Clive Best: Understanding the lapse rate

Posted: August 18, 2012 by tallbloke in atmosphere, Gravity

Reposted from Clive Best’s blog here. This is another take on the long running debate over the Loschmidt effect, and the recent work of Hans Jelbring and Nikolov & Zeller. There is also theoretical and modeling work in progress from several talkshop commenters, and I expect we’ll see them weigh in on this thread. I hope they’ll take the trouble to expand the condensed and abbreviated terms they use in their advanced technical discussion for the benefit of those who haven’t been following developments closely. Take it away boys…

Clive Best: Understanding the lapse rate

I am unhappy with the derivation of the dry adiabatic lapse rate given in all textbooks because it seems to me a somewhat circular argument. Are we really to believe that the lapse rate is caused by adiabatic convection? A  rising  adiabatic parcel of air in hydrostatic equilibrium  apparently produces the “correct formula” but it doesn’t really explain anything. I am sure that the lapse rate remains the same even with zero convection. It must be  gravity alone that  plays the crucial role in determining the lapse rate. Others have followed similar arguments to an extreme and even claimed that gravitational energy alone heats the bottom of the atmosphere.

Such arguments have then also been pillored for violating the second law of thermodynamics. However despite all this there is something not immediately obvious about the Earth’s atmosphere. In particular it is never in thermal equilibrium although it is in overall energy balance. The gound is directly heated by solar radiation and through conduction maintains the near surface layer of the atmosphere at a “fixed” average ground temperature of about 15 deg.C. Energy then flows from the surface upwards through the atmosphere. If we ignore greenhouse gases and radiative transfer for the moment, we can still ask how does that energy distribute itself through the atmosphere given that the temperature of outer space is 3K ?

I like to understand things simply at the molecular level. This  post  tries  to derive the lapse rate only using kinetic theory.

Fig 1: Thought experiment.

Consider a thought experiment as shown in figure 1. Lets imagine all the atmosphere contained within a skin of thickness ~ one meter such that the atmosphere reaches thermal equilibrium of 15 deg.C. Lets also assume a completely flat surface and fixed surface temperature and therefore no convection. The skin is instantaneously removed so the question is  how does the atmosphere evolve ? For simplicity we will take air to be a perfect gas and use maxwell-boltzmann distribution for velocities. Molecules rising up in the atmosphere will lose some kinetic energy to the gravitational field. The Boltzmann factor at height z gives a velocity distribution as follows

N(v,z) = N_{0} e^{-\frac{(mv^{2}+mgz)}{kT}}

At the molecular level temperature is related to the average energy per degree of freedom = kT/2. For a “monatomic gas” with  3 translational degrees of freedom.

\frac{mv_{rms}^{2}}{2} = \frac{3}{2}kT

For M-B gas the rms velocity v_{rms} = \sqrt{\frac{3kT}{m}}

So T = \frac{mv_{rms}^{2}}{3k}

Consider now increasing the height level by height \Delta{h} . It is assumed that locally for each level thermal equilibrium is reached. Some work is done to fill the new volume DU +DW = DQ.  The Barometric formula for pressure is P(z) = P(z_{0}) e^{\frac{-mg(z-z_{0})}{RT}}    so  dP = -\frac{mg}{RT}dz

mv'^{2} + dW = mv^{2} - 2mg\Delta{h}

T' = \frac{m(v_{rms}^{2}-2g\Delta{h})}{3k} -\frac{mg\Delta{h}}{3k}

\Delta{T} = T'-T = \frac{-2mg\Delta{h}}{3k} -\frac{mg\Delta{h}}{3k}

\frac{\Delta{T}}{\Delta{h}} = \frac{-g}{C_{p}} , where  C_{p}=\frac{5R}{2}

This is  the usual formula from thermodynamics based on the (constant temperature) hydrostatic equation and rising parcels of adiabatic air – \Gamma = \frac{-g}{C_{p}} .  My first attempt at the derivation simply ignored the work term Pdv and I got -g/Cv for the lapse rate. I am  still not fully convinced  that the work term is correct, since it  is a very long time since I studied statistical mechanics at university!

The conclusion is that  you don’t need convection to have a lapse rate on a planet. It is a consequence of gravity and a fixed surface temperature. Molecules high up in the atmosphere have “lost” average kinetic energy (temperature)  rising against gravity. Molecules from  the surface provide  a constant re-supply of energetic molecules from the tail of  a fixed temperature Maxwell Boltzmann distribution.

Gravity clearly can  heat gas (despite all the howls of violation of the  second law of thermodynamics). This is  how galaxies and stars form. Gravitational aggregation of  hydrogen gas clouds converts gravitational energy into kinetic energy which at sufficient pressure and temperatures ignites nuclear fusion – a Star.  On Earth however the energy source is the sun which (via greenhouse effects) keeps the surface at about 283K. This fixed surface temperature maintains the lapse rate, by providing a constant source of high energy molecules which can migrate to  the upper atmosphere against gravity.

References

  1. Wikipedia : Maxwell Boltzmann
  2. Kinetic Theory of Gases.
Comments
  1. tallbloke says:

    Harry Dale Huffman responded to Clive’s article:

    Harry Dale Huffman says:
    August 10, 2012 at 2:07 pm
    I heartily agree that it should be clear (but to most it is not) that the lapse rate is basically just -g/c, with c the effective specific heat, and gravity alone is responsible, not “adiabatic” convection. In fact, I emphasize, and have strongly (and so far as I know, originally and uniquely) suggested in my own writing, that the lapse rate should be known as the “hydrostatic lapse rate”, not the “adiabatic lapse rate”, because it follows basically from the hydrostatic condition.

    But you might just as well say the lapse rate is maintained by the mass mean tropospheric temperature, instead of the surface temperature. I say this, because in my comparison of temperatures in the atmospheres of Venus and Earth, the Venus/Earth temperature ratio is obviously just that due to the ratio of the two planets’ distances from the Sun, nothing else (and that means, there is No greenhouse effect, of increasing temperature with increasing carbon dioxide, at all). The explanation for this empirical and logical fact is that the two tropospheres must both be warmed by direct absorption of incident solar IR radiation–in fact, they both must directly absorb the same physical portion of that incident radiation (otherwise, the great difference in planetary albedo and physical surface–in addition to the great difference in atmospheric carbon dioxide concentration–would not allow their temperature ratio to reflect only their distances from the Sun). Consensus theorists, if they would dispute this conclusion about the fundamental warming of the troposphere, must explain, within their theory, why the Venus/Earth temperature ratio does in fact depend only upon the ratio of their solar distances, according to the most basic physics understanding–and, to avoid misunderstanding, see my linked article, for the simple Stefan-Boltzmann equations governing the mass mean tropospheric temperatures in the two planets, if they absorb, and are warmed only by, the same fraction f of the incident solar.

    From my Venus/Earth findings, it seems clear to me that the surface cannot warm the atmosphere, globally (only locally and transiently), and indeed, at night, it can and does COOL the near-surface atmosphere, so that many locations see a local temperature inversion around dawn.

  2. Stephen Wilde says:

    Gravity plus atmospheric mass plus solar radiation coming in as the energy source must be sufficient to create a lapse rate above a flat surface simply because there must be a transition distance between heated surface and the cold of space.

    Convection is not necessary to create the lapse rate but rather seeks to disturb it.

    However, cooling of parcels of air convecting upward is always equally matched by warming of parcels of air convecting downward for a zero net effect from convection.

    It may not even be necessary for there to be conduction from a heated surface which I think is what Harry contends. In fact we could subsume conduction and convection together because a heated surface causes uneven heating of the air above resulting in convection. Even on a flat surface a point source of energy would heat the surface unevenly.

    All that convection achieves is an uneven energy distribution and varying lapse rate within what would otherwise be a uniform distribution with an equally uniform upward lapse rate at all locations

    If one then adds a spherical shape and then a rotation the patterns produced within the uneven energy distribution caused by convection will result in latitudinal climate zones around the planet just as we observe on every planet with an atmosphere.

    The system energy content will never change as long as atmospheric mass, gravity and insolation remain the same.

    If anything other than those three factors changes, such as the composition (without an increase in total mass) of the atmosphere then the system energy content remains exactly the same but the air circulation changes to adjust the rate of energy transfer from surface to space thereby keeping system energy content stable.

    The atmospheric circulation (including the total volume of the atmosphere as per the ideal gas law) will always adjust so that at the top of the atmosphere energy in equals energy out and in the process the sizes, intensities and positions of the permanent climate zones change as necessary.

    There is only regional climate change. The system energy content and the lapse rate stay the same but the unevenness of the energy distribution within the atmosphere is reconfigured instead of the system temperature changing.

  3. tallbloke says:

    Hi Stephen, a nice summary, though there are a couple of points which need clarifying.

    You said:
    However, cooling of parcels of air convecting upward is always equally matched by warming of parcels of air convecting downward for a zero net effect from convection.

    A lot of the energy carried by upward convecting air parcels ends up in space, so I’m not sure what you mean by “zero net effect” – on the lapse rate I assume. If so I’m not so sure that’s right. Isn’t the upward energy flow part of the reason the observed environmental lapse rate is ~30% lower than the theoretical dry adiabatic lapse rate? Or is that due solely to humidity?

    You said:
    There is only regional climate change. The system energy content and the lapse rate stay the same but the unevenness of the energy distribution within the atmosphere is reconfigured instead of the system temperature changing.

    Did you mean surface temperature?

  4. Stephen Wilde says:

    Hi Rog.

    i) You might know a bit more than me on this so does adiabatic warming of descending air match adiabatic cooling of rising air or not ? I understand that it does (because of the lapse rate) and that only so much energy escapes to space as is matched by incoming insolation at top of atmosphere because the circulation always reconfigures to maintain that balance. So you can have energy going up and coming down as much as you like the balance will still be maintained at top of atmosphere. In fact the amount of upward, sideways and downward movement (the overall vigour of the atmosphere) will depend on how hard the circulation has to work to achieve that top of atmosphere balance. The amount of work the atmosphere has to do would be affected by the composition of the atmosphere so that, whatever the composition, the circulation does just what it needs to do to maintain top of atmosphere balance.

    ii) I find the idea of ‘a surface temperature’ difficult to define and ascertain because of the amount of variability across the entire surface. Thus I prefer the idea of system energy content (partly so that I can include the oceans) which leaves the so called surface temperature (whatever that is) to vary a bit whilst the circulation adapts to deal with whatever forcings may be acting on it at any given moment. There is never a true equilibrium so the circulation is always playing catch up which means there will be some variation in surface temperature whilst the process goes on. However in the end the circulation always keeps system energy content stable.

