Most of the absorption of the solar radiation is by the surface directly illuminated in line-of-sight with the sun. In comparison to the infrared-emitting surface area, this is reasonably consistent with the general models used by the catastrophic man-made global warming hypothesis.
The heat-emitting surface area is actually larger than is the absorbing, line-of-sight surface area. This is especially the case in land areas. A rough, rocky surface has a much higher surface area than does the surface of the perfectly smooth sphere used in the models. A vegetated area has heat emission from the ground and from every part of every plant on that surface. The stems and trunks emit heat. Both sides of every leaf emit heat. Let us say that the 71% of the Earth's surface which is water has a surface area about equal to that of the round, smooth surface as a simple base for further discussion, though even its surface area is slightly larger. This leaves 29% of the surface and those areas with vegetation may have a surface area which is 2 or 3 times the surface area of the smooth sphere in a given bordered area in 2-dimensions as viewed from space. Desert and arctic areas may only have an area 1.3 times as large. Every surface mineral particle in the desert with an air-exposed area will have a surface area much greater than the portion of the surface of a sphere covering the same periphery.
It is not at all unlikely that the average land area whose solar absorbing surface area is A, would have a heat-emitting surface area of about 1.6 A. Thus, the heat-emitting area including the 71% of the Earth's surface which is water and the nominal 29% which is land could readily be:
0.71 A + 0.29 (1.6) A = 1.17 A
Now, I am not claiming to know this effective emission area accurately. I most certainly do not know it accurately. But, if the science of the so-called greenhouse effect and its consequences for man-made global warming is a scientific consensus, as opposed to a political consensus, then this effective area is a well-known parameter and should be readily available to all interested parties.
As a scientist interested in the effects of carbon dioxide and other infrared gases upon the climate, I would have to know this effective Earth emission surface area to be a member of any scientific consensus of those effects on the Earth's climate. As a benevolent human being, I would also have to be very sure of this before I would become an advocate of killing off the many conveniences and life securing benefits of the use of fossil fuels, not to mention the jobs of those dependent upon the use of these forms of energy.
This issue of the effective Earth infrared emission surface area does not end here. No, it gets much more complex yet.
We have to remember, as far too few scientists seem to do, that infrared emission occurs because electric charges are accelerated with respect to one another, thereby creating dipole, quadrapole, and other higher order electromagnetic fields. The dipole field created by oscillating electric charges at the molecular level is the primary source of the resulting electromagnetic field, so I will just refer to these oscillating electric charge pairs henceforth in this discussion to keep things a bit simpler. The higher the temperature, the greater the acceleration and deceleration applied to the electric charges in each oscillating electric dipole because the frequency of the oscillation increases as the temperature increases. The greater these changes in acceleration are, the greater the strength of the dipole electromagnetic field created. The greater the strength of the electromagnetic dipole field, the greater the photon emission. At the temperature of the Earth's surface, the photon emission is in the mid infrared wavelength range. At the temperature of the surface of our Sun, the photon emission is in the higher energy and shorter wavelength range of ultraviolet, visible, and near infrared radiation.
Now if the Earth's surface interfaced directly with space and there were no water on the surface either evaporating or sublimating and there were no atmospheric molecules bombarding it, all of the Earth's surface area would emit infrared radiation in accordance with the Stefan-Boltzmann equation which is often utilized in the semi-scientific climate science discussions of infrared radiation from the Earth's surface. Of course as discussed above, the Earth's real surface area for that emission is not taken into account. No, in those discussions the Earth is replaced by a perfect sphere.
Our Earth has a surface which is not only not a perfect sphere, but 71% of it is liquid water and additional portions are ice. This portion of the Earth's surface has obvious cooling mechanisms other than the emission of infrared radiation. Most of the land surface covered by vegetation, animals, soil, and minerals also has considerable water present. Consequently, evaporation of water from these surfaces is a significant cooling effect. Plants and animals are mostly water. Soil and minerals absorb considerable water on the surfaces of the particles of which they are composed. Many of the minerals common in the Earth's surface have lamellar structures at the atomic level and absorb water and carbon dioxide between the layers of atoms of which they are composed and can be more or less hydrated depending on the humidity and time between rains. The evaporation of water provides a powerful cooling effect on almost every part of the Earth's surface.
Where does the energy come from that causes a water molecule to evaporate and become water vapor in our atmosphere? It has to come from the nearby atoms of the surface at the site of the evaporating water molecule. This is a clear requirement of the Conservation of Energy. In what form was that energy which has been taken up in the evaporation of our water molecule? It was the vibrational energy in the nearby atoms that was the same vibrational energy that caused them to create their contribution to the dipole electromagnetic field. As that energy is soaked up by the evaporating water molecule, the frequency of the oscillations of the nearby dipoles is reduced and the strength of the local electromagnetic field is decreased. The temperature of the local atoms is effectively reduced for a brief time before energy from the surrounding surface materials can flow into the local atomic area that just lost energy to the evaporation process. During this time, any infrared emissions from those lower frequency oscillating electric dipoles are those characteristic of a material at a lower temperature. To be sure, this time of reduced infra-red radiation energy loss is short, but then in many cases the time to the next case of a local water molecule evaporation may also be short. And what is very important here, the real surface area emitting infrared radiation characteristic of the Earth's surface temperature according to the Stefan-Boltzmann equation is reduced on the macroscopic level.
