## Thermodynamics 101: Compression increases temperature.

Posted: July 16, 2018 by tallbloke in climate, Clouds, Cycles, general circulation, Gravity, Ocean dynamics, physics, radiative theory, Temperature, Thermodynamics

Question: If I had a container, full with air, and I suddenly decreased the volume of the container, forcing the air into a smaller volume, will it be considered as compression, will it result in an increase in temperature, and why?

Answer on Stack Exchange by Luboš Motl: Yes, it is compression and yes, it will heat up the gas.

If there’s no heat exchange between the gas and the container (or the environment), we call it an adiabatic process. For an adiabatic process involving an ideal gas (which is a very good approximation for most common gases), pVγ is constant where γ is an exponent such as 5/3. Because the temperature is equal to T=pV/nR and pV/pVγ=V1−γ is a decreasing function of V, the temperature will increase when the volume decreases.

Macroscopically, the heating is inevitable because one needs to perform work p|dV| to do the compression, the energy has to be preserved, and the only place where it can go is the interior of the gas given by a formula similar to (3/2)nRT.

Microscopically, the gas molecules are normally reflected from the walls of the container with the same kinetic energy. However, the molecules that hit the wall moving “against them” during compression will recoil with a greater velocity. If one calculates the average energy gain for the molecules, one gets the same temperature increase as that which follows from the macroscopic calculation.

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Taking Luboš’ answer and applying it to the Earth’s atmosphere, we can start to understand why Ned Nikolov and Karl Zeller have been able to find a function which predicts surface temperature on rocky planets and moons throughout the solar system using insolation and surface pressure as explained in their 2017 paper.

The Sun heats the Earth’s land and ocean surfaces. They lose heat into the lower atmosphere via several energy transfer mechanisms, roughy 2/3 via evaporation and conduction, 1/3 via radiation. The rate of transfer via evaporation and conduction is dependent on another process; convection.

Convection arises due to the buoyancy of water vapour and warmer air, which are both lighter than the cooler surrounding air. In turn, buoyancy is due to the gradient of pressure in the atmosphere, and that gradient is due to gravity acting on the mass of the atmosphere. The surface air has all the mass of the entire column bearing down on it under the force of gravity, and so reaches the highest pressure, which reduces with altitude.

As you can see from the figure, pressure decreases exponentially with altitude, though it is fairly linear up as far as the tropopause, the boundary between the troposphere and stratosphere.

Because the pressure drops with altitude, the warm higher pressure air convecting up from the surface expands into this lower pressure regime at higher altitude and cools. The water vapour in the air condenses as the temperature drop to the dew point, releasing the latent heat of evaporation it acquired at the ocean surface as the latent heat of condensation. That heat is then efficiently radiated out to space from the cloud tops through the rarified upper atmosphere.

So far, so well known. A less commonly considered effect is that the rising warm air displaces cooler air from high altitude back down to the surface. On its way, it gets compressed by the higher pressure regime it is descending into. As Luboš explains, this causes the descending air to heat up. How big is this effect? The numbers on the right of the diagram at the head of the post tell us.

3.3 cubic metres of low pressure cold air from the tropopause get compressed into 1 cubic metre of air back down at the surface. It warms from a chilly 216K to a pleasant 288K. But Luboš tells us that to perform the compression, work must be done. So what is supplying the energy to do the work? The answer is the Sun, which drives this cycle of upward and downward convection. The hot dry air arriving back at surface at the boundary between the Hadley and Ferrel cells where the effect is particularly strong used to cause the dehydration and heat exhaustion of animals being transported by ship across the ‘horse latitudes’. That’s how they got their name.

Let’s imagine a world where this adiabatic cooling and heating didn’t exist.  Where the cold high altitude air returning to surface was still cold. That would create a big differential between the temperature of the surface air and the surface of the land and ocean. Where the temperature differential is large, conduction of heat is rapid, so the surface would cool quickly into the air. But because the descending air is adiabatically heated by compression, the differential is much lower, and this means conduction occurs slowly.

To be in equilibrium with the air, the surface has to lose heat as quickly as it gains it from the Sun. To do that it there has to be a sufficient differential in the temperature of the surface and the near surface air for conduction to happen fast enough.  if there isn’t sufficient differential, the temperature of the surface will be forced to rise until there is. This is a lot of the reason why the surface temperature of Earth is much higher than that of our airless Moon, despite the Moon being at the same average distance from the Sun and not having a 30% cloud albedo reflecting heat back out to space before it reaches the surface.

Of course, as the surface temperature rises, it will also radiate more energy as well as conduct more energy and it’ll also evaporate more water. The consequences of those effects will be covered in following Thermodynamics 101 posts.

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Disclaimer: No conservation of energy or other physical law was broken in the production of this post.

Comments
1. Ian W says:

It is a pity that the colloquial terms cools and heats are used as they imply removal and addition of energy from/to the volume of gas. What is actually happening is that there are less gas molecules in that volume when the pressure is reduced.

Temperature is a measure of the overall kinetic energy of the gas molecules in a defined volume of gas. If the pressure is decreased there are less molecules of the gas in the volume and the overall kinetic energy in that volume decreases in accordance with Charles Law.

2. tallbloke says:

You’re considering a fixed volume. My post as about ‘packets’ of convecting air with a fixed number of particles, but volumes which are expanding and being compressed. I agree there are all sorts of problems with loose use of language around thermodynamics, but I’m just trying to keep the science as accessible as possible to the lay reader. Another issue with your comment is that temperature is generally though to relate to the average kinetic energy of the particles in it, not the number of them. However, I think that definition has the implicit assumption of a fixed number of particles and probably a fixed volume too. Heat capacity is important for bulk temperature in the real world and that involves energy density as well as average velocity.

3. ferdberple says:

What about Potential and Kinetic energy? Consider an air molecule. At the surface this molecule has high kinetic energy and low potential energy, yielding a high temperature because temperature is due to kinetic energy alone.

At altitude this molecule will have lower kinetic energy and higher potential energy but the same total energy. This lower kinetic energy yields a lower temperature. Otherwise you would need to raise the total energy of the air molecules as they move higher.

4. ferdberple says:

Temperature is a measure of the overall kinetic energy of the gas molecules in a defined volume of gas
==========
Is this true? How does one explain million degree plasma in a near vacuum? Is the kinetic energy of individual molecules millions of times higher than a similar plasma at surface pressure?

5. cognog2 says:

A good article and I will accept the loose terminology used under the circumstances. Engineers tend to use the term enthalpy which encapsulates all the aspects of energy with temperature being but one.

My only query is the lumping together in the term “convection” of the rising of warm air with the rising of gaseous water. The latter process being a function of molecular weight differential rather than temperature. It is an important distinction. For example cold hydrogen will rise through a warmer atmosphere.

The reason why it is important lies in the part this plays in the atmospheric Rankine Cycle where work is done against gravity at the expense of the latent heat inherent in the gaseous phase albeit at the same temperature of the surrounding liquid and atmosphere. The work done, of course is reflected in the increase in potential energy of the water. The whole process ensuring that large energy fluxes are moved upwards towards the top of the troposphere and hence into space.

In rough terms some 680 WattHrs for every kilogram of water evaporated from the surface is dissipated into the atmosphere at various altitudes and space. Eventually when the water loses its energy and returns to its liquid or solid state, gravity returns it back to earth for the cycle to be repeated.

An excellent thermostat.

6. tallbloke says:

Ferd: At the surface this molecule has high kinetic energy and low potential energy, yielding a high temperature because temperature is due to kinetic energy alone.At altitude this molecule will have lower kinetic energy and higher potential energy but the same total energy.

Loschmidt would agree with you. Boltzmann and Maxwell (or at least the later interpretations of their work on statistical mechanics) would disagree. The argument is that molecules that managed to get high up in the atmosphere would have had higher than average kinetic energy to start with, so without convection, radiation and other energy transfer mechanisms, the atmosphere would be near isothermal.

7. tallbloke says:

Cognog: My only query is the lumping together in the term “convection” of the rising of warm air with the rising of gaseous water. The latter process being a function of molecular weight differential rather than temperature.

Good points well taken. I’m just trying to keep the concepts as clear and simple as I can, without misleading.

