Modeling Global Warming (Miskolczi Part 1)

A very interesting theory of global warming proposed by the Hungarian mathematician
Ferenc Miskolczi contains a simple proof that the greenhouse effect
is bound to a fixed value and cannot ‘runaway’, or even increase. In order to understand, or audit, parts of the theory I step through a simplified version of the derivation of his result below.

The first step in modeling a system’s dynamics is representing the main
constant relationships, usually based on conservation of energy.
The ‘big picture’ view of the flow of atmospheric energy consists of three
linked components: the Sun’s energy in, flux circulation within the atmosphere/surface system, and radiant heat out.

This view of the system as a linear converter of shortwave (SW) into longwave (LW) radiation is shown in diagram with the relevant symbols. Energy comes in
as SW energy (Fo), is circulated and transformed by surface (S) and atmospheric (E) fluxes, and goes out as LW energy (OLR).

Fo -> S,E -> OLR (1)

For these components to be in balance, the energy passing through each of the three components must be equal. We ignore geothermal energy at this stage (Po).

The internal energy of the surface/atmosphere system is also composed of a number of fluxes. Miskolczi represents the energy of the system by two main net fluxes. The first net flux is the difference between the surface up flux (Su) and the radiant energy down flux Fo. This net flux (Su-Fo) warms the atmosphere. If the atmosphere was non-absorbing then these would be equal and the net term zero.

The other internal energy term is the net flux down from
the warmed atmosphere. This is composed of up and down atmospheric components, Eu and Ed. The net flux (Ed-Eu) produces the increase in land surface temperature known as the greenhouse effect. If this net flux was zero, the land surface would be much colder than it is.

For conservation of energy, total energy input Fo, the total energy of the surface/atmosphere system, and also the total energy output OLR must all be balanced (illustrated in the Figure 1):

Su-Fo + Ed – Eu = Fo = OLR (2)

Slide1.PNG

This is the Miskolczi energy conservation equation 7.
Here it is assumed that the atmosphere is able to use all of the absorbed solar
flux density (Fo=OLR) to warm the system.

The factor missing is the transmittance (T) directly from the surface
to space without absorbance in the atmosphere. This is through
frequencies called the atmospheric window, and is why the
Miskolczi atmosphere theory is “semi-transparent” and not “infinitely thick”.
I will deal with transmittance in a later post, however for now we assume the
system is able to utilize St (surface radiation that would be transmitted
in a clear sky) and return it to the surface from the cloud bottom.
(2) is a unique equation for cloudy atmosphere. In the Earth you always have some transmitted flux density, meaning that OLR>Eu.

The expression (2) can be simplified using the Kirchoff law equilibrium
relationship: the energy balance at the ground Ed=Su and
the energy balance at the top of the atmosphere Eu=Fo=OLR. Miskolczi
explains that thermal equilibrium between the surface and the atmosphere is not self-evident, and in fact is one of the major innovations of his approach.
But I will return to his discussion of that issue in a later post.

Substitution of these into (2) gives SU-OLR+SU-OLR = OLR or

Su=3OLR/2 (3).

Miskolczi offers the following simple linear regression model as evidence of the
postulated relationship between Su and OLR based on actual radiosonde measurements (Figure 2 below).

earth_energy_cons.png

The relevant information on the figure is the a global average OLR at 61km of 250W/m2 and Su of 375 W/m2, confirming the 2/3 relationship. The spread of results about these values are due to latitudinal variation I presume (figure supplied by Ferenc). The comparable IPCC AR4 estimates (see FAQ and chapter 1) based on Kiehl and Trenberth are 235W/m2 and 390W/m2.

An easy way to get the greenhouse effect in terms of temperature is take the fourth root of the ratio of W/m2 (square root twice). This gives 1.106682 for the ratio of the increase in temperature due to the greenhouse effect. If the Earth’s temperature would be 257.7K without the greenhouse effect, with gives an expected increase of temperature of 27.5K due to greenhouse effect, which is comparable to estimates (see wikipedia).

