Since this controversial peer-reviewed paper was mentioned by Lubos Motl I have noticed increasing side-talk about it. It warrants more attention and effort to understand in depth.

While this is a mathematical paper, simple equations of radiative flux balance would present no challenge to people familiar with the field, although some of the concepts are new, such as the ‘virial theorem’. His previous paper, “The greenhouse effect and the spectral decomposition of the clear-sky terrestrial radiation (Miskolczi & Mlynczak 2004)“, provides a gentler introduction to the field of greenhouse spectral analysis, and is a better first read. As in this paper, he drops some real zingers. This paper redefines global warming. But not in a weird way. Of additional equations related to Kirchhoff’s law, constraining the atmosphere to be in thermal equilibrium with the surface, Miskolczi writes:

The physical interpretation of these two equations may fundamentally change the general concept of greenhouse theories.

The model suggests negligible sensitivity of 0.24C surface temperature increase to doubling CO2 increase.

For example, a hypothetical CO2 doubling will increase the optical depth
(of the global average profile) by 0.0241, and the related increase in the
surface temperature will be 0.24 K.

In understanding a theoretical model I like to look for the invariants, those quantities that remain stable despite perturbations of the system. In this model, optical depth emerges as the invariant. The optical depth, or opacity of the atmosphere to IR sits loosely in a kind of ’sweet spot’, making this another example of a niche model.

The system is locked to the optical depth
because of the energy minimum principle prefers the radiative equilibrium
configuration, but the energy conservation principle constrains the
available thermal energy. The problem for example with the highly
publicized simple ‘bucket analogy’ of greenhouse effect is the ignorance of the
energy minimum principle (Committee on Radiative Forcing Effects on Climate
Change, et al., 2005).

The climate system makes regulatory adjustment to compensate for changes in CO2 with changes in humidity and clouds, in order to most efficiently convert short wave incoming solar energy, into long wave outgoing energy. The problem with radiative models used until now is a discontinuity between the atmospheric and surface temperatures. This violates Kirchhoff’s law, that two bodies in thermal equilibrium must have equal temperatures, and is one of the reasons for mysterious unphysical behavior of climate models. Incorporating this simple constraint introduces an energy minimization principle that makes runaway greenhouse warming impossible. This corrects a major deficiency in the current theory, which doesn’t explain why “runaway” greenhouse warming hasn’t happened in the Earth’s past.

I find the argument compelling that problems of instability of global climate models stem from inadequate constraints. Miskolczi also presents considerable empirical data for both the Earth and Mars in support of the superiority of his new model of planetary atmospheres. The view of the atmospheric system as an equilibrated system occupying a kind of niche also appeals, although the challenge of this theory will be to explain temperature variability at longer scales adequately.

Moreover, Miskolczi’s approach to explaining the climate system illustrates the difference between a layman and a physicist. The layman tends to need a simple analogy to understand systems, such as the ‘leaky bucket analogy‘ for explaining the greenhouse effect, due to limited numeracy. The physicist explains a system simply as the solution set of necessary conservation laws. But simple analogies can be misleading, and sometimes wrong.

The popular explanation of the greenhouse effect as the result of the LW
atmospheric absorption of the surface radiation and the surface heating by the
atmospheric downward radiation is incorrect, since the involved flux terms
are always equal. The mechanism of the greenhouse effect may
better be explained as the ability of a gravitationally bounded atmosphere to
convert incoming to outgoing radiation in such a way that the equilibrium source function
profile will assure the radiative balance, the validity of the
Kirchhoff law, and the hydrostatic equilibrium.

If the model is correct, the real cause of recent warming is not related to the
enhanced greenhouse effect, as the surface temperature can only change through changes in the energy input to the system. Perturbations of the system by gases, or volcanoes, should result in small, rapid temperature spikes, followed by a reversion to equilibrium conditions. This describes exactly the current lack of global warming despite increasing CO2.

Another reason I think this paper is worth the effort to understand, is the conclusions are supported by other research. Steven Schwartz of Brookhaven National Labs, here gave statistical evidence that the Earth’s response to carbon dioxide was grossly overstated and explained why current global climate models predict more warming than observed.

