{"id":2690,"date":"2020-02-07T11:49:03","date_gmt":"2020-02-07T10:49:03","guid":{"rendered":"http:\/\/klima-fakten.net\/?page_id=2690"},"modified":"2020-08-20T22:29:43","modified_gmt":"2020-08-20T21:29:43","slug":"re-emission-demythologized","status":"publish","type":"page","link":"https:\/\/klima-fakten.net\/?page_id=2690&lang=en","title":{"rendered":"IR re-emission demythologized"},"content":{"rendered":"
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IR re-emission – the traditional explanation<\/h4>\n\n\n\n

The communicated common understanding of the greenhouse effect depends very much on the re-emission hypothesis<\/strong>: Molecules of greenhouse gases such as \"CO_2\" absorb infrared radiation, typically in the absorption band with the wavelength around \"16 \mu m\", reaching an excited state. After some time the molecules return to the „ground state“, thereby emitting infrared radiation of the same wavelength isotropically. This is typically interpreted as radiating 50% upwards, and 50% downwards. Due to the assumption that all \"CO_2\" molecules do this, it is imagined that approximately half of the upwelling IR surface radiation is radiated back to the surface, resulting in „downwelling“ IR<\/strong>. As this is additional heat reaching the surface, the surface is heated up. This is being called the „greenhouse effect“. Understandably the more \"CO_2\" there is in the atmosphere, the more it heats up.
With such a simple picture it is understandable that many claim that „the science is settled“. <\/strong><\/p>\n\n\n\n

Radiation is converted to thermal motion<\/h4>\n\n\n\n

A necessary condition for the behaviour described above to work, would be that the atmosphere was so thin that the probability for the decay of an excited \"CO_2\"-state is higher than the probability to collide with another gas molecule<\/strong>. In the real atmosphere, specifically the troposphere, the process is different. Let’s assume that \"CO_2\" molecules of the atmosphere are excited by infrared radiation (IR). This diagram shows,<\/p>\n\n\n\n

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Fig. 1: Life time of excited CO2 molecule (line) and mean time between collisions (grey area)<\/figcaption><\/figure>\n\n\n\n

that the lifetime of an excited \"CO_2\"-molecule for wavelength \"16\mu m\" is appr. \"10^{-4}\"s. But the time between collisions with neighboring molecules is between \"10^{-10}\" s and \"10^{-8}\" s, depending on air pressure. Therefore the probability to transfer energy by collision is 10000-1000000 times larger than by re-emission<\/strong>. Additionally, the probablity to collide with a non-\"CO_2\" molecule is \"99.96\"%.
Collisions are described by thermodynamics<\/strong>. From gas law and energy conservation in the thermodynamic equlibrium this results in a state distribution described by the adiabatic barometric equations<\/a>, essentially stating, that in an atmosphere subject to a gravitational field both density as well as temperature decrease with height above the surface<\/strong>. The temperature gradient is commonly called lapse rate<\/strong><\/a>. It is important to note that this temperature gradient is entirely caused by thermodynamics – it is the state of maximum entropy of a gas in a gravitational field, it has nothing to do with radiative forcing<\/strong>. For dry air the (dry adiabatic) lapse rate is \"\Gamma_d = \frac{dT}{dz} = - \frac{g}{c_p} = - 9.8 C/km\", only dependent on the gravitation constant and the specific heat, the moist adiabatic lapse rate <\/a>includes the condensation heat of water vapor, and is in the range of \"\Gamma_m = 4-9.8 C/km\", depending on the water vapor concentration.
Whereever heat is introduced into the atmosphere, it is forced to distribute thermodynamically across the whole atmosphere, with the equilibrium state of a temperature distribution according to the moisture dependent lapse rate.<\/strong> The so-called standard atmosphere<\/a> has a lapse rate of \"\Gamma = -6.4 C/km\", which is approximately the measured global average lapse rate<\/strong>. This „thermodynamic forcing“ is so overwhelmingly dominant (89%), that any other effects like radiative forcing are of minor significance within the troposphere<\/strong>. In the tropopause and above it is different. The atmosphere is so thin, that there is no thermodynamic equilibrium, and consequently the radiation effects dominate there. <\/p>\n\n\n\n

