Without an understanding of the basic physics which underlies the interactions between carbon dioxide and its resonant radiation field, as well as the processes involved in the transfer of energy between all of the components of the earth/air/radiation/Green House Gas (GHG) system, it is pointless for the many economists, biologists, geographers and even meteorologists, who engage in these discussions to provide confident statements as to the long term effects of the anthropogenic emissions of carbon dioxide.

I hope that at least some of them will come to this site and read Jennifer's article here, and think a little more about their own misgivings and perhaps their own very modest understanding of what lies at the basis of these most important discussions. The world economy and most importantly, the war on poverty, depends on that understanding.

The description of the process whereby the air near the surface of the earth produces cooling is complex and is often, too casually, explained by reference to the 'Second Law of Thermodynamics' which does in fact apply to the situation as always, but does not tell the whole story. For this reason, the common response is to revert to claiming, incorrectly, that the 2nd Law does NOT apply as has been the case among a few of the commentators on this blog.  If the temperature of the air above the earth is cooler than the earth, then the earth will continue to be cooled by its contact with the air, by the relaying of infrared radiation through emission and absorption to the GHG's, and by evaporation (some of it forced by wind) of water.  In spite of the plethora of commentators in the wider community, claiming otherwise, and trying to "correct" the statement by Senator Malcolm Roberts, what he says has provided a very valuable insight into the deeper world of basic global warming (or not!) theory.

However, in the absence of any greenhouse gases in the atmosphere, the cooling of the earth by radiation, which depends on the fourth power of the temperature T -

Power radiated by a "black body"(BB) per square metre = Sigma x T^4
[Note: A BB is one which absorbs and radiates electromagnetic radiation of all wavelengths {light of all colours!} equally readily]

where Sigma is Stefan's Constant and equal to 5.67 x 10^-8 where T is given in degrees Kelvin K which is 273 + the temperature in Celcius (C). Thus at 27 C (300 K), a common daytime temperature of the air which does not burn the skin nor feel all that uncomfortable even when walking under an umbrella, one will often find that the temperature of the surface of the ground is of the order of 65 C (338 K) earth.
 

So let us have a look at an example where only the sun, the ground's surface (approximately a BB), and the air (including some carbon dioxide) are involved - in the middle of the day, directly under a tropical sun

The power radiated by a square metre of that surface, (an approximate black body at infra-red wavelengths), can be found from the formula above to be about 740 Watts, compared with the sun's received power, with a perfectly clear mid-day sky, of around 1300 Watts per square metre. As the day progresses our bitumen surface does not become hotter but remains constant for a couple of hours before cooling slowly during the afternoon. What is happening to the initial solar power received at the surface, which is not re-radiated (1300 Watts -740 Watts = 560 Watts per square metre)?.

Some, a fairly small part of it, is absorbed by the ground itself.  The remainder is removed, mainly by the cooler air above it through conduction right at the interface, a few microns thick. Once that thin layer of air is heated, convective cooling of the surface then takes place, while, simultaneously, the GHG's are absorbing and re-emitting radiation upwards towards space and downwards towards the earth's surface.

Of the 740 Watts radiated from the bitumen, on our specifically clear day, with no water vapour, and assuming ONLY carbon dioxide of the GHG family being present, 72.3 Watts, a little less than 10% is absorbed by the 15 micron band of this gas and a much smaller power by the combination of its 4.7 micron and 10 micron bands. The remainder (conceptually without other GHG's and clouds) is radiated directly to space.

Thus we know from these fundamental calculations that the air above our bitumen is warmed
1. Because of contact and conduction which adhere to the Second Law of Thermodynamics 
2. Because of the uptake of radiation energy by carbon dioxide - being almost totally absorbed within the first 100 metres. 

Through turbulence and micro circulation, the heat from surface contact is also distributed well above ground level, so we can usefully look at the process, involving, say, this first 100 m, by assuming that the latter "contact induced" energy is also initially distributed through air up to that level - at a rate corresponding to an absorbed power of approximately 560 Watts + 72 = 632 Watts (Joules per second).
 