As well there is a very interesting back story in the DailyTech about how publication of the paper was blocked by NASA and the author resigned in protest. His story is similar to others’ treatment of controversial results.

NASA refused to release the results. Miskolczi believes their motivation is simple. “Money”, he tells DailyTech. Research that contradicts the view of an impending crisis jeopardizes funding, not only for his own atmosphere-monitoring project, but all climate-change research. Currently, funding for climate research tops $5 billion per year.

Miskolczi resigned in protest, stating in his resignation letter, “Unfortunately my working relationship with my NASA supervisors eroded to a level that I am not able to tolerate. My idea of the freedom of science cannot coexist with the recent NASA practice of handling new climate change related scientific results.”

The new climate theory of Dr. Ferenc Miskolczi

The greenhouse effect in a semi-transparent atmosphere with radiation equilibrium at the surface. On the basis of hundreds of measurements of real atmospheric profiles of temperature and humidity, in different seasons en on different latitudes.

Establishing the right theoretical basis for the relationship between greenhouse gas increase and climate change is so important, that we cannot allow ourselves to evade discussion about its physical foundation. The Netherlands, having a reputation of four centuries of criticizing established opinions, should organize this discussion on an appropriate scientific level.

Based on an original draft by Dr. Noor van Andel, Fiwihex, Wierdensestraat 74, Almelo, May 2008.
Synopsis

The standard theory of anthropogenic global warming is challenged by a new theory which is based on empirical evidence and a reevaluation of the Eddinger equations, using a different set of boundary conditions. In this exposition the Eddington radiation equilibrium equations (which apply to stars) are solved correctly for a planet with a semi-transparent atmosphere, like the Earth. The correct solutions predict that Earth's atmosphere holds an amount of greenhouse gases that maximize radiation of heat into space. It appears that the Earth has a self-regulation mechanism that allows increases of CO2 to exert only a very minor influence on the planet's temperature. Independent measurements give insight into the mechanism of how this self-regulation takes place. Still other measurements contradict the atmospheric heating that supposedly follows directly from standard climate models as a result of increased CO2 during the last few decades. Cooling is observed, instead. Due to the importance of the problem for policies that affect the well-being of the world's population, we conclude that there are now ample grounds to organize a discussion between the scientific proponents of these two theories.
Introduction

During the 2008 International Conference on Global Warming, Dr. Ferenc Miskolczi (FM) presented his radical new theory of the greenhouse effect [1]. Arthur Rörsch asked me to help him explain FM's theory in more common terms, and initiated a discussion with our national expert, Dr. Rob van Dorland, KNMI, the Dutch Royal Meteorological Institute, to critique FM's new theory. Of course, Ferenc Miskolczi himself participated in this e-mail discussion. Miskolczi's new theory predicts a much smaller effect (about 10%) from increased greenhouse gases on the mean temperature of the Earth, compared to the conventional global warming theory caused by anthropogenic greenhouse gases promulgated by the Intergovernmental Panel on Climate Change (IPCC).{refs needed} Rob van Dorland examined infrared atmospheric radiation, the greenhouse effect, and climate change as a function of greenhouse gas concentrations.{ref to dissertation, papers} My experience as a physicist is heat transfer in general, and the design of “energy producing greenhouses” by employing efficient heat exchangers [2].

While I have written many computer models myself, I am much more an experimentalist than a theorist. Thus I am suspicious of complicated numerical solutions. I was impressed by FM's theory because it gives closed form algebraic solutions that are quite open to inspection. However, FM's paper is not easily understandable without a good background in climatology. I found it somewhat difficult to read because a number of well-known physical laws are mentioned solely as illustrations, and not as part of FM's climate theory [3]. However, it is not too difficult to evaluate FM's theory with widely published measurements. These measurements support FM's new theory, albeit that the underlying physics of weather is too complex to be modeled in simple algebraic equations. Exception is the latent heat transfer form a wet surface upwards, that can be analytically explained from first principles. From this function a strong negative feedback to the influence of e.g. CO2 doubling can be derived.
Greenhouse heat transfer

A market garden greenhouse is not warm only because the glass cover is transparent for visible light & opaque for infrared radiation [IR]. The greenhouse is warm because the closed structure does not let out the warm and humid air. A greenhouse with walls and a roof that is IR transparent is only a little bit lower in temperature. This was demonstrated as early as the 1920's by experiments performed by Wood (ref?).