    The vast majority of the forcing processes that try to disturb equilibrium are from ocean internal variability and solar effects on the chemistry of the upper atmosphere. The contribution of human CO2 emissions will be present in the mix but imperceptible by comparison.

    Regional climate change is simply a change in the rate of energy flow from surface to space during the equilbriation process.

  5. Hans Jelbring says:

    To Clive Best

    You are saying that “I am unhappy with the derivation of the dry adiabatic lapse rate given in all textbooks because it seems to me a somewhat circular argument.”

    I certainly approve of the derivatione made by professor James R. Holton found in “An Introduction to Dynamic Meteorology.” and object to your statement.

    The following steps will be found:
    o The entropy form of the first law of thermodynamics is formulateed. (formula 2.43 page 48)
    o Considering an adiabatic case the formula can be rewritten as Cp (d(lnT)) – R d(ln(p)) = 0
    o This form can be integrated and the formula for potential temperature is derived (formula 2.44 and (Google Potential Temperature to see the formula)
    o Derivate formula 2.44 and an expression containing the derivative of the potential temperature will evolve (formula 2.47)
    o Since the potential temperature is constant in adiabatic processes its derivative will vanish (formula 2.47)
    o What is left is formula 2.48 which says that -dT/dz = g/Cp

    There is absolutely no circular reasoning in Holton´s derivation. It is strictly mathematical and relies on 1) the first law of thermodynamics, 2) the hydrostatic equation and 3) the ideal gas law.

    His comment after the derivation is: ” Hence, the dry adiabatic temperature lapse rate is approximately constant throughout the lower atmosphere”. Observe that he is restricting the validity to below the tropopause which is important.

  6. Hans Jelbring says:

    To Clive Best

    You are stating:
    “It must be gravity alone that plays the crucial role in determining the lapse rate.”

    First, the derived formula contains both gravity and Cp. Hence gravity and the chemical composition of the atmosphere are deciding the temperature lapse rate at an energetic equlibrium assuming that the atmosphere is adiabatically arranged (equal total energy per mass unit).

    Second, different planets have atmospheres that are arranging its energy per mass unit more or less away from a constant value per mass unit (equivalent with an adiabatic temperature lapse rate)

    Third, the atmosphere above the troposphere are dominated by other physical processes than an approximate energetic equilibrium and íts temperature will vary very much between day and nights.

    Fourth, a dense atmosphere such as the one on Venus will more easy develope an approximate total energy per mass unit than an antmospher which is thin (like the Martian one).

  7. Hans Jelbring says:

    To Clive Best,

    You are stating:
    “The conclusion is that you don’t need convection to have a lapse rate on a planet. It is a consequence of gravity and a fixed surface temperature.”

    I certainly agree with your statement in your first sentence. I have shown detailed calculations in two articles published by Tallbloke that this is the case in a STATIC atmosphere.

    I disagree with your second statement. What favours the development of an almost constant temperature lapse rate in a planetary atmosphere is that its total energy content (big mass) is large in comparison with its power flux in and out of the atmosphere (which is approximately equal). Then a constant surface temperature will evovle as it has on Venus and Titan.

  8. Hans Jelbring says:

    Stephen says:

    “I understand that it does (because of the lapse rate) and that only so much energy escapes to space as is matched by incoming insolation at top of atmosphere because the circulation always reconfigures to maintain that balance. So you can have energy going up and coming down as much as you like the balance will still be maintained at top of atmosphere.”

    Stephen, the balance is approximate on different time scales. Just look at day and night. During a glacial the solar power balance is different from what it is now. I chosed the title of my thesis “Wind Controlled Climate” for a reason. It is known that global winds were much stronger during glacials than now. The reason for that is not (well) understood. What is sure is that the ocean energy content will leave the ocean surface water much quicker when winds are hard and energy will not be able to go back into the water again (not easy anyway). The power release from the ocean surface is proportional to surface wind speed squared. Solar radiation can penetrate water quite easily (10 – 100 m) and thermal radiation (from clouds to earth) can only penetrate about 1 mm of the surface.

  9. Bryan says:

    The Carnot cycle(CC) gives the best basic structure to build atmospheric heat transfer theory around.
    Combine CC with parcel theory as used to derive the DALR

    Earth surface heated by Sun.
    Air parcel in contact with Earth surface will leave with the characteristic temperature of the surface.

    1. Isothermal expansion stage
    The concept of an air parcel is almost universally adopted to describe the temperature profile of the troposphere.
    The parcel expands isothermally absorbing heat from the Earth surface
    Air parcel considered to be in hydrostatic equilibrium is used to analyse thermodynamic behaviour of troposphere.
    Air parcel in hydrostatic equilibrium means it is either stationary or moving with constant velocity i.e. no unbalanced force acts on body.
    Given a small nudge the air parcel will rise under balanced forces as Newtons First Law states.
    The dry adiabatic lapse rate(DALR) can be derived for dry air by combining the laws of thermodynamics with the hydrostatic condition.
    DALR = – g/Cp = – 9.8 K/km
    Derived from stationary condition showing DALR does not depend on convection being present.
    Strictly speaking the term convection should be used when an unbalanced force acts on theparcel.

    2. Adiabatic expansion stage.
    For ascending parcel
    The air parcel does work Pdv in expanding the air parcel.
    This work is supplied by the internal energy of the air parcel causing the temperature inside the parcel to drop.
    This loss in internal energy is stored in the atmosphere (surroundings).

    3. Isothermal Contraction stage
    On ascending the slight loss of energy by radiation becomes much more significant at higher altitudes as heat is radiated to space.
    The thinner colder air becomes more ‘transparent’ to long wavelength infra red

    4. Adiabatic contraction stage
    For descending parcel (or back convection if you like)
    The air parcel is slightly denser than surrounding atmosphere and so descends.
    The surrounding atmosphere does work Pdv compressing the air parcel.
    This results in an increase in the temperature of the parcel.
    The internal energy of the air parcel rises causing the temperature inside the parcel is increasing.
    This gain in internal energy is matched by the loss of atmosphere(surroundings) energy.
    The parcel arrives back at the start of the cycle .

    The cycle can now be repeated

    With water vapour present in air lapse rate decreases and is called the environmental lapse rate and an average figure of around -6.5 K/km is obtained
    The average effective radiation altitude(AERA) is taken to be about 5 Kilometres where the temperature is 255K.
    By working back from AERA to the surface the air temperature increases to give the average surface temperature of 278K or 15C.

    Other points to notice is that during adiabatic stages no significant amount of heat enters or leaves the air parcel.

    Heat absorbed in the isothermal expansion at Earth surface
    Heat emitted during isothermal contraction at TOA.

    This means that near reversible conditions are observed for the whole cycle.
    No cycle can be as perfect as the Carnot cycle but the atmospheric transfer is reasonably modelled by it.
    The simple model can be extended for instance a Hadley cell type circulation can be added if there is an imbalance in the horizontal radiative emission at TOA.

  10. Stephen Wilde says:

    Hans said:

    “Stephen, the balance is approximate on different time scales. Just look at day and night. During a glacial the solar power balance is different from what it is now”

    I agree.

    My point is that over time the atmospheric circulation reconfigures to balance energy in and energy out at top of atmosphere. During the balancing process there will be variations on different timescales and in different locations.

    For example, day and night create an uneven energy distribution between the lit and unlit sides so the air circulation has to do the job of stabilising the system.

    Likewise during glacial epochs the air circulation must change to accommodate the effects of all that ice.

    I think that proposition is fully consistent with your ideas about wind driven climate. The harder the air circulation has to work to match energy in with energy out at top of atmosphere the more vigorous the circulation will be with more wind.

    But nonetheless system energy content will depend only on gravity, atmospheric mass and insolation at top of atmosphere.

  11. Stephen Wilde says:

    Bryan said:

    “This means that near reversible conditions are observed for the whole cycle.
    No cycle can be as perfect as the Carnot cycle but the atmospheric transfer is reasonably modelled by it.
    The simple model can be extended for instance a Hadley cell type circulation can be added if there is an imbalance in the horizontal radiative emission at TOA.”

    Yes.

    Thanks Brian, that is how I see it.

    The Hadley cell type circulation is always correcting for imbalances in the radiative emission at top of atmosphere.

    It will expand and contract as necessary to achieve the goal of energy balance at TOA.Indeed the entire atmosphere expands and contracts as necessary.

    However there is also evidence that solar effects from above upset the TOA balance (as do oceanic effects from the surface) by altering the vertical temperature profile of the atmosphere. When that happens the Hadley cell type circulation along with every other part of the air circulation shifts to restore balance at TOA.

    It never actually achieves balance because the rate of ocean heat release and the effect of solar spectral changes on the upper atmosphere are always changing and the air circulation is always seeking to catch up.

    However those solar and oceanic variations are never so large that the changes in the air circulation fail to smooth them out.

    All that changes on the surface is the positions sizes and intensities of the permanent climate zones and those changes are what we perceive as climate change.

  12. tallbloke says:

    So are winds stronger in glacials because there is less humidity? That would reduce vertical transport and radiation to space, making the circulation work harder to shift energy to the night side for easier loss to space?

  13. Stephen Wilde says:

    That would make sense since humidity takes latent heat upwards for faster radiation to space so that the circulation need work less hard to maintain TOA balance.

    All fits together nicely doesn’t it ?

    It also supports the N & Z concept of ATE because the surface temperature beneath the atmosphere has no need to be at the S- B temperature as obtained by back calculating at the lapse rate from the effective radiating height.

    The surface temperature can be anything depending on internal system characteristics.

    The S-B equation will only be satisfied at or beyond the point where energy in equals energy out. It tells us nothing about the surface temperature beneath an atmosphere.

    Within an atmosphere the Ideal Gas Law prevails (as modified by the internal system characteristics).

  14. Nick Stokes says:

    Clive,
    The conventional derivation of the DALR simply shows that it is a neutral value for advection. Gas that rises (or falls) adiabatically keeps the same temperature as the surroundings. It neither gains nor loses buoyancy. No work is done or needed.

    Your derivation just postulates a different kind of perturbation and shows that the DALR is neutral to that too.

    Some things to think about with a lapse rate:
    1. You have to work to maintain it. There is some conduction along any temperature gradient, and if the effective conductivity is k, then entropy is created at a rate k(∇T.∇T)/T^2. To keep a steady state, you have to do work to remove this.
    2. Related – you can show the DALR is a neutral point, but you also need to know that there is a mechanism that restores to that point if the lapse rate is different. That’s where advection (turbulence) comes in. The air motions do the work (and lose KE).

