More circular logic from the Science Deniers

I submitted my simple explanation as to why Earth's average surface temperature is what it is* over on hard-core pseudo-scientific Alarmist website Science of Doom.
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* Skip to next dashed line if you are familiar with this explanation, but here's the crash course:

A planet will settle at a temperature so that it is emitting as much LW radiation to space as it gets in SW radiation from its sun. On earth, only the cloud tops and the cloud free sea/land can directly absorb solar radiation coming IN (this is an agreed amount, 240 W/m2 average), and the self-same cloud tops and the cloud free sea/land surface have to emit the same amount of IR radiation directly OUT to space. Cloud tops and sea/land HAVE TO settle at the temperatures they are to maintain this balance.

There is a separate closed cycle that operates between clouds and the sea/land below them, which can be ignored when we look at LW going to space (yellow box in my third diagram in the first link). However this closed cycle works (it's heinously complicated), it will always be overridden by the fact that the temperature difference between sea/land and cloud tops is dictated by the lapse rate, which in turn is dictated by gravity; the specific heat capacity of the atmosphere; and the impact of the latent heat of evaporation (plus/minus a few other bits, like geo-thermal or electrical energy).

Imagine the lapse rate like the surface of a still reservoir. The water surface will be level. If you pump water from one end to another, it will not change the 'flatness'; the water will just sink back in the opposite direction and end up level again. Similarly, the atmosphere can 'pump' as much radiation energy down as it likes (cooling things higher up and warming the sea/land); an equal and opposite amount of energy will flow back up again to reinstate the fixed and known lapse rate (cooling the sea/land and warming things higher up).

Maybe the sea/land warms up the air above it by conduction/convection, which in turn warms the air above that, all the way up? Maybe there's more evaporation from the sea/land? Maybe the sea/land just reflect the radiation back up? Overall effect as measured by thermometers = net nothing.

And surely, it is only absolute temperatures that we care about, not the precise mechanism of how it happens?
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On with the story.

The comments and replies are difficult to follow because of nesting of replies-to-replies and because they simply deleted some of my replies. They started off by just calling me a Climate Denier etc, but one commenter, Frank, humoured me. His first attempt was "Why do you assume that cloud emissivity is 0.7? The Climate Models assume 0.95 or 1.0?" I just looked this up from sources dating back to the 1970s, when scientists wanted to find out stuff with being prejudiced as to the answer. I put him straight with half a dozen references and his last response is this:

Mark: There are two energy balances you need to deal with: the energy balance across the TOA and the energy balance at the surface. The [Kiehl and Trembert] energy budget has both. The existence of DLR is only important to the surface energy balance. You can only “prove” DLR doesn’t exist or transfer heat to the surface by studying the energy balance AT THE SURFACE.

I never said that there wasn't any downwards longwave radiation. I just said that you can ignore it when estimating likely temperatures - see my level reservoir example.

Energy balance across the TOA is the simplest because you only need to deal with radiation, which in principle can be calculated given the known temperature and composition of the atmosphere.

This seems to be his tacit admission that my simple calculation is in fact correct.

Calculating the energy balance at the surface is more complicated, because you need to add convection of latent and simple heat and DLR to the energy fluxes arriving at the surface. You completely ignore latent and sensible heat, and therefore CAN’T DRAW ANY CONCLUSIONS ABOUT DLR!

'Energy balance' is in fact very easy because you don't need to worry about what type of energy it is. You can work out from sea/land upwards, layer by layer, how much total energy each layer has - mainly thermal energy (warmth), with significant amounts of potential energy (gravitational energy - which goes up with increasing altitude/falling temperature) and latent heat (which is highest immediately above the oceans and tails off as you go up when gaseous water vapour releases that energy again by condensing).

And you find that the total energy at all altitudes in the troposphere is exactly the same, which is what you'd expect, it's like entropy. Radiation is just one of many mechanisms that works towards that balance, making sure that the lapse rate is maintained, radiation energy itself is not conserved or stored and does not show up in the overall balance (don't confuse stocks with flows!).

(NB This energy balance does not hold in the stratosphere, where the sunshine warms things from above when ozone absorbs it (converts it to thermal energy), so total energy goes up with increasing altitude - up to the point where the air is too thin and there is no measurable ozone. The same as oceans, which are warmed by sunlight from the top down. Water is not a gas, so there is no lapse rate. Again, red herrings.)

So... he believes in some magically self-reinforcing one-way energy transfer system and ignores all the other effects that cancel it all out again. it's like believing in the sloping water surface on a reservoir -and that once you have got a slope, it will become ever steeper of its own accord and you can turn off the pumps. Sorry, not good enough and it's obviously nonsense. It's an answer desperately looking for a question.

Onwards, ever onwards!

When being wrong has never felt so right.

At the very least, the correct answer should be "All four answers" but strictly speaking, it would be "All five answers" because the answer "All five answers" is itself correct.

Not comparing like with like

From the BBC:

Every year they stop an estimated two to three million deaths, preventing more than 20 life-threatening diseases, according to the World Health Organization (WHO).

Childhood illnesses that were common less than a generation ago are increasingly rare. And smallpox - which killed hundreds of millions of people - has been completely eradicated.

But these successes have taken decades to achieve - and many of us are now expecting effective coronavirus vaccines to have similar results in a radically shorter time frame.

Of course it took decades, because vaccinations against diptheria, whooping cough and measles were just given to young children on reaching a certain age, and it took a few decades before mass immunity against each of these was achieved.

If the UK government and/or NHS get things sorted out and manages to vaccinate [nearly] the whole population within a year, then surely we'll achieve in a year what used to take decades?

Those vaccination priority groups

There's some interesting discussion about this on gov.uk.

Broadly speaking, it makes sense to work backwards from the statistics on likelihood of death/serious illness and vaccinate people accordingly. So care home residents and their carers first; then frontline NHS staff and the over-80s; then over-70s and so on. NHS workers aren't particularly at risk, but a) they look after their own and b) they get vaccinated against and tested for all sorts of infectious diseases as a matter of ethos - it's not a good look to infect your own patients. Bus drivers (who were disproportionately affected) don't get a mention, poor sods.

