NASA Finally Produces A Realistic Energy Budget for the Earth

The Atmospheric Science Data Center of NASA has finally produced a realistic energy budget for the Earth.  [The link no longer works.  It is not surprising that the diagram fatal to the back radiation model of man-made catastrophic global warming due to back radiation acting on greenhouse gases is no longer publicized by NASA.  But I did find it in this educational product pdf file.  23 Feb 2013]  There is no back-radiation in this diagram due to greenhouse gases, or really due to infra-red absorbing gases, such as water vapor, CO2, and methane.  The new NASA energy budget is:

Note how remarkably different this is from the Kiehl-Trenberth diagrams NASA has previously been using:

I have discredited the Kiehl-Trenberth diagram in this post.

While the new NASA energy budget is much improved and has no back-radiation component, the web site I linked to above still talks briefly about greenhouse gases and some back-radiation effect.  As I have noted, any such effect is small and can only happen in a way to briefly slow the cooling of the Earth as solar insolation is being reduced from its maximum effect in the afternoon of a day.  Even then, infra-red absorption of incoming radiation from the sun may be greater than any back-radiation effect until evening.  The overall effect of IR-absorbing gases is a cooling effect as I have previously claimed it was.

Let us consider the new NASA Earth Energy Budget numbers.  The first thing to note is that the infra-red radiation from the ground is only 21% of the incoming radiation from the sun.  In the Kiehl-Trenberth diagram, the energy flux of out-going infra-red radiation (396 W/m^2) is actually greater than the total incoming solar radiation flux (341 W/m^2) and much, much greater than the energy absorbed by the surface from the sun (161 W/m^2).  This is patent nonsense.  Energy must be conserved and it is in the new diagram.

As I have claimed, the net effect of infra-red absorbing or greenhouse gases is that they absorb more energy from the incoming solar radiation through the course of the day than they absorb from the out-going infra-red radiation from the surface of the Earth.  In the new NASA diagram, the total radiation absorbed by the infra-red absorbing gases is 16% + 3% (clouds) = 19%.  Of the 21% of infra-red radiation emitted from the surface, only 15% is absorbed in the atmosphere.  Thus, the net absorption of incoming solar radiation at 19%, is 1.27 times greater than the net absorption of energy emitted by radiation from the ground.  This means the net cooling effect is at least 1.27 times greater than any warming effect could be.

Another point of great interest is that the new NASA diagram gets the fraction of the cooling of the surface of the Earth by infra-red radiation about right.  The fraction of surface cooling by infra-red radiation from the surface is 21% / 51% = 0.41.  This agrees with some calculations I have done based on molecular collision frequencies at the altitude in the atmosphere at which radiation competes evenly with molecular transport or movement.  The temperature of the Earth seen from space as a black body radiator is 255 K.  This is the temperature of the standard atmosphere at an altitude of 5 Km.  The altitude at which radiation cooling in the atmosphere is equal to the cooling caused by thermals, conduction, and the transport of water vapor is then a bit lower and proves to be about 4 Km.

Water vapor is the best long wavelength IR absorber and it is the best emitter of IR energy, but before it can commonly emit the energy it has absorbed from IR radiation, even it will likely suffer numerous gas collisions with much of its excess molecular energy being transferred in those collisions to the molecules which collide with the water molecule.  Nitrogen molecules are the most likely molecules to take up much of the energy from the water molecule, since nitrogen is 78.08% of the atmosphere.  Oxygen molecules are the next most likely colliders at 20.95% and then argon atoms at 0.93%.  Together, these three gases account for 99.97% of the U.S. Standard Atmosphere.  None of these gas molecules are very efficient IR absorbers in the long wavelength spectrum.

At sea level, the mean gas velocity is 459 m/s, the mean free path or distance between collisions is only 6.6 x 10^-8 m or 66 nm, and the collision frequency is 6.9 billion/s.  At an altitude of about 4000 m, the radiative transfer of energy competes about evenly with transfer by collisions.  At that altitude, the frequency of gas molecule collisions is about 4.4 billion/s.  We can use the equivalency of energy transfer by radiation and gas molecule collisions at the 4000 meter altitude to estimate the fraction of energy transfer by radiation of the total of energy transferred by radiation plus gas molecule collisions. At sea level, energy transfer by radiation is equivalent to about 4.4 x 10⁹ collisions per second, so the fraction of energy transferred by radiation is about 4.4/(4.4 + 6.9) = 0.39 of the total by gas molecule collisions and radiation.  This suggests that about 1.5 times as much energy is transferred by gas collisions as by radiation at sea level.  Note that this number is in good agreement with the fraction of the energy 0.41 given in the new NASA diagram.

This phenomenal number of atmospheric molecular collisions spreads the IR energy absorbed by a water molecule or a CO₂ molecule from the ground long wavelength IR emissions to the dominant nitrogen and oxygen molecules very, very quickly.  At an altitude of 5 km, the collision frequency is still 3.9 billion/s and at 10 km altitude it is 2.1 billion/s.  If a water molecule is to radiate energy away as IR emissions, it must do so very quickly!  If it were able to emit IR very quickly, then the atmosphere would cool down very quickly and effectively at night.  Indeed, cooling at high elevations in mountains by radiative cooling is more effective than cooling from sea level because less of the radiative energy of the ground is spread to many nitrogen and oxygen gas molecules which then tend to hold the energy near the ground.

Back radiation to the ground from an infra-red absorbing molecule such as water or CO2 is thus not a likely event.  To this, we must add the very important caveat that the Earth's surface can only re-absorb that energy if it has cooled since the emission of the radiation occurred.  Given the very short time scale between emission of radiation from the Earth and the re-emission from an atmospheric molecule such as CO2 or water, any such cooling is trivial.  Radiation from molecules in equilibrium with the cooler temperatures found as one goes higher into the atmosphere will not be absorbed at all, since infra-red radiation only flows from warmer to cooler bodies.  The reverse does not happen.  This is a law of thermodynamics often violated by greenhouse gas global warming alarmists.  Thus, any back-radiation effects were always trivial and more than compensated by the cooling effect of infra-red gases absorbing solar radiation before it could reach the surface of the Earth.