  15. Hans Jelbring says:

    To Clive and all,

    You are saying:
    “Such arguments have then also been pillored for violating the second law of thermodynamics. However despite all this there is something not immediately obvious about the Earth’s atmosphere. In particular it is never in thermal equilibrium although it is in overall energy balance.”
    Agree, and I have spent lots of time and efforts to investigate and solve problems relating to the theoretical and observational temperature lapse rat in our atmosphere. In my opinion you are pointing to the central reason for confusion among scientists in this paragraph. I will try to make my points as clear as possible below. Scientists seem to have very hard to separate kinetic energy (flow motion) from a static energy situation. Think of a river where water never will rest and think of a lake where there might be a slow redistribution of energy forming a temperature gradient from the surface to the bottom. It is hard to learn about the energy distribution in the lake by observing the river that might feed the lake. It will also be hard to derive any formula describing the temperature gradient by relating to micro concepts without relating to the macro world and the physical properties of water.

    In the atmosphere it is a similar situation. Nobody would deny that the atmosphere contains energy since it can cool down (ultimately to the absolute zero). The main question is to find out: How is the energy contained in the atmosphere distributed and what effect will that have on the temperature gradient? The title of this thread is: “Understanding the lapse rate”. Let us remember it.

    The obvious approach is to investigate what the (average) lapse rate look like in the real atmosphere at different locations. It turns out that it varies a lot. However, the temperature in the atmosphere gets lower at higher altitudes, at least in the troposphere. Most people wrongly conclude that the total energy per mass unit decrease by altitude since they mentally consider temperature and energy exchangeable.

    The truth is that the total energy content in any air parcel increases or is constant as a function of altitude wherever on earth we measure the situation in a stable atmosphere (for simplicity we disregard the influence of storm condition and condensation-evaporation processes).
    The second laws of thermodynamics states that if the atmosphere (of any planet) is energetically isolated at a specific moment, arbitrarily chosen, its energy content spontaneously has to equalize per mass unit as time goes by. After a about 14 days all winds have seized and the atmosphere would be calm. All physical processes in the atmosphere will cooperate to reach an energy equilibrium condition.

    At such a moment the energy content in any equal mass m0 will be approximately equal. The temperature gradient will be described by dT/dz = -g/Cp where T is temperature (K), z is altitude (m), g is the gravitational constant (m/s^2) and Cp is specific heat at constant pressure (J/kgK).
    The problem in any real atmosphere is that a pulsating energy source exists at any specific location on earth (day/night and seasonal reasons) plus there is a pure mechanical force which is moving the atmosphere around. The latter is mostly ignored by meteorologists and climatologists which is a big mistake as is the interactions between solar energy and tidal energy influences.
    A feasible scientific approach to solve the energy distribution problem in our atmosphere which is an open system is quite simple:

    1) Disregard that it is an open system and find out how the energy has to be arranged in a closed system containing the atmosphere
    2) Estimate how much the fact that the system is open affects the temperature lapse rate in relation to what is valid for a closed system
    3) Estimate how much condensation and evaporation processes do affect the open system
    4) Check the situation in other planetary atmosphere to see how much the STATIC solution affects the observed temperature lapse rate in our atmosphere and in any plane keeping an atmosphere.

    The answer is that the major physical process affecting the temperature lapse rate in the troposphere of our atmosphere is dissipation of energy to become distributed equally to all equal mass units as is required by the second law of thermodynamics.
    This statement is more true (the approximation is better) on Venus (much mass per unit area) than on earth which is better than on Mars (small mass per unit area). It should also be noticed that the statement is not valid in the tropopaus or in the stratosphere where the dissipation process never is coming close to a static energy equilibrium situation.

    This is essentially a description of what I have done within the topic of temperature lapse rate during the last ten years and my arguments are presented in two articles in a scientific form, both qualitative and quantitative at:

    http://tallbloke.wordpress.com/2012/01/01/hans-jelbring-the-greenhouse-effect-as-a-function-of-atmospheric-mass/

    and

    https://tallbloke.wordpress.com/2012/01/25/hans-jelbring-an-alternative-derivation-of-the-static-dry-adiabatic-temperature-lapse-rate/

    Best wishes relating to confusion minimization

    Hans Jelbring

  16. Bryan says:

    Nick Stokes says

    “It neither gains nor loses buoyancy. No work is done or needed.”

    This is not quite correct.
    An ascending parcel of air does Pdv work on the surrounding air during its expansion.
    This is at the expense of the parcels internal energy and so its temperature drops.
    A descending parcel of air has Pdv work on it by the surrounding air and is compressed.
    This is at the expense of the surrounding air causing the parcels internal energy to rise and so its temperature rises.

    The fact that the ascending work lost by parcel is exactly the same as same as the parcels gain in energy on descending is due to gravity being a conservative force.

    So work done up equals work done down on parcel.
    So during the adiabatic stages there is no NET work done.

  17. Nick Stokes says:

    Bryan,

    I meant that no work is done or needed to make it rise or fall, because there is no buoyant force.

    Yes, the rising air does work in expansion on neighboring air, whatever the temperature gradient.

  18. Clive Best says:

    Sorry for not responding earlier. I am in Italy where it is very hot, although luckily I can escape to a higher altitude thanks to the lapse rate. There are some great comments in this thread which I will need to think hard about before responding. The original goal was to try to understand the lapse rate on a molecular level rather than just using classical thermodynamics. Then the role of gravity is more explicit since molecules loose kinetic energy scattering upwards through the atmosphere against gravity.

    Does the lapse rate change with the addition of CO2 ? I think it must change because some IR photons emitted from the surface will now be absorbed by CO2 molecules. Part of this energy will be transfered to nearby N2 and O2 molecules, and the rest re-emitted as photons randomly. This essentially causes a gradient heat flow through the atmosphere. In the real world H2O completely dominates the environmental lapse rate, but could small CO2 effects be seen in deserts. Has the average lapse rate changed at all over the last 150 years ?

  19. Stephen Wilde says:

    “I meant that no work is done or needed to make it rise or fall, because there is no buoyant force”

    Water vapour being lighter than air there is a buoyant force so work is being done constantly but it the end what goes up must come down so the net effect is zero for the system as a whole but in the process regional climate differences are created.

  20. Nick Stokes says:

    Clive,
    “Does the lapse rate change with the addition of CO2 ? … This essentially causes a gradient heat flow through the atmosphere.”

    Yes, indeed. As I mentioned above, you not only need that the DALR is a neutral point; you need a mechanism to drive the lapse rate toward that point. You also need a heat pump to remove the entropy. The rate of entropy creation is proportional to the conductivity k, and the transmission of IR with GHG raises the effective conductivity.

    The heat pump is provided by vertical air movements (the energy comes from the KE lost). Heat is pumped down, balancing the conduction upward, and this is the mechanism pushing the lapse rate toward the DALR. Pump efficiency is proportional to the deviation from the DALR. So the actual lapse rate settles to a point below the DALR where the heat pump balances the conductive losses (including IR transport). Adding GHGs pushes that balance point further below.

    Stephen Wilde,
    “Water vapour being lighter than air there is a buoyant force “
    Moist air is lighter than dry, but what determines buoyancy of a moist air parcel is whether it is less dense than the surrounding air, which probably isn’t dry.

  21. Bryan says:

    Clive Best says:

    “Does the lapse rate change with the addition of CO2 ? I think it must change because some IR photons emitted from the surface will now be absorbed by CO2 molecules. Part of this energy will be transferred to nearby N2 and O2 molecules, and the rest re-emitted as photons randomly.”

    There are two main attempts at explaining vertical heat transfer in the troposphere.

    1.Thermodynamics plus a hydrostatic balance between a buoyancy force and gravity.
    All explanations for the DALR that I have read use this explanation.
    Notice the greenhouse effect has no place in this explanation.

    2. Use of the radiative transfer equations.
    This is the explanation favoured by the IPCC.
    The Earth surface radiates upward towards atmospheric slabs which re-radiate part up part down.
    This provides an explanation for a temperature gradient.
    This also provides the basis for the ‘greenhouse effect’ theory.
    This Radiative-Convective theory has no explanation for the DALR that I have come across.

    Why should that be?

    In DALR conditions the CO2 and H2O still have radiative effects in line with their temperature.
    Dry air does not mean no H2O molecules present, in fact they typically number more than 30 to one of CO2 .

    As far as I can make out the radiative effects of air are fully included in the bulk thermodynamic quantity Cp (the heat capacity).
    So great care must be taken in case the radiative component is counted twice
    For most of the atmosphere the radiative component for adjacent volumes of gas self cancels.
    Only at the TOA is there a significant net outflow outwards in the colder thinner conditions.

    Cp for air is almost constant for atmospheric temperatures (250K to 350K)
    Cp for CO2 changes by 13% for atmospheric temperatures (250K to 350K)

    If say atmospheric CO2 were doubled then since it is such a tiny fraction of air the effect on the capacity of air (Cp) would be negligible.
    Therefore the effect on the DALR would also be negligible.

  22. Stephen Wilde says:

    “Moist air is lighter than dry, but what determines buoyancy of a moist air parcel is whether it is less dense than the surrounding air, which probably isn’t dry.”

    There are varying amounts of water vapour within different parcels of air.

    Water vapour being lighter than air the more of it there is within a parcel of air the lighter the whole parcel will be and the more likely it is to rise due to increased buoyancy.

    Lighter generally means less dense.

  23. Clive Best says:

    Evaporation and convection of moist air reduces the lapse rate resulting in a negative feedback for increased CO2 forcing. An increase in CO2 concentration results in a rise of the effective radiation altitude (for CO2) because opacity increases. For a fixed lapse rate this new height is estimated to be increased by about 180m for a doubling of CO2 – see for example this discussion. This new height is colder so less IR radiation escapes to space than before. i.e. This is the classic AGW story…

    However, if increasing CO2 itself changes the lapse rate through thermalising absorbed IR with adjacent air throughout the atmosphere, then it too would provide negative feedback by reducing the lapse rate. In other words the effective radiation altitude where the CO2 fog clears is now slightly warmer than it was before (due now just to CO2). Perhaps this thermalising effect is already included in radiative transfer models, but I have never seen this stated explicitly.

    I have been told that for H2O the negative feedback from the lapse rate is almost exactly balanced by the positive feedback from extra greenhouse effect. If the same turned out to be the case for CO2 then we can all go home.

  24. Stephen Wilde says:

    “I have been told that for H2O the negative feedback from the lapse rate is almost exactly balanced by the positive feedback from extra greenhouse effect. If the same turned out to be the case for CO2 then we can all go home.”

    Quite, I’ve been saying for years that the thermal energy processed by more CO2 simply enhances the water cycle so that any slowing down of the rate of energy loss to space from more CO2 is offset by a speeding up of energy loss to space from a faster water cycle for a zero or near zero net effect.

