The Fraud of the Atmospheric Greenhouse Effect Part 7: The Tautology of GHE Math

I have likely mentioned a few times in this ongoing series that the atmospheric greenhouse effect is based on “tautologous”, illogical math.  In this post I will demonstrate and explain clearly what is meant by that, converting the math to much simpler words that anyone will be able to follow.  I’ll show the math, but I’ll convert it to a simple word-equations.

In my paper from last year, I presented the standard flat-earth model of “heat flow” which climate pseudoscientists use to create the appearance of a greenhouse effect.  This is a model which is found in actual textbooks that climate pseudoscientists use to teach each other and their students how the GHE works.  Criticism of the flat-earth model can be found between pages 7 & 15 of that paper.  References to various flat-earth models can be found in Appendix H of this most recent paper, and diagrams can be found on pages 72 & 73 of it.

There are many example of the flat-earth model creating the GHE, and this one below is representative.  Because it comes from a professor at Harvard University, we Slayers have come to call this the “Harvard Model GHE”:

In the textbook, all the numbers and figures in the diagram gets put into an equation as thus:


This equation is “supposed” to be a representation for the energy balance coming in and out of the system.  In words, it says: “The incoming solar energy is equal to the output from the surface plus the output from the atmosphere”.  Now that sounds totally legitimate, doesn’t it?  And it would be, except that the parameters of the equation don’t actually function in a logical way.  One big point is that the power of solar heating is reduced to one-quarter of it’s actual real-time value, and day & night have been utterly rejected as being a significant part of the climate!  This is what sets up the subsequent tautology, and the fraudulent creation of the greenhouse effect.

An entirely equivalent way to write the equation, in terms of the energy (and hence temperature) which is found at the surface (after all, the equation is supposed to tell us the surface temperature, not the temperature of the incoming sunlight which we already know), is:


What this equations says, is:  “The surface energy (temperature) is equal to the incoming solar energy plus the energy from the atmosphere”.  This is more to the point of what we actually want.  But here’s the catch: see the last term on the right-hand-side of the equation?  In the “Harvard Model”, this term gets replaced with another one, such that:


which says that the energy/temperature of atmosphere is caused (exclusively) by absorption of a fraction (f/2) of the energy radiated from the surface.

When you make the substitution, the equation now reads:


which therefore says that:

The energy/temperature of the surface is caused by the incoming solar energy, plus the energy/temperature of the surface.”

So do you now see the problem?  Do you see the self-referential tautology?  The energy/temperature at the surface is caused (in part) by the energy/temperature of the surface adding to itself!  It is generating its own temperature, and all you have to do is adjust “f” until it works out.  It says that any temperature is possible to self-generate, no matter how small the actual input is.  It is an equation for over-unity production of work, the most basic violation of the Laws of Thermodynamics.  There is no actual thermodynamics or heat-flow in this equation whatsoever, but climate pseudoscientists use it for teaching themselves how they think the climate must operate!  It is much more difficult to detect this problem when it is written in the way the Harvard Model textbook presents it, and that is likely for good reason.  I didn’t specifically write this all out in last year’s paper, so, now you see here it is: a temperature is increasing its own temperature.  That is exactly what the equation says.  You can go through pages 7 to 15 of last year’s paper to see further breakdown of the errors of the “Harvard Model”.

This relates precisely to the discussion of Godel’s Incompleteness Theorem written about in the last post.  The Incompleteness Theorem applies just as much to the language of mathematics as it does for “spoken” language.  You can write down a far greater number of equations that are false, than those that are true, but the false equations aren’t typically any easier to identify than the true ones.  Similar to the statement “this sentence is a lie”, the above equation is likewise meaningless because, even though it can be written down, and stated, it doesn’t actually obey basic logic and physics.  It is the nature of a “complete system” that it will allow “incomplete” statements; such are easier to identify in the more intuitive “natural” language, but doing it in math is a far greater challenge because math is so unintuitive (for most people, including me).

However, it is not like this entire scenario is unknown or new to science!  In my “Copernicus paper” I drew a comparison between the Ptolemaic Earth-centred universe, to that of the flat-Earth math of the GHE.  It has been well-known, for thousands of years no less, that sets of mathematics can be arranged to represent the appearances of any physical system, while not actually representing the internal physics of the system in any way whatsoever.  This is well known!  Competent scientists understand this stuff implicitly.  There is a difference between physics and mathematics: even though physics uses mathematics, physics is mathematics informed by the real-world and by the insight of the rational mind seeking an understanding of the Principle for why something is one way and not another.  Mathematics doesn’t do that by itself.  With Ptolemaic mathematics, you can create a mathematical model with the Earth being at the centre of the solar system, and the outward appearances work – predicting the positions of the planets.  This is analogous to how you can create mathematics where the ground heats itself up on a flat Earth – you succeed in matching the outward appearance, the surface temperature, but just because you can do so doesn’t mean that the way the math works actually represents the internal reality!  The Earth isn’t flat…Hello.