The original discussion also pointed out that people in 'BAME groups' are more likely to die or become seriously ill than whites, so maybe they should get priority. It didn't actually mention the fact that men seem to be worse affected than women, but the same principle applies. Neither of these factors made it through to the final priority list, which is a bit of a slap in the face.

They should have done a proper points system. Age-based points with additional points for BAME people and men. So, for example, a 50-year old black or Indian guy; a 55-year old white guy (i.e. me); and a 60-year old white woman rank rank equally and get invited for their jabs at the same time.

This would be the sensible thing to do, with the bonus fun factor that we'd see a bizarre coalition of racists and feminists whining and moaning! And probably the SJW finding some angle to moan about (it's condescending to BAME groups; it suggests that they can't look after themselves properly?).

Can you believe in six impossible things before breakfast?

I've done a lot more Googling and reading up on ozone depletion theory since I stumbled across it a couple of weeks ago. It seems to be a very plausible and mercifully simple explanation why the troposphere (lower atmosphere) has warmed a bit and the upper atmosphere (stratosphere) has cooled a lot over the past forty years. It might be correct, it might be nonsense, but it does appear to be the most likely explanation and the most worthy of investigation and exploration.

Most of the hits you get if you search the terms 'ozone depletion' or 'stratosphere cooling' are Alarmist websites and blogs (for example Skeptical Science and Science of Doom), all of which greatly play down the effects of ozone depletion.

Nonetheless, stratospheric cooling is A Thing, and the Alarmists see themselves obliged to explain it in terms of CO2 and radiation (for no obvious reason).

Do your own reading up and make up your own mind, but IMHO, here are the six impossible, or at least mutually contradictory, things Alarmists have to believe before breakfast:

1. CO2 'traps' some of the infra red radiation (IR) emitted upwards by land, oceans and clouds in the troposphere

As a result, the troposphere warms. To believe this, you have to ignore the fact that radiation does not have a temperature and is not thermal energy. Radiation has to hit something first, cease to be radiation and be converted from radiation to thermal energy ('energy is not created or destroyed' etc). You also have to ignore the fact that the total IR emitted to space is equal to the total IR emitted by land, oceans and clouds (give or take a couple of per cent, depending which assumptions you make - nobody knows and it's impossible to prove or disprove either way).

And as a secondary result, there is less radiation going up into the stratosphere, so the stratosphere cools. To believe this, you have to ignore the fact that the stratosphere is warmed from above by UV-C and UV-B interacting with oxygen (O2) and ozone (O3). Accepted science is that the high energy UV radiation split molecules, so the energy is converted to chemical energy (endothermic reaction), and when O and O2 recombine to form O3, the chemical energy is converted to thermal energy (exothermic reaction). There appears to be little interchange of thermal energy (whether by convection or radiation) between troposphere and stratosphere. That is why the temperature falls to its lowest at the tropopause (the boundary layer between the two).

2. The effect of more CO2 is to push the 'effective emitting altitude' (henceforth abbreviated to EEA to save me typing it out in full every time) upwards

This is a more sophisticated Alarmist theory than simple 'trapping'. It dismisses the 'trapping' idea and says IR at certain frequencies can only escape to space if the CO2 above it is less than a certain threshold in terms of density. CO2 is a fairly constant proportion of the atmosphere all the way up (about 1/25 of one percent) but the density of the atmosphere goes down as you go higher, and so does CO2 density per unit volume. Only IR emitted (by CO2 itself, natch) at or above the EEA at which CO2 density (in terms of CO2 per unit volume) is at that certain threshold can get to space. So more CO2 means the EEA is at a higher altitude.

This theory seems to accept the gravito-thermal effect aka the lapse rate. It also assumes that temperature and hence IR emitted at the EEA is a constant, so mathematically, if the threshold is one-sixth of a km higher (so it goes up from 5km to 5.166r km, for example), the surface is warmer by one-sixth of 6.5 K/km = about 1 degree warmer.

OK, but going back to 1, if the EEA is the same temperature and is allowing the same amount of IR to pass through and up, then the same applies to the tropopause (about 10 - 12 km up on average). If the stratosphere is warmed from below (which isn't true anyway), the lowest layer of the stratosphere would remain the same temperature. Which it clearly isn't doing. And we have a problem with the initial assumption that IR emitted at the EEA or tropopause goes out into space (instead of warming the stratosphere above it).

3. More CO2 in the stratosphere means it can radiate more out into space

According to this theory, nothing except GHGs can emit radiation (well apart from land, oceans and clouds, obvs), and certainly not nitrogen or oxygen/ozone. So you could heat air up as warm as you wished, and an IR thermometer would not be able to read a temperature. So all that thermal energy would be 'trapped' in the stratosphere. Along comes some extra CO2, which absorbs the thermal energy, turns it into radiation and biffs it up and out into space, it being above the EEA.

Or maybe it biffs some down into the troposphere to warm it a bit more. Apart from the fact that the net transfer of energy by radiation only goes from warmer to colder, and how does this radiation battle its way down through the EEA, which is impassable for radiation from below?

Either way, there is a neat double think that CO2 can 'trap' more radiation in the atmosphere and also  emit more out into to space.

4. If 2 and 3 are true, then perhaps there are two EEA's?

Theory 2 is based on the fact the temperature falls as you go up through the tropopause. Push the EEA higher and that leads to surface warming. Perhaps Theory 3 is that there is a separate EEA for the stratosphere. If you push this higher, by reverse logic, everything below the new EEA cools down a bit?

5. The troposphere and stratosphere are in thermal equilibrium. Or not, as the case might be

If the temperature of the two layers tends to even out (by layers emitting radiation at each other), then we wouldn't see one warming and the other one cooling. So that blows a hole in Theory 1. Unless CO2 increases the lapse rate. Even though the main GHG, water vapour, reduces the lapse rate. On the other hand, Theory 2 assumes that there is a 'sort of' thermal equilibrium i.e. the temperature at the tropopause stays constant, but only a weak link, so below and above that altitude, each layer does its own independent thing. But if the stratosphere above does its own thing, is that not a tacit admission that it is warmed from above?