So it seems that Miskolczi derives upper limits to the greenhouse effect in
a fairly straightforward way from the conservation of energy. Based on the rough calculations above the effect is also at a maximum, leaving no possibility of increases in temperature due to ‘enhanced greenhouse effect’ without violation of principles of conservation of energy.

Implications of Increasing CO2

The 2/3 value is the amplification of IR at the surface causing Su to be greater than OLR. This is related to the greenhouse effect caused by the absorption or optical depth of the atmosphere, called f. Greenhouse gases that increase the optical depth of the
atmosphere would change f, expressed as a positive derivative df/f.

The results of most general circulation models (GCMs) indicate such an increase df/f>0, would increase the temperature of the atmosphere
and hence the atmospheric flux down Ed, warming the surface. This is shown in the elevated curve in the
figure from Douglass et al. 2007
marked with a red arrow.

To examine changes in the system, Miskolczi takes a derivative form of (3) where f is the coefficient for 2/3:

df/f = dOLR/OLR – dSu/Su (4)

If df/f were positive, due to a sudden increase in a GHG say, then the dOLR/OLR must be
greater than dSu/Su. That is, (4) indicates that atmospheric temperatures
would increase faster than surface temperatrues, as shown in the
experimental results from GCMs reported in Douglas et al 2007
and reviewed here.

Slide11.png

However, (3) shows that the value of Su is locked to OLR which in turn is
locked to incoming radiation Fo. So such increases would be
temporary and the equilibrium would be reestablished with
f going back to its original value. This necessitates a fall in other
greenhouse elements, such as a decrease in water vapor in
the air, restoring the original optical depth.

The energy of
the surface/atmosphere system cannot continue increasing
as energy inputs and outputs must remain the same
to keep the energy of the system in balance. So the
temperature of the atmosphere must remain fairly constant.

This model provides an explanation for lack of troposphere warming despite increasing CO2.
as shown in the observed trends for the troposphere shown on the Douglass figure above (blue lines).

Next

Some outstanding issues need to be addressed, particularly the cloudy sky and Kirchoff equilibrium assumptions. In future posts, I want to get to claims such as the following:

The observed 5 % increase in CO2 can be compensated with ~0.005 prcm decrease in the global H2O content. This amount is so
small it cannot be measured or monitored.

This means that in the long run the Earth has a saturated greenhouse
effect with fixed optical depth, with profound consequences
for global warming. As long as we have an atmosphere with a virtually infinite
water reservoir, neither nature nor humans can influence the
greenhouse effect.

The only levers to play with that can alter surface temperatures
are the solar inputs Fo, geothermal
energy Po, and the distribution of heat within the system such as changes in albedo or
emissivity.

Next: The Virial Theorem in Miskolczi’s Atmosphere Theory

  • http://www.petergallagher.com.au Peter Gallagher

    David, thank you very much for this explanation/simplification of the Miskolczi thesis.

    I will need to read it again (and again) but one thing that puzzled me on first reading was: isn’t the conclusion (last para.) implicit in the first proposition that the energy balance of the system (global input=global output) is conserved? My knowledge of thermodynamics is no more sophisticated than Flanders & Swan’s. But I thought the premiss of energy conservation was applicable only to closed (i.e. ideal) systems. Should we readily accept that the earth is a thermodynamically closed system (this is meant as a naive question: I’m not sure)? If we should not–if the earth is only one small part of the relevant system–why is it not possible that it could store heat? That is why could it not be an energy trap, just as the ‘runaway’ greenhouse theory suggests perhaps balanced, in geological time, by some heat radiation mechanism so far unknown?

    I’m sure there’s an answer to this. Knowing it–or understanding why the question is confused–will help me understand this better.

  • http://www.petergallagher.com.au Peter Gallagher

    David, thank you very much for this explanation/simplification of the Miskolczi thesis.