The standard “man-made Global Warming” theory, in contrast to this experience, teaches us that the energy received from the Sun at Earth's surface is radiated into space through an atmosphere which contains infra-red absorbing gases (such as CO2 and H20), which absorb and “trap” some of the energy. Part of this energy is re-irradiated back to the surface, keeping it warmer than it would otherwise be. This is the current “greenhouse effect” concept. Therefore, this theory suggests that, if IR absorbing gases increase, more energy is “trapped,” and the surface temperature increases due to increased “back-radiation” and a hindrance to radiation to space. The “greenhouse” in this “greenhouse gas” theory replaces the glass in a greenhouse with a theoretical “blanket” of IR-absorbing gases.

(The astute reader will see immediately that the “blanket” analogy is really the same mistaken idea as the greenhouse analogy, since blankets also work primarily by reducing convection. But, regardless, it is postulated that the IR-active gases in the atmosphere trap the outgoing IR and send some of it back to the surface, thereby decreasing the amount of heat that would otherwise be lost–thereby creating a “greenhouse effect”).

FM's theory, in agreement with the actual empirically verified greenhouse mechanism, teaches us instead that the heat transfer from the surface is by non-radiative processes: vertical & horizontal convection, water evaporation, cloud formation, rain and snow. And FM teaches us more: Our atmosphere has, in the global and time-averaged mean value, a constant optical thickness, so, when more CO2 is injected, the atmosphere compensates by changing its water vapor content to regain the equilibrium.

The atmosphere optimizes its optical thickness to allow for the maximum heat transfer to space, by adjusting its IR absorbance.
Measurements

Thousands of atmosphere profiles are in the public domain, measurements by weather balloons of temperature, pressure, and relative humidity. Because of hydrostatic equilibrium, the pressure is a precise function of altitude, with only a small and well defined temperature correction term. The last 20 years satellites in orbit have carried Fourier Transform Infrared Spectrometers with high resolution, and so-called line-by-line computer programs that can translate atmospheric profiles to IR heat fluxes into heat flux (W/m2.), and can convert pressure (p), temperature (T), and relative humidity (rH) profiles into IR spectra and vice versa. FM is one of the few people that have written such a program, HARTCODE [4], which gives a detailed description of this 5000 line Fortran program, based on thousands of laboratory-measured absorption lines. Later, FM went to NASA Langley Research Center, where he published an extensive treatment of atmospheric heat fluxes, based on these thousands of atmospheric measurements [5], where the basic theory is already to be seen. In this 2004 paper, on p.242, he calculates an increase of global temperature of 0.482 °C as a result of doubling the CO2 concentration.

This is very different from what we learn from the standard theory. The methodological difference is, that the new theory starts with measurements, in contrast with the standard theory that starts with schematic atmosphere models like the Keihl-Trenberth scheme (need ref). The mathematical difference is that the new theory treats the atmosphere as semi-transparent, bounded, and in radiation equilibrium with the surface.

On page 233 we find the basic standard mathematics; OLR means Outgoing Longwave Radiation. The OLR is the only way the Earth can get rid of its heat received from the sun, and is well known to be 250 W/m2 as a global and seasonal mean. Optical thickness for IR is the natural logarithm of the IR absorption of the atmosphere, or the natural logarithm of the ratio of ingoing and outgoing radiation flux:



Figure 1. Equations of the standard theory.