This obsession with radiation as the main form of energy transfer in the atmosphere is baffling anyway. Simple conduction and convection are far more important:
- To feel the temperature of a warm object (poorly child's forehead or hot water bottle), you have to actually touch it = conduction.
- Put your hand one inch to the side of a hot object (hot radiator, candle flame etc) = radiation; then put it one inch above that object = convection, which feels a lot warmer than one inch to the side.
- You have to get really hot, like a bonfire, for radiation to outweigh conduction, and even then, it's a lot hotter directly above it (convection + radiation) than to one side (radiation).
- The atmosphere is on the whole a lot cooler than a poorly child's forehead, so we can safely assume that the majority of thermal energy transfers are by conduction and convection.

6. CO2 has a 'fingerprint' which can be observed from space. Or not, as the case might be.

The Alarmists make great play of the fact that CO2 absorbs (and emits) IR at wavelength 16 microns (sometimes expressed as 667/cm or frequency a bit less than 10^13 Hz) and that if you measure terrestrial radiation with satellites, there is a noticeable gap at that wavelength. Theory 1 says that if there is more CO2, that missing bit will be larger. But if Theories 2 and 3 are correct, then the extra radiation emitted by CO2 in the stratosphere above the EEA (whichever one) ought to fill up that gap again.

As a final thought, let's imagine a counter-factual where CO2 levels are increasing (true) and the stratosphere were warming instead of cooling. Would the Alarmists shout 'slam dunk!' or would they accept it as evidence against their basic assumption that CO2 is to blame for everything? It's poor science to look for evidence to support 'your' theory or even 'a' theory. You have to remain open minded and look for evidence against as well as for, or accept that you were barking up the wrong tree.
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Anyway, happy New Year's Eve to anybody who has read this far. I think I shall celebrate Indian New Year in half an hour (6.30 GMT) and then call it a night.

Lockdowns and the Sherlock Holmes principle

The Sherlock Holmes principle is, once you have ruled out the impossible, the remaining explanation, however unlikely, must be correct.

Applied to the question of what degree of lockdown* to impose, first you rule out the strategy that is doomed to failure, then you adopt the one that's left by default, however slim its chance of success might seem.

There are two basic strategies:
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1. The Swedish/Brazil "hope for the best" herd immunity strategy - this might or might not have been a good strategy given the lack of clear information at the time**. But it always had a theoretical chance of working and, with the benefit of hindsight, seems to be working, especially if you take into account the economic, social and educational damage that such countries have avoided. This of course involves the elderly and vulnerable voluntarily self-isolating, and it will cost money to employ people to do their shopping etc for them, but that is a small cost compared to the economic etc damage caused by a full lock down.
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2. The "suppress infections until a vaccine comes along" strategy which cannot ever work. I can sort of see the point of "flattening the curve" but they've done that. The NHS wasn't swamped and isn't being swamped.

a) Even if they develop a vaccine that works (unlikely) at some point in the future (months? years?), are we all going to take it (no)?

b) If immunity is only a few months after having caught it (the arguments AGAINST the herd immunity strategy), then the same will apply to people who have been vaccinated. So this will require endless repeat vaccinations.

So strategy 2 can only ever be delaying the inevitable and can never succeed.
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Ergo, given a choice between a strategy that MIGHT work (and appears to be doing so, with the benefit of hindsight) and one that CAN'T POSSIBLY work, surely you choose the former?

* It is a question of degree. Some things appear to worth trying where the economic cost is minimal, for example banning large gatherings (concerts and football matches); turning down music in pubs; face masks on public transport; encouraging people to work from home. Testing people for coronavirus after they get off an airplane or boat misses the point - it makes more sense to test people before they get on at the other end and to turn away passengers who test positive. Not sure on the logistics of this, but that's the principle.

Things like shutting pubs at ten o'clock are insane. Is the virus more infectious later in the evening? I think not. People under 30 are barely affected, so shutting schools and universities is also insane. The older teachers and lecturers will just have to take a sabbatical.

** The best information we had was the Diamond Princess. That was pretty much a Petri dish. 15% of the 1,045 crew tested positive and precisely none of them died (being presumably young and healthy). Twenty percent (or should I say "only twenty percent"?) of the 2,666 elderly passengers tested positive and twelve had died between the first positive test in early February and the end of March when most lockdowns were imposed (two more died in April).

Scaled up to the UK, we'd expect to see around 50,000 deaths among the elderly in the first two months, which is not far off the actual outcome. To paraphrase Prof Michael Levitt, that was the Grim Reaper taking all the people who would have died during the previous two years' flu seasons, but didn't because they were very mild. A year ago, UK undertakers were worrying about the low number of funerals!

Seriously, can anybody explain this?

From the BBC:

Employed or self-employed people who test positive for the virus are required to isolate for 10 days, so those eligible for the extra money will get £130. But members of the household of someone who has tested positive, who must self-isolate for 14 days, will be entitled to up to £182, assuming they also qualify for the payment.

As regards the £13 a day, we should be paying (or at least offering) that to everybody as a Citizen's Income anyway.

Once more unto the motherlode...

From Skeptical Science, another failed debunking which is so piss-poor that it makes whatever it is they are trying to debunk seem more plausible:

Over the last half million years, our climate has experienced long ice ages regularly punctuated by brief warm periods called inter-glacials. Atmospheric carbon dioxide closely matches the cycle, increasing by around 80 to 100 parts per million as Antarctic temperatures warm up to 10°C.

Undisputed so far.

Why do we have Ice Ages? To cut a long story short, the most likely explanation is that seemingly minor changes in Earth's orbit keep summers a bit cooler, so glaciers don't melt back in summer as much as they advance in winter. Glaciers reflect more sunlight back to space, which cools thing down further, and so on. Brrr, shit, Snowball Earth, half of everything dies.

