Hemispherical emissivity

Hemispherical emissivity of a surface, denoted ε, is defined as^[15]

${\displaystyle \varepsilon ={\frac {M_{\mathrm {e} }}{M_{\mathrm {e} }^{\circ }}},}$

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^[15]

${\displaystyle {\begin{aligned}\varepsilon _{\nu }&={\frac {M_{\mathrm {e} ,\nu }}{M_{\mathrm {e} ,\nu }^{\circ }}},\\\varepsilon _{\lambda }&={\frac {M_{\mathrm {e} ,\lambda }}{M_{\mathrm {e} ,\lambda }^{\circ }}},\end{aligned}}}$

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^[15]

${\displaystyle \varepsilon _{\Omega }={\frac {L_{\mathrm {e} ,\Omega }}{L_{\mathrm {e} ,\Omega }^{\circ }}},}$

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^[15]

${\displaystyle {\begin{aligned}\varepsilon _{\nu ,\Omega }&={\frac {L_{\mathrm {e} ,\Omega ,\nu }}{L_{\mathrm {e} ,\Omega ,\nu }^{\circ }}},\\\varepsilon _{\lambda ,\Omega }&={\frac {L_{\mathrm {e} ,\Omega ,\lambda }}{L_{\mathrm {e} ,\Omega ,\lambda }^{\circ }}},\end{aligned}}}$

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".^[13]

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.^[13] 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.^[22][23]

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.^[8]

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.^[24][25][26]

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).^[27] 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.^[28]

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.^[31] 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.^[32]

Atmosphere

A typical spectrum of infrared radiation transmittance through Earth's atmosphere. A 'window' can be seen between 8 and 14 μm that enables direct transmission of the most intense thermal emissions from Earth's surface. The remaining portion of the upwelling energy, as well as downwelling radiation back to the surface, undergoes absorption and emission by the various atmospheric components as indicated.

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.^[33] Nitrogen (N
₂) and oxygen (O
₂) - the primary atmospheric components - interact less significantly with thermal radiation in the infrared band.^[21] 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.^[34] 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).^[35] Carbon dioxide (CO
₂) and other greenhouse gases contribute about ε=0.2 to ε_a when atmospheric humidity is low.^[36] Researchers have also evaluated the contribution of differing cloud types to atmospheric absorptivity and emissivity.^[37][38][39]

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.^[35]

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.^[40]

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 ${\displaystyle \mathrm {OLR} =\epsilon _{\mathrm {eff} }\,\sigma \,T_{se}^{4}}$ where ${\displaystyle \epsilon _{\mathrm {eff} }\approx 0.6}$ is the effective emissivity of Earth as viewed from space and ${\displaystyle T_{\mathrm {se} }\equiv \left[\mathrm {SLR} /\sigma \right]^{1/4}\approx }$ 289 K (16 °C; 61 °F) is the effective temperature of the surface.^[41]: 934