The energy budget diagram implicitly states what you’ve made explicit. Evaporation shifts four times more energy aloft (85W/m^2) than the net upward transfer of the convection cycle (20W/m^2)

As I said at the bottom of the post, I’ll say more about evaporation and radiation in followup posts.

Thanks for your technical input.

8. gymnosperm says:

The sun supplies only half or the “work” of convection. The other half is supplied by gravity.

9. tallbloke says:

“Convection can be defined as vertical circulation that results from differences in density ultimately brought about by differences in temperature.”

http://www.scienceclarified.com/everyday/Real-Life-Earth-Science-Vol-2/Convection-How-it-works.html

I’m really cautious about ascribing “work” directly to gravity, but go ahead and flesh out your ideas. Gravity acts on atmospheric mass to create the pressure gradient that performs the compression on descending air, but it’s the Sun’s energy heating the surface that drives the convective circulation through that pressure gradient so far as I can see.

10. p.g.sharrow says:

It appears to me we are looking at 300 years of different explanations and formula on the behavior of gasses.
What is needed is a description that begins with energy in Atoms, and moves to energy in molecules, followed by energy of them in volumes as well as change in state. Considerable changes in energy can take place without change in temperature.
Energy is measured in “Temperature” in each of these but these “Temperatures” are not really measurements of the same thing. This results in confusion in communication. Apples, Oranges and Bananas all can be measured in pounds of weight, but a pound of Bananas is not the same thing as a pound of apples…pg

11. Hifast says:

Reblogged this on Climate Collections.

12. tallbloke says:

PG: I appreciate your point, but being trained engineer I find classical mechanics is the simplest way to explain things that happen in the observable world people have direct experience of. If we go down the subatomic rabbithole in search of the truth, we end up with a mouthful of quarks and ears stuffed with bosons.

The talkshop is open to any coherent and cogently argued line of reasoning though, so have at it if you wish. 🙂

13. cdquarles says:

It also seems that many keep using condensed form analogies to gases. These do not work very well. One reason for that is that the volume occupied by the particles is small relative to the total volume occupied; and that the particles are moving fairly rapidly, about 1 km/sec at Earth’s surface, at its surface temperature and the local atmospheric pressures in a gravity field. “Hot” gas moves faster than “cold” gas and “light” gas moves faster than “heavy” gas; but with the large numbers involved, buoyancy isn’t the same thing for gases, compared to liquids. Plus, for any sample, the overall kinetic energies will be similar throughout. Gases will completely mix, unless that’s physically prevented.

Yes, space is ‘hot’ in terms of kinetic energy of the species there. It is not ‘hot’, in the sense of total kinetic energy since the mass there is small. Density, mass per unit volume, is a function of numbers, too, since the number of particles * the unit mass = total mass and the volume is the 3D space occupied.

People also conflate the radiant color temperature with the thermodynamic temperature. NB that we do not actually measure temperature, which is the geometric mean (akin to the root mean square) of the kinetic energies of each particle. There are conditions where this is fine. There are conditions where it isn’t fine, if you want a highly accurate prediction with high precision and resolution.

Consider a mole of hydrogen atoms (a half mole of hydrogen molecules). That’s about 6.022 * 10 E 23 atoms. We can’t possibly measure each one accurately, with sufficient precision, to be able to do any kind of direct statistics on them. We use a proxy, the property of thermal expansion. That’s a complex function that depends on the sample’s composition in addition to environmental ones, such as pressure; but over a small enough range, we can approximate it linearly. That’s what the ‘thermometer’ measures, a linearized volume change.

For real gases, the van der Wall’s correction works better than the ideal gas laws, for high end analytical work. Sure, the ideal gas law is fine when applied to real gases, mostly, as a first approximation, at the limit ;).

In the real atmosphere, we can use the parcel analogy up to a point. So long as we keep in mind that in the real atmosphere, there’s no diffusion barrier between parcels; thus there is some physical mass exchange present, even if there is no overall energy exchange present.

14. tallbloke says:

cdquarles: Great to get such technical responses to this post, thanks for your input. You said

“…we can use the parcel analogy up to a point. So long as we keep in mind that in the real atmosphere, there’s no diffusion barrier between parcels; thus there is some physical mass exchange present, even if there is no overall energy exchange present.”

True, but given the relatively slow transfer of energy through air by conduction and radiation, compared to the speed of convection (often over 10m/s for moist updraughts at the centre of building cumulonimbus), I think there are valid reasons for meteorologists to frame their understanding of weather phenomena the way they do.

15. tallbloke says:

16. cognog2 says:

Re: Gravity, work etc.:

A quick calculation on a kilogram of water(ice, liquid, whatever) at some 12000 kilometres altitude reveals that it requires some 32688 WattHrs of energy to get it there. That is a lot of work. It is a problem that I have had for some time as nowhere can I find reference to this energy in the general calculations. Where does it come from and where does it go to? The answer of course lies in the clouds; but I am not equipped to chase that one, although I have doing a lot of guessing.

Anyone got any ideas on this?

Presumably it all comes back when it rains; but is that true ? A grave question excuse the pun.

17. tallbloke says:

Cognog: Is that just the energy required to evaporate the water? More required if it’s ice, as Ned will confirm when he gets here. No energy required for it to ascend to that altitude though, as buoyancy does that?

18. tallbloke says:

19. p.g.sharrow says:

Linear acceleration, gravity, provides for the packing of gasses and the energy they carry. Buoyancy of these gases cause by the energy they have accumulated provides for the lift needed to transport the energized gases up to the point the energy can be radiated into space.
Energy provided by gravity is countered by the resulting buoyancy. Energy in = energy out as work. Refrigeration at work. heating results in cooling. The main working fluid is water, where change of state greatly enhances buoyancy as well as the amount of energy transported…pg.

20. cognog2 says:

Sorry Tallbloke but must disagree here. raising a kilogram against gravity requires energy defined as kg. m or ft. Lbs. which may be converted to WattHrs.
The latent heat is only some 680 WattHrs. so would not achieve any great height by itself. Somehow addition energy is provided for the upward movement to continue which would probably be provided by insOlation and or upward radiation from the earth. in fact this movement sucks energy from the atmosphere, most of which gets returned when the water returns to earth. The process takes place I surmise? at constant temperature consistent with the behaviour of the phase change process; which probably explains why it does not appear in most of the calculations as it is a zero sensitivity process.
The buoyancy you refer to is only there if the water has been provided with the necessary latent heat to enable it to happen and which must be maintained as the movement ascends through the lapse rate height.
It is a matter of the difference between energy and enthalpy where enthalpy includes all aspects of a body’s State and not just aspects of temperature and radiation.
As I say I am not really equipped to take this much further so am raising the issue to seek advice from others.
Hope you can help.
My Regards.

21. EternalOptimist says:

TB. if I had a device that measured pressure via a pad and had it on my ceiling. stood on a chair and pressed up. the need le measures the pressure applied, then fall back to zero. Same on a wall, pressing sideways.
That’s measuring work ?
If it is..
I place the pad(scales) on the floor and stand on it, it measures the work but does not fall back to zero. Is this gravity continuing to produce work ?

22. Andrei says:

Hi there , can I translate this post to Portuguese ,with the only purpose of explain this topic to other chemystre undergraduate mates.I will not share with other purposes and I will always mention the disclaimer.

[Reply] Yes, and thank you for your interest.

23. dai davies says:

Roger, you and Ned both seem to be ignoring the diurnal cycle heating effect that he and Karl discussed in an earlier paper. Many people have done rough calculations on this including Roy Spencer, myself, and even ATTP, and all the results I’ve seen show it’s plenty strong enough to create Earth’s current surface temperature. And it’s pressure dependent!

See my article:
http://brindabella.id.au/BrindabellaArchives/Science/Climate/Atmosphere/Energy&Atmosphere.html
for more details.

The isothermal atmosphere idea is wrong. Great scientists often are, particularly in the early days of a field, as the climate debate has shown.

dai

24. tallbloke says:

Cognog: Sorry Tallbloke but must disagree here. raising a kilogram against gravity requires energy defined as kg. m or ft. Lbs. which may be converted to WattHrs.

The Sun’s energy inflates the atmosphere, and gravity sets up the pressure and density gradients which support buoyancy. Could it be that the energy required is accounted for in the energy budget by part of the 20% of incoming solar energy ‘absorbed in the atmosphere’? I don’t know the answer to this, so it’s worth thinking about.

