• Antero Ollila

The second law of thermodynamics and the so-called reradiation issue

Updated: Mar 31


The story of Dr. Spencer has commented my research study about the IPCC’s greenhouse effect definition in 12th of March The original story has been published in 16th of March on this blog page.

This story has raised now more than 570 comments. I reckon that it has been one of the most popular stories in WUWT. When it is a question about the GH effect, most of the comments and counter-comments are always about the so-called reradiation from the atmosphere to the Earth’s surface. It is the key feature of the GH effect because without this energy source to the Earth’s surface, there would be no GH effect.

There is a group of people – and only a few researchers – who claim that this is against the 2nd law of thermodynamics, which states that heat cannot flow from a cooler body to a hotter body. Because these people are stuck to this statement wording, they cannot admit that in the case of radiative heat transfer, this statement must be applied to the whole heat transfer process and not to the half part of it.

I could call these people “climate deniers” because they deny the existence of a very essential feature of the climate and by doing so, they also deny a few other physical laws and empirical observations. I think that many ordinary people reading these comments are utterly confused because they have no real knowledge and experience about these fundamental laws. That is why I have written this story to show that the reradiation follows the physical laws, but the IPCC’s GH effect definition is against these laws.

The basic laws of thermodynamics

In this section I try to summarize shortly the basic physical laws as they have been written in textbooks of physics and how professors have taught them in universities worldwide for a century or more. I use some references to textbooks for those people who think that I have invented these matters.

The First Law of Thermodynamics states that energy cannot be created or destroyed; the total quantity of energy in the universe stays the same. The Second Law of Thermodynamics applies to closed systems and it says that processes that involve the transfer or conversion of heat energy are irreversible. Heat always flows spontaneously from hotter to colder bodies, and never the reverse.

A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. It does not only absorb radiation but can also emit radiation. Although a blackbody does not really exist, we will consider the planets and stars (including the earth and the sun) as blackbodies. Even we would keep them graybodies, it would not destroy these laws and equations.

There is three heat transfer mechanism in the universe: conduction, convection and radiation. Convection is an essential part in sensible heating and in latent heating of the atmosphere. The net heat transfer rate of conduction and convection has the same form

Q = U A (T1 -T2) (1)

where Q is heat transfer (W), A is heat transfer area (m2), T1 is higher temperature (oC), T2 is lower temperature (oC). In heat conduction, U is a coefficient of thermal conductivity (W/(m^2K)), and in heat convection, U is convective heat transfer coefficient (W/(m^2K)). The essential feature is the temperature difference between the bodies.

Stefan-Boltzmann radiation law is in the focus of the GH effect. I quote a piece of text (italic) from the Indian textbook of physics therefore that its description is simple and univocal: Nonlinear Systems in Heat Transfer, 2018, Start of a quote:

3.1 Heat Transfer by Thermal Radiation

Heat transfer from a body with a high temperature to a body with a lower temperature, when bodies are not in direct physical contact with each other or when they are separated in space, is called heat radiation as schematically shown in Fig. 3.1. The Stefan–Boltzmann law of thermal radiation for a black body states that the rate of radiation energy from the surface per unit area is proportional to the fourth power of the temperature of the body:

(3.1) q=σAT^4

with q rate of energy emission from the surface, A surface area of the radiator and σ the Stefan–Boltzmann constant.

Figure 3.1. Heat transfer by thermal radiation between two bodies.

A black body is a perfect radiator. Real bodies, however, do not act like a perfect radiator and emit at a lower rate. To take into account the real nature of the radiant bodies, a factor ε, called emissivity, is introduced. Emissivity is defined as the ratio of the emission from a real “gray” surface to the emission from a perfect “black” surface. Then, the rate of radiation heat transfer from a real body at temperature T1 which is surrounded by a black body at temperature T2, is given by:

(3.3) q=σAε(T1^4−T2^4) (End of quote)

Those people who I call “climate deniers” simply say that this equation is against the 2nd law of thermodynamics. But it is not. Equation 3.3 above shows that also radiative heat transfer depends on the temperature difference of the bodies but in the case of radiation it is proportional to the difference of fourth power of temperatures because the physical phenomenon is different. Equation 3.3 means that the net heat flow is from a hotter body to a cooler body (T1 is higher than T1). Deniers say that this equation is wrong because it shows that there is also heat flow from a cooler body to a hotter body.