    I will need to read it again (and again) but one thing that puzzled me on first reading was: isn’t the conclusion (last para.) implicit in the first proposition that the energy balance of the system (global input=global output) is conserved? My knowledge of thermodynamics is no more sophisticated than Flanders & Swan’s. But I thought the premiss of energy conservation was applicable only to closed (i.e. ideal) systems. Should we readily accept that the earth is a thermodynamically closed system (this is meant as a naive question: I’m not sure)? If we should not–if the earth is only one small part of the relevant system–why is it not possible that it could store heat? That is why could it not be an energy trap, just as the ‘runaway’ greenhouse theory suggests perhaps balanced, in geological time, by some heat radiation mechanism so far unknown?

    I’m sure there’s an answer to this. Knowing it–or understanding why the question is confused–will help me understand this better.

  • jae

    David:I also thank you. I have a difficult time trying to digest that paper, and this really helps. I am very interested in this work, as it would explain my little dilemna regarding why it is not any hotter than it is in the moist tropics.

  • jae

    David:I also thank you. I have a difficult time trying to digest that paper, and this really helps. I am very interested in this work, as it would explain my little dilemna regarding why it is not any hotter than it is in the moist tropics.

  • pliny

    David, I’m puzzled about Eq 4. If Su = f * OLR, then isn’t it
    -df/f = dOLR/OLR – dSu/Su ?

  • pliny

    David, I’m puzzled about Eq 4. If Su = f * OLR, then isn’t it
    -df/f = dOLR/OLR – dSu/Su ?

  • http://landshape.org/enm admin

    #3 Pliny, f=2/3. I have tweaked the text. thanks

    #1 Peter, the argument here is that constant greenhouse follows from energy conservation (and Kirchoff). It is possible to store heat, in the oceans say, but this would only delay the equilibrium conditions assumed here. M’s paper has a geothermal term Po, and that is being neglected here also. These could be incorporated, but for starters I just wanted to go directly from conservation to constant greenhouse. Regards

  • http://landshape.org/enm admin

    #3 Pliny, f=2/3. I have tweaked the text. thanks

    #1 Peter, the argument here is that constant greenhouse follows from energy conservation (and Kirchoff). It is possible to store heat, in the oceans say, but this would only delay the equilibrium conditions assumed here. M’s paper has a geothermal term Po, and that is being neglected here also. These could be incorporated, but for starters I just wanted to go directly from conservation to constant greenhouse. Regards

  • http://landshape.org/enm admin

    #1 Peter, I should have also said that geothermal contribution on Earth is very low. Also, the three component system is like three metal cubes in contact in a row, insulated on the outside. You start heating one end and the heat flow through. At equilibrium the heat fluxes through each cube are equal, irrespective of the size of each of the cubes.

  • http://landshape.org/enm admin

    #1 Peter, I should have also said that geothermal contribution on Earth is very low. Also, the three component system is like three metal cubes in contact in a row, insulated on the outside. You start heating one end and the heat flow through. At equilibrium the heat fluxes through each cube are equal, irrespective of the size of each of the cubes.

  • cba

    On average, an energy balance will be reached. The sun provides 1361 W/m^2 on average and the Earth will shed itself at precisely this rate (on average) or it will heat up (if less is shed) or it will cool down (if more is shed). This will have to continue until a new balance is reached (again – on average).

    Conservation of energy is not just for overall systems like entropy but for any and every subsystem component. The energy in must balance with the energy stored + the energy out. Note that depending upon what one is talking about, energy may take on the forms of heat, kinetic energy, potential energy and even mass.

    I haven’t had time to analyze Miskolczi’s paper other than to briefly read over it. I think he’s right about some things but I’m not sure about all of it and he evidently has worked in the area which means some errors are going to probably be difficult to recognize. While his calculations and interpretations may be correct for his simplified model, I doubt that the Earth system is really going to behave as the model.