One final bit of sophistry indicated in the Harvard Model equation, alluded to earlier, is its presumption that the energy in the atmosphere is exclusively a result of radiative input and equilibrium from the surface.  In addition to the stupidity of one-quarter-power solar input, the flat Earth, no day & night, etc., this presumption is so devoid of any incorporation of any actual physics of the system it beggars belief that these people get away with it.  The reason why they do this is because it directly allows for the creation of a GHE where exclusively all of the temperature difference between the surface and the terrestrial average is caused by the surface heating itself up with its own temperature via the GHE.  First, the atmosphere gains a significant amount of energy directly from the Sun itself; second, the atmosphere gains heat energy by conduction with the warmer ground surface; third, the atmosphere gains energy from the latent heat of water vapour condensation.  The amount of energy gained by the atmosphere from the surface by radiation is only a fractional part of the total, not the exclusive part.

So, there you have it: tautological math, Godel’s Incompleteness Theorem found in an equation.  The basis of the GHE.  Do you know that the GHE-believing community has never been able to provide us with an alternative explanation, after we exposed this derivation of it to be a fraud?  Indeed 🙂

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15 Responses to The Fraud of the Atmospheric Greenhouse Effect Part 7: The Tautology of GHE Math

  1. John Francis says:

    Great post Joe. I have never understood how so-called physics professors can believe this stuff. My only negative observation is that your use of words like “stupid” practically guarantee that no mainstream media or bloggers are likely to re-post or link to it, no matter how justified the description is.

    [Reply: Thanks. And good point…I will try to be more civil :-)]

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  3. plus one, never go stronger than “erratic” or “flawed” or “lacking skill”.

    For how the atmosphere is really warmed, you may want to take notice of my “null hypothesis” that I posted earlier somewhere.

    Andre Bijkerk

    The real null hypothesis about greenhouse effect.

    Finding out the effects of a certain mechanism can be done by the null hypothesis, imagining what the situation would be, if the mechanism would not have been present. We are talking about the greenhouse effects. Climate text books and just about every blog about global warming illustrate this by considering the Earth as a black body under uniform solar radiation conditions, using the Stefan Botlzman law it is found that the black body temperature would be about -18 degrees Celsius, the average world temperature is about +15 degrees Celsius. Hence the greenhouse effect would accounts for 33 degrees? No, Wrong.

    Again for the null hypothesis, If you want to find out the effect, you’d have to remove exactly that effect but not more than that, hence, going to a black body model under uniform radiation is a bridge too far. You would have to consider an earth without greenhouse effect only –not a black body- but just without greenhouse gasses in the atmosphere and with a sun that shines during the day, -not an uniform radiation. That’s a big big difference.

    Now picture that null hypothesis earth, the sun shining on it. The hottest spot directly in zenith gets the full radiation of some 1365 w/m2, with the Stefan Boltzman law and the average reflectivity or albedo, that would mean a heating of some 87 degrees Celsius. Strange? No, just look at the bright side of the moon. That’s even warmer, over 100 degrees Celsius. Anyway, the heated Earth surface passes the heat to the lowermost molecules of the atmosphere by simple conduction, as there is no greenhouse effect, trapping radiation. But this warmed boundary layer decreases in density and becomes buoyant, it rises up, a well know process called convection, it transporting the heat away from the earth surface as new cooler air replaces it from above and gets heated in turn, sustaining the convecting. There is always an area directly in zenith under the sun, so the convection is constantly, non stop, putting heat energy from the surface into higher levels of the atmosphere.

    But what happens at the dark site of the earth? It emits infrared radiation into the cosmos and cools down, due to that energy loss. There is no greenhouse effect to counter that, so the earth will cool pretty quickly. Obviously, the lowermost boundary layer of the atmosphere transfers it’s thermal energy to the earth surface again by conduction, but cooling makes it more dense, heavier, not buoyant and it stays put. The warmer air aloft, heated during the day stays aloft and doesn’t cool down a lot by that conduction, since air is a poor conductor. This condition is known as inversion. So it turns out that this greenhouse gas free air is also unable to lose energy by radiation, because it’s the null hypothesis – no greenhouse effect either way, nor heating nor cooling.