Figure 1 shows the equations of the standard theory. With OLR=250 W/m2 and the global average atmospheric optical thickness (A = 1.86 we find the air temperature at the surface 282 K, and for the ground temperature 304 K. Here the standard theory is not consistent with what we all know: There is no 22 °C difference between ground and air.
A simple experiment

It is not difficult to measure the ground-air temperature differences, and get at least a qualitative impression of what goes on in a “real” greenhouse. We make 7 wells; 10 cm diameter and 4 cm deep, in a piece of EPS (Expanded Polystyrene), fix a temperature sensor on - Ordered List Item the center of each bottom, and cover some of the wells with windows that have a very different IR transparency. We lay a wet cloth on the bottom of half the wells. We make 7 temperature measurements every half minute, log the results, and see what happens night & day.





Figure 2.

Table 1. Experimental setup

Color cover, mirror, wet or dry, # of well

1.
Red: 2 mm PMMA cover, dry bottom 1
2.
Blue: 2 mm PMMA cover, wet bottom 2
3.
Orange: 6 µ PE cover, dry bottom 3
4.
Light blue: 6 µ PE cover, wet bottom 4
5.
Green: No cover, dry bottom 5
6.
Brown: No cover, wet bottom 6
7.
Violet: Aluminum mirror above well, not closed 7

—-



Figure 3. Evolution of temperature over time for seven greenhouses.

The experiment begins the 10th of May, 2008, on an open lawn at Fiwihex, Wierdensestraat 74 in Almelo. The sky is clear, it has been a sunny day, and the following day is sunny too. Quite un-Dutch weather. The experiment ends the 11th 13:00, because my daughter in law wanted to mow the grass by then.

Now, what do we see: After equilibration from installation, 21:00 in the evening, the PMMA [Perspex, or poly methyl methacrylate] cover, red and dark blue points, being black in the relevant IR wavelengths, keeps the well relatively warm. It does not matter if the bottom is wet or dry, however, because the temperature is so low, and the humidity so high outside and inside, that the wet-bulb temperature is equal to the dry bulb temperature.

We see also that, notwithstanding the greenhouse effect of the PMMA cover, the open dry well is slightly warmer that the PMMA greenhouse, and much warmer that the PE greenhouse. The warmest is the well with the mirror above it. How come?

This is, because the air, being composed of mainly a-polar gases like O2 and N2, and cannot radiate as strongly as a solid body, stays warm longer than any radiating solid or liquid. So, a sensor that is in open contact with the air, stays warmer too.

Now the coldest spot is the PE covered little greenhouse, wet or dry, because PE is transparent for IR radiation, so we have there a connection with the cold heavens, and insulation from the warm air by the cover. The well with the Al mirror is the opposite: here we have contact with the air, but the upward radiation is reflected back by the shiny metal. The difference is large; the PE greenhouse is about 10 °C colder than the mirror well.

Now the day comes, and we see a radically different pattern:

All covered closed greenhouses are very hot. We see a slight difference between the hottest, PMMA, 61 °C in the early afternoon, and the PE covered, 57 °C. The only well which is substantially less warm is the open well with the wet bottom. This well is able to cool itself by evaporation. We see also that a wet canopy, as every greenhouse gardener knows, lowers the temperature quite a bit in a greenhouse, because it is never completely closed, so the water vapor from the plants finds its way outside. In the blue case, the water was almost completely evaporated by 13:00, dry spots begin at 12:00 already.

Conclusion: what makes the surface, or climate, warm is the hindered convective heat transfer to up in the atmosphere. Not the hindered radiation heat transfer, this is much smaller.

1 A completely IR absorbing window, compared to a transparent one, increases the temperature only 5 °C, but as soon as water can be evaporated, we cool 20°C. Both covers hinder evaporation, and that is, why greenhouses can be very hot indeed. They are always being regulated, the normal greenhouse by opening the roof windows, the closed greenhouse by [fine wire] heat exchangers, cooling against ground water, condensing the evaporation from the plants, saving irrigation water and pest control chemicals and allowing CO2 fertilization in the process.