Ice Ages end for the equal and opposite reason. From the mother lode:

Inter-glacials come along approximately every 100,000 years. This is called the Milankovitch cycle, brought on by changes in the Earth's orbit... The combined effect of these orbital cycles cause long term changes in the amount of sunlight hitting the earth at different seasons, particularly at high latitudes.

For example, around 18,000 years ago, there was an increase in the amount of sunlight hitting the Southern Hemisphere during the southern spring. This lead to retreating Antarctic sea ice and melting glaciers in the Southern Hemisphere.(Shemesh 2002). The ice loss had a positive feedback effect with less ice reflecting sunlight back into space (decreased albedo). This enhanced the warming.

That's all you need to know, really. [Something] has an effect, the opposite of [something] has the opposite effect.
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What does this have to do with atmospheric CO2?

CO2 actually lags temperature by around 1,000 years. While this result was predicted two decades ago (Lorius 1990), it still surprises and confuses many. Does warming cause CO2 rise or the other way around?

As the Southern Ocean warms, the solubility of CO2 in water falls (Martin 2005). This causes the oceans to give up more CO2, emitting it into the atmosphere. The exact mechanism of how the deep ocean gives up its CO2 is not fully understood but believed to be related to vertical ocean mixing (Toggweiler 1999).

The process takes around 800 to 1000 years, so CO2 levels are observed to rise around 1,000 years after the initial warming (Monnin 2001, Mudelsee 2001).

So warming increases the amount of CO2 in the atmosphere, and cooling reduces it for the equal and opposite reason. There's a significant time lag either way (also appears to be undisputed).

The answer to their question is therefore obviously that warming causes CO2 levels in atmosphere to rise, and cooling causes it to fall. That explains everything, job done, you'd think.
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However, they answer their own question with "In actuality, the answer is both."

What? How?

The outgassing of CO2 from the ocean has several effects. The increased CO2 in the atmosphere amplifies the original warming. The relatively weak forcing from Milankovitch cycles is insufficient to cause the dramatic temperature change taking our climate out of an ice age (this period is called a deglaciation). However, the amplifying effect of CO2 is consistent with the observed warming.

It's strange that orbital changes are sufficient to trigger an ice-age (which is a feedback thin), but not strong enough to trigger the reverse (the feedbacks work in reverse). If you are going to do propaganda, then at least be consistent. They (whoever 'they' are) will have to add "falling atmospheric CO2 levels"' to the list of generally accepted reasons of why Ice Ages are as cold as they are and rewrite a lot of text books.

Which isn't beyond them, of course, but it all takes time to falsify.

Climate science - as easy as A, B, C.

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 (known figures) raises temperature of the 'surface' (as defined - see below) to whatever it needs to be to radiate the same amount of W/m2 back out to space.

The Consensus is that the entire 33K discrepancy is due to the presence of minor trace gases in the atmosphere, such as the +/- 2% water vapour or 0.04% CO2 ('greenhouse gases'). The surface converts short wave visible radiation from the Sun to longer wave infra red radiation, and this is trapped/absorbed or reflected by the 'greenhouse gases', which in turn warms up the surface even more, so it emits even more infra red in a vicious circle. Here is a typical article explaining this, which includes the energy budget diagram which doesn't add up as a bonus. Parts of that explanation are correct, parts are guesswork and assumptions, it is riddled with contradictions, leaves a lot of loose ends and unanswered questions, and overlooks some important basic physics.

Actually, if you sift out the basic physics from the guesswork and just apply the basic physics, it is quite easy to work out that the hard surface should be 45K - 50K warmer than the effective temperature. The formulas and calculations are the same whether or not there are any 'greenhouse gases', which suggest that they do not increase temperatures. As a matter of fact, there is only a 33K discrepancy, because water vapour and water in the troposphere have a moderating influence and reduce surface warming and temperature fluctuations (which accords with everyday experience and like-for-like comparisons of temperatures in humid and dry areas).

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 density 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, and atmospheric pressure falls by about 7% for each km you go up, at least for the first five or ten km (which is not far off actual measurements).

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

In an intuitive way, you can also guess that the temperature at the top of the atmosphere is close to the temperature of the nearly empty vacuum of space, which is either close to 0K or has no measurable temperature at all, depending on your point of view. So temperature falls the higher you go, as anybody who has been up a mountain knows.

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 of energy 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 T = J ÷ (m x cp)

We can simplify/merge those two equations as follows: T = (m x g x h)/(m x cp); cancel 'm' top and bottom; T = g x h/cp; divide both sides by h; T/h = g/cp.

(Thanks to Tallbloke for this short-cut - Wiki gives an explanation which is almost impenetrable to the layman, although it ends with exactly the same formula)

1 kg of air which is 1,000 metres higher up has got 9,807 more Joules of potential energy than 1 kg 1,000 metres lower down, so the air lower down must have 9,807 more Joules of kinetic energy (and vice versa).

How much warmer is the air 1,000 metres lower down?
Specific heat capacity of air = 1,006 J used/needed to increase 1 kg of material by 1K
T/1,000 = 9.807/1,006
T/km = 9.75K
Hence the predicted lapse rate = 9.75 K/km altitude.

[I think it makes more sense to a) use the specific heat capacity for constant volume rather than constant pressure, and b) to calculate J/m3 rather than J/kg. That means first using Barry to find pressure, at different altitudes and then finding the temperatures which balances Joules of kinetic energy and Joules of potential energy (basing calculations on density at different altitudes, not on pressure, so you need to know pressure and temperature to work out density, and the temperature is the thing you are looking for!), which is why the lapse rate I worked out was 8K/km. I'm not sure if my logic on a) and b) is 100% sound, but my method gives an answer which is closer to the real world observed typical rate of 6.5 K/km, so I'm happy with my method for now.]