    So if the atmosphere heats up by convection at day time but does not cool off a lot during night, we do have an unbalance and the heating of the atmosphere will only stop if the processes balance again, when the daylight convection offsets the night time conduction. But it also means that the atmosphere is considerably warmer than the earth surface on the average (-18C as a black body plus the conducted heat back from the atmosphere). How much, I don’t know. Theoretical maximum is some 80-90 degrees Celsius at ground level reduced by the cooling processes due to conduction to the surface.

    Now also take in consideration that if we talk about surface temperature, we actually talk about the temperature of the air molecules on some 1.5 meter above the ground and we are comparing that, not the actually contact temperature of the earth surface which can be significantly cooler than the air in the inversion conditions. Anyway, regardless of how you compare for the null hypothesis, the real surface temperature or the temperature at 1.5 meters will be higher than the Stefan Boltzman temperature for black body. Consequently, the greenhouse effect is less, much less than 33C. And if this cornerstone of the global warming theory is not as it should be, what would that do to the trustworthiness?

    [Reply: Thank for this, it is quite good and goes very well with my work. Cheers!]

  4. You’re welcome. Essentially it’s not mine, you would learn this with meteorology classes a few decades ago, when little attention was given to radiation, other than the cooling at night, leading to the inversion. I merely decided to call it the “null hypothesis”.

    Notice that the hot inert atmosphere would start losing the energy when greenhouse gasses are added and it can start radiation. I can’t see a simple way to deny that the biggest effect of greenhouse / radiative gasses is to cool the atmosphere, rather than to warm it. So what would happen if we increase the greenhouse gas concentration?

    Honest climatologists should be meteorologists first to know these basic processes



    [Reply: Yes indeed, excellent points. If the atmosphere has zero emissivity if no GHG’s are present, because by definition non-GHG’s can’t radiate (N2, O2), then if you add GHG’s the emissivity increases and thus the atmosphere can cool. N2 and O2 are the gases which trap heat, with their inability to radiate it away!]

  5. One little thing, all matters radiate, also N2 and O2, That makes the sky look blue. They have only few spectral emission/ absorption lines that can be ignored for practical purposes, But it should be mentioned to avoid strawman attacks.


    [Reply: Well to be sure, the blue sky is caused by preferential scattering of blue-frequency sunlight, i.e. Rayleigh scattering. But GHE adherents say that N2 and O2 don’t significantly radiate in comparison to GHG’s. If N2 and O2 thus have very low emissivity, THEY are the things which can hold a higher temperature for a given energy output rate. Some of the Slayers have long thought that the role of GHG’s is actually to cool. Carl Brehmer has recently been presenting a whole lot of data which proves that a higher presence of the strongest so-called GHG, water vapour, is always associated with lower temperatures, not higher.

    Between our comments here, would you be interested in putting it together as a “guest post”? It can go under the title “The Null Hypothesis”. If you wish, send it to and I will then post it.]

  6. Sorry about the rayleigh scatter goof. You’re right. I’d be happy to shape up the hypothesis a bit and then I’ll send it.

    About water vapor, I guess the most underestimated factor is the -latent- energy required to vaporize it. For instance, if you increase surface temperature, convection rate is increased which increases evaporation but if you try some reasonable numbers, you’ll find that the energy required for that is generally larger than the alleged increased energy with doubling CO2 ie 3.4-4 W/m2


    [Reply: Thanks Andre. Another interesting factor is that day-time evaporation is caused by input sunlight, which is quite hot and has the energy available to do so, and this occurs only at the surface. However, on the other hand, the major place where water condenses is in the atmosphere, thus providing heat (latent heat) to the atmosphere. So, the cycle of evaporation actually preferentially deposits heat into the atmosphere, thus keeping it warmer than otherwise…]

  7. Max™‮‮ says:

    I actually did a home experiment for school that I just completed.

    Basic setup is as follows: 4 lightbulbs of the same output (all 60 W frosted in my case) with a way to place them evenly above a surface, two insulated boxes (styrafoam shipping boxes for the gf’s medicine that has to stay cold) with windows cut in the roof, clear plastic to cover the windows, two thermometers, and then various modifications of the general setup were performed to test variables.

    One window has vents that allow air out without altering the light coming in (i.e. they overlap the edge of the window but aren’t taped down like the other sides) and I used that for convection/no convection tests.

