## Simple Time-Dependent Model Refutes the Atmospheric Greenhouse Effect

We must now look at Roy Spencer’s simple model of the greenhouse effect to see what he’s actually doing with it and what he actually thinks about it.

I have updated his current model but also have a copy from some time he did this before using a sphere with concentric shell as an example – they’re both updated with “reality” sheets and “Spencer” sheets.

We now get to see exactly what Roy thinks about backradiation, independent of all of the usual obfuscatory language, because we can refer directly to his mathematics.  Here is the relevant Excel equation from his most recent model:

B12 = B11 + (\$C\$2-C11+\$C\$5*0.0000000567*E11*E11*E11*E11)*\$C\$3/\$C\$4

Now this is an iterative equation and has Excel formatting, so I will rewrite it to look more like real math:

TSurf(i+1) = TSurf(i) + (FSun – FSurf(i) + ασTAtmo(i)4)*dt/Cp

We can simplify the appearance of this a bit with the atmospheric flux being FAtmo = ασTAtmo(i)4, so that

TSurf(i+1) = TSurf(i) + (FSun – FSurf(i) + FAtmo(i))*dt/Cp

And therefore, we now clearly see, that the atmospheric flux is being directly added in as heat.  It is precisely the same as the consensus radiative greenhouse effect diagrams such as this one.

Note what happens inside the brackets.  He takes the difference between the solar input and the surface output because, as is correct, the heat input from the Sun on the surface is the difference between the temperature of the solar radiation and the temperature of the surface, i.e., the difference between the solar input flux and the surface output flux.

But then, he goes on to add in directly the entire flux from the atmosphere, irrespective of the surface’s temperature.  In other words, the input flux is now the flux from the Sun and the atmosphere combined.  A slight rearrangement of terms shows this more clearly:

TSurf(i+1) = TSurf(i) + (FSun + FAtmo(i) – FSurf(i) )*dt/Cp

And so there you have it: the atmospheric flux is being added back in as input energy, as heat (or as whatever else you want to call it).

And that most certainly is in violation of the Laws of Thermodynamics and hence all of physics.

The approach isn’t even self-consistent.  If the heat input from the sun is given by the difference in flux between the solar input and surface output, FSun – FSurf(i), then why wouldn’t the heat input from the atmosphere be given by the difference between the atmospheric flux and surface flux, as in FAtmo(i) – FSurf(i)?  Why is the atmospheric flux being added back in directly irrespective of the temperature of the surface?  You see how the logic automatically begins to break down when you start violating the laws of existence.

So, let’s say we add in heat from the atmosphere in this “more appropriate way”.  We then have:

TSurf(i+1) = TSurf(i) + [(FSun – FSurf(i)) + (FAtmo(i) – FSurf(i))]*dt/Cp

= TSurf(i) + [FSun + FAtmo(i) – 2*FSurf(i)]*dt/Cp

If you modify the Excel sheet to match that, then the final surface temperature is -47°C!  Why so cold?  Because none of it makes sense.  Because the entire concept is not based in reality.

It’s not logically self-consistent, and it can’t be self consistent because it isn’t logically consistent with existence in the first place with the entry postulate that backradiation can cause further temperature increase than what the source initially provided.

That’s Ontological Mathematics philosophy right there for you.

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### 16 Responses to Simple Time-Dependent Model Refutes the Atmospheric Greenhouse Effect

1. Joe, you linked a nice set of heat equations, in a discussion with some fellow debating you, some time ago. Those various derivations of heat equations have no reference to the temperature of the emitter or absorber, but only the flux being emitted or absorbed. And they look just like the flux terms Roy used above. Why do you insist that the flux from the atmosphere not be included? Is that flux not made up of photons with momentum? Then they contain energy. HEAT is the result, positive or negative, of the total of all flux emitted offset by all flux absorbed. No heat equation contains only one term.

[JP: Tom said: “Why do you insist that the flux from the atmosphere not be included?”

Because read the article. The photons from the atmosphere are not heat. If you try to treat them as heat, you get a nonsensical result…and equation.

The correct heat equation doesn’t contain only one term. The heat equation includes the difference of two terms – the input flux and the output flux. The atmospheric flux is not an input – it can not transfer additional heat to the surface because it is lower in temperature, or at most equal in temperature, to the surface.

