## Definitive Refutation

This is something I wrote about long ago (reference pg. 16), but in a recent Slayer email exchange I re-realized just how important it was.  Hopefully any Slayers will follow up in the comments if anything else needs to be added.

In Misunderstood Basic Concepts and the Greenhouse Effect, it is stated:

“The tropospheric temperature lapse rate would not exist without the greenhouse effect. While it is true that convective overturning of the atmosphere leads to the observed lapse rate, that convection itself would not exist without the greenhouse effect constantly destabilizing the lapse rate through warming the lower atmosphere and cooling the upper atmosphere.”

However, let us look once again at the derivation for the lapse rate (also reference this previous post):

When there is no longer any gain or loss of energy in a column of gas (i.e., when it is in energy equilibrium), then the energy ‘U’ of an arbitrary parcel of gas is given by the sum of its thermal and gravitational potential energies.  The sum of thermal and gravitational potential energies is:

U = mCpT + mgh

However, this energy is constant since there is no other energy input (or loss), and so its differential is equal to zero:

dU = 0 = mCp*dT + mg*dh

which results in

dT/dh = -g/Cp

Note that this equation and its derivation has no reference to greenhouse gases or thermal radiation at all – the lapse rate is dependent only upon the gas’ thermal capacity, and the strength of gravity, and this will occur for any gas even if it is totally “radiatively inert”, and, even if the gas isn’t undergoing bulk convection; the lapse rate develops at the infinitesimal scale of the action of gravity on the particles of the gas.

Now I will simply quote my reference, with some editing:

This result is independent of any effect of greenhouse gases (GHG’s) as no consideration of those were made in the derivation.

Now, it is expected that GHG’s increase the temperature of the bottom of the atmosphere, while decreasing that at the top, and so this would require that the lapse rate of temperature to be larger than what was derived by means without reference to GHG’s.

That is, the lapse rate should be steeper than -g/Cp = -10 K/km because there is (ostensibly) already a GHE in operation in the atmosphere.

Yet this is clearly not the case because the fastest lapse rate derived and observed in meteorology is still that value as can be derived from -g/Cp, independent of any preexisting GHE.

Additionally, if we examine the effect of the strongest GHG on the lapse rate, which is water vapour, we find that it acts to reduce the lapse rate, not increase it, which is again in direct opposition to the requirements of the GHE postulate.

There is not any room for the postulate of a radiative GHE because observations from the real world, and mathematics, refute it.

The fact that the dry lapse rate of the atmosphere is -10 K/km, and not steeper, is a 100% refutation of the postulate of a radiative greenhouse effect.

The radiative greenhouse effect is predicated upon the requirement that it “destabiliz[es] the lapse rate through warming the lower atmosphere and cooling the upper atmosphere”.

That means that the greenhouse effect has to make the temperature gradient of the atmosphere to be greater than the lapse rate that is achieved by -g/Cp!  Yet, the lapse rate is not steeper than this, and, when the strongest greenhouse gas is present, the opposite occurs!

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### 19 Responses to Lapse Rate Refutes Radiative Greenhouse Effect

1. durangodan01 says:

Yes, it really is that simple! So we have dry air with a Cp of 1.01 kJ/kg K as our base case. Adding 2% water vapor with a Cp of 1.9 kJ/kg K raises this to about 1.028 kJ/kg K . For the lapse rate equation dT/dh = -g/Cp we see that this amount of water vapor reduces the lapse rate by nearly 2% just as reality exhibits. The effect of condensing water in an air column would further reduce this, but that’s beside the point. At 0.04% total CO2 in the atmosphere, the power of CO2 (Cp: 0.84 kJ/kg K) to increase the lapse rate is 0.03%. This is not measurable in terms of temperature effect! And once again this was considering all of the CO2, not the anthropogenic fraction.

2. Rosco says:

Hi Joe

It is simply amazing that people – even ones with PhDs, which I assume are virtually worthless in climate science and, while I quite like the guy, Roy Spencer is one of these – can make such an asinine statement such as that without greenhouse gases there would be no weather or no lapse rate !

Astounding – primary school children learn water forms rain – ie weather. So, yes, no water no weather – give the man a Nobel.

But they get even funnier when they claim a transparent non radiating atmosphere would be cold.

We have as close to a transparent non radiating atmosphere (if you believe climate scientists) in every significant desert location remote from the ocean as we are ever going to see.