C. What is the surface of the Earth?

The Consensus give a nod to Barry and the main 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 like the road sign saying turn left and the sat nav saying turn left, but turning right anyway. It's all about radiation from the surface being reflected back down by those dastardly 'greenhouse gases'! Any other explanation is heresy!

The Consensus' most heinous and borderline criminal obfuscation is in their definition of the 'surface'. They define 'the surface' as the hard surface at sea level, or the surface of the oceans (two-thirds of Earth's surface is ocean).

Here are a few reasons why that is wrong:

1. If you calculate the 'effective temperature', you should also be looking at 'effective surface', which is whatever the sun light hits first, Earth has a lot of clouds, so the 'effective surface' is NOT at sea-level.
2. If you approach Earth at speed from space, you feel it when you hit the atmosphere. That is the real surface.
3. If you scale down the earth to the size of a football, the troposphere is only 0.2 mm thick. You think it's thick when you look up at an airliner, but it's only 11 km away, you could drive that far in a few minutes.
4. There are about 10,000 kg of air (mass) for every m2 surface (see above)
5. 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 0.2 mm thick, the hard surface or sea-level is barely a couple of molecules thick.
6. When we talk about the surface of the ocean, we mean the top of the water, not the hard surface at the bottom.
7. When we talk about the surface of the Sun or a Gas Giant, we mean the surface of the atmosphere, not the hard surface lower down (to the extent there even is one). Why do we change the rules when looking at rocky planets with thinner atmospheres?
8. 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. It's usually the same temperature, and must be the same pressure.

Therefore, the real surface is the whole troposphere, not the hard surface or the surface of the oceans.

Summary

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 there is - a lapse rate. There are different ways of calculating/predicting it, and it can be observed/measured, so it's about 33K warmer than 255K at the bottom (the hard surface); it's about 255K half-way up (as defined); and it's about 33K cooler than 255K at the top of the troposphere.

Bonus

This A-B-C easy GCSE-level approach also explains a lot of things which the Consensus 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 peak 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 and there is plenty of radiation sloshing about).

5.  Why 'heat rises' is a truism only observed in enclosed spaces kept above the temperature of their surroundings (central heating in buildings; actual greenhouses/polytunnels) 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 - visible and infra red, kinetic energy, potential energy, latent heat of evaporation/condensation etc) is distributed in the troposphere (conduction, convection or radiation). All you need to know is that energy tries to distribute itself as evenly as possible (governed by the physical laws discussed here, or by winds/weather, if you want an everyday term for a complicated process).

7. Why the troposphere emits twice as much radiation towards the ground than it does out into space. This cannot be satisfactorily explained by 'greenhouse gases trapping and/or reflecting heat', it is because the troposphere at sea level is warmer and hence emits more radiation that the layer higher up, which is colder and so emits less radiation, see here.

8. Why water can't be a 'greenhouse gas', although this is based on observation rather than physics, which is really complicated with water vapour and water (see here).

9a. 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 at the same temperature. So even if N2 and O2 aren't emitting infra red themselves, the hard surface converts that warmth back to radiation anyway. The total infra red leaving the hard surface is the same whether it is bouncing back and forth as infra red between hard surface and troposphere (the Consensus), or whether the hard surface has to convert kinetic energy from N2 and O2 back into infra red first (the actual explanation).

9b. Why, even if the troposphere were indeed completely transparent to and unaffected by infra red radiation, incapable of absorbing or emitting it, the temperature at the hard surface would be the same as it is now. The hard surface would quickly reach 255K (accepted by the Consensus) and it would warm up the troposphere by conduction and convection until the whole troposphere (the effective surface) were 255K on average (it being incapable of radiating heat to space, that's the Consensus). That 255K would be the average, there would still be a lapse rate and so the temperature of the hard surface would increase to 288K (and the top of the troposphere would be about +/- 222K). The hard surface would then be warm enough to emit the required amount of infra red straight through the troposphere and back into space (not being able to lose any more energy to the troposphere by conduction or convection).

10. 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.

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

12. Why you can predict Venus' hard-surface temperature fairly accurately using the same basic physics (here). All you need to know is distance from Sun and albedo, from which you work out 'effective temperature'; the height of 'effective surface'; the acceleration duty to gravity and specific heat capacity of the gases in the atmosphere, from which you work out the lapse rate up- and downwards. Whether or not the constituent gases are 'greenhouse gases' is entirely irrelevant. Knowing the mass of constituent gases in kg/m2 helps as well for cross checking.

How to undermine your own argument.

From City AM:

Plans have been drawn up by the Treasury to hit businesses with a £2.7bn tax rise in this month's budget.

Nope. Businesses don't and won't pay any more tax. Business owners will pay a bit more tax when they sell up.

Chancellor Rishi Sunak is set to scrap entrepreneurs' relief, which gives a capital gains tax cut to people who start their own businesses.

Nope. It gives a CGT cut to people when they sell a business - whether they started it or took it over from somebody else. It comes at the end, not the beginning.

The scheme cuts the amount of capital gains tax paid, when they sell the business, from the usual 20 per cent to 10 per cent on up to £10m of lifetime gains.

Those selling now might have started their businesses pre-1998, when we had Retirement Relief. The first £750,000 of the gain was tax-exempt and the rest taxed at 40%, the normal CGT rate at the time. This didn't dissuade people then and upping the CGT rate to 20% won't deter them now.

Entrepreneurs' relief was brought in by Gordon Brown's Labour government in 2008 with the intention of encouraging people to start businesses.

Nope. It replaced - and was less generous than - Business Asset Taper Relief in 2008.

The scheme cost the government £2.7bn in tax revenues in 2018-19, up from £427m in 2009-09.

Ho hum. Is not taxing something really a "cost" and if so, to whom? How is it calculated? Compared to what?

A letter written by 150 prominent business owners...  read: "Other entrepreneurs have sold their business and are now currently considering whether to start a new business or not and the rate of tax is a very important factor."

It clearly isn't, or else nobody would have started a business pre-1998, when the very generous Business Asset Taper Relief replaced the rather stingy Retirement Relief, see above.