Dai: Thanks for the link, I’ll have a read. I tried to leave open that avenue by concentrating on temperature differentials between surface and near surface air, rather than discussing averages.

EternalOptimist: I don’t get why you think the pressure measuring pad would return to zero while you’re still pressing it, no matter which direction you’re pressing. Maybe you mean you don’t have to put any ‘work’ into continually pressing it on the floor because gravity is doing that with your body mass?

If so, then consider that the floor is ‘working’ to prevent you being accelerated towards the centre of gravity. That ‘work’ can be measured with a strain gauge. Things can be measured in various ways, but just because you can convert between units, doesn’t mean ‘gravity is expending joules’. If it was, it would all get used up and we’d float away. 😉

Gravity is a force, not an energy. Or if you want to get Einsteinian about it, gravity is an illusion brought on by the bending of spacetime… though he never told us what is doing the bending via the action of mass at a distance…

25. dai davies says:

Oldbrew,
May be getting wires crossed here, but I was using “isothermal” in the sense that the atmosphere would be the same temperature at all altitudes. Early on a few physicists thought that would be the default case.

dai

26. As some of you will know, I have been analysing these concepts for years now so it is good to see some traction developing here and elsewhere.

Here is a reminder of a relevant previous post on this site:

https://tallbloke.wordpress.com/2017/06/15/stephen-wilde-how-conduction-and-convection-cause-a-greenhouse-effect-arising-from-atmospheric-mass/

and I have a number of relevant articles here:

https://www.newclimatemodel.com/latest-articles/

and I raised the adiabatic issue here as long ago as 2012

https://tallbloke.wordpress.com/2012/12/14/stephen-wilde-the-ignoring-of-adiabatic-processes-big-mistake/

27. EternalOptimist says:

thanks for the reply TB. See, even a pea-brain gets treated with fairness and respect at Tallblokes Talkshop 🙂

28. Tallbloke said:

“The Sun’s energy inflates the atmosphere, and gravity sets up the pressure and density gradients which support buoyancy. Could it be that the energy required is accounted for in the energy budget by part of the 20% of incoming solar energy ‘absorbed in the atmosphere’? I don’t know the answer to this, so it’s worth thinking about.”

I would say yes.
During the very first convective overturning cycle which occurred at the formation of the atmosphere sufficient energy was conducted from surface to atmospheric mass to provide all the potential energy needed to place the mass of the atmosphere suspended off the surface in hydrostatic equilibrium.
Thereafter that same energy is recycled constantly up and down between KE and, PE and PE and KE forever until the atmosphere either escapes to space (via increasing insolation) or falls to the ground (via removal of insolation).

That energy is reflected in the atmospheric thermal enhancement at the surface.

Any radiative imbalances are neutralised by convective adjustments for a net zero effect on surface temperature.

29. EdB says:

Cognog ” Somehow addition energy is provided for the upward movement to continue”

Wrong.

Every surface parcel is touching the surface and floating in a fluid.(atmosphere). A tiny amount of extra water vapor, or conducted heat means it will float upwards. That extra water vapor or conducted heat is produced by the sun, and added to the parcel at the surface.

Thus it will rise by floating to the top of the troposphere. It has to, as it is relatively lighter at each millimeter of rise.. No more extra energy is needed.

30. Cognog ” Somehow addition energy is provided for the upward movement to continue”

Once adiabatic uplift begins no more energy needs to be added because the temperature and density of the parcel declines at the same rate as the temperature and density of the surroundings. The temperature and density differential that started the uplift therefore stays the same throughout.

In order to stop rising it has to reach a point where there is a thermal inversion such as the tropopause or at lower levels in localised scenarios such as at the base of high pressure cells at night or in winter when surface cooling reverses the thermal gradient in the vertical plane.

31. gymnosperm says:

Moist air is actually lighter and more buoyant than dry air, so by merely evaporating the ocean, the sun provides a boost to convection that gets accelerated by warming the boundary layer and by latent heat release at the condensation point.

Gravity is universal. It is not depleted by “work” it performs in warping spacetime. It is not understood. By all means, let’s avoid a mouthful of quarks. Roy Spencer has argued that adiabatic compression is impossible because no “work” is performed. Gravity does the work for free.

32. What Roy doesn’t seem to understand is that no ‘net’ work is done overall which is correct but the work done in uplift is equal to and opposite to the work done in descent.
Consequently, there is ‘positive’ work done in rising columns and ‘negative’ work done in falling columns. That is why gravity is not used up.
Nor does Roy accept that at any given moment half the atmosphere is rising within low pressure cells and half is descending in high pressure cells.
I’m surprised by his lack of meteorology knowledge. Probably due to being too narrowly specialised for too long.

33. cognog2 says:

It seems I have raised a few problems here in attempting to explain what is happening in clouds.
Clouds are a mix of liquid and gaseous water defined by moisture content. The phase change between the two involves an energy flux. if negative then condensation occurs and vica versa. It is only gaseous water that is buoyant; thus the mix determines equilibrium.with respect to gravity. ( buoyant or not)

The vapour pressure of water is determined by pressure which in turn is provided by gravity and the temperature at which evaporation is thus initiated and fixed. The rate of evaporation being controlled by the partial pressure of the gaseous water in the surrounding atmosphere.

Gaseous water contains latent heat and will rise due to its molecular weight until such time that the latent heat is expemded in doing work against gravity; when condensation will ocurr and prevent further rise. If however further energy is supplied via say InsOlation or upward radiation from the ground; then rising will continue. The whole process taking place at constant temperature at the micro level and thus my be deemed at zero sensitivity.

Radiation calculations which assume that radiation receipt automatically results in a rise in temperature are therefore at fault where water is present as a vapour. All that results here is that the water continues to rise rather than condensing.
Nothing comes free in the thermodynamic world and the potential energy provided by this absorption of radiation by water eventually winds up in our hydro power generators and will serve to heat our homes and warm our planet.

A quick look at the thermodynamics of the Dinorwic energy storage facility in Wales reveals much about this potential energy.

34. cognog2

i) latent heat is not expended if it does work against gravity. It remains present but as potential energy which does not register as heat and is recovered as heat in any subsequent descent.

ii) Condensation does not prevent further rise, in fact it accelerates it as observed in thunder clouds. The release of latent heat from the condensate goes partly to faster uplift and partly as radiation to space from the condensate.

iii) The potential energy in the atmosphere comes from two phenomena namely the movement upwards of molecules against gravity and from the moving apart of molecules as density decreases with height. The former is negligible but the latter is huge.

iv) Only that negligible portion is used as hydro power otherwise we would need no other energy source. Hydro power comes from water in liquid form that collects at a high location due to topography and then is allowed to fall in a controlled fashion. Not being a gas there is no significant moving together of water molecules during the descent so no potential energy can be derived from that source.

35. cognog2 says:

Stephen Wilde:

Re: your items:
i) Pedantically agree. Should have said moved to or morphed into or some such. A very valid point you make that the Potential Energy (PE) does not register as heat or do you mean temperature?

ii) The gaseous water that condenses no longer rises. The remainder continues to rise providing there is sufficient energy input to enable it. Mist hanging over a river stays there until it is “burnt off” by the sun. The same applies to hammerhead cumulus where gaseous water rises from a static vapour ; but I hesitate on this as an example as an inversion situation maybe involved here. The rate at which evaporation takes place being by the balance between the Vapour Pressure and the partial pressure of the water in the surroundings.

iii) The moving apart of molecules is irrelevant. A kilogram of water of whatever volume is still a kilogram of water, be it gas, liquid or ice. Potential Energy (PE) is measured in ft. Lbs, m.Kg and can be converted to WattHrs. but of course relates to the gravity situation involved.
If you drop a brick on your foot you become very aware of the energy involved.

iv) Not sure what you are getting at here. Agreed most of the original PE has been expended during the return to earth. What finds its way into elevated lakes etc. still has some left and it is that which is used to generate power.

Incidentally in this falling to earth, gravity uses the PE to increase the pressure and additionally energy is absorbed from the surroundings and these two comprise the feedpump and feedheater elements in the atmospheric Rankine Cycle Cycle. The whole process being fixed by the original boiler pressure of 1 atmosphere.