All of these display a similar lapse rate, all have significantly hotter summer air temperatures during the day and most maintain significant air temperatures overnight even though it can drop quickly – although this may probably be an urban heat island effect as most desert weather stations are located in cities – eg Baghdad.

Every day even our “wet” atmosphere increases in temperature despite >97% not absorbing IR to any great extent and every day the surface atmosphere cools by converting kinetic into gravitational potential energy – ie a lower temperature. To claim surface contact and convection play no part in this is stupid beyond belief !

But how would a transparent non radiating atmosphere ever cool if it can’t radiate to space ? We all know O2 and N2 can get damn hot – over 50 degrees C – but if they can’t radiate to space how would they ever shed “heat” ?

And yet these clowns argue that a completely transparent non radiating atmosphere must be cold – below minus 18 C ?

How does academia allow this totally unsubstantiated nonsense to continue unchallenged ?

3. markstoval says:

This is a wooden stake right through the heart of they CO2 warms the surface monster. But we have driven so very many stakes through the heart of the monster and yet the idiots still believe in it. I despair.

The fact the “climate scientists” treat the earth as a two dementional surface rather than a rotating sphere is enough to show me they are fools. And this post just adds to that.

4. durangodan01 says:

Let me translate what Joe Postma has stated in this article into plain English for the mathematically challenged.

The sun heats the Earth’s surface and the warm surface conducts heat to the boundary layer of air immediately at the surface. This now warmer air expands and becomes buoyant compared to the cooler and denser air immediately above it. It rises through the cooler air and by this process convection is induced. As this parcel of air (of fixed mass) rises, it carries the fixed amount of thermal energy it received at the surface. In accordance with the Ideal Gas Laws, the air expands in direct proportion to reduced air pressure as it rises. In order to conserve the amount of energy in accordance with the Law of Conservation of Energy, the temperature of this parcel must drop because its energy content, which remains unchanged, is distributed within an expanded volume. Also, because this parcel of air is now located higher above the surface, it has greater gravitational potential energy and this too must be physically expressed by a lower temperature. The equation dT/dh = -g/Cp , derived by Mr. Postma, merely shows that air temperature resulting from a change in altitude declines in direct proportion to the increased gravitational potential energy and in inverse proportion to the average specific heat capacity of the parcel of air at constant pressure. This change in temperature with altitude is known as the lapse rate. For dry air with a specific heat capacity of 1.006 kJ/kg K, the lapse rate is 9.8 C per km of altitude above sea level. Water vapor with a Cp of 1.93 kJ/kg K, significantly greater than that of dry air, can only reduce the lapse rate. CO2 with Cp at 0.84 kJ/kg K can only raise it while methane with Cp at 2.22 kJ/kg K can only lower it. The National Weather Service releases about 70,000 radiosonde equipped weather balloons each year. An examination of the data compiled from these readings is all that is necessary to conclusively demonstrate that Mr. Postma’s equation exactly fits this huge data set. Insertion of a radiative greenhouse effect into this equation can thus only serve to make the equation less accurate. The RGHE theorizes that surface heat, rather than convecting from the Earth’s surface, is radiated to the sky and back again to the surface. Under this scenario, the sky would have to become cooler and the surface warmer which if true would increase the lapse rate above the historically known and unchanging dry air lapse rate. Again, the data will refute this. So what do we do now that the RGHE is empirically proven to be false? It is after all the foundation upon which all anthropogenic climate change rests.

5. For an alternative derivation, see the Wiki page: https://en.wikipedia.org/wiki/Lapse_rate#Dry_adiabatic_lapse_rate

Note that the approach is seemingly quite different than the approach I’ve used here (which I learned from Hans Jelbring), yet it ends with the exact same terms and who’s derivation is likewise completely independent of consideration of the effect of greenhouse gasses or the greenhouse effect. Fascinating.

Also note, Dan, that the reference to water vapour is that it creates the wet lapse rate, which modulates the dry rate down to -6.5 K/km, whereas GHG and GHE theory says it should have made the rate steeper!

6. durangodan01 says:

Joe, The alternative Wiki derivation was quite good until I went a bit to far and ran into this:
Thermodynamic-based lapse rate: Robert Essenhigh developed a comprehensive thermodynamic model of the lapse rate based on the Schuster–Schwarzschild (S–S) integral equations of transfer that govern radiation through the atmosphere including absorption and radiation by greenhouse gases.[13] His solution “predicts, in agreement with the Standard Atmosphere experimental data, a linear decline of the fourth power of the temperature, T4, with pressure, P, and, as a first approximation, a linear decline of T with altitude, h, up to the tropopause at about 10 km (the lower atmosphere).”[13] The predicted normalized density ratio and pressure ratio differ and fit the experimental data well.[citation needed] Sreekanth Kolan extended Essenhigh’s model to include the energy balance for the lower and upper atmospheres.