The Federation of Small Businesses (FSB) also released a statement today, saying that scrapping the scheme would "destroy retirements".

No it won't. Say you get lucky and sell your business for £1 million. Clearly, you'd prefer to pay 10% CGT and keep £900,000; if you pay 20% CGT, you keep £800,000. Not the end of the world.

FSB national chairman Mike Cherry said "The vast majority of those who benefit from this incentive – 38,000 each year – are everyday entrepreneurs, those who see their business as their retirement plan, and who would lose an average of £15,000 each as a result of this change."

Ho hum. That would be a good argument for reducing the £10 million limit down to £1 million (similar to old Retirement Relief), so that 'the vast majority' with smaller gains are unaffected by the change.
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What they should have said:

1. The revenue-maximising rate of CGT is somewhere between 10% - 15%. At that level, people are happy to just pay it. People don't defer sales to defer or avoid the CGT. They don't get involved in other avoidance or deferral schemes, which cause further distortions elsewhere.

2. So by all means, scrap Entrepreneur's Relief as a separate relief and just reduce the main rate of CGT to 10% - 15%, everybody's [reasonably] happy.

3. The good news is, there would be no need for all the legal deferral opportunities either, as very few would want to use them. Hooray, more simplification. And people like me out of a job.

Well, duh.

From The Guardian:

The drought and water resources minister, David Littleproud, has acknowledged he “totally” accepts that worsening droughts are linked to climate change, as he signalled more taxpayer support for regional communities was coming as Australia’s big dry “escalates”.

Littleproud, who stumbled last month by first telling Guardian Australia he did not know if climate change was manmade, then later clarifying he had always accepted the science on the role humans play in the climate changing, told the ABC on Sunday he understood the link between global warming and drought because “I live it”.

The Guardinistas don't do subtlety or nuance.

Australia as a whole doesn't get much rain, and it appears to have had even less rain in recent years. Which is indisputably a "significant change in weather patterns which might or might not be long-term" or "climate change" for short.

But the article equates "climate change" with "man-made climate change" and so assumes that "minister accepts that climate change exists" to automatically mean "minister accepts that climate change is man-made" (which he was bullied into saying recently, but that's a separate topic), which is one heck of a leap of logic.

Diagonal Comparison

From The Guardian readers' letters page:

Nuclear power is helping to drive the climate crisis

Has the Confederation of British Industry got its head in the sand, or in the record levels of carbon-intensive concrete just poured at the Hinkley C nuclear site (Build more nuclear reactors to help climate crisis, says CBI, 28 June)?

Nuclear power, apart from destroying biodiversity throughout its life cycle, produces up to 37 times the CO2 emissions of renewable energy sources, owing partly to the mining and refining of uranium. The impact of this process on people and the environment is not included in the rationale for nuclear power in the UK...

Linda Rogers, PAWB (Pobl Atal Wylfa B/People Against Wylfa B)

Let's go with the prevailing narrative that today's temperatures are outside the normal range of fluctuations for the past hundred (or thousand, or whatever) years, and that carbon dioxide is causing them - and focus on that "37 times" number.

I don't know what she means by 'renewable energy', but presumably the net carbon dioxide emissions from these is close to zero - thirty-seven times close to zero is still a small number, and surely a few orders of magnitude less burning oil or gas (coal is hardly used any more in the UK).

Therefore, the headline that "Nuclear power is helping to drive the climate crisis" is nonsense. By all means, oppose it for other reasons (rightly or wrongly), but please accept that overall, it reduces carbon dioxide emissions.

More school statistics...

... which most people would have guessed anyway if they thought about it for a few moments, and which can be used to support any particular point of view/prejudice:

From The Telegraph:

Choosing a nursery could be more important than secondary school when it comes to ultimate academic achievement, a study has found. The contribution of a school to variation in pupil attainment is in fact “relatively small”, according to researchers at University College London's (UCL) Institute of Education. 

I wonder when another university will do the same analysis of whether universities make much difference either, for a given standard of student...

This means that sending children to what they regard as a “good” secondary school - meaning one that fares well in GCSE results and official progress measures - only adds a small amount more value than if they went to a “bad” secondary school.

The report, funded by the Nuffield Foundation, found that once you control for the characteristics of pupils within each school, the difference in attainment linked to school is below ten per cent of the total variance between children.

Professor Alex Bryson, UCL’s Chair of quantitative social science a co-author of the report, added: “Schools do still matter, but they don’t matter as much as people think. What perhaps is slightly surprising is that an awful lot of time and effort goes into trying to improve schools – but over the 13 year period we looked at, the variability accounted for by schools has remained fairly constant.”

Which would happen if all schools were to improve by the same amount, so this does not mean that schools haven't improved.

But:

Researchers found that school competition, measured by the number of schools within 5.5 kilometres of each school, accounts for up to seven per cent of the variation in pupils’ attainment.

That could be 'competition driving up standards' (hooray), or just as possible, slightly cleverer kisd getting into the perceived better schools and vice versa, leading to a widening gap between schools perceived as better or worse.

Meanwhile the pupil-teacher ratio - an indication of how well resourced the school is - only accounts for around one per cent of the variation. A report last year by researchers at King’s College London found that genetics are a bigger determinant of academic success than sending your child to a grammar school.

We could have guess the last bit, it's genetics and parents pushing their kids to do their homework etc.
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On the subject of competition between schools and/or competition for better pupils between schools, from the BBC:

Most families do not choose to send their children to their nearest school, shows the biggest ever study of state secondary school choices in England. More than 60% opt for a school that is further away - usually because it is higher achieving.

"Contrary to a widely-held belief, only a minority of parents choose their local school as their first option," say researchers.

Why would parents not put down a perceived better school as their first choice? Be daft not to; and what are the chances that the perceived best school within reasonable travel distance is not the nearest one? Fairly high, I would have thought. Bear in mind my point above that there is likely to be a wider perceived gap between two nearby schools than between two isolated schools which all children in an area attend, simply because there are is no realistic alternative.