    That assumes CO2 slows down energy loss to space in the first place but in fact there is a good case for saying that CO2 holding more energy in the air rather than letting it enter the oceans actually facilitates energy loss back tospace equally as much as it slows its transmission down through the atmosphere.

  25. Stephen Wilde says:

    A correction to my earlier comments.

    The point where energy in equals energy out is not at top of atmosphere but actually within the atmosphere.

    Nonetheless the air circulation always reconfigures so as to achieve that balance whatever forces try to disrupt it.

    Solar input determines the height at which balance is achieved whereas pressure at the surface determines the temperature achievable at the surface (averaged globally).

  26. br1 says:

    Clive:
    “Consider now increasing the height level by height . It is assumed that locally for each level thermal equilibrium is reached”

    Hi Clive,

    I’m a bit confused by this statement – what does ‘locally’ mean? I guess you mean just between heights z and z+Dz? But eventually all the layers will come into equilibrium with eachother, which gives an isothermal answer.

    In any case, your maths (apart from some slips, such as in the derivative of P, dP/dz, wich should maintain the exponential) seems to be about an isentropic expansion (both adiabatic and reversible) as in the case of the slow expansion due to a piston. In this case you will indeed get a cooling as the piston is withdrawn, but at each stage during a slow expansion the gas will be homogeneous and isothermal! So when the atmosphere is trapped in a 1m thick layer it will have one temperature, but when you expand the layer the whole atmosphere will cool, not just the bit nearest the top. Convection works against you here, as that will provide strong mixing. What also works against you is that the expansion only happens once – when the cap has reached full atmospheric height, no further cooling occurs. The full atmosphere then settles into being isothermal over all heights, unless there are other drivers.

    The standard explanation gets around this ‘only happens once’ expansion by invoking parcels, and one can generate new parcels so that when one has risen and dissipated, a different one can be formed and go through another rising process at a later time.

    My model, see for example https://tallbloke.wordpress.com/2012/06/28/graeffs-experiments-and-2lod-replication-and-implications/#comment-30327 and onwards, is for a 2D gas under gravity. The isolated case gives a practically isothermal solution even with very strong gravity – nothing close to a DALR. I can get circulations driven by temperature differences, but I don’t believe one can get a DALR unless one has pulses of heat to generate parcels. My opinion at the moment is that a DALR cannot be achieved with steady-state flows, such as a Hadley cell (!!! does this make me a heretic?), as for a steady flow the ‘expansion work’ is done only once in setting up the flow, but then forgotten, so that conduction always rules in the long term. I’m looking into day/night cycles being important in order to create fluctuations and ‘parcels’.

  27. Clive Best says:

    @br1 – I’m a bit confused by this statement – what does ‘locally’ mean?

    Sorry- I agree that the wording is not very clear. What I really mean here is that I assume a Maxwell Boltzman distribution with an equipartition of energy for each level in the atmosphere. For an increase in height DZ there is a loss in mean kinetic energy to the gain in gravitational potential energy.

    If the system were thermally isolated then you a right it would eventually reach isothermal equilibrium at a single temperature T with boltzman factor exp(1/2mv2 -mgZ)/kT. However the surface is held at a fixed temperature and heat/energy is flowing upwards. The (naive) picture then is each level is continuously being replenished with higher energy molecules from below, but you can still define a MB temperature for each level through equipartition as T = mv(rms)^2/3k.

  28. Clive Best says:

    I meant to add that the Nick Stokes picture of a heat pump seems rather attractive.
    “The heat pump is provided by vertical air movements (the energy comes from the KE lost). Heat is pumped down, balancing the conduction upward, and this is the mechanism pushing the lapse rate toward the DALR. Pump efficiency is proportional to the deviation from the DALR. So the actual lapse rate settles to a point below the DALR where the heat pump balances the conductive losses (including IR transport). Adding GHGs pushes that balance point further below.”

    A dynamic equilibrium is maintained between heat loss and heat gain throughout the atmosphere. DALR is an idealised equilibrium for a perfect gas. Add water and CO2 and the lapse rate changes.

  29. suricat says:

    Clive Best.

    “Add water and CO2 and the lapse rate changes.”

    This is also part of my problem with your article. You say “I am unhappy with the derivation of the dry adiabatic lapse rate given in all textbooks because it seems to me a somewhat circular argument.” and I concur because ‘water vapour’ is included in the ‘DALR’ (dry adiabatic lapse rate), but without its condensation/precipitation. However, your ‘perfect gas’ analogy divorces any resemblance of your model to a DALR.

    A true DALR incorporates a mix of gasses and should be analysed as such. From the ‘atomic weight’ of each element that constitutes the DALR make-up, a value for the element’s ‘gravitational attraction’ (weight) can be deduced. By undertaking this exercise it can be realised that water vapour exhibits ~3/5 the weight of the bulk of other atmospheric constituent elements. IOW, water vapour is ‘lighter than air’.

    This brings me on to the convection aspect. I understand two mediators of convection, forced and natural.

    A forced convection is mediated by an advected atmosphere that is forced to alter its altitude while negotiating the topography of the local landscape. The energy for convection here is provided by the advecting winds and is ‘~quid pro quo’ with losses to turbulence.

    A natural convection is more controversial to the ‘text book’ version and is mediated by specific gravity (see para 2 of this post). It’s natural convection that I want to discuss here because there is such belief here that the energy that produces the convection is supplied by the convecting parcel of air. It isn’t!

    Best regards, Ray Dart.

  30. Trick says:

    suricat 1:41am – “It’s natural convection that I want to discuss here because there is such belief here that the energy that produces the convection is supplied by the convecting parcel of air. It isn’t!”

    This is good.

    Given a rigidly enclosed, adiabatic m^2 column with initial condition of earth’s non-GHG dry air going up thru the troposphere w/o a heat source at bottom nor a heat sink at top, what then produces the energy for the natural convection?

    [Mod note] Rescued from spam, not sure why it ended up there. TB

  31. br1 says:

    This is me thinking out loud:

    In considering ‘what is a parcel anyway?’, I’m now coming to the opinion that they are very like bubbles you get in fizzy drinks. They probably start on the bottom surface, build up in size due to a local ‘bubble source’ (such as a hot section of ground), and then at some stage they will detach and rise in the atmosphere like a bubble. As they rise, they push against the surrounding ‘uniform’ air, expanding as they rise and losing energy to that work, thus cooling down. When they get to a similar density region of atmosphere, they stop rising and ‘pop’, becoming uniform with the surroundings. Presumably a similar thing can happen going down, but this may be more due to a very large area ground heating with cold air above, so that the cold air becomes unstable and forms a bubble which sinks (maybe).

    If there is a constant wind rising in the atmosphere, I feel the cooling process is very different – the wind will have a non-Maxwell-Boltzmann distribution (as it has a net velocity), and so this can also cool with altitude, but the rate will depend on wind velocity and so won’t be at the DALR.

    A continuous updraft shouldn’t give the DALR, as the expansion work is only done once in setting up the flow. After the flow is established, there is no further expansion work, and so the cooling rate must change away from the DALR. Imagine air flowing up a pipe – the pipe may change cross-sectional area, but once the flow-lines are established, the air does not do any work when changing cross-sectional area. There may be a small temperature effect due to the Joule-Thomson coefficient, but that is unrelated to g or Cp so should not give the DALR. During the starting and ending phases of a ‘continuous wind’, there may be a DALR effect as the stream has to fight to make a path through the surrounding air, but there won’t be a DALR during the steady-state wind phase.

    The effect of GHGs on DALR is not clear to me, will need to think more on that.

    Warning: above opinions subject to change without notice :)

  32. Bryan says:

    br1

    Whats wrong with the orthodox theory of an air parcel under thermodynamic and hydrostatic gravitational balance?

    There are several very similar derivations of the DALR using these constraints.

    This simple model gives the neutral atmosphere which is observed to be very stable at night.
    Introduction of horizontal wind and even winds with a vertical component will greatly complicate the picture.

  33. br1 says:

    Bryan:
    “Whats wrong with the orthodox theory of an air parcel under thermodynamic and hydrostatic gravitational balance?”

    Probably nothing, but what’s an air parcel?

    To me it seems like it has to be a bubble – a temporary thing with an enclosed boundary. Granted, the boundary is not solid and is rather vague, but if one considers by contrast a *continuous* rising air *stream*, I’m not convinced that one will get a lapse rate equal to the DALR. So for example, if one considers a Hadley cell, which I visualise as a continuous circulation, then I don’t think by itself it will give a DALR. So I guess I’m trying to draw a distinction between a bubble and a current.

    I could be wrong.

  34. Roger Clague says:

    Clive Best says

    “This fixed surface temperature maintains the lapse rate, by providing a constant source of high energy molecules which can migrate to the upper atmosphere against gravity”

    The surface temperature does not maintain the lapse rate. The lapse rate maintains the surface temperature.

    High energy molecules from the surface are not needed. THe total energy of the molecules does not change. Gratitation energy is changed to Kinetic energy nearer to the surface

    The mass not the composition of the atmosphere affects the surface temperature.

  35. suricat says:

    Trick.

    “Given a rigidly enclosed, adiabatic m^2 column with initial condition of earth’s non-GHG dry air going up thru the troposphere w/o a heat source at bottom nor a heat sink at top, what then produces the energy for the natural convection?

    Your scenario is for an ‘ideal gas’ and as such is a ‘text book’ ‘conundrum’ for a real scenario. GHGs (or ‘mixed’ gases) are a ‘real’ part of the DALR for a ‘real’ scenario and have to be included.

    The obvious answer to the ‘real’ scenario is the Sun, because without this there would be no atmosphere and this also provides the energy that elevates water to the phase of water vapour.

    On to your ‘parcel rise’ query.

    Water vapour exhibits a density property that equates to ~3/5 the density of the averaged bulk of all other atmospheric components. Thus, a parcel with more water vapour (non condensing) will climb to a greater altitude than a parcel with less water vapour as defined by Archimedes’ principle, so the buoyancy effect isn’t simply one of temperature and pressure.

    So it’s ‘gravity’ that expedites the afore mentioned ‘heat pump’ effect and not the energy within the parcel! :)

    (well spotted TB).

    Best regards, Ray.

  36. Trick says:

    suricat 2:42am – “..obvious answer to the ‘real’ scenario is the Sun…”

    Yes, indeed water vapor is lighter than air. However, water vapor is not required in the parcel to get natural convection and a DALR. All the DALR derivation needs is an ideal gas in hydrostatic equilibrium undergoing an approximate adiabatic process w/gravity and no condensation allowed.