  • cba

    On average, an energy balance will be reached. The sun provides 1361 W/m^2 on average and the Earth will shed itself at precisely this rate (on average) or it will heat up (if less is shed) or it will cool down (if more is shed). This will have to continue until a new balance is reached (again – on average).

    Conservation of energy is not just for overall systems like entropy but for any and every subsystem component. The energy in must balance with the energy stored + the energy out. Note that depending upon what one is talking about, energy may take on the forms of heat, kinetic energy, potential energy and even mass.

    I haven’t had time to analyze Miskolczi’s paper other than to briefly read over it. I think he’s right about some things but I’m not sure about all of it and he evidently has worked in the area which means some errors are going to probably be difficult to recognize. While his calculations and interpretations may be correct for his simplified model, I doubt that the Earth system is really going to behave as the model.

  • http://landshape.org/enm admin

    #6 Keep in mind the above is a part of the whole. He works through conjectures that are subsequently refined. More to come.

  • http://landshape.org/enm admin

    #6 Keep in mind the above is a part of the whole. He works through conjectures that are subsequently refined. More to come.

  • Hans Erren

    That this linear relationship holds is proven by the simple linear regression model of Su and OLR based on actual radiosonde measurements (Figure 2 below).

    Doesn’t this mean that BOTH OLR and Su are MODEL values based on the same measured radiosonde profile? What’s the error bar for the points in the cloud of fig 2?
    How do you calculate OLR with sufficient accuracy when eg the local distribution of tropospheric ozone is not known AT ALL, as it is not measured during a radiosonde launch?

  • Hans Erren

    That this linear relationship holds is proven by the simple linear regression model of Su and OLR based on actual radiosonde measurements (Figure 2 below).

    Doesn’t this mean that BOTH OLR and Su are MODEL values based on the same measured radiosonde profile? What’s the error bar for the points in the cloud of fig 2?
    How do you calculate OLR with sufficient accuracy when eg the local distribution of tropospheric ozone is not known AT ALL, as it is not measured during a radiosonde launch?

  • http://landshape.org/enm admin

    Hans, good questions. I am going to do some tweaking on this post. It is hard to tell in the paper what are real and what are modeled data. Some data are radiosone, selected for clear sky conditions say. OLR is stated to be from ERBE project (Earth Radiation Balance). Their previous paper has more on how the data are collected.

    It seems has budget differs in some ways from the Kiehl and Trenberth budget, but I haven’t sorted that out yet. The KT budget have a lot of guestimates too, as many of the quantities are not separably measurable. However until we get past the virial theorem where transmittance is brought in I think it would be jumping the gun to answer these and some other questions.

    BTW, What does the ozone concentration got to do with it?

    Regards

  • http://landshape.org/enm admin

    Hans, good questions. I am going to do some tweaking on this post. It is hard to tell in the paper what are real and what are modeled data. Some data are radiosone, selected for clear sky conditions say. OLR is stated to be from ERBE project (Earth Radiation Balance). Their previous paper has more on how the data are collected.

    It seems has budget differs in some ways from the Kiehl and Trenberth budget, but I haven’t sorted that out yet. The KT budget have a lot of guestimates too, as many of the quantities are not separably measurable. However until we get past the virial theorem where transmittance is brought in I think it would be jumping the gun to answer these and some other questions.

    BTW, What does the ozone concentration got to do with it?

    Regards

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  • ROD COLENDRINO DOMINGO

    Theories about global warming and climate change belong to the idiots who do not see realities. Send me your email address and I will send you real evidence on what is going on.

    I discovered true reasons of Global Warming being caused by acidic environment in 1985. Since then, so many fakist try to present their idiosm. ROD COLENDRINO DOMINGO

  • ROD COLENDRINO DOMINGO

    Theories about global warming and climate change belong to the idiots who do not see realities. Send me your email address and I will send you real evidence on what is going on.

