Skin Temperature (of An Atmosphere)
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The skin temperature of an atmosphere is the temperature of a hypothetical thin layer high in the
atmosphere An atmosphere () is a layer of gases that envelop an astronomical object, held in place by the gravity of the object. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A stellar atmosph ...
that is transparent to incident
solar radiation Sunlight is the portion of the electromagnetic radiation which is emitted by the Sun (i.e. solar radiation) and received by the Earth, in particular the visible light perceptible to the human eye as well as invisible infrared (typically p ...
and partially absorbing of
infrared radiation Infrared (IR; sometimes called infrared light) is electromagnetic radiation (EMR) with wavelengths longer than that of visible light but shorter than microwaves. The infrared spectral band begins with the waves that are just longer than those ...
from the planet. It provides an approximation for the temperature of the
tropopause The tropopause is the atmospheric boundary that demarcates the lowest two layers of the atmosphere of Earth – the troposphere and stratosphere – which occurs approximately above the equatorial regions, and approximately above the polar regi ...
on
terrestrial planet A terrestrial planet, tellurian planet, telluric planet, or rocky planet, is a planet that is composed primarily of silicate, rocks or metals. Within the Solar System, the terrestrial planets accepted by the IAU are the inner planets closest to ...
s with
greenhouse gas Greenhouse gases (GHGs) are the gases in the atmosphere that raise the surface temperature of planets such as the Earth. Unlike other gases, greenhouse gases absorb the radiations that a planet emits, resulting in the greenhouse effect. T ...
es present in their atmospheres. The skin temperature of an atmosphere should not be confused with the ''surface skin temperature'', which is more readily measured by satellites, and depends on the thermal emission at the surface of a planet. __TOC__


Background

The concept of a skin temperature builds on a radiative-transfer model of an atmosphere, in which the atmosphere of a planet is divided into an arbitrary number of layers. Each layer is transparent to the visible radiation from the Sun but acts as a
blackbody A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The radiation emitted by a black body in thermal equilibrium with its environment is ...
in the infrared, fully absorbing and fully re-emitting infrared radiation originating from the planet's surface and from other atmospheric layers. Layers are warmer near the surface and colder at higher altitudes. If the planet's atmosphere is in
radiative equilibrium Radiative equilibrium is the condition where the total thermal radiation leaving an object is equal to the total thermal radiation entering it. It is one of the several requirements for thermodynamic equilibrium, but it can occur in the absence of t ...
, then the uppermost of these
opaque Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shie ...
layers should radiate infrared radiation upwards with a flux equal to the incident solar flux. The uppermost opaque layer (the emission level) will thus radiate as a blackbody at the planet's
equilibrium temperature The planetary equilibrium temperature is a theoretical temperature that a planet would be if it were in radiative equilibrium, typically under the assumption that it radiates as a black body being heated only by its parent star. In this model, th ...
. The skin layer of an atmosphere references a layer far above the emission level, at a height where the atmosphere is extremely diffuse. As a result, this thin layer is transparent to solar (visible) radiation and
translucent In the field of optics, transparency (also called pellucidity or diaphaneity) is the physical property of allowing light to pass through the material without appreciable light scattering by particles, scattering of light. On a macroscopic scale ...
to planetary/atmospheric (infrared) radiation. In other words, the skin layer acts as a graybody, because it is not a perfect absorber/emitter of infrared radiation. Instead, most of the infrared radiation coming from below (i.e. from the emission level) will pass through the skin layer, with only a small fraction being absorbed, resulting in a cold skin layer.


Derivation

Consider a thin layer of gas high in the atmosphere with some absorptivity (i.e. the fraction of incoming energy that is absorbed), ε. If the emission layer has some temperature Teq, the total flux reaching the skin layer from below is given by: F = \sigma T_^4 assuming the emission layer of the atmosphere radiates like a blackbody according to the Stefan-Boltzmann law. σ is the Stefan-Boltzmann constant. As a result: F_ = \epsilon\sigma T_^4 is absorbed by the skin layer, while F_ = (1-\epsilon)\sigma T_^4 passes through the skin layer, radiating directly into space. Assuming the skin layer is at some temperature Ts, and using Kirchhoff's law (absorptivity =
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 n ...
), the total radiation flux produced by the skin layer is given by: F_ = 2\epsilon\sigma T_^4 where the factor of 2 comes from the fact that the skin layer radiates in both the upwards and downwards directions. If the skin layer remains at a constant temperature, the energy fluxes in and out of the skin layer should be equal, so that: \epsilon\sigma T_^4 = 2\epsilon\sigma T_^4 Therefore, by rearranging the above equation, the skin temperature can be related to the equilibrium temperature of an atmosphere by: T_=T_\left ( \frac \right )^ The skin temperature is thus independent of the absorptivity/emissivity of the skin layer.


Applications

A multi-layered model of a greenhouse atmosphere will produce predicted temperatures for the atmosphere that decrease with height, asymptotically approaching the skin temperature at high altitudes. The temperature profile of the Earth's atmosphere does not follow this type of trend at all altitudes, as it exhibits two temperature inversions, i.e. regions where the atmosphere gets warmer with increasing altitude. These inversions take place in the
stratosphere The stratosphere () is the second-lowest layer of the atmosphere of Earth, located above the troposphere and below the mesosphere. The stratosphere is composed of stratified temperature zones, with the warmer layers of air located higher ...
and the
thermosphere The thermosphere is the layer in the Earth's atmosphere directly above the mesosphere and below the exosphere. Within this layer of the atmosphere, ultraviolet radiation causes photoionization/photodissociation of molecules, creating ions; the ...
, due to absorption of solar
ultraviolet Ultraviolet radiation, also known as simply UV, is electromagnetic radiation of wavelengths of 10–400 nanometers, shorter than that of visible light, but longer than X-rays. UV radiation is present in sunlight and constitutes about 10% of ...
(UV) radiation by ozone and absorption of solar
extreme ultraviolet Extreme ultraviolet radiation (EUV or XUV) or high-energy ultraviolet radiation is electromagnetic radiation in the part of the electromagnetic spectrum spanning wavelengths shorter than the hydrogen Lyman-alpha line from 121  nm down to ...
(XUV) radiation respectively. Although the reality of Earth's atmospheric temperature profile deviates from the many-layered model due to these inversions, the model is relatively accurate within Earth's
troposphere The troposphere is the lowest layer of the atmosphere of Earth. It contains 80% of the total mass of the Atmosphere, planetary atmosphere and 99% of the total mass of water vapor and aerosols, and is where most weather phenomena occur. From the ...
. The skin temperature is a close approximation for the temperature of the
tropopause The tropopause is the atmospheric boundary that demarcates the lowest two layers of the atmosphere of Earth – the troposphere and stratosphere – which occurs approximately above the equatorial regions, and approximately above the polar regi ...
on Earth. An equilibrium temperature of 255 K on Earth yields a skin temperature of 214 K, which compares with a tropopause temperature of 209 K.


References

{{Reflist Temperature Atmospheric radiation