It is interesting that we have these different perspectives on this complex subject. I could learn a lot here.

My regards

36. cognog2

i) Best to just say that work with gravity, whether up or down simply TRANSFORMS energy rather than using it up. Temperature is our way of measuring heat which is simply the release of infra red radiation. Heat (KE which does radiate) reduces with height as it is transformed to PE which is not heat and does not radiate.

ii) The portion of the condensate that does not fall as precipitation is carried upwards until it becomes too heavy (via accretion) whereupon it falls to Earth. Mist over a river is condensate not water vapour and so is not lighter than air as is water vapour and it usually forms beneath an inversion so that the water droplets cannot be carried upward. A hammerhead cumulus actually contains both rising water vapour and rising condensate both of which spread out at an inversion layer before descending.

iii) When molecules move apart PE is derived from a weakening of the intermolecular attractive forces which is nothing to do with the PE formed when moving up against gravity. The former provides the vast bulk of PE in the atmosphere. When descent occurs the molecules move closer together and KE returns from PE as heat.

iv) All the PE derived from intermolecular energy returns to KE during descent but on average the temperature will follow the lapse rate slope downwards so there is no ‘extra’ heat at any given height from which one can derive power. The temperature of the lake will on average settle at the lapse rate temperature for its height. None of that energy is recovered as Hydro Power. Hydro Power is derived only from the subsequent descent of liquid water (not gaseous water vapour since the rules for gases are different) downslope which is where the other sort of PE (the minor part) becomes involved. Very little moving together of molecules of liquids or solids occurs during descent so no significant energy can be derived from that source.Hydro Power is derived only from the movement of a liquid or a solid descending under the force of gravity.

Gravity does not ‘use’ PE.
Gravity simply transforms KE to PE in uplift and PE to KE in descent and for an atmosphere in hydrostatic equilibrium (as they all are) the net outcome is zero but one still needs a surface temperature enhancement as an energy reservoir to support the energy demands of that net zero overturning.

Gravity and atmospheric mass together create the surface pressure and the surface pressure sets the rate at which the transformations occur between KE and PE with changing height.

37. p.g.sharrow says:

@Stephen, KE to PE, PE to KE.
interesting way to quantifying Gas pressure laws and buoyancy, gravity is just a constant on both sides of the equation. A big rubber band during heat energy conversions…pg

38. cognog2 says:

Stephen,

I suspect we are both saying the same thing but from a different perspective. I would however like you to define what you mean by KE which I assume is Kinetic Energy. Is this at the molecular level or reference to the movement of the whole mass involved? It seems you are referring to the former so you have me puzzled as the mass remains constant whatever the internal energy and hence the PE change is just a function of height.
Regards

39. Ned Nikolov says:

The classic adiabatic process in Thermodynamics provides a key to understanding the physical mechanism behind the empirical Eq.10a in our paper (https://tinyurl.com/ydxlfwn7), which was derived from NASA planetary data. The term “adiabatic>/i>” means without adding / subtracting heat or mass to/from the system in question. It’s important to realize that, during an adiabatic process, the internal kinetic energy and temperature of a gas system changes as a result of an internal pressure change.

Many people (including trained scientists) have difficulty understanding how the internal energy & temperature of a gaseous system could increase, for example, without adding heat from the outside environment. First, one must grasp the direct relationship between pressure (P), internal energy (U), and absolute temperature (T) of a gas mixture:

– T is proportional (linearly related) to U, i.e. U = a*n*R*T, where a = 5/2 for diatomic gases, n is the number of gas moles, and R is the universal gas constant;
– P is defined as a force applied to unit area;
– The overall gas kinetic energy (measured in Joules) is defined by the product PV (Pressure X Volume). This means that there cannot be gas energy (and therefore gas T) without pressure. That’s because energy cannot exist without a force!
– The gas law describes T as proportional to the gas kinetic energy P*V, i.e. T = PV/(nR). Thus, a change of the applied force (P) implies a change in the gas temperature (T). This also means that U is proportional to PV.

Secondly, we must understand the mathematical formalism of the adiabatic process. An adiabatic process is one, where PV^Y = constant (Y = 7/5 for diatomic gases and Y = 5/3 for monatomic gases), see https://en.wikipedia.org/wiki/Adiabatic_process. So, if we have a gas system that has made an adiabatic transition from state 1 defined by T1, P1 and V1 to state 2 defined by T2, P2 and V2, this means that P1*V1^Y = P2*V2^Y. We now ask the question, what’s the difference in kinetic energy and temperature between these two states of the gas system? To answer this, we examine the ratio of kinetic energies of the the two states, i.e. (P2*V2)/(P1*V1).

From the the adiabatic condition P1*V1^Y = P2*V2^Y, we can express V2 as a function of V1, i.e.

V2 = V1*(P1/P2)^(1/Y) (1)

Since, according to the Gas Law, gas temperature T is proportional to PV, we can write for the states of the system:

T2/T1 = (P2*V2)/(P1*V1) (2)

Replacing V2 in Eq. 2 with its equivalent from Eq. 1 produces:

T2/T1 = (P2/P1)^(1-1/Y) (3)

Clearly, if P2 > P1, then T2 > T1 under adiabatic conditions. In other words, the temperature of a gas mixture increases non-linearly with pressure during an adiabatic process! The graph of Eq. 3 above is shown in Fig. 7a in our 2017 paper.

Note that Eq. 3 has a similar mathematical form to our planetary Eq. 10a in the paper. The graphs of these two equations are qualitatively rather similar as well. That’s because both Eq. 3 above and Eq. 10a in the paper describe the direct thermodynamic (non-radiative) effect of pressure on temperature.

40. Ned Nikolov says:

Arguing that pressure cannot directly affect the temperature of a gas, because this would violate the 1st law of Thermodynamics as attempted by some scientists, really demonstrates a profound misunderstanding of basic Thermodynamics. It also reflects a bias of the Western education system in teaching climate science.

41. Hi Ned.
Thanks for your contribution albeit highly technical.
Do you accept that my layman’s version is correct in all essential aspects ?
Conduction from the surface of an unevenly irradiated sphere (which thereby results in convective overturning) and not radiative imbalances, being the source of the ATE?

42. oldmanK says:

Beg your pardon here. You have me somewhat baffled on thermo.

Adiabatic: (PVexp v)/T =nR; Change P and both V and T change.

P1V1 exp v = P2V2 exp v ——- isn’t that isothermal?

One cannot have both work in same process; mutually exclusive. Don’t know about climate but that what it was in Gas Turbine design.

Or is senility setting in??

43. cognog2 said:

“I would however like you to define what you mean by KE which I assume is Kinetic Energy. Is this at the molecular level or reference to the movement of the whole mass involved? It seems you are referring to the former so you have me puzzled as the mass remains constant whatever the internal energy and hence the PE change is just a function of height.”

The PE change is indeed just a function of height but there are two entirely separate components.

Due to the density gradient created by gravity the greater the height the further apart are the molecules. Greater distance between molecules creates PE at the expense of KE but in this case the KE is derived from the inter molecular forces which are stronger at lower heights as molecules become closer to each other. Thus there is more total energy in a given volume at lower levels and the temperature rises (more KE). At a greater height there is less total energy in a given volume and the temperature falls (less KE). That is what you mean by the molecular level.

The energy required to move a liquid or a solid up against gravity is a separate process and very much smaller because it does not involve a change in the distances between molecules since liquids and solids are magnitudes less compressible than gases. That is what you mean by the movement of the whole mass involved.

Two entirely distinct processes for the creation of PE from KE but the molecular aspect relates only to gases because of their vastly greater compressibility.

44. dai davies says:

Stephen,
Due to the density gradient created by gravity the greater the height the further apart are the molecules. Greater distance between molecules creates PE at the expense of KE but in this case the KE is derived from the inter molecular forces which are stronger at lower heights as molecules become closer to each other.

Inter-molecular forces are only significant within distances of a few molecular diameters. The separation of molecules on the atmosphere are, on average, vastly greater than this. The PE involved is that required to lift up against gravity.