Here I could stick to the word “heat”. Actually, it is not heat that flows between the bodies, it is energy. Energy has been transferred in the form of photons, the workhorses of the universe. When a photon has been absorbed, it is transformed into energy. A photon cannot be absorbed partially. Material has three options in treating photons: reflection, absorption, and transmission (transparent material).

Now I take in a way one step backward to explain what happens in radiative heat transfer between two bodies. Stefan introduced his law in 1979 and Boltzmann in 1884 but the law of S-B can be concluded from the more fundamental law of Max Planck published in 1901 by integrating his equation (1) over all wavelengths

E = ((8¶hc)/λ^5) * 1/(e^(hc/(kTλ))-1) (1)

where E is the energy radiated per unit volume by a cavity of a blackbody, h is Planck’s constant, c is the speed of light, λ is the wavelength, k is the Boltzmann constant, and T is the absolute temperature. Planck’s law means that the material in emitting radiation depends only on the temperature of an emitting body and in the case of a grey body also emissivity.

Planck’s law can be used to explain what happens in the radiative heat transfer of three bodies as schematically illustrated in Fig. 1.

Fig.1 A schematic figure of radiative heat transfer of three bodies with different temperatures.

Fig.1 shows that all three surfaces emit and absorb infrared (longwave) radiation according to their temperatures. It is a scientific fact that Planck’s law is the reality in the real world. Climate deniers say that it is not going to happen that a body with a temperature of 15 °C could absorb radiation from the body of 7 °C (black body temperature of the atmosphere emitting 345 W/m2 to the surface). According to the radiation laws, it will happen. A black body will absorb all radiation frequencies. In Fig. 2 I have other evidence.

Fig. 2. Radiation intensities according to surface temperatures of 7, 15 and 25 Celsius degrees.

In Fig.2 we can see that the radiation intensities according to surface temperatures vary significantly from 7 °C to 25 °C but the wavelength range is practically the same from 3 to 50 micrometers. What would be theoretical possibilities of the 15°C surface to make a difference between photons arriving from the 25°C surface or the 7° surface? The 15°C surface should have a capability to analyze the wavelength (frequency) and the intensity of each photon with a remarkable accuracy and then to have a capability to absorb or reflect a photon based on this rather complicated process happening with the speed of light. This all is impossible, and it has been stated in all textbooks of physics that a black body absorbs all photons. Simple like that. But deniers deny all these facts. They have their own laws of physics and therefore the conversation is impossible – it is harping on both sides, because the common basis is missing.

All this confusion could have been avoided if the wording of the 2nd law of thermodynamics would be like “there is no net heat flow from a cooler body to a hotter body”. This wording would notify the fact that cooler bodies emit radiation and it will be absorbed by hotter bodies.

Reradiation – observation or calculation based?

Two comments based on the empirical observations. All people living in the countryside of Scandinavian countries have learned that in wintertime when the sky turns cloudy, temperature will increase. This is based on the fact that clouds absorb totally LW radiation emitted by the surface and this will increase the LW flux from the atmosphere to the surface. In these countries, carports are popular because they prevent not only snowing on cars but also during cold cloudless nights the windows of cars will not be frozen even this happen to cars nearby without these open carports. The scientific explanation is the higher temperature of the roof above in comparison to the black night sky with very low temperature reading.

There is still an issue, which has been claimed to be fabricated by a few climate deniers and it is if the reradiatio flux from the atmosphere is really 345 W/m2. The accuracy of this value is not an issue in this case but if this radiation flux is a real thing. Here is a link to an article, which describes the ground-based network of measurement stations called Baseline Surface Radiation Network (BSRN). This network with 59 stations (Fig.3 ) is hosted at the Alfred Wegener Institute (AWI) in Bremerhaven, Germany since 1992. Link:

Fig. 3 Baseline Surface Radiation Network (BSRN) in 2017 for measuring radiation fluxes at the surface.

