is generally used to describe a simple, homogeneous surface such as silver. Similar terms, emittance and thermal emittance, are used to describe thermal radiation measurements on complex surfaces such as insulation products.<ref>"ASTM C835 - 06(2013)e1: Standard Test Method for Total Hemispherical Emittance of Surfaces up to 1400°C". ASTM International. Retrieved 2014-08-09.</ref><ref>Kruger, Abe; Seville, Carl (2012). Green Building: Principles and Practices in Residential Construction. Cengage Learning. p. 198. ISBN 9781111135959.</ref><ref>Saad, Abdullah A.; Martinez, Carlos; Trice, Rodney W. (2023-02-13). "Radiation heat transfer during hypersonic flight: A review of emissivity measurement and enhancement approaches of ultra-high temperature ceramics". International Journal of Ceramic Engineering & Science. 5 (2). doi:10.1002/ces2.10171. ISSN 2578-3270.</ref>

Measurement of Emittance

Emittance of a surface can be measured directly or indirectly from the emitted energy from that surface. In the direct radiometric method, the emitted energy from the sample is measured directly using a spectroscope such as Fourier transform infrared spectroscopy (FTIR).<ref>Saad, Abdullah A.; Martinez, Carlos; Trice, Rodney W. (2023-02-13). "Radiation heat transfer during hypersonic flight: A review of emissivity measurement and enhancement approaches of ultra-high temperature ceramics". International Journal of Ceramic Engineering & Science. 5 (2). doi:10.1002/ces2.10171. ISSN 2578-3270.</ref> In the indirect calorimetric method, the emitted energy from the sample is measured indirectly using a calorimeter. In addition to these two commonly applied methods, inexpensive emission measurement technique based on the principle of two-color pyrometry.<ref>Saad, Abdullah A.; Martinez, Carlos; Trice, Rodney W. (2023-02-13). "Radiation heat transfer during hypersonic flight: A review of emissivity measurement and enhancement approaches of ultra-high temperature ceramics". International Journal of Ceramic Engineering & Science. 5 (2). doi:10.1002/ces2.10171. ISSN 2578-3270.</ref>

Emissivities of planet Earth

The emissivity of a planet or other astronomical body is determined by the composition and structure of its outer skin. In this context, the "skin" of a planet generally includes both its semi-transparent atmosphere and its non-gaseous surface. The resulting radiative emissions to space typically function as the primary cooling mechanism for these otherwise isolated bodies. The balance between all other incoming plus internal sources of energy versus the outgoing flow regulates planetary temperatures.<ref>"Climate and Earth's Energy Budget". NASA Earth Observatory. 14 January 2009. Retrieved 10 October 2022.</ref>

For Earth, equilibrium skin temperatures range near the freezing point of water, 260±50 K (-13±50 °C, 8±90 °F). The most energetic emissions are thus within a band spanning about 4-50 μm as governed by Planck's law.<ref>Petty, Grant W. (2006). A first course in atmospheric radiation (2 ed.). Madison, Wisc.: Sundog Publ. p. 68. ISBN 978-0972903318.</ref> Emissivities for the atmosphere and surface components are often quantified separately, and validated against satellite- and terrestrial-based observations as well as laboratory measurements. These emissivities serve as input parameters within some meteorlogic and climatologic models.

Surface

Earth's surface emissivities (ε_s) have been inferred with satellite-based instruments by directly observing surface thermal emissions at nadir through a less obstructed atmospheric window spanning 8-13 μm.<ref>"ASTER global emissivity database: 100 times more detailed than its predecessor". NASA Earth Observatory. 17 November 2014. Retrieved 10 October 2022.</ref> Values range about ε_s=0.65-0.99, with lowest values typically limited to the most barren desert areas. Emissivities of most surface regions are above 0.9 due to the dominant influence of water; including oceans, land vegetation, and snow/ice. Globally averaged estimates for the hemispheric emissivity of Earth's surface are in the vicinity of ε_s=0.95.<ref>"Joint Emissivity Database Initiative". NASA Jet Propulsion Laboratory. Retrieved 10 October 2022.</ref>

Atmosphere

Water also dominates the planet's atmospheric emissivity and absorptivity in the form of water vapor. Clouds, carbon dioxide, and other components make substantial additional contributions, especially where there are gaps in the water vapor absorption spectrum.<ref>"Remote Sensing: Absorption Bands and Atmospheric Windows". NASA Earth Observatory. 17 September 1999. Retrieved 28 October 2022.</ref> Nitrogen (N
₂) and oxygen (O
₂) - the primary atmospheric components - interact less significantly with thermal radiation in the infrared band.<ref name="hopfner">Höpfner, M.; Milz, M.; Buehler, S.; Orphall, J.; Stiller, G. (24 May 2012). "The natural greenhouse effect of atmospheric oxygen (O₂) and nitrogen (N₂)". Geophysical Research Letters. 39 (L10706). Bibcode:2012GeoRL..3910706H. doi:10.1029/2012GL051409. ISSN 1944-8007. S2CID 128823108.</ref> Direct measurement of Earths atmospheric emissivities (ε_a) are more challenging than for land surfaces due in part to the atmosphere's multi-layered and more dynamic structure.