2 The air in those “greenhouses” with wet surfaces has temperatures which are lower than the air temperatures in the “greenhouses” which have dry surfaces. It is important to note that the “floors” and the air in the greenhouses are at the same temperature (in thermal equlibrium) and thus have to also be in radiative equilibrium. This does not appear to conform with the standard theory, because in that theory (Kiehl and Trenberth, e.g.), the upward radiation is 65 W/m2 larger than the downward radiation, which means a 12 °C higher ground temperature than the effective atmospheric downward radiation temperature. In FM's theory, like in the “greenhouses,” there is radiation equilibrium between ground and atmosphere. So, there is no persistent higher ground temperature.

So, there is no net radiation transport from the ground, other than the radiation through the infrared window. Can the atmosphere then regulate our temperature? Yes, because as soon as the temperature lapse rate becomes greater than the temperature lapse rate by adiabatic expansion of dry air; 1°C per 100 m, or air in which humidity is changing phase 0.29 °C per 100 m at 320 K, 0.42 °C per 100 m at 300 K, .74 °C per 100 m at 250 K, the atmosphere becomes instable. Large amounts of heat escape to many kilometers altitude, where the radiation away into space is much easier; the atmosphere is thin and much more IR transparent. And, in most cases, the top of the rising air column is a cloud, reflecting most of the incoming solar radiation.

We live in an atmosphere where the temperature lapse rate due to IR radiation equilibrium is always steeper than the adiabatic one. So, as soon as there is radiation inequilibrium, the atmosphere tends to instability. The more IR active gases in the air, the steeper the radiation lapse rate, and the sooner the real cooling comes into action. The warmer it is, the less steep the adiabatic lapse rate, and the sooner instability - and cooling - starts.

We also live on a planet with an abundance of liquid or solid water, be it in the oceans, in the plant canopy, or in ice. The only really dry place is the desert. There, we have a climate that depends on radiation, and the surface can be much hotter than the air above it (you can even fry eggs on the surface, sometimes!). But the temperature of the surface on most of the planet is controlled by evaporation of water and convection of air.

But how can we quantify these air and water thermostats? And how can we estimate the influence of an few hundred ppm extra anthropogenic carbon dioxide? For the first time, Ferenc Miskolczi has solved this enigma in an analytic way.
The Cabauw measurements

The 200 m high radio broadcast transmitter in Cabauw, near Lopik, the Netherlands, can be used, like a weather balloon, to measure atmosphere profiles, albeit only up to 200 m high. Rob van Dorland has measured these profiles and has provided the data. The actual ground temperature was not been measured; instead, the air temperature, T, at 2 m is used. The humidity was measured, too. From these profiles, the LWD or Longwave Downward Radiation was calculated, according to the Stefmann Boltzmann Law, using the measured temperature, atmospheric transmittance, Ta, water content expressed in precipitable centimeters, and an assumed emittance of 0.96. This LWD was also measured, using a pyrgeometer. Now we ask, is one of the basic assumptions made by the new theory–that radiation between the air and the surface is in equilibrium–true? Plotting these calculations against the measured LWD, the following one-to-one correlation results, indicating that the assumption is true:



Figure 4.

Miskolczi terms the radiation absorbed by the atmosphere as Aa. Because the calculated absorbed radiation, Aa, always equals the measured downwelling radiation, we see that, indeed, the radiation equilibrium extends to the surface. No net IR radiation heat flux reaches the atmosphere from the ground. It is either transmitted through the atmospheric window, or completely compensated by the LWD, or ED, in FM’s terms. The conclusion is that Rob’s Cabauw measurements support Ferenc Miskolczi’s major assumption.

In fact, the graph illustrates simply that, because the mean free path of the photons that interact with atmospheric components is so short, on the order of meters, no appreciable temperature differences along that path occur. We call this Local Themodynamic Equilibrium. These results are contrary to the prevailing theory, which indicates an imbalance in the radiation, with a net upward component of about 25 watts/m^2.