    Of course, the sun is necessary to provide at least earth’s hydrostatic equilibrium assumption in the initial conditions. My question remains to discuss what about natural convection in air w/o water vapor or other GHGs?

    ————————————————-

    br1 1:03pm – “…what’s an air parcel?”

    Parcels of gas are just thought up by humans. Parcels are fuzzy but useful concepts as control volumes for energy, N et. al. accounting. Despite years of observations, meteorologist parcels have not been seen in the wild.

    The derivation of the observed DALR from human’s concept defn. of a finite life unseen parcel works b/c the parcel needs to live for only that very brief moment where the math is based on instantaneous rate of change of a parcel’s T wrt z. Once the math work is finished, the parcel can disappear into thin air as it is no longer of interest leaving behind an intact approximate (DALR = g/Cp) math result.

  37. Brian H says:

    NS;
    “the transmission of IR with GHG raises the effective conductivity.”
    I have long considered this to be the mechanism for the startlingly uniform day/night temps on Venus. CO2↔CO2 transmission would be very efficient at the densities and temperatures on the surface there — a kind of “short circuit”.

  38. Bryan says:

    Trick makes a valuable observation

    “The derivation of the observed DALR from human’s concept defn. of a finite life unseen parcel works b/c the parcel needs to live for only that very brief moment ”

    Given the very low vertical speeds of air motions it would take months to complete a surface to TOA transit in ideal conditions.
    Day/night differences, winds, humidity rule all that out.

    Its remarkable in that ‘brief moment’ given correct observational values that the thermodynamics plus gravitation theory works.

    The mystery is where is the ‘greenhouse effect’?

  39. suricat says:

    Trick.

    “All the DALR derivation needs is an ideal gas in hydrostatic equilibrium undergoing an approximate adiabatic process w/gravity and no condensation allowed.”

    I assume “w/gravity” = “with gravity” and isn’t a mathematical statement of “w over gravity”. If it is, what does “w” represent?

    You also say: “My question remains to discuss what about natural convection in air w/o water vapor or other GHGs?”

    Again, does “w/o = “without”, or is it a mathematical term? However! :)

    The ‘ideal gas’ scenario is used to educate school children on the merits of Boyle’s and Charles’s laws and their ‘provenance’ (derivation) for the ‘PVT’ formula (one of the few physics formulae that can provide a mathematical ‘proof’). However, if Earth’s atmosphere was assumed to be devoid of ‘all’ GHGs, the residue would still not provide an atmosphere that could meet the criterion for an ‘ideal gas’! Again, however:

    Without GHGs, Earth’s atmosphere wouldn’t radiate well. We wouldn’t observe any cooling of a parcel as a convective plume rises from the surface of the planet, other than the expected effects from turbulent mixing. The surface would provide most of the radiative cooling ability, with the atmosphere only radiating energy to space at the rate limited by the molecular kinetic level (black body).

    What does this have to do with Earth’s DALR and where is Clive Best? I think Clive shares my concerns. :)

    Best regards, Ray.

  40. br1 says:

    suricat:
    “Without GHGs, Earth’s atmosphere wouldn’t radiate well.”
    For sure.

    “We wouldn’t observe any cooling of a parcel as a convective plume rises from the surface of the planet”
    I disagree. The theory behind why rising parcels cool is that there is expansion work done against the surrounding air. This is like a bubble rising in a fizzy drink, which also expands as it rises and so must also cool a little bit (I wonder if anyone has measured that!).

    “The surface would provide most of the radiative cooling ability”
    Without GHGs, the surface would provide practically all of the radiative cooling. Note that atmospheric convection currents would still be expected, as these can be driven by ground temperature differences as well as vertical temperature differences, so one will still get parcels (=bubbles) moving around the atmosphere.

    I had said above that I visualise a Hadley cell as a continuous circulation, but that may be incorrect. Maybe it is more like a series of bubbles rising at the equator, and a series of bubbles sinking in the higher latitudes? The average may look like a circulation, but the atmosphere may be more like a fizzy drink than I previously thought. And when a bubble rises in a fizzy drink, where does the energy come from? :)

  41. br1 says:

    My new line of research into bubbles quickly revealed a whole new topic, called ‘fizzics’. This is important stuff with surprising consequences! For an aperitif, have a read of the following article:

    http://www.world-science.net/exclusives/120524_beer.htm

  42. br1 says:

    tallbloke:
    “Good one br1. Take a read of this article too:”

    Doc Brown makes a good point that needs answering. Complicated things, atmospheres.

  43. Trick says:

    suricat 2:19am – Yeah, I mean “with gravity”.

    In this top post I note Clive Best started it out “If we ignore greenhouse gases and radiative transfer…”

    Seems this non-GHG situation is less complicated in theory. If enough informed, critical posters can achieve common text book agreement of basic atm. thermo (with non-GHG assumption) before moving on to much tougher physics of infrared active gases (IAG more precise than GHG) then so much the better for common progress. The T lapse = g/Cp derivation doesn’t need infrared active gases so far as I can see in the text book top post math.

    All matter above 0K will radiate so the radiative transfer to space heat sink won’t cease if the infrared active gases are theoretically removed from the atmosphere. Approximate troposphere equilibrium T lapse = g/Cp would still be valid in a column of non-IAG air. So would the exact equil. lapse T(z)/To = (P(z)/Po)^R/Cp.

    Also non-IAG atm. – the (mostly N,O) radiative atmosphere “residue” – would still be an ideal gas so I am curious as to what criterion you are writing about.

  44. ferdberple says:

    br1 says:
    August 21, 2012 at 10:01 am
    As they rise, they push against the surrounding ‘uniform’ air, expanding as they rise and losing energy to that work, thus cooling down.
    ===================
    The problems in duplicating the DALR with the sim do raise question. The surrounding air must equally be warmed as the rising air is cooled.

  45. br1 says:

    ferd:
    “The surrounding air must equally be warmed as the rising air is cooled.”

    yes, and in a closed container this always leaves the steady-state condition warm-on-top. Unless there is cooling from the top or course, but that is trivial. Applying pulses of heat to create bubbles is another idea I’m looking at, but nothing to report so far. Probably needs lots more molecules which may be beyond the easy reach of the sim.

  46. suricat says:

    br1.
    “I disagree. The theory behind why rising parcels cool is that there is expansion work done against the surrounding air.”

    That theory is false! The energy causing a parcel to rise is supplied, free of energy budget cost to the parcel, by ‘gravity’ per se. However, it’s difficult to isolate a parcel from it’s environment to accurately observe and measure which attractors drain energy to whatever element of the environment, but a conclusion can be made by gathering evidence from various experimental data.

    The most prominent attractors are turbulent mixing (cause by the parcel rising in the atmosphere), seconded by IR radiation (which also plays an active part within the turbulence generated by the parcel rising) which has a very short ‘depth to extinction’. Gasses are ‘bad’ conductors of thermal energy due to their ‘disconnected’ molecular structure and/but their high rate of absorption to thermal (IR) radiation both hinders/helps energy transfer depending on the scenario being appraise. In turbulent air IR helps, but in static air IR hinders energy transfer (as an ‘attractor’).

    Probably the least prominent attractor would be the energy expended by the parcel to increase in volume. We’re looking at the energy needed to move a small amount of an identical gas at ~equal pressure, ‘hydraulically’, to accommodate the expansion of ‘the parcel’.

    However, this isn’t what this thread is about and I’ve already ‘trolled’ too much (apologies to Clive), but I’ll not post here again without the thread author’s participation. :)

    Best regards, Ray.

  47. tjfolkerts says:

    The cause of the temperature difference between the bottom of the troposphere and the top of the troposphere is differential heating. The bottom is heated by contact with the sun-warmed ground; the top is cooled by thermal IR to space. Therefore the top must (at least on average) be cooler than the bottom.

    The temperature gradient from bottom to top is determined by the properties of air. If the differential heating/cooling is small enough, then energy will be transmitted only by conduction. When the heat flow is larger, convection sets in (because the air becomes unstable). Convection is a powerful way to transmit thermal energy, and effectively caps the gradient.

    It is kind of like pumping air into a large tank with 1) a small leak (like conduction that can handle small flow rates) and 2) a pop-off valve (like convection, which only occurs for large enough pressures, but then can let a lot of air out ). If the air is pumped slowly enough, then the leak can handle the air flow. The faster the air flows, the larger the pressure becomes inside the tank. Once the air flow is large enough, then the pop-off valve opens, limiting the pressure.

    The convection is a “pop-off valve” that kicks in when the temperature gradient tries to rise above the adiabatic lapse rate. For this reason, the lapse rate can be well below the adiabatic lapse rate (over even reversed with “inversions”), but the lapse rate can never be much above the adiabatic lapse rate.

  48. Stephen Wilde says:

    “If the differential heating/cooling is small enough, then energy will be transmitted only by conduction”

    You have to consider horizontal temperature differences not just vertical ones.

    ANY unevenness in energy distribution horizontally will give rise to convection and illumination is always uneven around a sphere even if the surface were to be perfectly smooth.

    “The convection is a “pop-off valve” that kicks in when the temperature gradient tries to rise above the adiabatic lapse rate”

    No popping off is called for. Convection is ever present and continuous where heating is not perfectly even in all three dimensions and it never is.

    “the lapse rate can never be much above the adiabatic lapse rate.”

    There is certainly a basic lapse rate set by pressure at the surface plus insolation. Definition seems to be a problem though. Some don’t like the term adiabatic, The term hydrostatic has been suggested where water vapour is present. As you say, any deviation from the lapse rate is negated by movement within the body of air.

    However where the actual lapse rate is less than the adiabatic lapse rate such as beneath an inversion that difference has to be compensated for somewhere else within the system so that energy in continues to match energy out. The necessary balancing act is achieved by contraction or expansion of the atmosphere or by portions of it. Therefore on average globally you can’t have less than the lapse rate either.

    That is what has led to the need to distinguish between the actual environmental lapse rate which varies from place to place and from time to time in all three dimensions and the adiabatic lapse rate which is set for the system as a whole by pressure and insolation.

    “The bottom is heated by contact with the sun-warmed ground; the top is cooled by thermal IR to space. Therefore the top must (at least on average) be cooler than the bottom.”

    Correct.There has to be a distance across which the transition occurs but there is an interesting issue arising.

    Is it actually necessary for there to be conduction at all ?

    Harry Huffman points out that temperatures seem to be the same at the same atmospheric pressure on any planet adjusted for distance from the energy source.

    That implies direct heating of the air (of whatever composition) by the energy source simply as a result of mass / density with radiative qualities being irrelevant.

    However, personally I think you could get that result from surface to air conduction initially but then with the lapse rate doing the necessary ‘work’ to merely maintain such a vertical profile.