The Warmists certainly know how to cover the bases, but “comprehensive thermodynamic model”? Cmon!

7. Max™ says:

I suppose I should thank you, Joe, for helping me break my habit of tilting at strangely radiative windmills. I accidentally ended up starting into a tirade on the subject on another forum and just don’t care to try to sift through the folks who dismiss me off-hand, and the folks who think they agree with me but actually don’t.

The sad fact is these people don’t care. You try to show someone the facts about the atmosphere and heat exchange, even though it is good news for those you’d expect to be “on our side” they don’t want to let go of their radiatively insulative blankets.

Incidentally on the other threads I checked out just now I saw discussions about the Q = Th^4 – Tc^4 derivation.

The entire spectrum of a body a Tc lies below the curve of the Th body (barring weird spikes due to material properties) and thus is less energetic.

It is ok to describe a body at Tc to emitting photons towards a body at Th, and it is ok to describe a body at Th absorbing those photons.

There’s no magic rejection or sorting of photons taking place, but every time said Tc -> Th exchange occurs, there will always be a greater (in quality and/or quantity*) exchange in the Th -> Tc direction, and there will not be an increase of the internal energy within the body at Th as it is losing heat to the body at Tc.

*By which I mean 1 or more shorter wavelength/more energetic photon(s) leaving Th being “replaced” by each longer wavelength/less energetic photon arriving from Tc.

8. Nice to see you again Max. And yes you are right, and it makes this whole debacle absurd beyond the unrealistic – they don’t care, and they seem to have a fundamental and totally dominating inability to care or to think critically or rationally or consistently about it. People much smarter and more capable than us have come up with terms such as “pearls before swine” long long before us…and we’re not casting pearls.

9. jerry krause says:

Hi Joe,

Jerry

10. I’ll get back to you tomorrow Jerry.

11. jerry krause says:

Hi Joe,

I have scanned the references you included in this posting and I found no direct reference to observed data of any sort. Of course to refer to the lapse rate and not refer to actual observations is not unique to you. I have not yet discovered anyone discussing the lapse rate relative to the greenhouse effect referring the temperature inversions that are formed during cloudless nights as observed by atmospheric sounding made after midnight or a few hours later.

While I do not know where you live, I have read you are a Canadian. So I have just reviewed the sounding made at three sites (71722 WMW Maniwaki, 72747 INL Int. Falls, 71203 WLW Kelowna Apt) whose latitudes range from 48.3 to 49.9 degrees north during the nighttime for the past five nights.

Maniwaki
5/20 5.4C at 189m (surface), 14.8C at 498m, (maximum temperature of inversion) 5.8C at 1545m (Below the greatest altitude there are no temperatures, except that of the surface)
5/21 9.4C at 189m, 16.4C at 701m, 10.2C at 1519m
5/22 12.0C at 189m, 8.7C at 451, 9.8C at 914m, 7.2C 1524m RH(ice) 100+ 7200m to 7467m
5/23 7.0C at 189m, 16.2C at 437m, 7.9C at 1829
5/24 8.8C at 189m, 19.0C at 591m, 10.3C at 1829m

Int. Falls
5/20 9.4C at 357m, 16.8C at 728m, 10.4 at 1523m
5/21 9.8C at 357m, 18.4C at 683m, 11.2C at 1560m
5/22 9.2C at 357m, 20.4C at 551m, 11.8C at 1524m
5/23 19.4C at 357m, 18.2C at 610m, 11.8C at 1418m 99-100% RH 2249m to 4469m
5/24 12.8C at 357m, 18.6C at 868m, 13.6C at 1457m

Kelowna Apt
5/20 9.0C at 456m, 6.4C at 914m, 3.0C at 1425m
RH 98+% at 1425m to 1502m
5/21 10.2C at 456m, 7.8C at 914m, 4.4C at 1400m
RH 98+% at 1555m to 3048m
5/22 11.2C at 456m, 9.8C at 914m, 4.2C at 1524m
RH 98% at 2743m to 2951m
5/23 11.6C at 456m, 9.0C at 914m, 4.2C at 1524m
RH 98% at 2743m to 2965m
5/24 12.0C at 456m, 10.0C at 914m, 4.0C at 1762
RH(ice) 98+% at 3658m to 3726m

The implications of this sounding data seems to be self-evident. And it easy to find, in other sounding data, nighttime temperature inversions when there is no indication of cloud cover and no temperature inversions when there are indications of cloud cover.