Atmospheric profiles translated into IR spectra

These relationships can also be shown by calculations using existing computer programs, such as HARTCODE. The following two figures are taken from FM, and are examples of typical IR spectra decomposed in the relevant heat fluxes. A very warm climate, and a very cold one. The x-axis is the wavelength expressed as the number of wavelengths per cm, as usual in IR spectroscopy. The list of decomposed heat fluxes is:

* SU is the blackbody radiation from the surface upwards. Light blue line. A continuous spectrum because the ground is solid, or liquid sea surface. * ED is the long wave downward radiation from the atmosphere to the ground. * OLR is the sum of the heat fluxes ST and EU into space * ST is the heat flux radiated through the IR window and through other partially transparent parts of the atmosphere, from the ground directly to space * EU is the heat flux from the atmosphere itself into space.



Figure 5. Typical IR spectra of a warm climate decomposed in the relevant heat fluxes.

At around 650/cm lies the major absorption of CO2. EU is very much hindered there. The back radiation ED, is here large, almost as large as the upwelling radiation SU. In the second figure we are in Antarctica. There it is 232.2 K of -41.2 °C cold, we see that the sharp molecular line at 650/cm of CO2 in a climate that is cold enough to exclude almost all water vapor, extending even above the continuous spectrum of the snow. We see even the Ozone peak, around 1000/cm, in this dry climate. In both graphs we see the profiles where they are derived from. CO2 is not indicated because the concentration is the same everywhere. The adiabat is clearly visible, 110K/15 km=7.3K/km in the first, and 70 K/10 km in the second graph. We see that even in the polar climate, we have less than the dry adiabat.



Figure 6. Typical IR spectra of a warm climate decomposed in the relevant heat fluxes.

Kiehl-Trenberth is the scheme most used in the standard theory. Such schemes do not compare with measurements, because they are modified to be also 100% correct radiation budgets. Local profiles do not have to conform an energy budget, because there is also a large horizontal convective heat transfer. A LBL program such as HARTCODE does not depart from such schemes at all, using atmospheric profiles, that are measured, and converted using a straightforward method into radiation heat fluxes. We see that the standard K-T scheme has a large deviation from the measured profiles, that have a much higher flux in the IR window. taojag95
The standard theory

We need to be aware of the variation between the standard theory, that works with an atmospheric scheme, such as the K-T scheme, and radiation relations that come out of the study of many measured profiles.

From the PhD thesis of van Dorland we take the following figures that show the standard scheme with an overall heat flux balance is 343=83+20+40+200 W/m2. Note the net 355-330=25 W/m2 heat flow through the absorbing atmosphere from surface to space.


Figure 7. Standard radiation balance.

The next figure of the standard theory of van Dorland shows how IR active gases come to influence the surface. The x-axis is in Kelvin/day, so the temperature of the system is only stationary if zero. We see that water[vapor] absorbs sunlight [S H2O] and so heats the atmosphere with half a degree per day, but we see also that in the IR region [L H2O] water has a cooling effect. We see that in the stratosphere Ozone is a heater. This gas absorbs UV light from the Sun and therefore the stratosphere becomes so warm, that a stable inversion forms, on 12000 meter, the tropopause.


Figure 8.

We are interested in the climate at the surface, that is at zero height. We see that CO2 heats there, but cools on great height, which we saw in the spectra. It is striking, that the large warming at 2-3 km height, which could be easily measured by satellites, is not there in reality. On the contrary, a cooling is measured as a result of increased CO2 . We see also, that there is a net shortage of heat. That comes from the sun, shining on the surface. This is much more than the necessary 1.5 °C/day, so there is a large term, vertical convection, that balances the climate.



Figure 9. In this graph we see the heat fluxes upward and downward as a function of height. At 1000 hectopascal we are on the surface. The scheme is a good illustration of the unphysical strong discontinuities assumed at the surface by the standard theory. These are the reason for the large influence of extra greenhouse gases in the standard theory.

In the new theory there is no such discontinuity. This discontinuity arises from boundary conditions used in solving the Eddington equation, taken from the conditions in the Sun. There we have no surface, there we have an infinite atmosphere, so the solution takes the form:

OLR=2/[1+tau A]·SA for the lowest atmospheric layer, OLR=2/[2+tau A]·SU for the liquid or solid surface.

In the new theory:

SA = SU = SG and ORL=2/[1+tau A+TA]·SU.

