Yesterday I proved that global temperature is controlled by the equation:

T_{0} = L.h_{trop}/{1- (P_{trop}/p_{0})^(R_{0}.L/g.M)}

Where

p = pressure at height h (pa) .. or …

P_{trop} = pressure at troposphere (assumed to be 0.1bar)

p_{0 }= pressure at surface (pa)

L = Lapse rate (=g/C_{p}) (J/(kg.K)

h = height (m)

T_{0} = Temperature at surface (k)

g = gravity (m/S^{2})

M = Molar mass of dry air (0.0289644 kg/mol)

R_{0}. = Universal gas constant (8.31447 J/(mol.k)

This apparently shows that the temperature at the surface is purely a function of pressure and gas constants and is not related to solar radiation. This goes a long way to explain the apparent relationship found by Ned Nikolov & Karl Zeller.

Now, however, I will try to demolish that “proof”. Let’s start by finding those that are determined by fixed attributes of the planet, its gases, gravity etc.

### Pressure

Is simply the gravity times the weight of atmosphere over a unit area. So it is:

p = n.M.g / Surface area of planet

Where n is total mols of atmosphere so n.M is total mass.

### R_{0}.L/g.M

As I showed yesterday this can be expressed purely in terms of heat capacities of the atmosphere:

(R_{0}.L/g.M) = (C_{p} – C_{v})/C_{p} = 1 – C_{v}/C_{p}

where *c*_{p} is the specific heat for a constant pressure and *c*_{v} is the specific heat for a constant volume. And because lapse rate L = g/C_{p} (gravity divided by specific heat capacity for a given mass)

### Lapse Rate

Is the rate at which potential energy is converted to heat and is the energy used to raise a kg of gas, divided by the energy needed to raise one kg of gas by one degree. So it is:

L = g/C_{p}

**“when you have eliminated the impossible, whatever remains, ***however improbable*, must be the truth”

*however improbable*, must be the truth”

There is only one parameter left and this is (as I describe it) the troposphere height. However, if could be any arbitrary height in the atmosphere so long as we also know the pressure. What this shows is that there is a close relationship between the height of a particularly pressure level and the temperature.

In effect, the planet itself is acting like a huge bulbous thermometer. As the ground temperature rises, the activity of the gas increases, the pressure is set by the mass of air, so there is only one way to adjust and that is for the volume of the atmosphere to increase. So as radiation heats the globe, the atmosphere expands such that the same pressure level is found further from the surface.

However … this now provides an ideal way to assess global temperature:

## The use of isobaric pressure height to determine global temperature

For a constant global temperature, the height of a particular pressure level will be the same. That also means that if we know the height of the 0.1bar “isobar” (and ground pressure & gas composition of atmosphere) we can work out the surface temperature. **However, it also means that if the relationship between pressure and height remains constant, then there has been no change in global temperature.**

There is a international standard agreement on the relationship between pressure and height: ISO 2533:1975 which apparently has not needed to be changed since 1975. And I can find no suggestion that the relationship has changed. Proving:

- Alarmists don’t understand atmospheric physics

(otherwise they’d have adjusted the standard just to make the point). - There has no been a significant change in global temperature

(otherwise they’d have had to adjust the standard even if they didn’t understand why)

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“It’s an interesting equation – I’d be interested to see whether you agree with the general view on the next article”

(“It’s an interesting equation – I’d be interested to see whether you agree with the general view on the next article”)

“Pressure Is simply the gravity times the weight of atmosphere over a unit area. So it is: p = n.M.g / Surface area of planet. Where n is total mols of atmosphere so n.M is total mass.”

I have no idea why you even think Earth’s atmosphere exhibits ‘weight”, the atmosphere is everywhere self-buoyant. Instead under the compressive force of gravity acting on the mass of the compressive fluid atmosphere, is expressed statically (no phase change or expansion) by the results in a gas law triplet of density, pressure, and temperature. Density and pressure lapse rates with altitude are exponential functions each with its own exponent. The ratio of those two functions results in an almost linear temperature lapse with altitude. This is sometimes called in meteorology the dry adiabatic laps rate (dalr) for no understandable reason.

The pressure at any altitude is indeed a function (product)of both gravitational attraction and the columnar mass, however, for pressure such has a theoretical scaling factor of PI, due to projective geometry. Thus meteorology claims an air-mass three times what it actually has. Can’t do better accuracy than that as air-mass refuses to be ‘static’. Surface pressure (sea level) seems to everywhere remain at 101,325 Pa ±35 Pa except for extreme weather. No one knows why surface pressure remains so very stable! Meteorology has many many fantasies about such, none demonstrable!

“ISO 2533:1975 which apparently has not needed to be changed since 1975. And I can find no suggestion that the relationship has changed. Proving:”

Absolutely nothing of how this atmosphere operates! It is never the actual pressure, temperature lapse at any location. ISO 2533 is a committee agreement as to the required calibration of aircraft barometric altimeters. Once so calibrated aircraft operating at different “indicated” altitudes cannot collide. This is quite separate from actual height above sea level. Any other use for the USA std atmosphere, may have a political function but never a scientific reason!

Mike, I try to express here how very little is known about about earth’s atmosphere. Perhaps we should ask the Albatross and Eagles!Scottish Sceptic, thanks for taking the time to post this interesting consideration of atmospheric physics. In considering this matter I suggest it is useful to try to apply any formulae or theory derived for our own planet to that of another, specifically Venus. We have, from NASA probes, accurate information on height,pressure, temperature in the Venusian atmosphere. Many of us will know that Venus has an atmosphere of 96.5% CO2 and has clearly therefore suffered an exceedingly catastrophic case of extreme thermal runaway from the Greenhouse Gas Effect of the dreaded CO2 which has resulted in a VERY hot surface temperature (go look it up if you don’t know).

So if we apply your maths to Venus we will be able to see how the ACTUAL OBSERVATIONS of temperature, pressure, height for a nearly pure CO2 atmosphere are far removed from your theory thus proving the massive effect of the GHE.

Or possibly not.

Have a go with the maths and the actual observations on Venus and let us know what you find . GHE or no GHE ?

Hi Badger, as I show in the previous post (http://scottishsceptic.co.uk/2017/03/27/predicting-planetary-temperature-without-referring-to-radiation/) using very “off the shelf” data the temperature of Venus is not that different from what you would expect from the equations.

What this shows is that Venus is very stable and has at no time suffered any “runaway greenhouse effect”. Instead it is the stable temperature it would always be with that atmosphere.

Indeed, when you get to an atmosphere that thick a “greenhouse” is such a bogus analogy that it gets to be laughable – only fit for “cartoon science”.

The problem with the radiation “capture” model is that it takes no account of the atmospheric temperature – the temperature is in effect ignored. So as a first approximation (because the atmosphere is cooler), it behaves at a first glance like it is “capturing” IR. But when you get a thick atmosphere like Venus, almost non of the radiation goes direction from the surface out to space. So the effect of the atmosphere is no longer a minor change in what escapes, instead almost all the IR leaving the planet originates from the atmosphere – do then you’ve got to include the temperature of the atmosphere in the modelling and calculations.