It also debunks the idea that richer families are more engaged with choices... Despite any assumptions about the "sharp elbows" of middle-class families, there was no significant difference in behaviour between wealthier and more disadvantaged parents.

Again, that doesn't really prove anything.

If a school is perceived as good, then higher income families will choose to move near it and will drive out lower income families from the area. This leads to the self-enforcing gap between the areas. Higher income families, having paid over the odds to access the 'free' education they've paid for two or three times over (income tax and higher house prices) will of course send their children to the nearest school - because that one is perceived as best (or else they wouldn't have moved there etc).

The reverse applies to low income families where parents 'just want the best for their children'. They can't afford to live close the perceived best schools, but they can still put them as first choice on their applications.

And so on. All quite fascinating in a Freakonomics kind of way.

Surely a ten-year old can see that this is complete and utter nonsense?

From one of my favourite Warmenist Porn sites:

Climate Myth:

Water vapour is the most important greenhouse gas. This is part of the difficulty with the public and the media in understanding that 95% of greenhouse gases are water vapour.

The public understand it, in that if you get a fall evening or spring evening and the sky is clear the heat will escape and the temperature will drop and you get frost.

If there is a cloud cover, the heat is trapped by water vapour as a greenhouse gas and the temperature stays quite warm. If you go to In Salah in southern Algeria, they recorded at one point a daytime or noon high of 52 degrees Celsius – by midnight that night it was -3.6 degree Celsius.

That was caused because there is no, or very little, water vapour in the atmosphere and it is a demonstration of water vapour as the most important greenhouse gas. (Tim Ball)

Basic rebuttal written by James Frank:

When skeptics use this argument, they are trying to imply that an increase in CO2 isn't a major problem. If CO2 isn't as powerful as water vapor, which there's already a lot of, adding a little more CO2 couldn't be that bad, right?

What this argument misses is the fact that water vapor creates what scientists call a 'positive feedback loop' in the atmosphere — making any temperature changes larger than they would be otherwise.

How does this work? The amount of water vapor in the atmosphere exists in direct relation to the temperature. If you increase the temperature, more water evaporates and becomes vapor, and vice versa.

So when something else causes a temperature increase (such as extra CO2 from fossil fuels), more water evaporates. Then, since water vapor is a greenhouse gas, this additional water vapor causes the temperature to go up even further—a positive feedback.

How much does water vapor amplify CO2 warming? Studies show that water vapor feedback roughly doubles the amount of warming caused by CO2. So if there is a 1°C change caused by CO2, the water vapor will cause the temperature to go up another 1°C. When other feedback loops are included, the total warming from a potential 1°C change caused by CO2 is, in reality, as much as 3°C.

Has he not heard of the concept of an equilibrium?

There are two ways of interpreting the rebuttal:

1. There is no equilibrium. So a CO2 induced increase of 1C leads to an overall 3C increase. Which in turn would lead to another 9C increase. Which would lead to a further 27C increase. And then we'd all be boiled alive. Clearly not true.

2. There is an equilibrium, and 3C warmer is the 'new normal'. OK. But the Warmenists insist, with calculations, that the entire 1C increase since the Little Ice Age is down to increases in CO2, with water playing little or no role.

In which case, why isn't it already 3C warmer? That's clearly not true.

If they insisted that of the 1C increase, 0.3C was due directly to CO2 (this is in fact just about plausible) and the rest was due to water vapour "and other feedback loops" (as yet unspecified), well fine, but none of them has ever said that.
--------------
Finally, he does not give a starting point for the CO2 level at which such positive water/CO2 feedback kicks in.

Let's change his wording slightly: "So when something else causes a temperature increase (such as extra CO2 from fossil fuels bright sunlight or atmospheric pressure), more water evaporates. Then, since water vapor is a greenhouse gas, this additional water vapor causes the temperature to go up even further—a positive feedback."

That's clearly nonsense.

Should we assume that up to 'pre-industrial levels' of 280 ppm of CO2, there is no positive feedback, and it starts at 281 ppm? Or current levels of 420 ppm (and rising)? Or does the positive feedback start at 1 ppm?

The Brooklyn 99 Twelve Islanders problem.

The problem is:

1. There are eleven islanders who all weight exactly the same and one who is either heavier or lighter than those eleven.
2. You have a see-saw with accurately marked seats that you can use as weighing scales.
3. You have to find out which islander is a different weight, and whether he/she is heavier or lighter than the others.
4. Can you always solve it in a maximum of three comparisons?

After four or five hours of trial and error, I have found that the answer is "yes" and come up with an easy to follow mechanical system (no doubt one of dozens). Pdf below (click to enlarge).

Worked example
You start by numbering the islanders 1 to 12.
Let's assume 6 is heavier, but you don't know that yet.
Test 1 is always 1,2,3,4 on one side of the see-saw against 5,6,7,8 on the other.
Result 1 is 5,6,7,8 are heavier, so go to the second table.
Test 2 is 1,2,5,6 against 3,7,9,10.
Result 2 is 1,2,5,6 are heavier.
Test 3 is 3,5 against 7,9.
Result 3 is both sides weight the same
Answer is then read off in the bottom row of the second table, "6 H"

If anybody spots a mistake, please leave a comment :-(

Truncated Y-Axis Of The Week

From Watts Up With That:

The greenhouse gasses keep the Earth 30° C warmer than it would otherwise be without them in the atmosphere, so instead of the average surface temperature being -15° C, it is 15° C. Carbon dioxide contributes 10% of the effect so that is 3° C. The pre-industrial level of carbon dioxide in the atmosphere was 280 ppm. 

So roughly, if the heating effect was a linear relationship, each 100 ppm contributes 1° C. With the atmospheric concentration rising by 2 ppm annually, it would go up by 100 ppm every 50 years and we would all fry as per the IPCC predictions.