    I discovered true reasons of Global Warming being caused by acidic environment in 1985. Since then, so many fakist try to present their idiosm. ROD COLENDRINO DOMINGO

  • David L. Hagen

    David S.
    Per your citing Douglas et al. 2007, I found Miskolczi’s (2007) comment:

    “Note that there are accumulating evidence of long term negative surface
    pressure trends all over the southern hemisphere, (Hines et al., 2000), which
    may be an indication of decreasing water vapor amount in the atmosphere.”
    citing Hines, K.M., Bromwich, D.H., and Marshall, G.J., 2000: Artificial surface pressure trends in the NCEP-NCAR reanalysis over the southern ocean and Antarctica. J. Climate 13, 3490-3952. http://polarmet.mps.ohio-state.edu/PolarMet/PMGFulldocs/hines_bromwich_jc_2000.pdf

    Confirmations that such decreasing pressure is related to decreasing specific water vapor trend would appear to support M’s theory. They might also support Douglas’ results showing declining atmospheric temperature trends compared to greenhouse models based on CO2 projecting increasing trends in the atmosphere.

    This could be a major distinguishing feature between conventional Eddington-Milne based CO2 tuned climate models vs climate models based on perturbations around Miskolczi’s equilibrium Kirchoff based theory with long range trends due to solar and cosmic ray forcing.

  • David L. Hagen

    David S.
    Per your citing Douglas et al. 2007, I found Miskolczi’s (2007) comment:

    “Note that there are accumulating evidence of long term negative surface
    pressure trends all over the southern hemisphere, (Hines et al., 2000), which
    may be an indication of decreasing water vapor amount in the atmosphere.”
    citing Hines, K.M., Bromwich, D.H., and Marshall, G.J., 2000: Artificial surface pressure trends in the NCEP-NCAR reanalysis over the southern ocean and Antarctica. J. Climate 13, 3490-3952. http://polarmet.mps.ohio-state.edu/PolarMet/PMGFulldocs/hines_bromwich_jc_2000.pdf

    Confirmations that such decreasing pressure is related to decreasing specific water vapor trend would appear to support M’s theory. They might also support Douglas’ results showing declining atmospheric temperature trends compared to greenhouse models based on CO2 projecting increasing trends in the atmosphere.

    This could be a major distinguishing feature between conventional Eddington-Milne based CO2 tuned climate models vs climate models based on perturbations around Miskolczi’s equilibrium Kirchoff based theory with long range trends due to solar and cosmic ray forcing.

  • http://landshape.org/enm admin

    David, you may be right. I would like to see something like that. We (blog world) have been increasingly interested in the water vapor confirmation as you can see from more recent posts.

  • http://landshape.org/enm admin

    David, you may be right. I would like to see something like that. We (blog world) have been increasingly interested in the water vapor confirmation as you can see from more recent posts.

  • http://heliogenic.blogspot.com jblethen

    Regarding equation (2) in your post, the conservation of energy equation, Miskolczi’s equation (7): is there a proof of this equation, or is it only qualitative?

  • http://heliogenic.blogspot.com jblethen

    Regarding equation (2) in your post, the conservation of energy equation, Miskolczi’s equation (7): is there a proof of this equation, or is it only qualitative?

  • Jan Pompe

    jblethen #17

    Eqn 2 is M7-7 simplified.

  • Jan Pompe

    jblethen #17

    Eqn 2 is M7-7 simplified.

  • http://heliogenic.blogspot.com jblethen

    Miskolczi doesn’t derive his eq. 7, he states it after discussing the two flux terms of his eq. 6.

  • http://heliogenic.blogspot.com jblethen

    Miskolczi doesn’t derive his eq. 7, he states it after discussing the two flux terms of his eq. 6.

  • Anonymous

    jblethen: See Zagoni for a derivation http://hps.elte.hu/zagoni/MET-ZM_v08c_eng.pdf

  • http://landshape.org/enm admin

    jblethen: See Zagoni for a derivation http://hps.elte.hu/zagoni/MET-ZM_v08c_eng.pdf

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