Thermodynamics of Global Climate

The atmosphere of the Earth transports the heat energy absorbed by the Earth surface (and lower levels of the atmosphere) from insolation, to higher levels where it is radiated back into space.

The 2nd Law of Thermodynamics  for a gas subject to gravitation but without external heat sources, as formulated in Computational Thermodynamics, takes the form 

                                  dK + dP = W - D,          dE = - W + D,

where dK, dP and dE is the rate of change of kinetic energy K, potential energy P and internal (heat) energy E, W is rate of work and D is the rate of turbulent dissipation. See The Atmosphere as Air Conditioner.

We identify two extreme cases:

• D = 0: isentropic expansion/contraction: dK + dP = W, dE= - W: lapse rate = -10 C/km
• D=W: maximal turbulent dissipation: dK + dP =0, dE =0: lapse rate = 0,

where lapse rate is vertical temperature gradient. The case D = 0 represents a lossless cyclic motion of ascending/expanding/cooling and descending/contracting/warming flow. The case D = W represents a motionless isothermal state maintained by maximal turbulent dissipation. 

The observed lapse rate - 6 C/km rate lies between these extreme cases, connecting 15 C at the Earth surface with - 57 C at the tropopause over a height of 12 km.

In this analysis there is no external heat source and the non-zero lapse rate results from internal  thermodynamics of bouyancy-driven light hot air at the Earth surface which rises under expansion and cooling, combined with cold denser air which descends under compression and heating.  

In particular this analysis shows that a vertical temperature gradient can be maintained without both incoming and outgoing radiation, in particular without any effect of socalled greenhouse gases. 

The above model is compatible with radiative heat transfer with the Earth surface radiating

all incoming radiation into space without interaction with the atmosphere, in particular without interaction with socalled greenhouse gases. 

The model may also be combined with partial heat transfer by evaporation/condensation.

Note that conduction as well as radiation is compatible with a constant lapse rate, without however determining the magnitude of the lapse rate, which can be anything from zero to 

minus inifinity. This is because both conduction and radiation in a layered atmosphere satisfies a heat flow balance law of the form (in a basic case):  

                                         E(z-h) - 2 E(z) + E(z+h) =0,

with  E(z) heat energy  at height z and h is a layer thickness. The effective lapse rate is then determined  by a boundary condition of the form    - c (E(h) - E(0))= Q with c a coefficient of 

conduction/radiation and Q a heat source. Typically  c  would be small, which would define

much more negative lapse rate than observed. 

We learn from this analysis that the 15 C at the Earth surface is not necessarily related to the presence of any socalled greenhouse gases in the atmosphere. Similar conclusions have been drawn in The Thermodynamic Atmosphere Effect, by Heinz Thieme.

Note that scientific evidence (experimental or theoretical) of major effects of greenhouse gases on the Earth surface temperature, seems to be lacking. The evidence put forward consists of differentiating Stefan-Boltzmann's Radiation Law which connects  socalled "radiative forcing" dQ to surface temperature change dT by the simple relation dQ = 4 dT.

However, this evidence is not convincing, to me at least, because  Stefan-Boltzmann's Radiation Law concerns a simple system (one black-body) and not a coupled system of planet + atmosphere with internal temperature gradient.

It is surprising to see large parts of the scientific community including academies of sciences embracing a hypothesis of global warming from atmospheric CO2, without any convincing scientific support. It appears that the mere mentioning of Stefan-Boltzmann's Radiation Law has been enough to annihilate any further demands of scientific evidence. 

This may be a result a 2oth century physics education with both the Radiation Law and  the 2nd Law of Thermodynamics being based on statistical mechanics not understood by anybody. In any case, the acceptance by the scientific community of CO2 climate alarmism without physical basis, needs to be understood and corrected.

I agree with Roy Spencer in The Missing Climate Projections:

• It is time to return to the scientific method before those who pay us to do science — the public — lose all trust of scientists.
  

Compare with IPCC's description of the "greenhouse effect" in FAQ 1.3:

• Much of this thermal radiation emitted by the land and ocean is absorbed by the atmosphere, including clouds, and reradiated back to Earth. This is called the greenhouse effect. The glass walls in a greenhouse reduce airflow and increase the temperature of the air inside. Analogously, but through a different physical process, the Earth’s greenhouse effect warms the surface of the planet. Without the natural greenhouse effect, the average temperature at Earth’s surface would be below the freezing point of water. 
  

The different physical process is thus described as reradiation back to Earth.

But what is the physics of this reradiation, and how big is it? Physics books do not seem to 

give any clue, so where is then the evidence?