    I had a third thermometer set nearby but not directly lit for a room temperature control.

    I then ran numerous cycles with the following methodology: prime the thermometers to 72 with water from the faucet, insert them with whatever factors were included, turn on the lights and close the door.

    I would run for an hour with 2 bulbs, checking temp at start, 30 mins, and the end, and I would run for 30 minutes with 4 bulbs, checking the temp at start, 30 mins, and the end.

    I later lined the bags with black trash bags to see what effect it would have, it helped improve the seal for the no-convection lid some so I left it for the remainder of the closed/open tests.

    Ran some with just the thermometer on the surface, the thermometer on the surface in a bag filled with water, thermometer on top of the window, and then I had some more specific variables I wanted to test besides the usual attempts to eliminate instrument error (swapping boxes, swapping thermometers, changing the ordering of the runs, and even doing them during the day and night when the house was warmer and colder to record that effect to account for it, heck, I even did a set of runs with 240 Watts for an hour and 120 watts for 30 on/off for completeness) and that is where the most interesting results came out.

    In general the expected was found, 30 minutes at 240 Watts gave a peak 4 or 5 degrees higher than the 60 mins at 120 Watts, and in some runs the 30 minutes at 0 Watts cooled it enough to match the average of the 60 min runs, not all, and only a couple of times did both boxes match in the same run like this.

    What really turned out neat was when I began testing specific parts of the GHE, so I set up the convection/no convection boxes, and after having swapped things around decided to go full on/off for each variable.

    No Convection/Convection wound up around you’d expect, with the box that could convect ending cooler than the other.

    Adding an open tray of water to the convection box and the same tray empty to the other produced more cooling (and yes I tested the other way, didn’t have much effect, canceled somewhat, I think the runs with open water and no convection were the hottest overall) I expect that due to the mass of the water itself absorbing energy and then what did evaporate wound up not condensing as it was carried out with the convective currents, this makes sense. Not particularly interesting.

    The last GHE component test though, I had done this in various forms before, but with the full setup it was pretty clear what is going on.

    Getting CO2 content controlled is difficult, but I had a method I used before, freezer bags and a soda bottle, put the bottle inside, suck the air out with a straw and seal it snug, then shake the bottle up and bit by bit let it inflate the bag without getting soda in it (as that is a variable I didn’t want to account for here) and you get a higher CO2 content than the regular air. Put the same type of soda in the same condition in a bag that is just puffed out by hand and sealed, then run the cycles.

    Putting convection, open water, and CO2 under illumination vs no convection/dry/air wound up knocking 2 to 4 degrees off:

    240 W runs, 30 mins on, 30 off:
    GHE on — GHE off
    –72 ———-72–

    120 W runs, 60 mins on:
    GHE on — GHE off

    So water vapor, CO2, and convection all appeared to help cool the box more effectively than not, particularly when combined (most other runs were within 1 or 2 degrees of each other, the 4 degree difference was large enough I had to reset and run it again later after swapping boxes/thermometers to make sure it wasn’t a fluke, same result)… who knew?

    [Reply: At a wedding…will have to read this again later for more input 🙂 ]

  8. Max™‮‮ says:

    Oh a wedding, do you know them or did you just wander in and say “oh, it’s ok, I’m an astrophysicist”, because I know for a fact stuff like that works. I mean, I’m not actually a physicist, but people kinda go “uh… oh, he probably knows what he’s doing here, I’ll leave him alone”… hah!

    Submitted the above experiment for grading earlier, wish me luck.

    [Reply: Hillarious…hehe :-)]

  9. Have a great time at the wedding. The season is also delaying my very basic null hypothesis elaboration. But nevertheless it’s in good progression. Give me a few more days.

    About evaporation, some numbers. The oceans together evaporate roughly about 1.8 meter water per year. Several sources can confirm this. Hence1800 liter per m2 per year, this is 0.057 cc (cubic cm) per second. One cc evaporation requires about 2500 joules, Hence the average energy required for oceanic evaporation is 143 W/m2. Now what would you think an alleged increase of 3.4 watt for doubling CO2 is going to do for evaporation rate to get that alleged imposible positive feedback?