Upper and lower limits have been measured and calculated for ε_a in accordance with extreme yet realistic local conditions. At the upper limit, dense low cloud structures (consisting of liquid/ice aerosols and saturated water vapor) close the infrared transmission windows, yielding near to black body conditions with ε_a≈1.<ref>Liu, Lei; Zhang, Ting; Wu, Yi; Niu, Zhencong; Wang, Qi (2018). "Cloud Effective Emissivity Retrievals Using Combined Ground-Based Infrared Cloud Measuring Instrument and Ceilometer Observations". Remote Sensing. 10 (2033): 2033. Bibcode:2018RemS...10.2033L. doi:10.3390/rs10122033.</ref> At a lower limit, clear sky (cloud-free) conditions promote the largest opening of transmission windows. The more uniform concentration of long-lived trace greenhouse gases in combination with water vapor pressures of 0.25-20 mbar then yield minimum values in the range of ε_a=0.55-0.8 (with ε=0.35-0.75 for a simulated water-vapor-only atmosphere).<ref name=hitran>Mendoza, Victor M..; Vallanueva, Elba E.; Garduno, Rene; Sanchez-Meneses, Oscar (31 January 2017). "Atmospheric emissivity with clear sky computed by E-Trans/HITRAN". Atmospheric Environment. 155: 174–188. Bibcode:2017AtmEn.155..174M. doi:10.1016/j.atmosenv.2017.01.048. ISSN 1352-2310.</ref> Carbon dioxide (CO
₂) and other greenhouse gases contribute about ε=0.2 to ε_a when atmospheric humidity is low.<ref>Staley, D.O.; Jurica, G.M. (1 March 1972). "Effective atmospheric emissivity under clear skies". Applied Meteorology and Climatology. 11 (2): 349–356. Bibcode:1972JApMe..11..349S. doi:10.1175/1520-0450(1972)011<0349:EAEUCS>2.0.CO;2.</ref> Researchers have also evaluated the contribution of differing cloud types to atmospheric absorptivity and emissivity.<ref>Graham, Steve (1 March 1999). "Clouds and Radiation". NASA Earth Observatory. Retrieved 28 October 2022.</ref><ref>Cox, Stephen K. (1 February 1976). "Observations of cloud infrared effective emissivity". Atmospheric Sciences. 33 (2): 287–289. Bibcode:1976JAtS...33..287C. doi:10.1175/1520-0469(1976)033<0287:OOCIEE>2.0.CO;2.</ref><ref>Chylek, Petr; Ramaswamy, V. (1 January 1982). "Simple approximation of infrared emissivity of water clouds". Atmospheric Sciences. 39 (1): 171–177. Bibcode:1982JAtS...39..171C. doi:10.1175/1520-0469(1982)039<0171:SAFIEO>2.0.CO;2.</ref>

These days, the detailed processes and complex properties of radiation transport through the atmosphere are evaluated with radiation transport codes and databases such as MODTRAN/HITRAN.<ref name=hitran />

For many practical applications it may not be possible, cost-effective or necessary to know all emissivity values locally. "Effective" or "bulk" values for an atmosphere or an entire planet may be used. These can be based upon remote observations (from the ground or outer space) or defined according to the simplifications utilized by a particular model. For example, an effective global value of ε_a≈0.78 has been estimated from application of an idealized single-layer-atmosphere energy-balance model to Earth.<ref>"ACS Climate Science Toolkit - Atmospheric Warming - A Single-Layer Atmosphere Model". American Chemical Society. Retrieved 1 December 2022.</ref>

Effective emissivity due to atmosphere

The IPCC reports an outgoing thermal radiation flux (OLR) of 239 (237-242) W m^-2 and a surface thermal radiation flux (SLR) of 398 (395-400) W m^-2, where the parenthesized amounts indicate the 5-95% confidence intervals as of 2015. These values indicate that the atmosphere (with clouds included) reduces Earth's overall emissivity, relative to its surface emissions, by a factor of 239/398 ≈ 0.60. In other words, emissions to space are given by <math>\mathrm{OLR} = \epsilon_\mathrm{eff}\,\sigma\,T_{se}^4</math> where <math>\epsilon_\mathrm{eff} \approx 0.6</math> is the effective emissivity of Earth as viewed from space and <math> T_\mathrm{se} \equiv \left[\mathrm{SLR}/\sigma\right]^{1/4} \approx</math> 289 K (16 °C; 61 °F) is the effective temperature of the surface.<ref name="ipccAR6WG1">IPCC (2021). Masson-Delmotte, V.; Zhai, P.; Pirani, A.; Connors, S. L.; et al. (eds.). Climate Change 2021: The Physical Science Basis (PDF). Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press (In Press).</ref>^: 934