The heat equation gives the heat flow between two specific objects. The Sun and the Earth surface for example. If you add in the energy from a third object, firstly it is not being accounted for as heat but is being simply directly added in, and secondly adding in a 3rd object is nonsensical to the equation itself because the equation is only between two other specific objects. If one wishes to know the heat flow between the Earth’s surface and atmosphere, then a new heat equation must be formed for these two specific objects, and of course the heat flow will be only from warmer to cooler, generally from surface to atmosphere. The heat flow between surface and atmosphere might also be zero, if the atmosphere is warm enough. And the heat flow between sun and surface might also be zero, if the surface is hot enough. Incoming or ambient energy can have no heating effect at all, even though it is present.]

2. geran says:

In his spreadsheet, Spencer also violates the laws of quantum physics. He does the infamous “divide-by-4” calculation, which confuses energy with photon flux.

[Joseph has covered this several times before, but for anyone new here, Earth’s “disk” receives about 1365 Watts/m^2. After albedo, that leaves about 960 Watts/m^2. Considering the 960 as energy, and Earth’s surface is a sphere (4 times the area of a “disk”) then dividing 960 by 4 yields 240 Watts/m^2. And, the “240” figure is what Spencer uses in his spreadsheet for “absorbed solar”.

The problem is that once you treat the flux as energy (divide-by-4), you can NOT go back and consider it as flux. That is, you can NOT use the new value (240 Watts/m^2) in the S-B equation. The S-B equation is only valid for the EXACT flux impacting the surface, not an average!]

So, Spencer violates the laws of thermo, AND the laws of quantum physics. He gets it all WRONG. Pseudoscience at its best!

3. That’s pretty good Geran thanks. I’d never put it in those terms. Good one.

4. Rosco says:

Slight error in your quote of Spencer’s equation –

B12 = B11 + (\$C\$2-C11+\$C\$5*0.0000000567*E11*E11*E11*E11)*\$C\$3/\$C\$4

Should be –

B12 = B11 + (\$C\$1-C11+\$C\$4*0.0000000567*E11*E11*E11*E11)*\$C\$2/\$C\$3

Probably should fix it on PSI as well.

5. Rosco says:

Joe has already pointed out the duplicitous nature of Spencer who always says his “version” of how things work does not transfer heat from cold to hot and then he just goes and does it anyway !

Geran has succinctly pointed out the fraud inherent in using an “average” input solar flux – this has long been a source of criticism of the models used by “greenhouse effect” acolytes.

I noted on Spencer’s site a whole host of smug acolytes pouring scorn on any who could dare to question the “prophet”. By this action they reveal that this is the teachings of a “religion” – not science.

I’ll mention another problem with Spencer’s “Physics” AND “Maths”. This one is such a basic FAIL that it beggars belief.

Chapter 1.4 of Young and Freedman – a BASIC introduction to Physics – states in part :-

“An equation must always be dimensionally consistent. You can’t add apples and automobiles; two terms may be added or equated only if they have the same units. For example, if a body moving with constant speed travels a distance d in a time t, these quantities are related by the equation

d = vt

If d is measured in meters, then the product must also be expressed in meters.”

Force and bending moment are used extensively in engineering. Force has units of newtons and bending moment has units of newton metres BUT there isn’t an engineer on Earth that would add these in an “equation” despite their obvious relationship to each other.

If you look at the equation Joe quotes from Spencer’s spreadsheet you will notice :-
1. That it purports to add temperatures expressed in Kelvin.
2. That the term inside the brackets evaluates to units of W/m2.
3. That the term inside the brackets is multiplied by a time constant over “heat capacity”.

Spencer lists the units of his heat capacity – \$C\$3 in his spreadsheet as J per degree per cubic metre.

Hence \$C\$2/\$C\$3 has units of sec*K*m3/J

So it is simple to check dimensions of units that Spencer has quoted. Doing so reveals Spencer sees no problems in adding Kelvin – B11 in the spreadsheet – to the term in the brackets – W/m2 – times sec*K*m3/J.

B12 [Kelvin] = B11 [Kelvin] + (\$C\$1-C11+\$C\$4*0.0000000567*E11*E11*E11*E11) [W/m2]*\$C\$2/\$C\$3[seconds*K*m3/J = seconds*K*m3/(W*seconds)]

This evaluates to Kelvin (B11) + metreKelvin (W/m2 * seconds * K * m3/W.seconds) – a hitherto unknown unit.

