I have spent another few days trying to reconcile all the logical and mathematical contradictions in Alarmist climate science, and it is impossible. You nail down one contradiction and try and find out how they reconcile it, only to find two more sticking plasters of logic (usually different people advancing opposite theories to explain the same thing, at least one of which must be wrong). Then you try and reconcile the sticking plaster contradictions to find two more papering over those cracks, and so on *ad infinitum*. Strip them all away, and there is pretty much nothing left.

We all accept that the actual average sea-level temperature of the Earth (288K) is about 33K higher than its 'effective temperature' i.e .what it would be if Earth had no atmosphere (255K). That's basic physics - average incoming solar radiation in W/m2 minus amount reflected as light (a known figure) raises temperature of the surface to whatever it needs to be to radiate the same amount W/m2 back out to space.

The Alarmist view is that the surface converts short wave visible radiation to longer wave infra red radiation, and this is trapped/absorbed or reflected by 'greenhouse gases' (minor trace gases such as the +/- 2% water vapour or 0.04% CO2), which in turn warms up the surface even more, so it emits more infra red in a vicious circle. Parts of that explanation are actually true, but the precise mechanism (conduction, convection or radiation) is fairly irrelevant as we shall see. Suffice to say, we know how many W/m2 come in from the Sun, and we can work out the 'effective' temperature of the surface.

Anyway, I am sick and tired of the topic now, and hopefully this will be the final time I feel compelled to address it.

Actually, it is all very easy and you can pretty much work out the reason for the 33K discrepancy for yourself, once you've sifted out the hard physics from the bullshit. They could and should teach this as part of GCSE level physics, it wouldn't take more than two or three lessons.

__A. Barry__

__
__ You can easily work out that there are about 10,000 kg of air (101,325 Pascal ÷ 9.807 m/s/s) for every m2 surface. We know that 1 m2 of air at sea-level has a mass of 1.293 kg. So if atmosphere were same pressure and density all the way up, with a hard edge, it would be 7.7 km high.

You can guess intuitively that the atmosphere gets thinner as you go up and gradually tapers off into space and that there is no hard edge. So let's assume actual average pressure (and density, which is closely correlated but not the same thing) is half that at sea-level, a reasonable guess is that most of the mass of the atmosphere is up to an altitude of 15 km or so (which is not far off).

If you want to calculate this properly, you use the Barometric Formula (or 'Barry', as I affectionately call it) which is based on actual ideal gas laws and gives you reasonably accurate predictions for pressures at different altitude, at least for the troposphere (which is all we really care about, i.e. is the bottom 11 km, others say bottom 13 km, it's thicker at Equator and thinner at the Poles). The formula is very clever. I can just about understand how they work it out, but I would struggle to reverse engineer it or explain how to derive it.

__B. The lapse rate__

More basic physics. Remember that 'energy cannot be created or destroyed, it merely changes from one form to another'. Air at sea level as thermal energy (aka kinetic energy) and no potential energy (it can't fall any further down). Air higher up has the same amount of total energy - less kinetic energy and some potential energy. it is reasonable to expect the total amount to be the same at different altitudes.

Once you accept this, you can work out the lapse rate. I'll show you how, just for fun and

**because it is important**:

Potential energy in Joules = mass x gravity x height.

So J = m x g x h

Joules required to increase temperature of 1 kg of a substance by 1K = specific heat capacity ('cp' )of that substance.

So J = T ÷ (m x cp)

We can simplify those two equations to T/h = g/cp

(Thanks to Tallbloke for this short-cut)

1kg of air which is 1,000 metres higher up has got = 9,807 more Joules of PE, 9,807 J less kinetic energy than 1kg at sea level..

Specific heat capacity of air = 1,006 J used to increase 1 kg of material by 1K

How much warmer is the air 1,000 m (i.e. 1 km) lower down? It has used/converted 9,807 J from PE to kinetic energy.

T/1,000 = 9.807/1,006

T = 9.75.

Hence the predicted lapse rate = 9.75K/km altitude.

(Personally, I think it makes more sense to use the cp for constant volume rather than constant pressure, and to calculate J/m3 rather than J/kg, which is why the lapse rate I worked out was 8K/km, which is actually slightly closer to the real world measured typical rate of 6.5K/km).