History

The concepts of emissivity and absorptivity, as properties of matter and radiation, appeared in the late-eighteenth thru mid-nineteenth century writings of Pierre Prévost, John Leslie, Balfour Stewart and others.<ref>Prévost, Pierre (April 1791). "Mémoire sur l'équilibre du feu". Observations Sur la Physique (in français). XXXVIII (1): 314–323.</ref><ref>Leslie, John (1804). An Experimental Inquiry into the Nature and Propagation of Heat. Edinburgh: J. Mawman.</ref><ref>Stewart, Balfour (1866). An Elementary Treatise on Heat. Oxford, Clarendon Press.</ref> In 1860, Gustav Kirchhoff published a mathematical description of their relationship under conditions of thermal equilibrium (i.e. Kirchoff's law of thermal radiation).<ref>Kirchhoff, Gustav (1860). "Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme and Licht". Annalen der Physik und Chemie. 109 (2): 275–301. Bibcode:1860AnP...185..275K. doi:10.1002/andp.18601850205.</ref> By 1884 the emissive power of a perfect blackbody was inferred by Josef Stefan using John Tyndall's experimental measurements, and derived by Ludwig Boltzmann from fundamental statistical principles.<ref>Boltzmann, Ludwig (1884). "Ableitung des Stefan'schen Gesetzes, betreffend die Abhängigkeit der Wärmestrahlung von der Temperatur aus der electromagnetischen Lichttheorie" [Derivation of Stefan's law, concerning the dependency of heat radiation on temperature, from the electromagnetic theory of light]. Annalen der Physik und Chemie (in Deutsch). 258 (6): 291–294. Bibcode:1884AnP...258..291B. doi:10.1002/andp.18842580616.</ref> Emissivity, defined as a further proportionality factor to the Stefan-Boltzmann law, was thus implied and utilized in subsequent evaluations of the radiative behavior of grey bodies. For example, Svante Arrhenius applied the recent theoretical developments to his 1896 investigation of Earth's surface temperatures as calculated from the planet's radiative equilibrium with all of space.<ref>Svante Arrhenius (1896). "On the influence of carbonic acid in the air upon the temperature of the ground". Philosophical Magazine and Journal of Science. 41 (251): 237–276. doi:10.1080/14786449608620846.</ref> By 1900 Max Planck empirically derived a generalized law of blackbody radiation, thus clarifying the emissivity and absorptivity concepts at individual wavelengths.<ref>Planck, Max (1901). "Über das Gesetz der Energieverteilung im Normalspektrum". Annalen der Physik. 4 (3): 553–563. Bibcode:1901AnP...309..553P. doi:10.1002/andp.19013090310.</ref>

Other radiometric coefficients

Radiometry coefficients
v
t
e
Quantity		SI units	Notes
Name	Sym.	SI units	Notes
Hemispherical emissivity	$ε$	—	Radiant exitance of a surface, divided by that of a black body at the same temperature as that surface.
Spectral hemispherical emissivity	$ε ν$ $ε λ$	—	Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface.
Directional emissivity	$ε Ω$	—	Radiance emitted by a surface, divided by that emitted by a black body at the same temperature as that surface.
Spectral directional emissivity	$ε Ω, ν$ $ε Ω, λ$	—	Spectral radiance emitted by a surface, divided by that of a black body at the same temperature as that surface.
Hemispherical absorptance	$A$	—	Radiant flux absorbed by a surface, divided by that received by that surface. This should not be confused with "absorbance".
Spectral hemispherical absorptance	$A ν$ $A λ$	—	Spectral flux absorbed by a surface, divided by that received by that surface. This should not be confused with "spectral absorbance".
Directional absorptance	$A Ω$	—	Radiance absorbed by a surface, divided by the radiance incident onto that surface. This should not be confused with "absorbance".
Spectral directional absorptance	$A Ω, ν$ $A Ω, λ$	—	Spectral radiance absorbed by a surface, divided by the spectral radiance incident onto that surface. This should not be confused with "spectral absorbance".
Hemispherical reflectance	$R$	—	Radiant flux reflected by a surface, divided by that received by that surface.
Spectral hemispherical reflectance	$R ν$ $R λ$	—	Spectral flux reflected by a surface, divided by that received by that surface.
Directional reflectance	$R Ω$	—	Radiance reflected by a surface, divided by that received by that surface.
Spectral directional reflectance	$R Ω, ν$ $R Ω, λ$	—	Spectral radiance reflected by a surface, divided by that received by that surface.
Hemispherical transmittance	$T$	—	Radiant flux transmitted by a surface, divided by that received by that surface.
Spectral hemispherical transmittance	$T ν$ $T λ$	—	Spectral flux transmitted by a surface, divided by that received by that surface.
Directional transmittance	$T Ω$	—	Radiance transmitted by a surface, divided by that received by that surface.
Spectral directional transmittance	$T Ω,ν$ $T Ω, λ$	—	Spectral radiance transmitted by a surface, divided by that received by that surface.
Hemispherical attenuation coefficient	$μ$	m⁻¹	Radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume.
Spectral hemispherical attenuation coefficient	$μ ν$ $μ λ$	m⁻¹	Spectral radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume.
Directional attenuation coefficient	$μ Ω$	m⁻¹	Radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.
Spectral directional attenuation coefficient	$μ Ω, ν$ $μ Ω, λ$	m⁻¹	Spectral radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.

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