\"Dieses
Fig. 2: Temperature Gradient (Lapse rate) for standard atmosphere<\/figcaption><\/figure>\n\n\n\n

Thermal motion is converted to radiation<\/h4>\n\n\n\n

Obviously the process also works in the other direction. A \"CO_2\" molecule may get excited by collisions and then radiates. But from the numbers above it is fairly clear, that direct re-emission plays a neglegible role in the interior of the troposphere<\/strong>: Any excited greenhouse gas molecule is overwhelmingly likely to distribute its additional energy to its neighbor molecules by collisions, the result is a local state of thermodynamic equilibrium. <\/strong>This is usually called „thermalisation<\/a>“ (interestingly Wikipedia does not mention atmospheric processes – honi soit qui mal y pense<\/em><\/a>) . Therefore any selected volume sufficiently large to have a thermodynamic equilibrium can be regarded as an independent Planckian emitter of (infrared) radiation. So it is possible that a volume absorbing IR with \"CO_2\" is later emitting IR of another wavelength from water vapor (and vice versa). Thermodynamics permanently re-arranges the gas volume towards the local thermodynamic equilibrium. Any absorbed energy is locally quickly distributed across all neighboring molecules , some of which can radiate IR, and most others can’t. From such a volume you get a Planck emission spectrum involving all local greenhouse gases, not only \"CO_2\".
Re-emission can therefore not be defined on a single molecule but emissions are independent of absorptions and are defined on a large enough volume to have a thermodynamic equilibrium<\/strong>. <\/p>\n\n\n\n

Downwelling radiation and heat transport<\/h4>\n\n\n\n

According to Planck’s law a volume with higher temperature emits more radiation at all wavelengths. Volumes from higher altitudes emit less radiation because of temperature and densitiy gradients. <\/strong>Therefore upwelling radiation is always larger than downwelling radiation, with the important consequence that – under the condition of a lapse rate – there is no radiative heat transport from higher altitude to lower altitude<\/strong>. This is in accord with the 2nd law of thermodynamics<\/a>, according to which heat can never flow spontaneously from a colder system to a warmer system. <\/p>\n\n\n\n

Radiation at the boundary of the atmosphere<\/h4>\n\n\n\n

As soon as we are „close enough“ to space, i.e. within 1 optical depth<\/a> (which is wavelength dependent), then actual emission into space becomes possible, and takes place, because there are not enough suitable molecules above to absorb all radiation<\/strong> .  Water vapor is by far the most relevant absorbing and emitting gas. Fig. 3 shows that there is a sharp drop of water vapor density at about 5 km altitude. <\/p>\n\n\n\n

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Fig 3: Measured ater vapor density profile of the atmosphere<\/a><\/figcaption><\/figure>\n\n\n\n

Radiative equilibrium at top of atmosphere<\/h4>\n\n\n\n

Whereas all energy-relevant interactions inside the atmosphere and between the atmosphere and the ground are based on convection(67%), evaporation\/condensation(22%), and radiation(11%)<\/a> – dominated by convection, the interaction with empty space is restricted to radiation<\/strong>. From the previous arguments it is clear, that relevant radiation is restricted to the „top of atmosphere“. To be precise, it is the range with less than 1 optical depth „distance“ to empty space. This „distance scale“ depends strongly on the wavelength<\/strong> of the infrared light. <\/p>\n\n\n\n

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Fig. 4: Example of an actual infrared emission spectrum observed by the Nimbus 4 satellite over a point in the tropical Pacific Ocean. Dashed curves represent blackbody radiances at the indicated temperatures in Kelvin. (IRIS data courtesy of the Goddard EOS Distributed Active Archive Center (DAAC) and instrument team leader Dr. Rudolf A. Hanel.)<\/em>] <\/figcaption><\/figure>\n\n\n\n

From the emission spectrum of Outgoing Longwave Radiation (OLR) we can infer essentially 3 cases:<\/p>\n\n\n\n