If you have a bouncing ball then, neglecting friction with air, its energy is constant and it will go on bouncing. At ground level, all KE. At the top of its rise, all PE. A circulating air mass, again neglecting friction, is exactly the same. Because in reality there’s lots of friction with the ground and turbulence dissipating the flow it needs heating at the surface to maintain it. As with the ball, there is no energy generated in the motion.

My Lapse Rates article goes into this in depth, and also provides a mathematical proof that the gravitational derivation of the lapse rate is fundamentally identical to the traditional rising adiabatic air packet model used by meteorologists. One is a molecular level calculation, the other a bulk gas approach.

Molecules behave just as balls do. After collisions, half move upward and decelerate, the other half move down and accelerate, losing and gaining KE respectively. The net effect in a still atmosphere is that lower is hotter than upper. You don’t need circulation to get the lapse rate which is why the isothermal (constant T across altitude) idea is wrong.

Actually, both lapse rate models are wrong if there are radiative gasses present because that transfers energy in and out of the packet. At ground level only less than 100m but increasing mean free path as it rises, with infinity for some photons in the upper troposphere that escape to space.

Heat (KE which does radiate) reduces with height as it is transformed to PE which is not heat and does not radiate.

Strictly speaking, KE doesn’t radiate. Some gets converted to ‘internal’ energy of radiative gasses (vibration, rotation) in collisions. Most of this is returned to KE in a subsequent collision, but some gets radiated. The natural lifetimes of the excited states is longer than the mean time between collisions.

dai

45. tallbloke says:

Stephen: Do you accept that my layman’s version is correct in all essential aspects ?
Conduction from the surface of an unevenly irradiated sphere (which thereby results in convective overturning) and not radiative imbalances, being the source of the ATE?

Hi Stephen. In your previous post on the talkshop, you theorise that the descending compression heated air warms the surface on the night side and then advects to the dayside. I think there are a couple of problems with this.
1) Air has little heat capacity
2) Wind speeds would have to be huge and are not observed.

I think that rather than directly warming the surface to any great extent, the bulk of the ATE is caused by the descending compression heated air suppressing or impeding the conduction of heat by reducing the temperature differential. Rather than directly warming the surface, it is reducing the rate of cooling of the surface. That forces the temperature of the surface to rise until it is warm enough to lose heat as fast as it gains it. Just feel the temperature of bare rock under sunlight. It’s a lot hotter than any descending air on the dayside, let alone air making its way round from the nightside.

Two other things to remember.
1) 70% of the surface is water. I’ll be covering evaporation in the next post.
2) The ‘slowing the rate of cooling’ argument is also used by some of the radiative enthusiasts, which maybe why sceptics are resistant to it. Nonetheless, I think my impedance of conduction argument is about a much larger effect than any radiative effect (and there is at least some radiative effect).

46. cognog2 says:

tallbloke:

May I challenge your statement that 70% of the surface is water?

If you observe the leaves on a tree you will be looking at a huge area where water is in close proximity with the atmosphere and this applies to all living matter including yourself. This area is mind boggling large.

I suspect this consensus 70% figure has generated problems in understanding the climate primarily as water vapour is decidedly NOT a perfect gas and is totally ubiquitous.

47. tallbloke says:

Cognog: Point taken. Evaporation occurs over much more than 70% of the surface.

48. Rog,

i) I don’t think I specified that the descending air warms the surface directly. I’m sure that I’ve said somewhere that the compression heating of descending air partially offsets the radiation of the surface to space so that the surface and the air immediately above it rise to a higher temperature than the S-B (purely radiative) prediction. That less cold air then feeds around to the sunlit side to raise that surface temperature by the same amount.

ii) The strength of the winds that are necessary would be less in a water world simply because water in all its forms aids the redistribution of energy around the globe and thence to space so that convective overturning does not need to work so hard to achieve the necessary redistribution of energy. On Mars, which has no water, we see that despite a very thin atmosphere the winds can become powerful enough to raise dust storms around the entire planet when radiative imbalances develop.

Don’t forget that my previous post on the subject is an idealised scenario which strips out the complexities arising from planetary rotation and diurnal temperature ranges. In the end they matter not anyway because those effects always net out to zero.

49. dai,

You can argue that the effect derived from intermolecular forces declines with density as the molecules move apart with height but the fact remains that the effect is greatest at the surface and least at top of atmosphere.
However the effect is much greater in the densities of the tropopause where all our weather occurs than is the PE created from uplift alone.
An example is the concept of CAPE (convective available potential energy) which is at the heart of storm system analysis.
If you study that concept you will see that it is all related to density differentials rather than heights and it is density differentials that involve variations in the distances between molecules. Indeed, if you expand a gas then it cools irrespective of height as per the gas laws so it cannot be primarily a matter of PE derived from uplift alone. KE in an expanding, cooling gas becomes PE whether there is uplift going on at the same time or not.

50. nickreality65 says:

PV = nRT explains the relationship between these variables, e.g. compressed air compressors, receivers, HEXs, etc. It says exactly zip about the temperature of the atmosphere.

The pressure does NOT cause the temperature.

The lapse rate of the atmosphere is no different from the lapse rate through an insulated wall.

The atmosphere is little different from a basic ME HVAC problem describing the heat from the warm inside to the cold outside.

Q = U A dT

51. nick

Mass and gravity create the surface pressure at any given level of insolation.
Pressure simply determines the mass density of the gases in contact with the surface.
Greater density allows more effective conduction so that the surface temperature must rise.
Therefore a pressure measurement pressure tells us how favourable the surface conditions are for conduction since higher pressures create greater densities.

One could say that pressure indirectly causes the temperature rise by creating greater surface densities.

After that the gas laws govern the thermal behaviour of gas parcels, which have received conduction from the surface unevenly so as to create density differentials in the horizontal plane, moving up and down within the mass of the atmosphere.

The lapse rate through an insulated wall does not involve any similar adiabatic movement and the gas laws do not apply.

52. cognog2 says:

Stephen and dai:

I think that much of this debate suffers from not recognising that water vapour is NOT a perfect gas; so these gas laws are not very useful in homing in on energy movements. For instance if you look at the steam tables you will observe that in the simple gas law pv/t = k you will find that this k is not constant. Also the universal gas constant is not appropriate as you have difficulty in establishing what the equivalent molecular weight is as the vapour is only partially a gas. The joker in the pack being Latent Heat which pops in and out of the equations at constant temperature and mucks up the assumptions.

Generally the use of the equation delta Flux = KT by the IPCC where K is called the Climate Sensitivity has much to answer for; as the presence of water means that this K is zero in many of the calculations involving energy transfers and I suspect the lazy assumption that this equation is appropriate is a bit endemic and gets locked into many of the computer models.

However, not being equipped to answer these questions I can but only raise the issues for greater minds than mine to ponder upon.

Meanwhile I stick with my contention that PE has little to do with molecular activity within the parcel being considered where gravity is concerned as all the molecules are influenced, whatever their respective energies. This, of course is not true where say the PE relates to the strain in a compressed spring and this might be considered as a factor in the compression/ expansion process within a gas or vapour. Two very different scenarios.

53. nickreality65 says:

How about gasses through a double glass pane window?
A box with a bazillion molecules given a bazillion kJ will be 1/10th cooler than 1/10th bazillion molecules given 1 bazillion kJ.
No way can 0.04% of the atmosphere handle 396 W/m^2 at actual tropospheric temps.

Furthermore:
“I would rather have questions that can’t be answered than answers that can’t be questioned.”

― Richard Feynman

For the greenhouse theory to operate as advertised requires a GHG up/down/”back” LWIR energy loop to “trap” energy and “warm” the earth and atmosphere.

For the GHG up/down/”back” radiation energy loop to operate as advertised requires ideal black body, 1.0 emissivity, LWIR of 396 W/m^2 from the surface. (K-T diagram)

The surface cannot do that because of a contiguous participating media, i.e. atmospheric molecules, moving over 50% ((17+80)/160) of the surface heat through non-radiative processes, i.e. conduction, convection, latent evaporation/condensation. (K-T diagram)

Because of the contiguous turbulent non-radiative processes at the air interface the oceans and lands cannot have an emissivity of 0.97.

No GHG energy loop & no greenhouse effect means no CO2/man caused climate change and no Gorebal warming.

54. BigWaveDave says:

It is refreshing to find a discussion about atmospheric physics.