    I’d be interested to hear Harry’s take on that suggestion.

  49. br1 says:

    Thinking about this some more has led me to another approach to getting the DALR.

    While my model can impose temperature differences at ground level, and temperature differences between ground and altitude, and I can plot all the circulations, I have been having a hard time reproducing the actual DALR. I have no problem getting temperature gradients, but they can be greater or lesser than the DALR – there seemed to be nothing special which clamps the gradient at the DALR.

    However, I realise now that setting the *temperature* of the ground is not the right condition. I should still be setting the *temperature* at altitude (I think), but I should set the *heating rate* of the ground. This is quite different, as the ground temperature can then find its own equilibrium, and the temperature gradient is more liable to clamp near the DALR. Maybe.

    This will require some changes to the sim (give the ground a thermal heat capacity and calculate all the energies of the molecule/floor collisions and emissions). Should be fun!

    I might have to change the ceiling boundary condition too, but I’ll start simple.

  50. tallbloke says:

    Hi br1; I haven’t been following the sevelopment of your model, so let me ask a dumb question.

    Is the model dynamic in the sense of throughput of energy?

    If as you say, you let the surface temperature float up to equilibrium temperature by setting it’s characteristic response to energy input, and fix the rate of incoming energy as an analogy to the amount of sunlight getting past the cloud albedo, might that enable your model to become more ‘realistic’?

  51. br1 says:

    Hi Tallbloke,

    The model has got this far:
    1, A 2D gas of finite sized molecules in a box,
    2, Gravity present,
    3, Temperature of floor of box can be set, including different sections of the floor having different temperatures,
    4, Ceiling temperature can be set,
    5, Wall collisions can be mixed between reflective and thermal.

    After some re-writes, the physics of point 1 is now exact – molecule-molecule and wall collisions are dealt with, and the molecule density can approach a fully packed ‘solid’ situation without any compromise, the simulation is always exact. Likewise the temperature interactions with the walls is dealt with exactly, and gravity can be set as high as you like.

    Some things the simulation doesn’t include are molecule-molecule attraction, rotational degrees of freedom, and radiation.

    Under these conditions, there is practically no temperature gradient with altitude. If there was some intrinsic reason for a temperature gradient, such as ‘molecules lose energy with height under gravity, therefore higher up should be colder’, or ‘temperature is related to pressure’, or such as Clive Best is asserting in this thread (that rising molecules must perform work against the molecules above them??? I’m not quite sure what the assertion is), then I would expect the simulation to see it. But it doesn’t – the profile is isothermal with height. When all the walls are reflective, there is a very very small temperature gradient due to Velasco1996, but this is really negligible on the scale of what we are looking for and doesn’t apply to the atmosphere anyway.

    The model has enough physics to exhibit the DALR given the right conditions. However, I have not pin-pointed what those conditions are! So now I’m trying to home in on what those conditions are. Having an energy budget is one condition I have side-stepped so far. I had previously set temperature in the hope that convection would kick-in at some stage to clamp the gradient at the DALR, but I have found it is not so simple! You get convection alright, but the temperature gradient can easily exceed the DALR. My next step is to put in energy flows – this might change the situation because heat transfer is likely not a linear function of temperature difference. If heat transfer speeds up at higher temperature differences (due to ‘extra’ convection, or bubble generation, whatever), then this will tend to clamp the temperature gradient. I’ve yet to see it though, so my opinion is still very much subject to change!

  52. br1 says:

    Stephen Wilde:
    ” Convection is ever present and continuous where heating is not perfectly even in all three dimensions and it never is.”

    My simulation agrees with this – one doesn’t need a critical temperature difference before convection sets in, any small difference will do.

    This may be a point overlooked in the usual ‘convection roll’ experiment, where the base of a pan of water is heated, and above some critical temperature difference between base and surface a convection roll will set in. The reason this requires a minimum critical temperature difference is that due to symmetry, one needs an instability to self-accelerate away from the symmetric condition. But if you apply heat to half the bottom of the pan, then there will be a convection roll anyway at much smaller temperature gradients, as the asymmetry already drives it. As air is very low viscosity, it will start to roll at very small temperature gradients, much less than the DALR. And I have the sim to prove it :)

    Which is one of the reasons I’m finding it difficult to get a clamped DALR.

  53. Tim Folkerts says:

    Stephen says:

    “ANY unevenness in energy distribution horizontally will give rise to convection and illumination is always uneven around a sphere even if the surface were to be perfectly smooth.”

    Actually, I think that only a forced temperature gradient with heating at the bottom and cooling at the top will drive convection. Discussing the details would take more time than I have now (and i need to think thru all the concepts better myself) . However, in practice heating one part of the surface and cooling another part of the surface will will create the requisite vertical gradients and create convection, so the difference is mostly academic.

    No popping off is called for. Convection is ever present and continuous where heating is not perfectly even in all three dimensions and it never is.

    I disagree. Consider the situation where the TOP of a fluid is uniformly warm and the BOTTOM is uniformly cool (which certainly qualifies as “not perfectly even in all three dimensions”). In this case there is no convection. The hot, low density air is already at the top and “wants” to stay there.

    If the top and bottom are the same temperature, there will be no convection (no energy to drive the bulk motion).

    The basic theory of convection and adiabatic lapse rate (presented earlier by others) says that until the actual lapse rate exceeds the theoretical adiabatic lapse rate, then the thermal energy will simply go into conduction and NOT convection. I recognize that the energy needed to exceed the adiabatic lapse rate is very small, so convection is very common, but in principle (according to the standard theory), there could be small temperature gradients where no convection is created.

  54. Tim Folkerts says:

    BR says: “My simulation agrees with this – one doesn’t need a critical temperature difference before convection sets in, any small difference will do.”

    I would enjoy knowing more details here. Part of my intuition says this should be right, and part of my intuition says this should be wrong. Of course, intuition can be a dangerous thing, and minor details could change the answer in situation like this.

  55. br1 says:

    Tim Folkerts:
    “I would enjoy knowing more details here.”

    I will have to rebuild my sim a bit to show you exactly what I’m referring to. I had quite a refined version but then my USB stick died and I had to revert to a more primitive one. At least the physics is now beyond question. Unfortunately it might be early next week before I can rebuild it and get back to you.

    I calculated the expected DALR here: https://tallbloke.wordpress.com/2012/06/28/graeffs-experiments-and-2lod-replication-and-implications/#comment-30610

    I thought I saw one here: http://s1257.photobucket.com/albums/ii503/brspics/?action=view&current=DALR_10g.png
    but I’ll have to change that commentary as it is all wrong – I’m pretty sure this is not a DALR at all.

  56. Stephen Wilde says:

    br1,

    Maybe one cannot ever get a ‘clamped’ DALR.

    Instead one always gets areas with a steeper gradient and areas with a shallower gradient but between them always averaging out to the DALR.

    The reasons being:

    i) Heating can never be uniform around a sphere or even on a flat surface if the energy is from a point source and ANY unevenness in heating will cause density differentials leading to convection.

    ii) Once a parcel of air rises by convection another equal sized area has to descend to make room for it and the energy lost by the expansion of the first parcel is exactly offset by the energy gained by the compression of the second parcel.

    iii) You can have the actual lapse rate varying all over the place in all three dimensions but as long as it all averages out then energy into the system will always match energy out of the system.

    iv) As soon as there is any imbalance between energy in and energy out the size of the entire atmosphere changes to eliminate the difference and in the process the pattern of circulation changes.

    v) Since the revolving sphere forms climate zones within the atmosphere then whenever there is any adjustment required to maintain balance the sizes, positions and relative intensities of the climate zones will change too.

    vi) So you can have a theoretical DALR derived from the numbers for the intensity of the gravitational field, the total mass of the atmosphere and the amount of insolation but find that it is never actually maintained from any given point on the surface.

  57. Stephen Wilde says:

    Tim said:

    “Actually, I think that only a forced temperature gradient with heating at the bottom and cooling at the top will drive convection

    Isn’t that implicit in what say ?

    The surface is warmed initially by incoming solar, the lapse rate is created by the fact that it takes time for energy to travel upwards through the atmosphere towards the cold of space whether that travel be via radiation, conduction or convection.

    and:

    i said:

    “No popping off is called for. Convection is ever present and continuous where heating is not perfectly even in all three dimensions and it never is.

    Tim replied:

    I disagree. Consider the situation where the TOP of a fluid is uniformly warm and the BOTTOM is uniformly cool (which certainly qualifies as “not perfectly even in all three dimensions”). In this case there is no convection. The hot, low density air is already at the top and “wants” to stay there.

    My response:

    Not applicable on a revolving sphere heated constantly and non uniformly by a point source of energy and surrounded by an atmosphere.

  58. Trick says:

    br1 1:53pm: “…(sim) very small temperature gradient due to Velasco1996, but this is really negligible on the scale of what we are looking for and doesn’t apply to the atmosphere anyway.”

    In the top post Clive Best shows one of the 2 ways to derive earth atmosphere 3D approx. ideal dry lapse = g/Cp = 9.8oK/km. So of course a lapse is negligible on the order of the limited for calc. speed sim height (or Graeff’s container). Velasco 1996 derives the exact ideal lapse rate (eqn. 8) which is ideally applicable to earth and is higher than the empirical 1992 US Standard Atmosphere lapse.

    For example, the tropospheric part of the Standard Atmosphere measured T between pressures P1 = 1013.25 hPa and P2 = 264.36 hPa empirically lapses ~ 63K where the Velasco eqn. 8 exact ideal lapse is faster lapsing ~73K. The real atm. lapse rate being lower than ideal due to effects from insolation & forced convection non-equilibrium, infrared active gas PPM, aerosols, et.al.

    ————————————————

    Stephen Wilde 7:46am: “…temperatures seem to be the same at the same atmospheric pressure on any planet adjusted for distance from the energy source.”

    Yes of course and empirical vs. ideal lapse profiles still exist. I’ve been pulling some of the original papers on the radio occultation experiments from the orbiting Venus probes. They report measuring Venus’ atm. refraction and convert that to the atm. gas density continuous with altitude down to a lower limit cutoff. The ideal gas law is then used with ideal lapse rates to convert to the Venus T profile from an assumed or Venera measured To and Po at surface or other beginning altitude.

    That Venus thermometer measured troposphere empirical profile can be compared to exact or approx. theory Venus lapse rate = g/Cp ~ 10.5K/km faster than Venus empirical ~8.5K/km vs. Earth approx. ideal ~9.8 and empirical ~6.5 avg. lapses. Interesting to compare these so as to try and learn the effects from the infrared active gases (IAG) et. al. b/c I expect a better understanding of the atm. lapse rates & IAG effects to come from examining lapse data & theory from both planets.