But the relationship isn’t linear, it is logarithmic. In 2006, Willis Eschenbach posted this graph on Climate Audit showing the logarithmic heating effect of carbon dioxide relative to atmospheric concentration:



As you can sees the, y-axis goes from 230 to 270, that's key to this.
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We can assume that W/m2 are related to temperatures. As a guide, from Wiki: When 1361 W/m2 is arriving above the atmosphere (when the sun is at the zenith in a cloudless sky), direct sun is about 1050 W/m2, and global radiation on a horizontal surface at ground level is about 1120 W/m2.
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From Skeptical Science:

After publishing my experiences talking to science 'dismissives' (or 'skeptics', or whatever you'd like to call them) and then participating in the excellent Denial101x course, I was invited to join the volunteer team at SkepticalScience last year.

Good start, a few ad hominems (refreshingly absent from the first article) to strengthen your case. Einstein famously opened his Theory of General Relativity with "Sit on this and swivel, Newton, you wig-wearing English prick!" Back to the article:

But before all that, one of the dismissives drew my attention to a climate science paradox... Scientists agree that the greenhouse effect is approximately logarithmic — which means that as we add more CO2 to the atmosphere, the effect of extra CO2 decreases.

In the last million years, CO2 levels have cycled between about 180 and 280 ppm during cycles about 100,000 years long. Because this happened in the steep part of the curve, a change of only 100 ppm (together with the Milankovich cycles) was enough to move the world in and out of the ice ages. Even though humans have increased the CO2 concentration by 130 ppm already, this extra 130 ppm has a smaller effect than the 100 ppm that was added naturally before.

But let's zoom in on the part that we actually care about: the modern era:



After zooming in, the logarithm doesn't make such a big difference: it's not far from a straight line. 560ppm will probably take us well beyond the Paris target of 1.5°C, so the 280-560 range is key; we would be unwise to let our civilization go beyond 560.
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Sure, looked at close up, any part of any curve looks like a straight-ish line. But look at the y-axis, it goes from 0 to 4.5. The W/m2 increase (resulting from a CO2 increase from 280 to and 560 ppm) of just under 4 agrees to the first chart, which shows an increase from 257 to 261. But the y-axis is a tad misleading, to say the least.

They are also (deliberately?) confusing units. Fag packet* says 3.7 additional W/m2 = temperature increase (if CO2 levels doubled from pre-industrial levels) no more than 1C.

* Average earth surface temperature 288K ÷ 1,120 W/m2 (when sun directly overhead in a cloudless sky) x 3.7 W/m2 = 0.95K or 0.95C.

If we go by the first, more optimistic chart, the increase would be barely measurable, but let's give the warmenists the benefit of the doubt.

It's Opposites Day!

From a blatantly biased article at the BBC:

Leo Varadkar restated his commitment to an open border in Ireland with free movement of people and frictionless trade, with no tariffs and no checks.

Sounds excellent, but wait...

He added: "We don't want Ireland to become a back door to the single market in the event of a hard Brexit."

Isn't that more or less the opposite of the first statement? Or at least, near the other end of a continuum between 'free trade' and 'hard border'? Or what? The more you try and read it in context, the more ambiguous it becomes. Is it OK for the I/NI border to be a 'back door' if there is a 'soft' Brexit, in which case, how 'soft'?

Reader's Letter Of The Day

From today's City AM (my emphasis):

Re: Deadlocked MPs reject soft Brexit as Tory MP quits party in protest

It is a sad comment on the state of our politics when 261 MPs are prepare to vote for a proposal which is a legal impossibility.

I refer to the crazy plan promoted by Nick Boles MP, under which we would join the European Free Trade Association (EFTA) and therefore be required to remove all customs duties on goods from other EFTA states, while continuing to allow the EU to determine what customs duties we would apply, including on imports from other EFTA states.

So, to take on example, the EU dictates that we must impose a 13 per cent tariff on Norwegian smoked salmon and continuation of that tariff would obviously be incompatible with the zero tariffs which operate within EFTA.

The legal impossibility of this 'compromise' scheme was pointed out by a Norwegian politicans in a UK national newspaper as far back as December [2018] saying: 'It is not an option for the UK to stay indie the customs union... if you are part of the EFTA platform.'

But Mr Boles chose to ignore that, and now his suggestion has rightly been rejected.

Dr D R Cooper, Maidenhead

I emailed Denis Cooper to say well done, he said he didn't think rejoining EFTA was a good idea anyway, so we disagree on that, but hey - I always thought there was something fishy about Boles' plan.

Fun with numbers

From The Guardian: On 27 March, MPs voted against 'Motion B: no deal in the absence of a withdrawal agreement' by 400 to 160.

Also from The Guardian: The Cooper bill [ruling out 'no deal'] has passed its third reading with a majority of only one vote, 313 to 312

So there must be a significant number of MPs who voted against 'No Deal' but also voted against 'No no deal'. The mind boggles. Maybe there are some who just vote against every proposal by force of habit?

The funny things that the Warmenists say...

From The Royal Meteorological Society (in 2011):

If Earth’s atmosphere contained no GHGs, all the IR radiation would be propagated directly to space and would be ‘lost’. The world would be cooler than it is by around 33 degC, having an average temperature of around –18 °C instead of its present +15 °C, for reasons that will now be explained.

That is the most outrageous claim the Warmenists have ever advanced, it does not fit in with any of their other claims.

But let's  test the claim against "what we know" and, for sake of argument, allocate half that 33 degC to the effect of water vapour and half to CO2, 16C each. That means our current 400 ppm CO2 = extra 16C.

Assuming a linear relationship, when CO2 was only 300 ppm, the surface temperature would have been on average 4C lower, which it clearly wasn't, and to get the so-called 2C 'tipping point' increase, CO2 levels would only have to increase to 450 ppm (which they probably will in the next twenty years or so, in which case we'll find out one way or another).

Assuming a logarithmic relationship, it would have been 0.8C cooler with 300 ppm*, which is quite possibly true, but to get to the so-called 2C 'tipping point' increase, CO2 levels would have to increase to 846ppm**, which they simply will not do.

* Log(300) ÷ log(400) x 16C = 15.2C
** 10^(log(400) x 18C/16C) = 846