Here is a link to an article published in 2008, where major flux values of the Earth’s energy balance are calculated utilizing the BSRN network: According to this study, the reradiation flux values have been 338.6 W/m2 and the surface emitted flux value 398.8 W/m2. The latter value is close to the black surface radiation value of 15…16 °C. The present-day values are little bit different, because of improved measurements and slightly changing solar insolation.

The definition of the greenhouse effect

I think that I have addressed all the major issues in this reradiation case. The comments following Dr. Spencer’s story were almost all about the issues introduced by “climate deniers” and those people trying to defend real science. If I would have been somebody belonging to the inner circle of the climate society endorsing the climate change story of the IPCC, I would have been very pleased after reading the comments. I would have been thinking that these skeptical people are no real threat because these people have their own laws of physics and they have their own strange ideas belonging to conspiracy theories that the Earth’s energy balance is not based on the real measurements etc. In doing so these skeptical people do not notice real tricks like the IPCC’s GH effect definition. That is what happened also in the story of Dr. Spencer. Therefore, I would like to analyze the GH effect definitions of the IPCC and mine, Ref.1.

Fig. 4 The Earth’s energy balance in connection to the GH effect.

Dr. Spencer wrote like this: Dr. Antero Ollila, who claims that the energy budget diagram somehow violates the 1st Law of Thermodynamics, i.e., conservation of energy, at least in terms of how the greenhouse effect is quantified.” This clause has two inaccuracies. I have not written that this diagram violates the 1st law of thermodynamics but I have claimed that the IPCC’s GH effect definition violates this law. Somebody had misunderstood that Fig. 4 somehow represents the IPCC’s GH effect definition. No, it does not do so, because in this diagram is nothing against the laws of thermodynamics. Because of these inaccuracies, it looks to me that the whole conversation went on the backroad.

I this diagram of mine is a decisive difference in respect to all other energy balance diagrams. I have shown the existence and the magnitude of the LW absorption by GH gases and clouds. In other diagrams like those of Kiehl & Trenberth, Wild, and Stephens, this feature has not been shown and I come later to this issue. This absorption flux is essential thinking of the GH effect that is the most important feature of our climate.

The starting point in this GH effect definition is that of the IPCC. If somebody thinks that there is a generally accepted definition by the well-known climate researchers, it is not true. If you find any other definition, please submit an email to me. I have found that of Hartmann, and it is different. The definition of theIPCC’s GH effect, according to AR5 / p. 126) is: “The longwave radiation (LWR, also referred to as infrared radiation) emitted from the Earth’s surface is largely absorbed by certain atmospheric constituents - (greenhouse gases and clouds) - which themselves emit LWR into all directions. The downward directed component of this LWR adds heat to the lower layers of the atmosphere and to the Earth’s surface (greenhouse effect).”

In a definition, every word has its meaning, and also words missing.

Just by looking at Fig. 1 it is clear to anybody with basic knowledge of physics that the IPCC’s definition means that the atmosphere by absorbing 155 W/m2 cannot emit the LW radiation flux of 345 W/m2 to the surface as stated by the IPCC. The IPCC does not introduce any other sources of energy for creating the reradiation flux of 345 W/m2. Somebody may ask, is it really so that the calculation basis of the GH effect by the IPCC is this 155 W/m2. There is no doubt about it; Schmidt et al. 2010, Ref. 2.

This is the reason, why the researchers of the climate establishment do not want to show this flux of 155 W/m2, because it would be too easy to notice this cheating. Another observation of mine is that hardly anybody has ever read the IPCC’s definition. If you have done so, please submit an email to me. The reason is simple. Those who know this cheating do not want to refer to it, and nobody else ever noticed. How come? Because there are only two-three contrarian researchers who have ever calculated the contributions of the GH gases needing this calculation basis. I have found only three names who have published studies both on energy balance and on the contributions of GH gases and they are Kiehl, Trenberth and me.

