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An asymmetry in the up- and downwelling eigen radiation (only from atmosphere) will be found with a stronger contribution in downward direction, which is caused by the lapse rate as well as the density profile over the atmosphere with higher temperature and pressure at lower atmospheric layers and therefore a higher net downward radiation. Calculations for the radiative forcing at doubled CO2 concentration and at an average cloudiness give a 30% smaller forcing than applied by the IPCC.
Thermal radiation is electromagnetic radiation and no heat. Therefore, in the same way, as radio waves can propagate from a colder antenna to a warmer receiver, microwaves can be absorbed by a hot chicken, or CO2-laser radiation (10.6 μm) can be used for welding and melting of metals up to several thousand °C, so any back radiation from colder and higher atmospheric layers can be absorbed by the lower and warmer layers, and this back radiation can also be absorbed by a warmer surface of the earth without violating the 2nd law of thermodynamics. As long as the surface is assumed to be a black or gray absorber, it does not filter any frequencies of the incoming radiation, in the same way as it does not reject any frequencies of the broad Planck spectrum of a thermal radiator, independent, if it has a higher or lower temperature than the earth. Radiation converts to heat after an absorption, followed by an emission in accordance with a newly adjusting thermodynamic equilibrium, which only requires that the net energy transfer is in balance.
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From
https://www.hindawi.com/journals/ijas/2013/503727/
This is a pretty thorough analysis of radiation and energy movement into, through, and out of the atmosphere. And the mechanisms by which the energy is constantly being switched back and forth into different forms.
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The radiation in upward direction is the only possibility to render any absorbed energy to space and by this to keep the atmospheric temperature in balance with all the supplied direct and indirect energy from the sun. On the other hand, the downwelling part determines the back radiation from the atmosphere to the earth’s surface, which is the source term of the so heavily discussed atmospheric greenhouse or atmospheric heating effect.
While the upwelling radiation only contributes to cooling, as long as the radiation can escape to space, the downwelling part only causes heating, when it reaches the surface.
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This has to be taken in context. It is describing the two possible exits for energy contained in the atmosphere. Either it is lost to space or returns to the surface.
The surface expels energy by radiation, conduction and convection (containing latent heat). Only some of the radiation can escape to space causing cooling of the system, the rest is absorbed by the atmosphere, which warms in response.
The atmosphere expels energy by radiation and conduction. These are the only paths. Conduction can only return to the surface, therefore cannot cause cooling of the total Earth system. Radiation can cause cooling but only if it escapes to space. Some of the radiation produced by the atmosphere does escape, some returns to the surface, but most is simply reabsorbed by the atmosphere.
The energy absorbed by the Earth system swirls around being transformed back and forth into different forms. Whenever it takes the form of radiation that can escape through the atmospheric window, it leaves (if it is traveling in the right direction). Radiation can also escape if it emitted high up in the rarified atmosphere and doesn't get reabsorbed. Those are the only two escape routes, the only way to cool the Earth system.