My comments after reading through

The enormous volume difference between water and water vapor may not be getting the all the attention it deserves, when considering the effects of evaporation and condensation on local pressures and temperatures.

Someone mentioned the Earth is a 1 atm. boiler (sorry, I can’t remember who) . I agree, I would add that clouds can be secondary boilers at sub atmospheric pressures. The vertical flow of solar generated water vapor (steam) suspends liquid droplets and solid ice.

The diurnal process often gets neglected, and gets substituted with equilibrium, which doesn’t exist in the atmosphere.

I’m looking forward to more on this.

55. dai davies says:

Stephen, inter-molecular forces in air are only significant when molecules collide, and the collisions are best viewed as billiard ball collisions. On average molecules are separated by about 10 times their diameter. I’ve just calculated that two ways: comparing the mean volume occupied by each mol. from the density of air divided by the mass of a molecule which gives 3.7*10^-26 m^3 or 3.3*10-9 m per side. Diameter of N2 is 3*10^-10 m. Ratio is 11.
Alternatively the density of liquid Nitrogen is 800 kg/m^3 and for air is 1.3 kg/m^3. Ratio is 615 and cube root of that is 8.5, so more densely packed than the diameter which is a bit arbitrarily defined as atoms aren’t really billiard balls.
The inter-molecular force is neglible beyond a molecular diameter or two. The calcs are for surface, so separation increases as density drops.

As for necessary wind speed to travel half the Earth’s circumference (20,000 km) in 12 hours is 1667 km/h.

I’m not trying to be argumentative, but when I see physics misrepresented in public I feel the need to say what I think most physicists would agree with. I’ve had five years teaching undergraduate physics – three hour laboratory sessions wandering about helping students understand the physics behind the experiment they’re doing. This doesn’t make me right as an argument from authority, and it was decades ago, but you do need some real physics not just intuition.

dai

56. dai davies says:

Roger, your diagram above is missing the absolute surface radiative fluxes, up and down, of 380 and 340 W/m^2. The significance of these figures is that they represent by far the main thermal coupling between surface and lower atmosphere, and are the main driver of the diurnal heating effect which comes from the nonlinearity of thermal radiation from solids E=aT^4, or (trying HTML) E=aT4.

To briefly review the process for viewers who are unfamiliar, a 1C drop in daytime surface T through transfer to the atmosphere has a greater effect in dropping surface radiation than a 1C increase of a lower surface T at night when the transfer is air to surface. The mean surface T must rise to regain balance.

As I said above, the effect is easily able to replace what was assumed to be the greenhouse effect, so I’m puzzled that people are still trying to find another cause. It can give the casual observer the impression that we’re still struggling to come up with an alternative. I don’t think we need to. I think we’ve won the debate. The ball is in the alarmist’s court for them to show that the GHE is significantly greater than the 0.14C I’ve calculated it to be.

More broadly, there’s still a major task ahead to get this message out to the general public. One thing that would help is an agreement on a basic message – that the table has been flipped as far as the science goes.

dai

57. gallopingcamel says:

While Lubos Motl is an effective advocate for “Climate Realism” and against “Catastrophic Anthropogenic Global Warming”, he is also an intolerant jerk. He has mental issues that prevent him from understanding people who disagree on any detail of his world view.

Don’t get too enamored with his BS.

58. tallbloke says:

GC: I take it you’ve had a run-in with him then. 🙂
What he says about temperature and pressure at the head of this post (and what Ned has said further down in comments) is pretty uncontroversial though, wouldn’t you agree?

StephenW: I’m sure that I’ve said somewhere…

FInd it, quote it and link it for us. 🙂

NickR: PV = nRT explains the relationship between these variables, e.g. compressed air compressors, receivers, HEXs, etc. It says exactly zip about the temperature of the atmosphere.

PV=nRT Seems to work fine for the tropopause and surface temperatures/pressures/volumes at the right hand side of my energy budget diagram above. What’s the problem?

Dai: Roger, your diagram above is missing the absolute surface radiative fluxes, up and down, of 380 and 340 W/m^2. The significance of these figures is that they represent by far the main thermal coupling between surface and lower atmosphere,

Yes, I took them out to make room for the thermodynamic processes that usually get ignored. 🙂
And also to make the point that the net flux is upwards, and smaller than convection plus evaporation by a factor of ~two. If radiation was “by far the main thermal coupling”, you wouldn’t be getting convective updrafts in excess of 10m/s under building cumulonimbus in the tropics whizzing vast amounts of latent heat 12 km straight past all that 0.04% of CO2 and ~0.5% of other water vapour in the air, up to the tropopause would you? I’m asking, not telling.

59. dai

I’m always open to change of terminology but if it is not a matter of inter molecular forces then you tell me what it is that causes molecules closer together to vibrate more and heat up whereas molecules further apart vibrate less and cool down. That applies from the depths of space at near absolute zero to the interior of suns at the point where fusion processes start.
One alternative I have heard is that the temperature rises when there is more matter in a given space because there is then more total energy held within that more limited space but even then it must be the case that there is some sort of interplay between molecules to cause them to vibrate more when closer together. Your input on that issue would be appreciated.

As regards wind speeds I see no reason why a 12 hour time limit is required for an individual warmed molecule to travel from one side to the other when the advection process is a continuous flow running as part of a huge convective overturning pattern. Please explain and note that my idealised description was for a non rotating planet so there is no diurnal range to consider.
Once the overturning cycle completes and becomes fixed in place at overall hydrostatic equilibrium then from that point onwards a warmed molecule reaching the ground on the unlit side is immediately matched by a wamed molecule arriving at the opposite side so there is no need for the powerful winds that you suggest.

60. Rog,

I think I said it in informal comments somewhere but it is implicit in the old article of mine that you linked to because it is well established science that air has a much lower heat capacity than the ground.
What happens is that compression warming heats the near surface air beneath descending columns to a point where that air temperature matches the surface temperature with its ATE and if the system has arrived at hydrostatic equilibrium the ATE on the unlit side (caused by compression warming partially offsetting radiation to space) will have raised the surface ground temperature to match the temperature of the descending compressed air.
So, you don’t get direct conduction from air to surface but rather the outcome of two combined processes equalling each other when hydrostatic equilibrium is achieved.
The compression warming on the unlit side partially offsetting radiation to space comes to exactly match the decompression induced reduction in radiation to space on the illuminated side for a balanced system overall.
So, you have a reduction in radiation to space on each side with those reductions in radiation to space being equal at hydrostatic equilibrium and there you have the ATE.

61. Rog,

You might wish to consider this:

https://www.newclimatemodel.com/correcting-the-kiehl-trenberth-energy-budget/

from April 6th 2014 and which is very similar to your head post.

62. tallbloke says:

StephenW: Thanks for the link. I had a quick skim, and it looks pretty good, but I want to develop my own line of thinking over the next couple of posts so I won’t study it closely for now. That way there’s a better chance of us adding to each others’ thinking, rather than reaching premature ‘consensus’.

63. gallopingcamel says:

@Tallbloke,
When it comes to “String Theory” I take Lubos seriously. He has an Ph. D in physics while I have a humble M.A. (Cantab) in physics and electrical engineering.

Lubos is on our side in the Climate wars but he should have a better grasp of thermodynamics than his tweets indicate. He should be better than that.

Yes, I did have a run in with Lubos and was excommunicated from his blog. Lubos has an ego that brooks no dissent…….his way or the highway! Something like Michael Mann.

With regard to Ned Nikolov his ideas on the dominant role that pressure plays make perfect sense to me. However we do have some disagreements on details. For example I contend that the rate of rotation has a significant effect on the temperature of airless bodies. Ned has my respect because he is still talking to me even though I don’t accept everything he says. IMHO that is how real scientists behave.

64. gallopingcamel says:

@Tallbloke’
“PV=nRT Seems to work fine for the tropopause and surface temperatures/pressures/volumes at the right hand side of my energy budget diagram above. What’s the problem?”