  59. Tim Folkerts says:

    BR1

    I think an interesting scenario to try would to to have all the wall reflective, but have *part* of the floor be adjustable in temperature (say the left 1/4). Suppose you start at equilibrium between the gas and the floor section. Then raise the temperature of the floor section.

    I suspect that you would quickly observe convection rising up the left side as the air on the left warms at the bottom and rises. The interesting question is “how long will that convection continue?”. Because eventually the whole system should return to thermal equilibrium at the new higher temperature. Once that “angular momentum” is established, it might continue for quite a while before it dies out.

    The “relaxation time” for the system to return to equilibrium then becomes an important concept. If convection continues for a long time, then the relaxation time is long and any “experiment” would need to run at least that long to have a chance to be back to equilibrium. And I suspect that it might take even longer for the conduction equilibrium to be reached. You would have to be careful that any results you get are not transient, non-equilibrium conditions, rather than the true thermodynamic equilibrium.

  60. Stephen Wilde says:

    “Once that “angular momentum” is established, it might continue for quite a while before it dies out. ”

    It continues forever or until the sun goes out or the atmosphere escapes to space.

    It is a constant transfer from surface to space of energy arriving unevenly at the surface.

  61. tjfolkerts says:

    TIM>>“Once that “angular momentum” is established, it might continue for quite a while before it dies out. ”

    STEPHEN> “It continues forever or until the sun goes out or the atmosphere escapes to space.”

    Perhaps you misunderstood me. I am talking about the angular momentum of the gas within BR1’s model. If the gas is initially at thermal equilibrium at some temperature T1 (equal to the temperature of the bottom corner), then pretty my by definition there can be no organized motion (ie no convection and no circulation).

    When the bottom corner is warmed, it should create convection initially. This should set up the same sort of circulating pattern BR1 described. But this is NOT thermal equilibrium!

    Eventually, the whole system should come to equilibrium at the higher temperature. At this point there should once again be no organized bulk motion. All circulation and convection will cease.

    If the model DOES show bulk motion, that is a clear indication that not enough time has been given for the model to achieve thermal equilibrium.

  62. tjfolkerts says:

    BR1 says: ” I have no problem getting temperature gradients, but they can be greater or lesser than the DALR – there seemed to be nothing special which clamps the gradient at the DALR.”

    I suspect your model is WAY too small to recreate the DALR. The “A” part is, after all. “adiabatic”. For the theory to hold, a “parcel” of air must be able to rise (or fall) without exchanging thermal energy with the “surrounding parcels”. For “large” parcels (say 10’s of meters across) found in updrafts/downdrafts in the atmosphere, the air molecules in the center are well insulated from the surrounding air, so MOST of the “parcel” can be pretty well approximated as “adiabatic”.

    In this model, the “parcel” of air is only a few molecules wide. There is no “insulated center of the parcel” of air since even the molecules in the center of the rising column are “close” to the surrounding air and can exchange thermal energy.

  63. tallbloke says:

    br1 says:
    August 29, 2012 at 1:53 pm
    Hi Tallbloke,

    Thanks, that’s a nice clear exposition of where it’s at and when you want to go with it. Good luck and keep at it!

    It’ll make a great post in its own right once you have it to a stage where you think its telling us something definitive.

  64. suricat says:

    Wot, still no Clive? OK. Here goes with friendly banter.

    Stephen Wilde.

    “ii) Once a parcel of air rises by convection another equal sized area has to descend to make room for it and the energy lost by the expansion of the first parcel is exactly offset by the energy gained by the compression of the second parcel.”

    IMHO you are confusing two different systems in your statement that averages the overall energy budget and confuses the detail of the issue. The ‘energy’ that ‘moves’ a parcel is subordinate to the energy ‘within’ the parcel and any vertical movement by that ‘energy that moves’ depends entirely on the properties of the parcel per se.

    The ‘gravity heat pump effect’ depends upon the ‘Sg’ (specific gravity) of the parcel within it’s local environment and may well not be entirely reliant on the temperature of the parcel. Thus, the ‘buoyancy potential’ (Sg, or ‘gravity potential’) is a ‘property’ of the parcel that the ‘gravitational system’ will act upon. This is where ‘adiabatic’ behaviour and ‘atmospheric’ behaviour becomes divorced.

    ‘Adiabatic’ behaviour prohibits any loss/gain of thermal energy from/to the parcel, but ‘atmospheric’ behaviour exhibits both losses and gains from/to the parcel! Thus, I can’t talk of DALR as an ‘adiabat’ when I know that the ‘ELR’ (environmental lapse rate) is all that exists for the discussion of an atmosphere. An adiabat lives in a totally ‘closed system’, whereas an atmosphere is an open system that lives within an ‘enclosed, or finite, atmosphere’.

    br1.

    I also believe your model to be on a ‘microscopic scale’, for which it is difficult to accurately portray most ‘macroscopic’ properties/phenomena for atmospheric behaviour. I’ve not read further than this thread, but perhaps you should consider more than one ‘box’ in your model. Somehow I get the ‘gut instinct’ that your model is based more on a ‘fluid parcel’ than an ‘air parcel’.

    Best regards, Ray Dart.

  65. br1 says:

    Tim Folkerts:
    “I think an interesting scenario to try would to to have all the wall reflective, but have *part* of the floor be adjustable in temperature (say the left 1/4).”

    My expectation here is the same as yours, provided there is only one temperature source and everything else is reflective. This is a good ‘experiment’ to characterise the system, and I expect the initial circulation to die out after a while. Appreciating how the thermal interaction at a wall can kill angular momentum is one insight I have gained from this model.

    Your suggestion is different than the model DALR picture I linked above, as the rest of the floor was at a lower temperature (as opposed to being reflective). If one has a high temperature section and a low temperature section on the floor, then you always get a persistent circulation, no matter how low the temperature difference is (as far as I can see). This makes sense to me, but I’m not sure if there is a difference betwen a ‘diffusion current’ and a ‘convection current’. It is also different from the ‘classic’ convection roll setup where the whole floor is one temperature and the whole ceiling a lower temperature. So to prove this I will run your single-temperature suggestion and then compare it to a two-temperature simulation.

    “I suspect your model is WAY too small to recreate the DALR.”
    probably – I have made this same comment several times now. Still, it shows that there is a difference between an updraft and a rising parcel, so that may be a useful distinction.

    I would still like to say that I can create a ‘parcel’ with my model, and find out what it takes to generate one (pulses of heat might do it, but I don’t think continuous heat will). I’ll continue for a while at least, but may be forced to either give up or find a supercomputer…

  66. br1 says:

    tjfolkerts:
    “For “large” parcels (say 10′s of meters across) found in updrafts/downdrafts in the atmosphere, the air molecules in the center are well insulated from the surrounding air, so MOST of the “parcel” can be pretty well approximated as “adiabatic”.”

    Further up this thread I was trying to draw a distinction between a continuous current and parcels. It still seems to me that parcels=bubbles, whereas a continuous current is a stream which doesn’t necessarily contain parcels.

    For example:

    https://tallbloke.wordpress.com/2012/08/18/clive-best-understanding-the-lapse-rate/#comment-30919

    “A continuous updraft shouldn’t give the DALR, as the expansion work is only done once in setting up the flow. After the flow is established, there is no further expansion work, and so the cooling rate must change away from the DALR… (and rest of post)”

    What do you reckon?

  67. tjfolkerts says:

    BR1,

    In my view, “parcel” simply means a given “subsystem”. It is very common in thermodynamics to define such subsystems and to see how each subsystem behaves. The boundaries of such a subsystem could be fixed in place or mobile; they could be rigid or flexible, they could be permeable of impermeable.

    So an insulated cylinder with a moveable piston could be such a subsystem. A large thin plasctic bag full of air could be such subsystem (either of these would be very close to “adiabatic” and could be used to predict the properties of the DALR); or the subsystem could simply be an imagined boundary. Typically each subsystem is considered small enough that the properties are similar across the subsystem (but that wouldn’t have to be the case).

    So an individual bubble could certainly be considered a “subsystem”. An updraft could be considered a whole series of subsystems (or even one large subsystem, but that might not be so productive).

  68. br1 says:

    tjfolkerts:
    “In my view, “parcel” simply means a given “subsystem”. ”

    I thought that too until I thought about it a bit deeper. Then it started to seem to me different if one has a continuous flow or if one has bubbles. A continuous flow doesn’t seem to assure a DALR (although there will be a lapse rate, it just has no requirement to be *the* DALR as there is no expansion work done), whereas a bubble seems to ensure a DALR (as there is expansion work done).

    Anyway, I’ll tweak about with the sim some more and let you know how I get on.

    p.s. Thanks to ferd berple and Q. Daniels for also pursuing the sim side of things, I think we have it cracked now.

  69. tjfolkerts says:

    ” Then it started to seem to me different if one has a continuous flow or if one has bubbles.”

    Of course, a continuous flow is simply a series of adjacent bubbles. :-)

  70. tjfolkerts says:

    The “story” behind the DALR is one that even a 12 year could grasp (but of course the details take a bit more sophistication).

    * Start with some large volume of gas at equilibrium. The only detail at this point that is important is that the pressure will drop as you go up.

    * Collect a “bag full of air” (ie a “parcel of air”) somewhere near the bottom. It will have the same pressure, temperature and density as all the other air at that altitude.

    * Heat the air in the “bag”. The air will have higher temperature, lower volume, and the same pressure as the air around it.

    * At this point, the air could cool by contact with the surround air and/or rise due to buoyant forces (it is less dense than the air around it). Since air is a very poor thermal conductor, there will be little cooling, so (to a first approximation) we can assume the “parcel” (or “bubble” or “bag”) of air will rise without any heat exchange with the surrounding. (This is where gravity comes into play — the buoyant force is a function of “g”).

    * As the air rises, it expands. As we all know, when air expands, it cools (this is where the heat capacity comes into play).

    * If is rises far enough, it will cool to the temperature of the surrounding air. At this point, the parcel of air will be the same temperature and pressure and density as the surrounding air. With the same density, it will stop rising.

    The rate that the insulated PARCEL cools as it rises is the DALR. If the gradient is ALREADY larger than the DALR, parcels near the ground will spontaneously start to rise and continue to rise (until they reach a place where gradient is smaller). This will carry heat from the ground, until eventually the ground cools and atmosphere warms, diminishing the gradient. (This is the “pop-off valve” I mentioned earlier. If a large gradient is somehow created, convection will spontaneously occur, quickly working to drop the actual lapse rate back to the DALR.)

  71. tchannon says:

    “. The air will have higher temperature, lower volume, and the same pressure as the air around it.”

    ??

  72. suricat says:

    tjfolkerts.