The density of molecules in the air at ground level is very close to 2.5 x 10^ 25 m^-3 so that our 100 metre column of cross section 1 m^2, contains 2.5 x 10^27 molecules. Ignoring the difference in heat capacity for variation in volume or pressure, we may write the change in energy E of the 100  m^3  of air in our column corresponding to a change in its temperature T of Delta_T, from the formula E = Nk x Delta_T or 2.5 x 10^27 x 1.38 x 10^-23 x Delta_T from which the change in temperature, Delta_T = E/(3.5 x 10^4).

Thus the air will be warmed above the temperature of "surrounding" air, the inverted commas indicating that we cannot define definitively the dimensions of this surrounding air, although we do know that the result will be a rising of the hotter air sample at a rate commensurate with its increase in temperature.  However, in such a simple calculation as this, it is not appropriate to make any positive claim regarding the characteristics of that rise. (From experience with wind measurments over flat farm land, as the sun rises over a paddock where herbicides are being sprayed in the early morning, it is known that soon after sunrise the convection, somewhere, will give rise to a wind of some 15 km /hour or 4.2 metres per second.

Suppose that we err on the conservative side and assume that the upward flow of air from convection of our heated sample is only one quarter of this speed or 1 metre per second. Thus our sample of air may be assumed to rise at this speed, so that the 100 metre column of warmed air is replaced every 100 seconds. In that time, the 632 watts being transferred to it from the ground, will add 63,200 Joules of energy which is distributed amongst the 2.5 x 10^27 molecules providing a temperature rise of 63,000/(3.5 x 10^4) = 1.8 C.

The quantities used above are rough and ready, but provide a skeleton over which to drape a "skin" that demonstrates the type of detailed calculation neededt before one can simply dismiss the statements as being implausible. The result of 1.8 C may be very different - but not TOO different - from the result we might expect to observe in the temperature of the air as we stand above a hot bitumen surface!!!  And of course all of the above figures will change dramatically as we relocate our position to all the many locations on earth between the equator and the poles, as well as taking account for the different characteristics of the solid surface.

And what about the effect of the carbon dioxide in that air? You may well ask.
Calculations of a more accurate nature and making full use of the quantum mechanical representation of appropriate parameters for the measured (and calculated) characteristics of carbon dioxide in the sample of air, shows that yes, all this while this Green House Gas is radiating energy within its spectral bands, both upwards towards space and downwards towards the earth, at a rate commensurate with its temperature and density. It is this downwards radiation which is correctly identified as restricting the rate at which the surface of the earth will cool, compared with the rate which would persist were no carbon dioxide present.  It is indeed a rate which depends critically on the gas temperature and its own concentration and at our nominated temperature of 300 K (27 C) has a calculated value of 86.8 Watts per square metre, which, when added to the power of the sunlight - 1,300 W/m^2 - gives a total of 1386..8 W/m^2, providing a very local, of course, contribution to the surface temperature, corresponding to that considered as representing the standard Green House Effect of Arrhenius.

For our piece of bitumen under the full, unimpeded, sunlight intensity of 1300 Watts, the equilibrium temperature is 389.13 K or 116.13 C, while that for the sunlight plus "Back radiation" of 1386.8 is simply 6.3 C higher, at 395.46 K. This is commensurate with other estimates of the temperature increase to the measured 288 K, which is 33 K (or 33 C) above the solar equilibrium temperature of 255 K which is widely quoted in published reports.   which provide details of the ultimate determination of the temperature increase from the, (the average temperature for the earth, taking account of losses from sunlight because of cloud, aerosols etc. leading to an earth albedo of 0.3), to that higher after taking account of conduction and the effects of vaporization from water and re-condensation in the formation of clouds.