__C. What is the surface of the Earth?__

The Alarmists give a nod to Barry and the real reason for the lapse rate. They don't deny they exist, they give the formulas but then downplay them as irrelevances and draw no conclusions from them. It's all about radiation from the surface being reflected by those dastardly 'greenhouse gases'!

Their most heinous and borderline criminal obfuscation is in their definition of the 'surface'. They define 'the surface' as the hard surface or sea level.

Here's are a few reasons why that is wrong:

1. If you approach Earth at speed from space, you feel it when you hit the atmosphere. That is the real surface.

2. If you scale down the earth to the size of a football, the atmosphere is only 0.2 mm thick.

3. There are about 10,000 kg of air (mass) for every m2 surface. (see above)

4. The sun only warms the top few inches of the hard surface (or water), that's a few kg of mass per m2. So if the atmosphere is 0.2mm thick, the hard surface or sea-level is barely a couple of molecules.

5. So as far as heat distribution goes, we might as well treat the top few inches of the hard surface as the bottom part of the troposphere.

6. So the real surface is the troposphere, not the hard surface or sea-level.

__Conclusion__

The troposphere

*is*the surface, and as a whole and on average, is the temperature you would expect from incoming solar radiation = 255K. This is what you would expect, and this is what you get. I don't see why anybody taking this view should be on the defensive in a discussion. It is those trying to say otherwise who are struggling.

The troposphere itself, it is not a constant 255K. There has to be - and is - a lapse rate, so it's 33K warmer at the bottom (the hard surface or sea level) than at the middle/the average, and the top of the troposphere is also about 33K cooler than the middle/average.

__Bonus__

This A-B-C easy GCSE-level approach also explains a lot of things which the Alarmist explanation can't and doesn't (and by and large, just glosses over to save embarrassment), for example:

1. Why the top of the troposphere (or the peaks of a very high mountain) is colder than the 'effective' temperature, i.e. colder than it would be if Earth had no atmosphere.

2. Why the day/night temperature range on Earth (+/- 15K) is so much smaller than the day/night temperature range on the Moon (+/- 300K).

3. Why, despite the 'greenhouse effect', Earth's day-time temperatures at the surface are

*lower*than what they would be without an atmosphere.

4. Why the 'greenhouse effect' is much stronger at night (i.e. actual temperature minus expected temperature of the night side of Earth if it had no atmosphere) than in the day time (when the Sun is blazing down on us).

5. Why 'heat rises' is a truism only observed in enclosed spaces kept above the temperature of their surroundings (central heating in buildings) and why convection doesn't actually transfer heat upwards. For sure, there are thermals above hot surfaces (like square miles of dark tarmac at airports, which can make landing trickier than it need be on hot days), but for every molecule that goes up, one has to come down. One molecule converts kinetic energy to potential energy and the one coming down does exactly the opposite.

6. Why there is no need to get tied in knots over which methods energy (in its various forms - kinetic energy, potential energy, latent heat of evaporation/condensation etc) is distributed in the troposphere (conduction, convection or radiation). Energy tries to distribute itself as evenly as possible (governed by the physical laws discussed here, or by winds, if you want an everyday term for a really complicated process)

7. Why it is irrelevant that N2 or O2 are transparent to, and cannot absorb or emit infra red (even if this were true, which is questionable). They can certainly warm up, and they in turn keep the hard surface or sea-level at the same temperature. So even if N2 and O2 aren't emitting infra red themselves, the hard surface or sea-level converts that warmth back to radiation anyway. The total infra red leaving the surface is the same whether it is bouncing back and forth as infra red between hard surface or sea-level and troposphere (the Alarmist theory), or whether the hard surface or sea-level has to convert kinetic energy from N2 and O2 back into infra red first (the actual explanation).

8. Why there is a lapse rate on all planets with an atmosphere, even Gas Giants (Jupiter, Saturn), which have no hard surface (and if they do, radiation from the Sun never gets there) and which consist mainly of non-greenhouse gases (mainly hydrogen and helium); why they are insanely hot at their centres; and why those Gas Giants are actually emitting more radiation to space than they get from the Sun.

9. Why the 'greenhouse effect' on Mars is barely measurable (max 5K), even though there is forty times as much CO2/m2 surface area than there is on Earth.