The total energy flux absorbed by the surface is 165 + 345 = 510 W/m2. The net solar energy flux absorbed by the Earth is 240 W/m2. The difference between two energy sources if 510-240 = 270 W/m2 that is the magnitude of the GH effect. The LW flux emitted by the atmosphere is 345 W/m and it includes 75 W/m2 of the SW radiation absorbed by the atmosphere, and therefore it is not a part of the GH effect.

Dr. Spencer did not approve of this definition of mine, so I understood. He wrote like this: “How can 240 W/m2 of solar input to the climate system causes 395 W/m2 of IR emission by the surface? Or 345 W/m2 of downward IR emission from the sky to the surface? ALL of these numbers are larger than the available solar flux being absorbed by the climate system, are they not? But, as I have tried to explain from the above, a 1-way flow of IR energy is not very informative, and only makes quantitative sense when it is combined with the IR flow in the opposite direction. If we don’t do that, we can fool ourselves into thinking there is some mysterious and magical “extra” source of energy, which is not the case at all. All energy flows in these energy budget diagrams have solar input as the energy source, and as energy courses through the climate system, they all end up balancing. There is no violation of the laws of thermodynamics.”

It looks like we both agree that there is no violation of the laws of thermodynamics in Fig. 4. On the other hand, Dr. Spencer questions that how can 240 W/m2 of solar input cause energy fluxes of 395 W/m2 or 345 W/m2 in climate. Because he raises this question and does not give any explanation, I could conclude that he does not approve of the existence of these two fluxes. In this connection, he also refers to a mysterious and “magical” source of energy, which is not the case at all.” It is true that I have used the term “extra energy” in describing this energy flux of 270 W/m2 absorbed by the surface because it really exists and most of all, it is not part of direct solar insolation. I need not start to defend if this “extra energy” flux exists or not because it is a part of 345 W/m2 and it has been measured and calculated by the leading researchers of the climate community without addressing the GH effect at all. Majority of climate research papers are neutral without addressing the issue of the global warming cause.

How we can explain this flux and why we have fluxes like 345 W/m2 and 395 W/m2 which are much greater than the net energy received from the sun? Dr. Spencer writes that this is too complicated to explain what happens in the atmosphere. Yes, it is true that emission and absorption phenomena happening in the atmosphere are very complicated. But the end results are not complicated at all. Nobody (except a few deniers) deny the existence of the outgoing LW flux of 240 W/m2 emitted into space. It is the result of similar complicated phenomena. This applies also the 345 W/m2. The phenomena and calculations may be complicated, but the results are observation-based and univocal. It can be said that the surface does not care and it does not know what is going on above its surface; it reacts on the incoming energy fluxes and on the outgoing energy fluxes.

The most important thing affecting the surface temperature is the amount of total radiation which is 165 + 345 = 510 W/m2. Dr. Spencer writes that “But, as I have tried to explain from the above, a 1-way flow of IR energy is not very informative, and only makes quantitative sense when it is combined with the IR flow in the opposite direction.” As we know the surface is in the energy balance meaning that the incoming and outgoing energy fluxes are exactly the same.

There are two things I disagree with Dr. Spencer. Thinking about the GH effect, the IR flow (LW flux upward of 395 W/m2) is only a part of the energy fluxes having its cooling impact on the surface. There are also sensible and latent heating fluxes – totally 115 W/m2 – closing the overall energy fluxing leaving the surface. If these fluxes were not there, the surface temperature would increase continuously. Because the surface is in energy balance, the “opposite direction” energy fluxes have no role in calculating the GH effect, and they cannot be calculated to be a part of the GH effect magnitude. The energy fluxes leaving the surface are the outcomes of the GH effect. In the end, when we consider the whole GH effect, it is a recycling phenomenon and therefore its magnitude depends solely on the incoming energy amount to the surface.