Yes, PIVnRT works well in the tropopause because pressure broadening kicks in so that less and less IR escapes into space as pressure increases (inverse pressure squared dependence). When energy can’t escape you have an adiabatic situation as mentioned by oldbrew and Ned above. OK that is “Hand Waving” so for a mathematical model take a look at the appendix to this NatGeo letter:
https://arxiv.org/abs/1312.6859

The radiative-convective model described has one radiation “down” channels and two “up” channels. Although that paper was paid for with your tax dollars it is now hiding behind a paywall. If any of you care enough I can email you the entire 35 page document. My public email is info(at)gallopingcamel.info

65. Q. Daniels says:

Lubos Motl wrote:

So the Sun is only needed for the circulation not to *stop* by friction – the Sun creates temperature non-uniformities which are needed for the circulation.

I don’t think this is exactly correct. The scintillation of dust is an observable consequence of the random movement (velocity fluctuations) of small parcels of air. These fluctuations are not driven by any external source, but rather are a consequence of being a gas. Further, there are wave (density) fluctuations as well, ranging from infra-sound to ultra-sound.

Boltzmann tried to prove the Second Law based on the assumption of ‘molecular chaos’. That is, that there is no correlation between the velocities of molecules. This is visibly and experimentally false.

66. dai davies says:

Roger, decluttering – fair enough. My comments could be summarised as wanting to see more decluttering of the whole debate.

The diagram is global, seasonal, diurnal means. Local extremes vary. Under tropical conditions evaporative cooling of the surface could triple to match radiative emission.

According to the Engineering Toolbox (https://www.engineeringtoolbox.com/evaporation-water-surface-d_690.html) it’s linear for wind speed and the difference between actual air humidity and the saturation level for that temperature which is higher for high air temperatures.

It also depends on water temperature, which they mention but don’t include in their formula. As I discuss in the above linked Energy and Atmosphere article, it’s highly nonlinear and shoots up at 30C water temp to create the thermostat effect (that regulates Earth’s surface temp). So in a tropical storm with locally descending air that’s just dumped its water in the upper troposphere and water temps typically 30C, evaporative cooling could well dominate.

dai

67. dai davies says:

Stephen, “The compression warming on the unlit side partially offsetting radiation to space comes to exactly match the decompression induced reduction in radiation to space on the illuminated side for a balanced system overall.”

Atmosphere smoothing the daily cycle, local or global, in itself doesn’t cause net surface warming. For that you need to include the Stefan–Boltzmann law – the nonlinear radiative effect of E=σT^4.

“I’m always open to change of terminology but if it is not a matter of inter molecular forces then you tell me what it is that causes molecules closer together to vibrate more and heat up whereas molecules further apart vibrate less and cool down. That applies from the depths of space at near absolute zero to the interior of suns at the point where fusion processes start.”

Yes, terminology is important here. Your use of “vibrating” is incorrect or misleading for a gas. Most of the time, molecules in a gas are moving in parabolas in a vacuum like the bouncing ball under the influence of gravity – except when they collide which is brief.

Re molecules in space to suns, the best intuitive image I have of that is solar system formation. Starting simply with just two particles alone, they are attracted to each other by gravity. They are drawn together, accelerating as they go (Newton’s law, F=m*a, or a=F/m, and gravitational law, F=G*m1*m2)/d^2).

If they were initially moving in exactly the same speed and direction (velocity) they will collide (messy) or if not they will go into orbit around each other. Shift to a gas cloud and the ones with near equal initial velocity will start to coalesce in the centre as a liquid trapping any others that hit it. All their KE is turned to short distance collisions or thermal energy. In a liquid or solid, “vibration” is the correct term because they are constantly influencing each other – definition of a gas is where they aren’t.

Then comes the interesting bit that’s been on my mind a lot – chaotic dynamics and the formation of attractors. Those particles that don’t join the centre mass collide repeatedly as a gas circulating the centre and jostle each other into orbits that minimise collisions – one mode of attractor formation. First they form a disc, then they coalesce radially into planets and moons.

There’s an excellent animation of this from the California Academy of Sciences
at https://www.youtube.com/watch?v=yXq1i3HlumA. OT for this post but relevant for site interests. Phi comes into planetary and planetary ring formation because orbits differing by the golden mean interfere minimally.

dai

68. tallbloke says:

GC: Yes, PV=nRT works well in the tropopause because pressure broadening kicks in so that less and less IR escapes into space as pressure increases (inverse pressure squared dependence). When energy can’t escape you have an adiabatic situation as mentioned by oldbrew and Ned above.

Maybe the tropopause is where it is because that’s where the ‘knee’ in the exponential pressure-altitude relationship is. Below the tropopause, the increase in pressure with the reduction in altitude is fairly linear, and so is the lapse rate, unlike the inverse square radiative relationship you mention. Isn’t that why the dry lapse rate is defined in terms of gravity and specific heat relative to volume, rather than by a more complex inverse square relationship? Or is it just that the approximation we use to define the lapse rate is older and better established than radiative transfer physics?

69. tallbloke says:

Dai: Most of the time, molecules in a gas are moving in parabolas in a vacuum like the bouncing ball under the influence of gravity – except when they collide which is brief… In a liquid or solid, “vibration” is the correct term because they are constantly influencing each other – definition of a gas is where they aren’t.

Lubos Motl commented on Twitter that where gas molecules are moving in parabolas rather than colliding is where you get an underlying thermal gradient rather than an isothermal atmosphere. So the question becomes one of density. At what point does the gradient regime transition to the isothermal regime?

OT for this post but relevant for site interests. Phi comes into planetary and planetary ring formation because orbits differing by the golden mean interfere minimally.

Thanks for that, great animation.

So in a tropical storm with locally descending air that’s just dumped its water in the upper troposphere and water temps typically 30C, evaporative cooling could well dominate.

It’s fascinating that boundary conditions are bumped into around Earth’s surface T&Ps such that different mechanisms dominate in different areas.

70. cognog2 says:

dai Davies. re: 21 July 2.22 am:

You raise an interesting point here. I have noticed that maximum sea temperatures tend to hover about the 30C level and wondered why.

I suspect it is due to Dalton Law of Partial pressure in that the rate of evaporation depends on the balance between the Vapour Pressure of water and the Partial Pressure. Once the Partial Pressure reaches a maximum then the rate of evaporation becomes a function of the rate of the energy input.
I suspect this occurs at sea level around this 30C level; but have not yet attempted to put any figures on it.
All I know is that my kettle never boils above 100C, however much I turn up the heat. Perhaps we have a similar situation prevailing at 30C; but at a lower level and not necessarily equating evaporation rate with heat input; but rising along with it.

Just a thought. Got any views?

Regards

71. tallbloke says:

Dai: Phi comes into planetary and planetary ring formation because orbits differing by the golden mean interfere minimally.

I know we’ve been saying this for a long time here, but have you found any references for this in the literature? Links please!

72. gallopingcamel says:

@Tallbloke,
“Or is it just that the approximation we use to define the lapse rate is older and better established than radiative transfer physics?”

Robinson and Catling have demonstrated that their radiative-convective model degenerates into -g/Cp in the troposphere in agreement with classical thermodynamics. My “Cliff’s Notes” explanation is that the troposphere becomes increasingly opaque to thermal IR radiation as pressure rises. When energy can’t leave the system you have an adiabatic process.

In the stratosphere, pressure broadening is not significant so gases absorb in proportion to pressure which means that energy can more easily be lost via radiation. This is why the R&C model shows a positive lapse rate for six of the seven bodies in our solar system that have dense atmospheres.

The exception is Venus that has an anomalous (negative) lapse rate in the stratosphere owing to the high concentration of CO2. Robinson and Catling discuss this issue in their NatGeo letter.

73. tallbloke says:

GC: My “Cliff’s Notes” explanation is that the troposphere becomes increasingly opaque to thermal IR radiation as pressure rises. When energy can’t leave the system you have an adiabatic process.

Yes, thermal energy and latent heat can and do convect to the top of the troposphere regardless of the problems IR has getting through dense air. So increasing opacity isn’t a severe restriction. As the day gets warmer, convection gets stronger. Why wouldn’t additional CO2 simply cause additional convection and evaporation?

74. wildeco2014 says:

For a non radiative atmosphere IR has no problem getting in whatever the pressure.
However, it does have a problem getting out because the higher the pressure, the greater the density and the more outgoing IR can be diverted to conduction and convection.
It is the delay in IR getting out that causes the surface temperature to rise above S-B.
The surface temperature will rise until the energy diverted to conduction and convection is able to escape and that only happens at hydrostatic equilibrium.
That point is reached only when kinetic energy returned to the surface by compression heating is equal to the kinetic energy taken from the surface by decompression.

