Greenhouse Heat Engine

In reviewing the points of controversy raised here in Miskolczi’s controversial theory of (almost constant) greenhouse effect and the impossibility of runaway global warming, I thought about the role of convection.

Convection is a heat engine. A heat engine is defined as a device that converts heat energy into mechanical energy. In this model, the circulation of the air is analogous to a Stirling or other simple heat engine, producing work as the result of temperature differential between the earths surface and the edge of the atmosphere. The diurnal cycle plays a large (but not complete) role in the operation of the engine, creating a cycle of heating and cooling air packets.

Keep in mind convection is not the only thermal process in the atmosphere. While convection is necessary, the following does not represent the totality of the energy conservation relationships governing the atmospheric system. As Miskolczi says:

If you like to put that way, the su=3olr/2, su=2eu, su=ed/a and
su=olr/f relations are for convective-radiative-hydrostatic equilibrium
global average atmosphere which is in total energy balance.

Treating convection as a heat engine is not a new idea and a research field has developed in the area of thermodynamics of natural convections (e.g. Renno). I don’t think it has been discussed in relation to Miskolczi’s theory though, and below I go through some of the ways it could potentially apply. I refer to comments by Nick Stokes and Pat Cassen in previous simple descriptions of parts of the theory.

Below is a schematic of natural convection as a heat engine. The source of heat at the surface, cooling and work output is shown. Wikipedia has a good article on different types of heat engines, and natural convection is probably most similar to the Brayton cycle (adiabatic/isobaric/adiabatic/isobaric).


Figure: The model of convection as a heat engine, much like a Stirling or Brayton engine, work is done by across a temperature potential. In the atmosphere, absorbed heat performs atmospheric work of raising packets of air to the colder upper atmosphere Eu.

Points of comparison with Miskolczi’s theory are as follows:

Conservation of Energy

M’s equation (6) is F = (Su-F) + (Ed-Eu) where F is the solar isolation on the surface, Ed and Eu are down and up atmospheric radiation, and Su is the radiation up from the surface. This equation asserts the existence of an Su-OLR flux term that heats the
atmosphere, and the existence of the Ed-Eu flux term that heats the

If Ed-Eu can be equated with work done, and Su-F with internal energy, and F with heat added to the system, then the equation describes the first law of thermodynamics.

ΔQ = ΔU + ΔW

Pat Cassen expresses a concern here

Equation 7 expresses the balance of energy of…what? I don’t know.

M’s equation could describe the first law of thermodynamics relating conversions of energy from one form to another via mechanical work.

The Virial Theorem

The virial theorem mentioned by Miskolczi relates kinetic and potential energy in gravitationally bounded systems to the proportion 2KE=PE. The natural convection engine could be analyzed for kinetic and potential energies, where the moving parts are the KE, and the potential energy is the gravitational field.

Here Pat Cassen also was concerned as:

I cannot figure out how Miskolczi is applying the virial theorem, or why it is necessary for any planetary atmosphere.

The virial theorem is applicable to convection — the atmospheric heat engine would not work if there was no gravitation. Air parcels could not rise without gravity.

Kirchhoff’s law

Nick Stokes was concerned that he should:

use Kirchhoff properly, which he doesn’t do (no mention of gas emissivity).

From Wikipedia, Kirchhoff’s law states the emissivity of a body (or surface) equals its absorptivity as at thermal equilibrium. However, the origin of the law is in the description of what was originally a mysterious process where an object in side a cavity achieved thermal equilibrium. Study of this leads to theories of black body radiation, and eventually to Planck’s and Einsteins treatment of radiation as quantized energy.

Local Thermodynamic Equilibrium (LTE) in the atmosphere requires the
equality of the absorbed and emitted radiation, that Su=Sa=Sg (on the average) and the simulation results in the related figures demonstrate this relationship to hold.

Kirchhoff’s law can be related to thermal equilibrium via radiative (black body) emission, and this is the context I think M intends here. In the atmospheric heat engine, the temperature of the gas inside the engine at the lowest point in the cycle is equal to the temperature of the surface (i.e. isobaric).

Optimal optical path

Pat Cassen also expressed concern at M’s radiative equilibrium equations showing that the system acts to optimize the conversion of solar energy into heat at the edge of the atmosphere Bo. Because of the cloudiness – the Earth-atmosphere system may convert Fo to OLR in such a way that the effective absorption coefficient is 1.

A heat engine is a also converter of solar energy into heat, which through M’s equations may be self-regulating. A self-regulating engine will not run faster (in this case due to solar energy constraints), or run slower (in order to utilize available energy). The Earth’s convection engine is currently at maximum greenhouse effect, and cannot be increased (the engine can’t run faster) or decreased (the engine can’t run slower) except through changes to the overall energy input to the system.


This just sketches out a model for natural convection in the atmosphere. Contrasting the heat engine model with the ‘steel shell‘ model of Willis Eschenbach, and another model of greenhouse warming applied to ice beads called the solid-state greenhouse effect, would demonstrate different types of greenhouse effect.

Pat and Nick seem to be concerned with lack of good motivation for these relationships in the paper. At this stage, I can’t see that they constitute errors that undermine the theory.

It might be argued that it is the greenhouse effect that drives the atmospheric heat engine and not the other way around. Perhaps IR greenhouse helps get the engine started. If there was no atmospheric heat engine driving warm air packets into the upper atmosphere, the atmosphere would like as a stable layer on the surface. Heat would transfer by thermal conduction, and temperature would be driven by the coefficient of conductivity of the air. This is describing an inversion condition, an occasional but not widespread phenomenon.

The predictions of GCMs due to increased greenhouse gases shows increased heating in the troposphere, kind of like a temperature profile of inversion conditions. The measurements of actual air temperature are as predicted by Miskolczi’s theory: Douglass et al 2007 show increased surface temperatures, but little increase in tropospheric temperatures. I wonder if anyone has made the connection between the profile of GCM’s and inversion conditions. This suggests a major source of lack of realism in GCM’s is inadequate representation of convection processes.