Have a good day, Jerry

12. jerry krause says:

Hi Joe,

I have discovered I posted comments related to the previous post here to your post Slayer Double Victory on 5/25/2016 at 1:11PM.

Have a good day, Jerry

13. nabilswedan says:

Joe, this is a good demonstration. You will find it stated in words under discussion of
Swedan, N. (2015) Anthropogenic and Natural Forcings as Functions of Emission Time. Development in Earth Science (DES) 3, 1-7.

14. PA says:

durangodan01 says:
The Warmists certainly know how to cover the bases, but “comprehensive thermodynamic model”? Cmon!

“Sigh”. Essenhigh is a mechanical engineering professor with BS/MS degrees in “Natural Science” and a PHD in “Fuel Technology and Chemical Engineering”.

He explicitly does not believe in global warming theory.

http://www.desmogblog.com/robert-h-essenhigh
“On the issue of carbon dioxide and global warming, the question at issue really is, ‘Does carbon dioxide emissions from fossil fuel combustion cause global warming?’ There does appear to be a common consensus view; but, the available data not only does not support this common consensus view, but supports the contrary position.

Yeah, he probably has developed a fairly accurate model since engineering applications (unlike science applications) need accurate models. No, it probably doesn’t support warmist claims.

15. Chic Bowdrie says:

“When even Google gets the definition so wrong, how can mere mortals be expected to understand it?”

Dr. Spencer asks the wrong question. How can anyone discuss the greenhouse effect without explaining what their definition of it is? By inference, I assume the definition adopted in this post is that of a concept which does not exist. Dr. Spencer’s definition apparently involves radiative transfer processes causing Earth surfaces to be warmer than they would otherwise be without IR-active gases. A more basic definition is one that makes no assumption about reasons the atmosphere is generally cooler above than below.

It is no use to argue that radiative processes should make lapse rates greater than theoretical when your opponent believes the atmosphere would be isothermal be it not for the radiative convective processes. Allegedly, radiative transfer alone produce lapse rates greater than theoretical, while convection and evaporation bring the lapse rate down to those observed.

16. Jan Stunnenberg says:

It should also be noted that the reason for the difference between dry- and wet lapse rate, is because H2O on earth, is not an ideal gas. The ruling Law is for ideal gases only.
H2O exist in all 3 phases, gas (steam), fluid (water) and solid (ice) on earth.
Phase changing binds, holds and releases lots of latent energy and is so decreasing the dry- into a wet lapse rate. Greenhouse gases do not exits. There are however ideal- and non ideal gases. Whether a gas is ideal or not, depends on the temperature range of any planet.
Trying to explain earths atmosphere temperature with ‘radiation physics’ can of course be done.
As long as the outcome is the same as by just simply applying the ‘Gas Law’, its fine.
But why should you even try? Occam told us not to do so.

17. Before I had brushed up on my O level grade B maths and physics. Before I had read any work’s from Slayers or any other skeptic. I had gone back to my earliest memory of hearing about a “runaway greenhouse effect”, which was on Carl Sagan’s show Cosmos when I was 11 years old about the planet Venus. One look at the basic information of Venus’s atmosphere created the greatest paradigm shift of my life. A lifetime of support for Greenpeace and Green political groups disappeared in an instant. To me is was so blindingly obvious. 96 times the atmospheric mass, slightly less gravity and 92 times the surface pressure of earth. I cannot understand how any educated person could not see the obvious link to temperature.
It has taken me a few years to understand the physical mechanisms and maths behind them and I rarely trust myself to reproduce the maths in debate but this is as obvious to me as it is to the boy who saw the emperor had no clothes on. I feel like that little boy. I have had so many arguments with people with PhDs now. The more I do it, the more convinced I become that the education system is broken. I am so glad I slacked off at school after age 16 and kept my mind independent.

18. Always lovely to hear a story of awakening wickedwenchfan. Indeed, the more you argue with them the better you become, and the more you exceed them and realize just how absolutely ridiculous, stupid, and unconscious they are!

Sounds like your mind is switched ON 🙂

Perfect!