75. Q. Daniels says:

@tallbloke

I’ve worked through this math several times over the years, until it finally made sense.

The parabolic loss of energy exactly washes out with reduced population for non-interacting particles, resulting in a uniform temperature. This is not correct, but it is easy.

Doing the math properly for interacting particles is hard. I gave up after many hours.

One could try adding fluctuations to Navier-Stokes for a compressible gas. I’m pretty sure that isn’t solvable with any known math, and possibly not at all. There’s a huge cash prize for proving Navier Stokes is or is not generally solvable.

One could try producing a canonical ensemble with additional populations of phonons and other quasi-particles that capture the effects of correlations. I think this is merely very hard.

This leaves us with a situation where it’s easy to do the math wrong, and beyond our skill to do it right. This situation has persisted for ~150 years.

76. gallopingcamel says:

@Tallbloke,
“Why wouldn’t additional CO2 simply cause additional convection and evaporation?”

The Robinson and Catling model is derived from first principles using equations that govern radiation and convection.

R&C don’t address the issue of phase change (specific heat of evaporation and latent heat of fusion) from “First Principles”. They introduce a constant which they call “alpha” that has the effect of reducing the Dry Adiabatic Lapse Rate and it is needed or bodies that have oceans, specifically Earth and Titan.

It was my intention to improve on the R&C model by using FEA (Finite Element Analysis) to model clouds and ice (processes involving phase changes) but have made little progress. I miss Tim Channon.

77. gallopingcamel says:

@wildeco2014,
We are in close agreement on most issues so I try not get into disputes over trivial details. That said I have some problems with this:

“For a non radiative atmosphere IR has no problem getting in whatever the pressure.”

While this is true it is somewhat misleading as there are no bodies in our solar system with “non radiative atmospheres.

While incoming IR accounts for ~54% of the energy delivered by the sun another 42% arrives in the form of visible light and ~6% as UV radiation.

It is really difficulty to explain in words why temperature varies with altitude as it does so I don’t want to criticize the explanation that you gave. My explanation in my reply to Tallbloke was not any better. My recommendation is to admit that “Equations Speak Louder Than Words” on the issue of atmospheric temperature.

78. dai davies says:

Roger, Maybe the tropopause is where it is because … At what point does the gradient regime transition to the isothermal regime?.
The way I view it, and and I guess it can be viewed differently and equivalently, is that the lapse rate drops to zero around the tropopause because that’s where water vapour has dropped off (precipitated) and the mean free path (mfp) of IR emitted upward gets longer than downward. This can be seen from this OCM display:

The red plots are mfp distributions. At the surface they are almost symmetric bell curves. By the tropopause they are highly skewed. The dotted line gives the skew for IR that doesn’t escape to space (mfp is meaningless if path is infinite). This net upward transfer of energy causes the lapse rate to drop to zero (light blue).

references for this in the literature?
I must have some somewhere but since I tidied my file structure in a machine change I can’t easily find anything. I’ll look.

Re thermal vs radiative transfer, radiative for saturated air is a few hours to tropopause (3 km/h) – fast enough to cause insignificant heating (0.14C). Mean global or even equatorial humidities are lower, so transfer is proportionally faster.

dai

79. dai davies says:

Q. Daniels, you might like to try my OCM (Open Climate Modeller) at:
http://brindabella.id.au/BrindabellaArchives/OCM/OCM_170402.html
Other parameters can be displayed: pressure, density, water density, etc, and latitude can be changed. Equations used are in the javascript source code with a bit of documentation.

dai

80. tallbloke says:

GC: While incoming IR accounts for ~54% of the energy delivered by the sun another 42% arrives in the form of visible light and ~6% as UV radiation.

This statement might be somewhat misleading. Here are the blackbody curves for Sun and Earth (Sun scaled down by a factor of 1,000,000)

Solar IR is on a very different set of wavelengths to the IR emitted by Earth’s surface. A lot of it is absorbed by water vapour in the atmosphere, almost none by CO2.

My recommendation is to admit that “Equations Speak Louder Than Words” on the issue of atmospheric temperature.

I think this is where the problem has arisen. Climatologists work out the temperature profile in terms of radiative transfer, with inconveniences like latent heat bolted in as constants. They end up believing radiation is the cause of the temperature instead of its effect, because they ignore the adiabatic compression heating of downwardly convecting air and its effect on surface conduction rates, and despite the fact that the net upward flux of radiation is only around half that of the net upward flux of convection plus latent heat.

81. tallbloke says:

Dai: This can be seen from this OCM display:
http://brindabella.id.au/BrindabellaArchives/OCM/plots/OCM-AirPlot-DsTLS.gif

Kudos to you for your computational work, but I find the graph hard to understand. It might help if your three x axis scales had coloured numbers and units to help identify and relate them to the curves?

82. tallbloke says:

Dai: Re thermal vs radiative transfer, radiative for saturated air is a few hours to tropopause (3 km/h) – fast enough to cause insignificant heating (0.14C). Mean global or even equatorial humidities are lower, so transfer is proportionally faster.

https://en.wikipedia.org/wiki/Cumulonimbus_and_aviation
Supercell thunderstorms or derechos can have gigantic updraughts at this altitude, updraughts with speeds that can exceed 40 metres per second (78 kn). Such an updraught speed corresponds to the wind speed of a small hurricane. The speed can even exceed 50 metres per second (97 kn).

That’s 3 kilometers a minute, 60 times faster than radiative transfer.

83. oldbrew says:

There seem to be quite a few of these high pressure domes around at the moment…

– – –
The culprit: a “heat dome.”

It’s a real meteorological event — the National Oceanic and Atmospheric Administration even took the time to define it in the agency’s warning this week:

“A heat dome occurs when high pressure in the upper atmosphere acts as a lid, preventing hot air from escaping. The air is forced to sink back to the surface, warming even further on the way.”

http://www.npr.org/sections/thetwo-way/2016/07/22/487031278/heat-dome-causing-excessive-temperatures-in-much-of-u-s

84. Q.Daniels you might like to look at this site if you want to learn more about fluid dynamics and computation of fluid problems https://claesjohnson.blogspot.com/ . Look on the left side for various topics, presentations, downloadable books etc eg https://claesjohnson.blogspot.com/search/label/Navier-Stokes. Many of his publications have been peer viewed. He was awarded a Prandtl medal. He is amongst the world’s top mathematicians.

85. dai davies says:

Roger, x axis tricky with 3 scales to handle 21 possible graphs. I’ve tidied it up a bit with 0-10, 0-5, and 0-2 scales to handle all.
Now reminded myself that I still haven’t got condensation realistic, and the tropopause is too high.

86. gallopingcamel says:

@Tallbloke,
Nice graph! If you agree that IR starts at 750 nm it is clear that the area under your yellow curve from 750 nm to 4000 nm amounts to less than 50% of the total radiation. Likewise if you agree that UV starts at 380 nm it is clear that UV amounts to less than 10% of the total solar radiation.

The visible spectrum (380 to 750 nm) accounts for more than half of incoming solar radiation. We seem to be in agreement.

You said;
“Climatologists work out the temperature profile in terms of radiative transfer……..”

They may do that but their models don’t match observations as closely as Robinson & Catling who take radiation and convection into account.

87. tallbloke says:

GC: Yes. Around 20% of the incoming solar is absorbed in the atmosphere. Mostly in clouds, which then radiate up, down and sideways. Modelers were surprised to learn clouds account for 35W/m^2 more than they thought from theory.
https://tallbloke.files.wordpress.com/2012/11/cess.pdf makes interesting reading.

Dai: Keep going, great work!

I’m away for a fortnight. Will check in when I can.

88. oldbrew says:

Is this another way of saying: lack of convection?
– – –
Report – The big heatwave: from Algeria to the Arctic. But what’s the cause?

“The jet stream we are currently experiencing is extremely weak and, as a result, areas of atmospheric high pressure are lingering for long periods over the same place,” added Mitchell.

http://www.theguardian.com/world/2018/jul/22/heatwave-northen-hemisphere-uk-algeria-canada-sweden-whats-the-cause
– – –
Guardian waffle about ‘carbon emissions’ excluded.