    [Reply: Looking forward to the null hypothesis, but please do enjoy the holidays. Thanks for those numbers on evaporation etc…very useful! Assuming a general equilibrium, that same amount of energy is also constantly coming back out, into the atmosphere itself, as I mentioned previously that the cycle must preferentially deposit energy into the atmosphere. In other words, evaporation is roughly equal to condensation; evaporation occurs at the surface itself but condensation occurs in the atmosphere. Thus 143 W/m^2 additional input, in-situ to the atmosphere itself. That’s about 12.35 MegaJoules per day, which is ~60% of what sunlight introduces. This is very interesting…I had never though of this before until reading your comments…a whole new line of physics to consider!]

  10. Max™‮‮ says:

    I just went over this with the gf earlier.

    Today it was around 8 C when we got up (a bit late, were up til morning) and it was raining til the sun went down, now it’s 11 C.

    I asked her why, she said “hmmm, because the sun was shining all day?”, and I told her that I can’t say that is wrong, she did have the right answer in a roundabout way.

    She was a bit lost there, so I pointed out that the sun was shining over the pacific all day, and that means evaporation. Evaporation cools a surface, and the water vapor is carried around with the winds.

    The water vapor that we had dropped on us didn’t originate near here, most of it probably came out of the pacific ocean, and the energy that warmed it up after the sun went down didn’t originate near here either… it came with the water.

    She was a bit dubious at this point, but I just had her think about why evaporation cools a surface, she suggested that it got rid of the heat, sounds reasonable enough, right?

    But I told her that’s a problem, we can’t just get rid of energy, and heat is just a flow of thermal energy… so if the heat isn’t flowing in an obvious manner, it must be hidden somehow, right?

    She started to follow along, and I connected the last couple of dots, water vapor could be thought of as water + hidden heat, so when water vapor turns back into water, the hidden (or latent as I explained later) heat is transferred into the atmosphere, and that is responsible for warm muggy nights like tonight!

    It’s warmer than it was this afternoon because the sun was shining all day, but it was a couple of days ago, and it was over the pacific ocean… and that wound up making it warmer here in Memphis today. 😀

    [Reply: Nice]

  11. John Francis says:

    Lovely, Andre!
    Makes a great deal is sense.
    Looking forward to Joe’s detailed comments

  12. You’re welcome, spread the word.

    Quickly then – not a lot of time
    To further on the numbers, like the average 134 W/m2 required to keep the evaporization of the oceans going, it can be read at several places that it is assumed that the positive feedback of water vapor means that the average relative humidity remains constant. Which means at higher temperatures that there is more water vapor in the air.

    Let’s see what this means for energy. With this very useful tool we can calculate some rough magnitude numbers. Select on the right a relative humidity of 50%, in the middle a temperature of 15C (about the Earth’s average) and ask for the absolute humidity output. That gives us a value of 6.49 gram per cubic meter. Now, if we increase the temperature one degree, we get 6.84 g/m3; that’s a 6% increase. If we go for the alleged 2.5 degrees mean increase for doubling CO2 we get at 17.5C a value of 7.49 g/m3 and that’s a 16% increase.

    Obviously one cannot assume that these 6% and 16% are also true for the required increase of that 134 W/m2 evaporation energy to sustain that higher absolute humidity, since a lot more factors are working, like wind speed and mixing air in turbulence etc, but it’s hard to see it being done with that 3.4W/m2 and still have energy left to raise the temperature.


  13. Max™‮‮ says:

    Always seemed odd to me to suggest constant relativite humidity, isn’t that rather like directly pegging temperature and the water content of the atmosphere together?

    Seems like an unphysical assumption used for modeling, a rise in temperature doesn’t magic water vapor into the air immediately, and the processes which add water vapor tend to locally reduce temperatures, while the processes that remove it work the opposite way, don’t they?

    [Reply: Indeed, they do.]

  14. Rosco says:

    The model is so obviously wrong it is amazing that people do not fall about laughing that anyone could consider it science.

    Energy in x ( 1 – albedo) x pi x r^2 = energy out x 4 x pi x r^2 shows that they are not calculating the temperature that the solar radiation is capable of generating.

    All their sophistry shows is that to balance an input of ~1000 W/sq metre over a disk profile of a sphere the sphere only needs to radiate 1/4 of the input over a surface area 4 times the size.

    What if the Earth was cube shaped – would one use a factor of six instead of four to calculate the “blackbody” temperature ?

    [Reply: You know that’s such a great point! Never thought of it that way. That is exactly what they would do! Then sunshine would be heating to -43C instead of -18C, and they’d still be so confused as to the why the sun-facing side was so much hotter. This all stems from them using simple linear algebra to describe a process, heat flow, which can only be described with differential equations.]

  15. Pingback: Logical Physics Maths | Climate of Sophistry

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