This the essential difference between the standard theory and that of Miskolczi.

In the graph of the standard theory of van Dorland that follows, we see the influence on heat fluxes of a CO2 doubling. We see a -4.5 W/m2 decrease in the upward flux outside the window region, and only a +1.7 increase in the downward flux. Here we have the standard “Anthropogenic Global Warming” theory. In the new theory, these two fluxes are equal to each other, and that does not change at all, not with water content, nor with extra CO2. The typical “forcing” due to CO2 on 700 m height, is conspicuously absent in satellite measurements in the last 25 years. We will see that the 1.7 W/m2 radiation forcing at the surface due to doubling of the CO2 concentration is largely compensated for by the increase of latent heat transfer with increased temperature.



Figure 10.
Miskolczi's new theory

Miskolczi's new theory does not start with schemes, but from measured atmosphere profiles. It seeks relations between the heat fluxes per profile. In the following graphs, every point represents one profile. The locations are as far apart as they can be. The coldest point is from the polar night, the warmest point is from a hot day over the tropical pacific ocean. From studying the relationships between the heat fluxes, surprising new insights come to light.



Figure 11.

Figure 11 reveals a strong correlation between the downward atmospheric radiation ED , the transparency of the atmosphere (Ta) and the upward surface radiation SU. While all three vary strongly with latitude, they follow the relationship ED = SU·[1-Ta] at all places. FM calls this “Kirchhoff’s Law”, because of the equality of the radiation. The use of this term should not be confused with the usual understanding of Kirchoff's Law, which is that emissivity = absorbtivity. It appears to be an additional constraint, due to a special property of the atmosphere. This is the major difference between Miskolczi's theory and the standard theory, which assumes a fairly large, 25 W/m2, net flux from the surface into the absorbing atmosphere.

In the standard theory, absorption by the atmosphere increases with an increase in the amount of greenhouse gases, so the net upward flux is hindered, increasing the atmospheric and surface temperatures. In the case of the relationship ED = SU·[1-Ta], there is no net upward IR heat flow other than that which passes through the IR window, which is much less dependent on increased greenhouse gas concentration. In other words, the upward radiation in the atmosphere depends almost entirely on the transmissivity of the air and only to a very minor degree on the amount of greenhouse gases.

This relation is true for every height, not only on the surface. It is also true for Mars, with its tenuous atmosphere. It is simply equivalent to Local Thermodynamic Equilibrium, or LTE within a layer that is not thicker than the mean free path of an interacting IR photon.

From this relation it follows that the OLR can be thought of as being constituted from three parts: The radiation through the window, the absorption of visible sunlight into the atmosphere, and the vertical convective heat transfer when the adiabat is exceeded.

Note, also, that the expression (1-Ta) is equivalent to (1-exp(-tau A)), where tau A is the optical thickness. Thus, the y-axis could be expressed as ED/(1-exp(-tau A)). This means that the empirical data indicate a constant optical thickness. Although not shown directly by the data in this graph, that optical thickness turns out to be 1.87.

This measured value is precisely equal to the theoretical value he found by solving the Eddington radiation differential equation with the boundary condition on the surface of ED = SU·[1-TA] and with a partially transparent atmosphere that is bounded in height. All these are natural boundary conditions, and none of them are applied in the standard theory.

In the geologic history of the Earth, the CO2 concentration increased a hundredfold during the Paleocene-Eocene Thermal Maximum, about 55 million years ago. The oceans were so acid then, that we find no calcium carbonate sediments, but a reddish clay instead. The large amount of CO2 was caused by a temperature increase of about 6 °C globally, the arctic polar sea was not saline and was full of floating Azolla ferns, now found in rice paddies. Their fossil remains are now found in the North Sea bottom.



Figure 12.

Second, it appears that the upward IR flux from the top of the atmosphere EU, that is, the OLR minus the window radiation, is roughly one half of the surface upward blackbody radiation Su. FM calls this the “Virial Law.” Note the similarity of the Eu = Su/2 to the viral law, which states that potential energy = twice the kinetic energy. Eu is closely related to the total internal energy of the atmosphere and is half the total energy input to the system, Su. The Eu = Su/2 relationship appears to be a special property of our atmosphere, resulting from complex heat transfer mechanisms.