How do we explain that there really are greater energy fluxes than 240 W/m2 received from the sun? Has the energy created from the void? The violence of energy conservation laws? The essence of the GH effect is right here. This is my explanation. Firstly, all energy in the climate comes from the sun (almost all, 99.97%). As we know, the received energy from the sun goes back into space, because the Earth is in energy balance. Also, this “extra energy” which I could call also the GH effect energy (GHEE) recycles between the atmosphere and the surface. It is in a trap. It cannot escape into space, because the TOA keeps the outgoing flux at the same magnitude as the incoming flux. In the balance, the GHEE cannot either enter into land or into oceans or into space. It is in a trap. The magnitude of the GH effect depends on the three energy fluxes: LW absorption, sensible ja latent heating. Because the climate is in balance, the magnitude of the GH effect is pretty much stable.

The final question is in which way this GH effect and the GHEE involved ever came into existence? I think that the answer is in the laws of nature and in the existence of the atmosphere and the oceans. Oceans provide water, which partially evaporated into the atmosphere and so clouds, and the latent heating came into existence. We can assume that this all started in the tropics where solar insolation is strongest. The water vapor and other GH gases started to absorb the LW radiation emitted by the warm surface. And the warmed-up surface created sensible heating phenomenon in the tropics. These phenomena created this GHEE and the atmosphere could not emit this energy into space. We do not know in which order this all happened and how rapid what this formation of the GH effect but the crucial matter is that this GHEE was trapped between “the sky and the Earth” as it is now and it cannot escape. There is no mysterious extra source of energy, but it originates from the sun.

The name of “greenhouse effect” has been criticized that the analogy is no good at all. The criticizers say that the real greenhouse works on the different principle: cooling is largely reduced because the glass roof prevents heat transfer by convection (warmed air cannot escape). The GH effect is also based on the reduction of the cooling effect but in this case, there is not roof. There is “an invisible roof” which totally prevents cooling by convection and conduction, and it is space. The only heat transfer mechanism working in space is radiation. The third element restricting the cooling of the atmosphere and the Earth is the 1st law of thermodynamics: the amount of heat radiation into space must be the same as the incoming (240 W/m2 net). There is cooling also in a real greenhouse, and it is heat transfer by conduction through glass walls and roof. The analogy of GH effect is a very good one.

What are the processes creating the LW flux emitted by the atmosphere to the surface? It can be calculated by the spectral analysis method applying average global atmospheric conditions. I have carried out tens of calculations and as far as I know, I am now a days the only contrarian researcher still publishing these studies. Miskolczi and Mlynczak has published several laudable papers about the LW fluxes in the atmosphere based on emission, absorption, and transmission processes. Only a few people understand or know that the LW absorption by GH gases is a very nonlinear process, Fig,5.

Fig. 5. The total absorption by GH gases for the LW radiation emitted by the surface.

Absorption starts right after the surface and at the altitude of 10 meters already 34% has happened, at 100 meters 67%, at 1 km 89%, at 2 km 95% and at the tropopause 98% in the clear sky conditions. Spectral calculations show that the total absorption is about the same as the LW flux downward, and it is also according to the Kirchhoff’s radiation law. Somebody could ask if this is true, where is the effect of latent and sensible heating if the LW absorption can explain the LW flux downward. All four energy sources – SW absorption, LW absorption, sensible and latent heating – maintain the temperature profile of the atmosphere. If the temperature would be lower, the total absorption would be smaller.

Wikipedia shows that the GH effect is the same as the total absorption, and its value is 350 W/m2 (coming from the energy balance of Kiehl & Trenberth). Why does Wikipedia want to show this value as the measure of the GH effect? People have no idea that they are cheated because this value is not the measure of the GH effect according to the IPCC. Researchers have used the value of 155 W/m2 in calculating the contributions of GH gases. In this way Schmidt et al. have calculated the contribution of carbon dioxide to be 19 % and by using my definition the same contribution is only 7 %. Carbon dioxide is a weak GH gas. For hiding this fact, the IPCC has defined the GH effect in the wrong way violating the physical laws.


1. Ollila A. The greenhouse effect definition. Physical Science International Journal, 23(2), 1-5, 2019.

2. Schmidt GA, Ruedy RA, Miller RL, Lacis AA. Attribution of the present-day total greenhouse effect. J Geophys Res 115,D20106:1-6, 2010.

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