Yes, those local atomic environments within the macroscopic area where no water molecule has evaporated will emit radiation in accordance with the Stefan-Boltzmann equation. But other local atomic environments having just given up energy to the evaporation of a water molecule cannot do so, at least not at the normal temperature of the Earth's surface. At any given time, the fraction of the area of the Earth's surface emitting radiation in accordance with the Stefan-Boltzmann equation for the average Earth temperature of 288K, must be less than 1. And of course, any scientific consensus in favor of the catastrophic man-made global warming hypothesis would include knowledge of just what this fraction is. At some point, this would have been a hot topic of discussion. This issue having been resolved, every advocate of the truth of catastrophic man-made global warming will be able to discuss this intelligently with any inquirer.
Now this is not the end of the surface area of infrared emission story. To this point, we have not considered the bombardment of the Earth's surface by air molecules. According to the usual theory of the large greenhouse gas effect on the climate, the primary reason the Earth's surface has an average temperature of about 288K is the absorption of radiation from the sun directly and the absorption of an even larger amount of radiation energy from the atmosphere. See the viewpoint expressed in the Earth energy budget below:
All of the energy that warms the surface is in the form of these two radiation sources, with the back radiation from the atmosphere being 2.08 times the direct solar radiation absorption according to this NASA Earth energy budget. This is entirely false, which I have explained many times. This viewpoint is based on the wrongheaded idea that the Earth's entire surface emits radiation as though it were in a vacuum and absorbs massive radiant energy from a generally cooler atmosphere which is even greater than the energy absorbed from the Sun. In reality, the Earth's surface emission is much, much less than shown in this diagram and the back radiation is much, much, much, much less than is shown. In fact, back radiation is actually limited to those cases of atmospheric temperature inversions, which do occur in a dynamic atmosphere, but have a much smaller effect than that claimed. The principal the Earth's surface is as warm as it is is due to being in equilibrium with the temperature of the warm air molecules that bombard it.
Why are these air molecules warm enough to establish an equilibrium temperature with the surface which is much higher than that of the Earth system equilibrium temperature as seen from space? Primarily because of the action of the Earth's gravitational field on the molecules of the atmosphere. At the altitudes from which the Earth's atmosphere emits infrared radiation into space from water molecules, carbon dioxide, and other infrared-active molecules, the atmosphere is much cooler than is the surface of the Earth. The Earth's surface also emits a large fraction of the infrared radiation it does emit directly into space, because much of its spectrum of radiation is not absorbed by the infrared-active molecules of the atmosphere. The fraction of the Earth's surface emission absorbed by the atmosphere is much smaller than is shown in the NASA Earth energy budget above.
The temperature of the atmosphere at the altitudes from which its infrared emission into space occurs is fixed by that process and depends upon the concentration of the infrared-active molecules with altitude. The energy of an air molecule at that altitude is given by E = Kinetic Energy + mgh, where g is the gravitational constant (actually very slightly reduced with altitude from the surface value) and h is the altitude. The gas molecules in our atmosphere are very nearly perfect or ideal gases in their behavior, Consequently, the temperature of those gas molecules is proportional to the Kinetic Energy of those molecules. This is a property of ideal or perfect gases.
Of course every good scientist knows both that the gas molecule kinetic energy in the atmosphere varies with altitude due to the potential energy term mgh and every one of them knows that the temperature of a perfect or ideal gas molecule is proportional to its kinetic energy. Consequently, any respectable scientist understands that the temperature of an air molecule at the surface of the Earth is much higher than its temperature at an altitude of say 7000 meters where atmospheric radiation into space largely occurs. Do we not see this discussed all the time in the consensus viewpoint supposed to back the catastrophic man-made global warming hypothesis?
In fact, simply due to this gravitational action on gas molecules in our atmosphere, the temperature of gas molecules on average at the Earth's surface and in equilibrium with the Earth's surface raises the surface temperature more than does the directly absorbed radiation from the Sun. It is only when the Earth's surface temperature is higher than the temperature of gases at the bottom of the atmosphere that heat flows from the surface to the atmosphere. This happens when the surface is warmed by sunlight. At night, as thermal radiation from the surface cools the surface, it is kept from cooling very much because the air molecules bombarding it tend to maintain the temperature the gravitational field imparts to them. These effects on the surface temperature are not indicated in the NASA Earth energy budget. The only role that the Earth's molecules striking the surface plays in the NASA "consensus" viewpoint is the loss of heat by the subsequent creation of thermals. The primary reason for the Earth's high surface temperature is converted into a minor heat loss.
If the only effect of gas molecules bombarding the Earth's surface were a heat loss, then each instance of a gas molecule striking the surface would remove heat locally and act much like the evaporation of a water molecule described above. Each such event would locally lower the surface temperature and reduce the energy loss due to the emission of infrared photons. This would reduce the effective area emitting radiation in accordance with the Stefan-Boltzmann equation. And, being conscientious scientists, those claiming they were part of the scientific consensus on catastrophic man-made global warming would have come to a conclusion, known to all of them and available to every interested inquirer, about the effect on the fraction of the surface emitting energy in accordance with the average temperature by Stefan-Boltzmann radiation and the fraction emitting infrared radiation characteristic of lower temperatures due to energy loss to bombarding air molecules.
So, I ask you if those scientists who ascribe to what has been frequently claimed to be a scientific consensus have indeed considered the critical scientific issues I have discussed above? It is not as though these are difficult issues to recognize as critical if one has both some understanding of very basic principles of science and a scientific mind. It would be a terrible travesty of science and good government if the United States government has spent many tens of billions of taxpayer dollars on backing catastrophic man-made global warming and yet has not considered the basic science I have tasked them with here.
Interestingly enough, in the the 1950s through the 1970s, the U.S. government funded the computation of tables for the U.S. Standard Atomsphere which did recognize the gravitational source of the temperature of the lower layer of the Earth's atmosphere, the troposphere. How odd that the government has forgotten that science. I have been reminding people about this since 2010, with little effect.