This relationship applies to cloudy skies, wherein all radiation from the surface is absorbed by the atmosphere. Under clear sky conditions, some IR is transmitted directly from the surface to space via the “window” regions, which are those portions of the spectrum where there is no absorption by the gases in the atmosphere. Miskolczi also derives the following relationship for cloudy skies, which simply expresses the conservation of energy: Su -Fo + Ed - Su = Fo = OLR. In this equation Fo is the energy received from the Sun, and OLR is the outgoing longwave radiation to space.

Miskolczi shows, as do the results of the greenhouse experiments discussed earlier, that there must be thermal equilibrium between the surface and the air above the surface. This means that Ed = Su, under cloudy conditions. Moreover, for cloudy conditions, Eu = Fo = OLR, at the top of the atmosphere. Substituting these relationships in the energy conservation equation above gives the relationship Su – OLR + Su – OLR = OLR, or, Su = 3/2 OLR. Besides deriving this relationship mathematically, Miskolczi shows this relationship to be true empirically for the Earth (see Figure 22).

But what about the case of a clear or partly cloudy atmosphere? In this case another term must be introduced to account for the window radiation. Miskolczi uses the term St for this transmitted surface radiation, and in this case, OLR becomes the sum of Eu and St. Using the above relationship, then, Su = 3/2(St + Eu). As shown in the above figure, Eu = ½ Su. Substituting this relationship into the Su = 3/2(St + Eu) equation gives Su = 6 St. By definition, optical depth = -ln(St/Su) = -ln(1/6) = 1.79, which is in fair agreement with his Hartcode calculations and the empirical relationship shown in Figure 11.

By definition the transparency Ta = St/Su. Notice that under cloudy skies, St and Ta are both = 0; whereas, under clear skies, Ta = Su/6. The Earth's atmospheric system has on average a partial cloud cover with 0 ⇐ Ta ⇐ Su/6. This elevates the optical depth from 1.79 to 1.87.

Using Miskolczi's new theory we can calculate the influence an extra amount of greenhouse gas would have on the optical thickness. Starting with an optical depth of 1.86, and it follows that removal of all CO2 reduces the optical thickness to 1.73 for a perturbation of -7%. Conversely, a 100-fold increase in CO2 concentration increases the optical thickness to 2.29, a perturbation of +23%.



Figure 13. Perturbations of optical depth by greenhouse gasses.

The figure shows the same perturbation for Ozone or O3, and for water vapor holding all other concentrations being equal. However, as a consequence of Miskolczi's theory, the atmosphere responds by reverting to an optical thickness where the maximum heat transfer to space takes place, i.e. at the optimal optical depth of 1.86. This has influence on the SU/EU = 2 equation, see the graph of the calculated functions above. Water below the tropopause has a cooling effect, as shown in Van Dorland’s figure 2.4. We see that water vapor cools, while the other two gases CO2 and O3 heat the atmosphere, like we saw in Rob van Dorland's graph. When we increase the CO2 to 3%, 100 times what we have now, the atmosphere increases its water content about 5% to regulate back to the optical depth of 1.86.
Measurement of absolute humidity, ORL, surface temperature, compiled by NOAA.

To illustrate the large difference between the new theory and the standard theory, we now give a few examples, taken from the database of NOAA, all numbers averaged from 1948 to 2007 or 2008. What we see is the physics underlying FM's theory, indicating unambiguously that a wet planet regulates its own temperature, by compensating for large spatial differences in heat input. Like a pan with boiling water, it does not change its temperature with the heating rate. The underlying heat transfer mechanisms are much more complex than the simple statements by FM, but indeed they support his hypothesis clearly. We begin with a history of water content in the atmosphere on a height of 300 mB: (NCEP Reanalysis data provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their Web site at http://www.cdc.noaa.gov disregard “up to 300 mB”).