Even using the standard definition of heat capacity of J/K the result of the dimensional analysis is still wrong.

\$C\$2/\$C\$3 has units of sec*K*/J = sec*K/W*sec = K/W
and
B12 [Kelvin] = B11 [Kelvin] + (\$C\$1-C11+\$C\$4*0.0000000567*E11*E11*E11*E11) [W/m2]*\$C\$2/\$C\$3 [K/W]

evaluates to W/m2 (the term in brackets) * Kelvin/W = W/m2 * Kelvin/ W = Kelvin/m2 ??

I am sorry to point out the obvious but you CANNOT just write “equations” that are not dimensionally consistent and have any credibility.

I know all of the acolytes, maybe even critics, will excuse this and deny it is even a problem BUT it FAILS the fundamental principle of Physics as quoted from Young and Freedman – consistency in units in equations.

You cannot even call ANY of the expressions Spencer uses in his spreadsheet “equations” because they are NOT !

This isn’t science !

6. No it’s because I added a row at the top on Spencer’s sheet.

7. ScottM says:

“TSurf(i+1) = TSurf(i) + (FSun + FAtmo(i) – FSurf(i) )*dt/Cp

And so there you have it: the atmospheric flux is being added back in as input energy, as heat (or as whatever else you want to call it).

And that most certainly is in violation of the Laws of Thermodynamics – all of them.”

Please explain how this violates the zeroth law of thermodynamics.

Please explain how this violates the first law of thermodynamics (which can be expressed without any reference to heat). I think it is saying exactly what the first law says: The change in internal energy (here taking the form of a temperature increase, dTsurf * Cp) is equal to the total of energy added (including work done on the system), minus the total energy leaving (including work done by the system). In this case, I think there’s an implicit stipulation is that no work is done in either direction.

Please explain how this violates the second law of thermodynamics. If you are successful in finding a violation of the second law, then please explain how to reformulate the first law so that an equation consistent with the first law does not violate the second law. Otherwise, you will have discovered a counterexample to the first law.

Please explain what this has to do, even remotely, with the third law of thermodynamics.

8. From Wiki:

“The zeroth law of thermodynamics may be stated in the following form: If two systems are both in thermal equilibrium with a third system then they are in thermal equilibrium with each other.”

Spencer’s equation states that no three systems can ever be in thermal equilibrium, since the coolest of the 3 systems will cause the warmer ones to rise in temperature. If they all start off at equal temperature, then they will heat each other and raise in temperature which violates the definition of heat and the definition of thermal equilibrium. Spencer’s equation thus violates the zeroth law.

“First law of thermodynamics: When energy passes, as work, as heat, or with matter, into or out from a system, the system’s internal energy changes in accord with the law of conservation of energy. Equivalently, perpetual motion machines of the first kind are impossible.”

Spencer’s equation states that energy from a cold object will pass to a warmer object and raise its temperature which means that such energy is heat, which violates the definition of heat. Spencer’s equation thus violates the 1st law.

“Second law of thermodynamics: In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases. Equivalently, perpetual motion machines of the second kind are impossible.”

“Third law of thermodynamics: The entropy of a system approaches a constant value as the temperature approaches absolute zero. With the exception of non-crystalline solids (glasses) the entropy of a system at absolute zero is typically close to zero, and is equal to the logarithm of the product of the quantum ground states.”

The violations here for 2 & 3 aren’t as clear, and so my quoted statement is in the general sense that if you violate one subsection of physics, you violate all of physics. Thus I will edit the statement from “all of them” to “and all of physics”. Thanks for helping make that clear!

9. ScottM says:

In row 461 of your spreadsheet, the model is supposed to be at equilibrium, but the net energy flux into the surface (column I) is 96 W/m^2. Yet the surface temperature is unchanging, and no work is being done. Where is that 96 W/m^2 going? Is there a miscalculation?

10. ScottM: There is an error in Spencer’s calculation, unrelated to what you ask above, which was missed and is now corrected on the “Reality” tab.

Note that the flux emitted by the atmosphere is always less than the flux emitted by the surface, and therefore the atmosphere can not transfer heat to the surface.

11. ScottM says:

The question was, where does the 96 W/m^2 go?

12. It goes to outside the Earth, to space.

13. Tom in Oregon City says: