Wednesday, 8 July 2020

Potential temperature

I have tried to stay off posting about 'climate science' because I lost my audience months ago, but I have kept digging in my own time. I stumbled across another meteorological concept recently (3 below) and I have added another paragraph to my summary on why the Earth is 33K warmer at sea level (288K) than its effective temperature (255K, the temperature we would expect it to be from incoming solar radiation and 'albedo' alone).

The Holy Trinity of basic atmospheric physics are (is?) three formulae or concepts. These are all text book physics and they are mutually supporting and internally consistent (as well as matching up well with observations).

The starting point is to realise that
a) potential energy (due to altitude and gravity) is equivalent to and inter-changeable with thermal energy and increases the total amount of energy in the atmosphere, and
b) the average temperature of the atmosphere = the effective temperature. There is nothing special about sea level! It just a good reference point (most of us live there or near there), which happens to be about 5 km below the mid-point of the atmosphere.

1. The lapse rate (this is the easiest to calculate, it's just acceleration due to gravity ÷ specific heat capacity or air). To get it to match the real world observed moist lapse rate and to take latent heat of evaporation/condensation into account, you have to bump up specific heat capacity from just over 1,000 J/K/kg to about 1,425 J/K/kg.

2. The Barometric Formula (aka 'Barry'), which predicts local atmospheric pressure at a given altitude, based on pressure and temperature at sea level (and various constants, heinously complicated to calculate). This overstates pressure at high altitudes, but such is physics.

3. Potential temperature, a term which meteorologist use to describe the sum total of the actual temperature plus the 'latent heat of convection' (i.e. the potential energy) of air at a given altitude (fairly easy to calculate). You can use the same inputs as for the lapse rate and Barry, and then use the pressure at altitude from Barry to predict the potential temperature of air at the given altitude.

To tie them in, you can predict local actual temperature using 1, sea level temperature - (altitude x lapse rate) or combine 2. and 3 and deduct the potential energy at that altitude from the potential temperature. Both answers match up and are a good prediction of actual temperature.

There, that's all you need to know, that's where the extra 33K or 33C at sea level come from (and also why it is about 33K colder than the effective temperature at the top of the troposphere). Has nothing to do with 'Greenhouse Gases' or 'radiative forcing' or all these other made-up, non-scientific terms.
The real science deniers, i.e. the Alarmists, are capable of believing two impossible things before breakfast. These things are not only impossible, they are mutually exclusive:

A. In the absence of 'Greenhouse Gases', the temperature in the atmosphere would be a constant 255K all the way up. To believe this you must also believe that pressure and density are constant all the way up. In which case, where is the 'top' of atmosphere? Does it go up forever, like the aether that they believed existed until 1887?

B. In the absence of 'Greenhouse Gases', the temperature at sea level would be 255K, but there would still be a lapse rate (from 1). Good old Skeptical Science actually bite this bullet (and break a tooth on it, as per usual). This is slightly more plausible, but you also have to believe that the average temperature of the atmosphere should be lower than its effective temperature, despite it being incapable of losing energy to space by radiation (in the absence of 'Greenhouse Gases') and despite the potential energy, which can only be positive and add to the total energy in the atmosphere (like gravity, which is only ever positive).


Lola said...

You haven't lost me as an audience. I just haven't commented. I would quite like all the climate posts grouped in one list, so I could re-read them more easily.

Mark Wadsworth said...

L, this has been a long messy process. So my earliest posts are pretty useless. I gradually narrowed the whole greenhouse effect post by post. The one worth reading is the Number 1 under "quick links" (if you are looking at this on a PC). I might just delete all the earlier ones.

Dinero said...

As you have noted, the gravity lapse rate idea is not a new idea , and there is a refutation of it on Watts up with that .

If you have a closed tube of air on its side with a heat source at one end , it eventually becomes an isothermal condition from conduction. If you then rotate it to the vertical position then the influence of gravity is introduced but it will become isothermal again from conduction.

Mark Wadsworth said...

Din, I've read many articles like that. They are clearly nonsense, they are true for small tubes but not on the scale of kilometres where you can't ignore potential energy.

Dinero said...

Specifically for the temperature gradient, the effect of gravity is comparable to adding a second heat source, and so the isothermal situation is re - established for the same reason that it is established for a heat source at one end of a volume of gas.

Mark Wadsworth said...

Din, gravity/potential energy is NOT a 'second heat source'. It is a second ENERGY source.

So the atmosphere has a certain total energy - thermal energy + potential energy.

Energy (of both types) tries to equalise.

It is inevitable that the air higher up has more potential energy.

So the thermal energy manifests itself lower down to balance out.

At each altitude, total energy is the same, and total energy = thermal energy plus potential energy.

IF you go with the Alarmist, non-scientific view that thermal energy must be the same way up

THEN you must be capable of believing that POTENTIAL energy is the same way up.

Which is clearly bollocks.

Potential energy is dictated by altitude. And the higher layers are clearly higher than the lower ones.

Dinero said...

Potential energy is not a characteristic of objects, in this case air molecules. the phrase Potential energy is an abstract description used in science to describe a dynamic situation where their is potential for movement and so you have to careful how you apply it.

If you heat up a rod of steal in a gas flame and the rotate it to the vertical the highest point does not become colder due to PE.

Mark Wadsworth said...

Din, you're an Alarmist and a science denier, I know where you are coming from. But deep down, you know I'm right.

Bayard said...

"If you heat up a rod of steal in a gas flame and the rotate it to the vertical the highest point does not become colder due to PE."

If you heat up a steel rod and pivot it about the centre, the PE gained at the top is exactly equal to the PE lost at the bottom. If you raise the entire rod, you are doing work against the force of gravity and therefore adding energy. That's your PE. If you did the same amount of work on the steel rod without lifting it, the rod would warm up. Therefore, by lifting the rod, the rod becomes cooler than it would have been if it wasn't lifted and had the same amount of work done to it. Look up the First Law of Thermodynamics.

Bayard said...

"If you then rotate it to the vertical position then the influence of gravity is introduced but it will become isothermal again from conduction."

The difference between "equal" and "having a difference too small to be measured" is not always appreciated. If you have two containers. Both contain 1000 litres of water, but one container has one molecule of water more than the other. It is not possible to measure the difference in volume or water between the two containers, but it still remains a fact that the mass of water in one container is greater than the mass of water in the other.

Lola said...

A steel rod is not analogous to a column of gas? just asking.

Mark Wadsworth said...

Din, that is the worst analogy you could have thought of!

1. The Ideal Gas Laws do not apply to solids, by definition. if I trap some air at sea level in a container and carry it up a mountain, the air cannot expand so will not cool either (well it probably will cool, but for other reasons).

2. If you lift the rod, you are applying external energy to it. When warm air rises and cools, no energy is being added, the air converts thermal energy to kinetic energy. When cold air falls, the reverse happens, it gets compressed and warms up. Potential energy is converted to thermal energy. This is how we derive the equation for the lapse rate!!

3. Although the mechanism is a bit more complicated with air, this is the same as throwing a ball upwards. Kinetic energy is converted to potential energy, until it is completely stationery for a split second (max PE, zero KE) and then it fall again and the reverse happens. It's about 'conservation of energy', see the Wiki explanation for 'potential temperature' which is established and accepted physics.

L, no it certainly is not! See my reply to Din.

Bayard said...

L, insofar as it is a movable mass being acted on by a force (gravity), it is, otherwise not.

Bayard said...

"Potential energy is not a characteristic of objects,"

I am not sure what you mean by this, but you are almost certainly wrong. Any mass in a force field like gravity has potential energy.

" in this case air molecules. the phrase Potential energy is an abstract description used in science to describe a dynamic situation where their is potential for movement and so you have to careful how you apply it."

How is a ball sitting on top of a cupboard, stationary for the last year, considered "a dynamic situation"? It is completely static, yet a tiny shove will cause the ball to attain a far greater speed than can be attributed to the shove itself, as the ball falls off the cupboard. Where does the kinetic energy for that move come from, if not from the ball's potential energy? The air molecules you so carefully exclude from the ability to possess potential energy to move, don't move, not because they lack potential energy, but because they are surrounded by other air molecules, which would have to move up as they moved down, therefore the potential energy lost as the air molecules moved down is exactly balanced by the potential energy gained by the other air molecules move upwards. You have to consider why things float in a fluid.
Similarly, if you erected a tube full of hydrogen from the ground to the top of the atmosphere and opened the top, the molecules of air adjacent to the top of the tube would then sink down to the bottom of the tube in exactly the same way as water would fill a tube full of air if you submerged it in the sea with its top just under the surface. If they have no potential energy, where do they get the energy to move down the tube?

Dinero said...

As I said in my first comment I acknowledge the effect gravity has, but the point remains from the article I linked , conduction is still available to make it isothermal.

Mark Wadsworth said...

Din, pressure and density gradually fall as you go upwards, because of gravity (and without gravity there would be no atmosphere).

Why are so many people incapable of realising that temperature falls for vaguely similar, gravity-related reasons?

How do they think gas giants form, and why they are so hot in the centre? How stars form seems to pretty widely accepted, the same applies to gas giants/failed stars and the same applies to any atmosphere.

B, thanks, excellent examples.

Bayard said...

"conduction is still available to make it isothermal."

In that case, why is the air not the same temperature all the way up to the top of the atmosphere?
We observe that the atmosphere is colder at the top than it is at the bottom. From this we can deduce that a tube of air, however, small, must be colder at the top than the bottom, otherwise how long is the tube where the air stops being the same temperature all the way up and starts being colder at the top? The small tube of air may appear to be the same temperature, but that just means the difference is too small to be measured, see my example of the two containers of water earlier.

Mark Wadsworth said...

B, don't pick on Din. A lot of Alarmists seem to genuinely, devoutly believe that without "greenhouse gases", temperature would be the same all the way up. Gas giants don't count, for some reason,and can be ignored.

Bayard said...

"genuinely, devoutly believe"

I keep forgetting that Alarmism is a religion, not a science.

Dinero said...

Bullet point one has a bit missing. For the gravity lapse rate in bullet point one to work, it needs to explicitly include some continuous heating from the hard surface.

Mark Wadsworth said...

Din, "it needs to explicitly include some continuous heating from the hard surface"

No it doesn't. In the context of Earth, that is stating the blindingly obvious. That would be as trite as explaining that gravity pulls things towards the centre of the earth.

(I'm not sure it's even true on a really large scale - see "how stars form" or "why is it so hot in the middle of Gas Giants?".)

Dinero said...

Well do you recognize that a gravity lapse rate requires the presence of continuous heating.

Mark Wadsworth said...

Din, that is a moot point. When gas clouds coalesce to form stars or gas giants, then no.

In the context of Mars, Earth, Venus, of course 99.9% of the thermal energy comes from the sun. Gravity doesn't add to total thermal energy, it gives rise to potential energy which squidges thermal energy downwards. Please see new widget in side bar which has lots of different explanations for this, and go and argue with the US Air Force or somebody if you think they are wrong.

Dinero said...

It is referred to the second link of the Widget. Claes Johsnon. - " In the presence of (small) heat conduction, it appears that a (small) external source will be needed to maintain the lapse rate. Of course, in planetary atmospheres external heat forcing from insolation is present."

Not sure about his use of the term compression rather than acceleration but on this particular
point that is an aside.

Mark Wadsworth said...

Din, does it matter? For the third time, in the context of Earth, thin atmosphere near a bright Sun, we can take that as a given.