Thus we see that the logic of radiation calculations, relating to a pseudo "experimental" arrangement of a patch of bitumen lying peacefully under a tropical sun, provides results which are totally consistent with experimental values found regularly in other situations. However, we have not yet dealt with the key feature of any discussion on global warming, or rather, that which should always be the key feature, but which is so often rejected as inconsequential compared to those more "important" considerations used to "demonstrate" the apparent consequences of the anthropogenic production of carbon dioxide in the atmosphere.  Such "observations" as decaying coral reefs, movement of species to "cooler" climes (when temperatures appear to increase in habitats by 0.1 C), unprecedented droughts, higher rainfall, cold winters, unprecedented snow falls in Europe and devastating floods in China, are all evidence that carbon dioxide increases are already causing global warming.  This "anthropogenic" warming is obviously far more destructive of our planet than those changes brought about by variation in the sun, so clearly demonstrated by Henrik Svensmark and co-workers at the Danish National Space Centre in Copenhagen, and by the ongoing effects of the components of the Milankovic cycles, which in appropriate combination produce the repeated Ice Ages and Holocenes.  These important influences which are continuously active in modifying the earth's climate, seem to be excluded from any conversation on Climate Change.  Why is this so?.    Simply because the goal in the climate research units has been:
        1. To find a value of the climate sensitivity representing the temperature increase to be expected from a doubling atmospheric carbon dioxide, using atmospheric modelling of the kind used in modern weather forecasting.
         2.  To study the expected devastation which a warmed earth will likely cause, ensuring a governmental support which continues to grow, in spite of the uncertainty which now persists after more than forty years of dedicated research in an effort to improve the ability of the models.
        3.  To explain away an 18 year "pause" in warming, which defies earlier confident predictions.
        4.  To find excuses for the inability of any one of 122 models which contributed to the IPCC AR5 report of 2013/14, to pass an "experimental" test of hind-casting, a test which had been declared as "absolutely essential" in the scientific section (8.1.1.1 and 9.1.2.2) of AR4, 2007. 

In terms of our reasonably successful "pseudo-experiment", we demonstrated how the power returned to the earth from carbon dioxide could be determined theoretically.  We applied this method for the current known concentration of N(co2) = 1.0064 x 10^22 molecules per cubic metre.  It is time to look now at the effect on the temperature of this same sample of the earth's surface, as a result of a doubling of this concentration.

Calculations, in concert with the analysis described above, but which now involve the use of the well-known Schwartzchild equation for the transfer of electromagnetic radiation through an active, gaseous medium, show that for the model described above, an increase in the density of a Green House Gas in the atmosphere, does lead to an increase in the "downwards radiation" described earlier as having a value of 86.8 W/m^2.    The revised value is 87.19 W/m^2, an increase in this case of 0.4 W/m^2. On its own, this leads to an estimable temperature increase for our bitumen surface from 395.46 to 395.49 or 0.03 for the case of carbon dioxide in air, making use of a full quantum mechanical model of radiation being transmitted through a mixed gas system with experimentally known temperature and pressure variations,

While the increase in CO2 leads to a very small increase in the net equilibrium temperature of the surface. the radiation upwards from the carbon dioxide in the air above this surface, increases from 87. 3 W/m^2 to 90.6 W/m^2, or by 3.3 W/m^2, again a very small amount, but with a higher value than that for the "back radiation".   This difference is to be expected from the obvious fact that for radiation from a given slice of the atmosphere, the more dense gas below that slice will more readily absorb the radiation travelling towards the earth than will the lower density layers above it absorb the radiation of similar wavelengths travelling towards outer space.

There is obviously a lot more that can and needs to be said on this topic. Hopefully these few comments may stimulate a more focussed analysis of the difficult processes to be discussed than the superficial presentations provided so far by the IPCC, CSIRO and the many Units at Universities in Australia, whose research, it is claimed at least, is directed towards studying "quantitatively" the magnitude of global warming to be expected from a doubling of atmospheric carbon dioxide.

Experimental evidence tends to favour the results of the above analysis, as demonstrated clearly by the pause in warming over the past, approximately, 19 years, during which time the density of carbon dioxide in the atmosphere has measurably increased at an accelerated rate.

Next Time:
          A discussion to follow the effects of radiation to free space from
          the upper atmosphere and general effect of circulation - processes
          which continue both day and night and which cool the air that eventually
          returns to the surface with much less energy than it contained when
          convection took it up through the clouds to the "tropopause".
To help clarify further the basis of the discussion on Global Warming or climate change, and to demonstrate the real issues involved in this important analysis, I have attempted to set out as briefly as possible the fundamental physics which is continually referred to by proponents of the Global Warming Crisis, but for which no coherent or logical description has ever been presented by the IPCC reports nor by any of the hundreds of mainly geographers, working in the many University and research establishment "climate" groups around the world.
  John Nicol