    “* If is rises far enough, it will cool to the temperature of the surrounding air. At this point, the parcel of air will be the same temperature and pressure and density as the surrounding air. With the same density, it will stop rising.”

    Herein lays the problem! If we assume the ‘parcel’ has a lower density than the surrounding atmosphere (perhaps due to a higher temperature, or a different gas content) the ‘parcel’ becomes an anomaly to the ‘surrounding’ (environmental) DALR and rises. If we must, and should, assume that the DALR is stable for all altitudes we have a problem with the adiabatic ‘state’ (property) of the parcel because, if the ‘parcel’ is truly adiabatic it’ll end up at ‘TOA for convection’ (tropopause), and the only scenario I can envisage to achieve this involves a ‘thunder-head’ anvil configuration. This scenario provides enough insulation from the environment to permit parcels central to the convective plume to display a similarity with an adiabat.

    Most convections are not so dramatic and air ‘parcels’ tend to have ‘leaky boundaries’ so can’t be candidates for ‘adiabatic’ properties, but they do rise to a point where their buoyancy is lost to other attractors. They’re something else. :)

    DALR is a global construct and doesn’t educate anyone on how it is derived. It’s an average of the global ‘ELR’ (environmental lapse rate), doesn’t relate to any global region and confuses convection potential.

    IMHO we need to observe the ‘ELR’ (environmental lapse rate) to distinguish/demarcate convective activity. :)

    Best regards, Ray Dart.

  73. suricat says:

    tchannon.

    “??”

    Yes. The atmosphere is ‘virtually’ an ‘open system’ with regards to pressure. This means that when a region of atmosphere is warmed, it’s expansion from warming is extended to its neighbouring regions.

    Best regards, Ray.

  74. Stephen Wilde says:

    “This will carry heat from the ground, until eventually the ground cools and atmosphere warms, diminishing the gradient”

    Not if there is a constant flow of new energy into the system it won’t. In that case the ground and the air above it stay the same temperature and the upward / downward motion cycles indefinitely at whatever net average speed is necessary to maintain energy out equal to energy coming in.

    “DALR is a global construct and doesn’t educate anyone on how it is derived. It’s an average of the global ‘ELR’ (environmental lapse rate), doesn’t relate to any global region”.

    Yes. There is no need for it ever to be achieved at any specific place or time. However the net average globally will always be what we would term the DALR and that figure is the figure required to achieve energy out equalling energy in.

  75. br1 says:

    tjfolkerts:
    “Of course, a continuous flow is simply a series of adjacent bubbles”

    well, no, my point was that a continuous flow does not do expansion work.

    Anyway, must get back to simulating – hopefully this weekend.

  76. tallbloke says:

    Ray said:
    tchannon.
    “??”

    Yes. The atmosphere is ‘virtually’ an ‘open system’ with regards to pressure. This means that when a region of atmosphere is warmed, it’s expansion from warming is extended to its neighbouring regions.

    So how is it going to occupy a smaller volume as Tim Folkerts claims? Warming a gas always caused it to expand when I was at school.

    Tim F said:
    Heat the air in the “bag”. The air will have higher temperature, lower volume, and the same pressure as the air around it.

  77. tjfolkerts says:

    tchannon says: August 31, 2012 at 3:23 am

    “. The air will have higher temperature, lower volume, and the same pressure as the air around it.”

    ??

    Sorry — that was suppose to be “… higher temperature, lower DENSITY, and the same pressure… “

  78. tjfolkerts says:

    br1 says: “well, no, my point was that a continuous flow does not do expansion work.”

    The rising stream of gas will still expand (unless it is somehow confined to a pipe so that it cannot expand). For example, the rising gas inside a thunderstorm definitely expands and cools as it rises. It expands sideways, doing work on the gas beside it, losing energy, and cooling in the process.

  79. tjfolkerts says:

    Suricat says: “IMHO we need to observe the ‘ELR’ (environmental lapse rate) to distinguish/demarcate convective activity.”

    We need knowledge of both. The ALR gives the maximum stable lapse rate. The ELR gives the actual lapse rate. When ELR > ALR, the air becomes unstable. This is basic meteorology. Googling “unstable air” gives lots of simple explanations, starting with this one:

    http://www.weatherquestions.com/What_is_an_unstable_air_mass.htm

  80. tjfolkerts says:

    One last quick comment for now. It is important to know both the underlying principles and the actual conditions to explain what is happening on earth (and other planets for that matter). I have been concentrating on the principles that lead to the existence of the DALR — which is merely an idealization like “a frictionless surface” or “a massless pulley”.

    Understanding DALR is merely a first step toward understanding earth’s atmosphere. But if you don’t understand the idealization, then I don’t think you can hope to understand the actual atmosphere (at least as far as convection goes). I concentrate on the principles (since that is my background).

  81. Bryan says:

    ttjfolkerts says:

    ” lead to the existence of the DALR — which is merely an idealization like “a frictionless surface” or “a massless pulley”. ”

    There is a physical reality behind the idealisation of (for instance) frictionless conditions.
    It often comes down to what level of detail is acceptable for the idealisation.
    The DALR formula is obtained by balancing hydrostatic buoyancy force against gravity.
    It would appear to be satisfied by stationary or constant vertical speed movement of the air parcel.

    The stationary condition is interesting.

    On a night (because these conditions are most likely to be present) when there is almost no vertical air movement of dry air we have a neutral atmosphere.
    Two thermometers one Kilometre vertically separated should differ by 9.8K

  82. Clive Best says:

    I have slightly changed my views since writing the above piece. The analysis described above is true for a once only expansion of an atmosphere against gravity if that atmosphere was thermally isolated from above. This is because conduction of heat from the surface would eventually bring the atmosphere to an isothermal constant temperature roughly the same as the surface unless energy escapes from the atmosphere to space. To maintain a planetary lapse rate energy must continuously flow through the atmosphere. I think this is the crucial point that in my opinion is not properly described in text books.

    Gravity is essential for a lapse rate because it compresses the atmosphere resulting in the hydrostatic pressure gradient. In bulk thermodynamic terms – air that rises up against gravity looses energy by doing work and air that falls gains energy by having work done on it. The best derivation of the resultant dry adiabatic lapse rate I have found is given by Nasa here as follows.

    from the first law of thermodynamics
    dQ = dU + dW = n·cv dT + PdV = 0
    where cv is given in units of erg/K/mole and n is the number of moles. The derivative of the ideal gas law, PV = nRT, is
    VdP + PdV = nRdT
    equating PdV and noting that R = cp – cv yields
    dQ = n cv dT – V dP + n (cp-cv) dT
    dQ = n cp dT – V dP = 0 for adiabatic
    Cp = cp/ and = n · /V so that
    dT/dP = V/(n · cp) = 1 /(Cp · )
    From hydrostatic equilibrium and the gas law we can convert from pressure to height coordinates: dP = – g dz
    dT/dz = -g/Cp

    However this does not explain why does convection occur anyway? It seemingly only occurs because there is a lapse rate and warmer air rises because it is less dense than colder air. Here is the circular argument again – The lapse rate is caused by adiabatic expansion of convective air and convection occurs because air above it is colder. This almost seems to imply that the lapse rate boot straps itself into existance. However this is just not true. A lapse rate can only exist if energy is being directly transfered through the atmosphere with continuous energy loss from the top of the atmosphere into space. If there were no bulk movement of air in the atmosphere there would be no lapse rate and conduction would eventualy tend toward an isothermal atmosphere.

    On Earth the majority of solar energy is absorbed by the surface raising its temperature whcih re-radiates IR. Greenhouse gasses throughout the atmosphere absorb some of this IR radiation from the surface eventually radiating a fraction of this to space from the upper atmosphere. This causes an initial temperature gradient. We now need gravity to compress the atmosphere near the surface creating a pressurae/density gradient for the lapse rate to function.

    Air that rises does work against the surrounding air and losses energy.
    Air that falls has work done on it by surrounding air and warms. Exactly at the dry adiabat no heat is transfered but in the normal “stable region” below the dry adiabat, heat is transfered downwards as discussed by Nick Stokes here. It is like a giant “carnot cycle” heat pump. Once convection starts it will drive then lapse rate towards but not quite reach the dry adiabatic value. The net effect is to pump heat down to the surface. Latent heat from surface evaporation also moves heat upwards thereby reducing the environmental lapse rate. It is a dynamic system just like the weather. Gravity must plays an important role in the whole convection cycle because it will ensure that an equal amount of air falls to that which rises.

    It may not actually be necessarily have to be greenhouse gases that generate an initial atmospheric temperature gradient for convection to start, but I now believe that there must be some radiating mechanism for the atmosphere to lose energy into space in order for there to be a lapse rate.

  83. Bryan says:

    Clive Best says:

    ” If there were no bulk movement of air in the atmosphere there would be no lapse rate .”

    This is clearly not correct.

    There are occasions where there is no bulk transfer of air.
    This is called by meteorologists as the ‘neutral atmosphere’.

    It is precisely in this condition that for dry air the lapse rate is – 9.8K/km

  84. br1 says:

    tjfolkerts:
    “The rising stream of gas will still expand (unless it is somehow confined to a pipe so that it cannot expand). For example, the rising gas inside a thunderstorm definitely expands and cools as it rises. It expands sideways, doing work on the gas beside it, losing energy, and cooling in the process.”

    that’s not what I’m getting at – I gave a link in my post of Aug30, 11:07 am to a previous post (all on this thread):
    “For example:

    https://tallbloke.wordpress.com/2012/08/18/clive-best-understanding-the-lapse-rate/#comment-30919

    “A continuous updraft shouldn’t give the DALR, as the expansion work is only done once in setting up the flow. After the flow is established, there is no further expansion work, and so the cooling rate must change away from the DALR… (and rest of post)” ”

    This consideration arose because the simulation I was using steady heat sources, and waiting for steady-state to see what the gradient is. In steady-state, a rising stream of gas does no work even though it transports heat, so one will get a lapse rate but there is no reason it should be the DALR.

    This led me to the possibility that to get the DALR in practice, one needs unsteady heat sources.

  85. tchannon says:

    So if this parcel of air gets bigger it consequentially raises the rest of the whole atmosphere against gravity, hydraulics, which also means the rest cools. Ever so slightly is not zero.

    That is a static view but all the same this ought to be happening. Maybe I should keep away from the subject.

  86. Stephen Wilde says:

    “If there were no bulk movement of air in the atmosphere there would be no lapse rate and conduction would eventualy tend toward an isothermal atmosphere. ”

    I think you need to preface that with an assumption that the surface heating (and cooling) were to be perfectly even in all directions at all times.

    It is the unevenness of heating on a revolving sphere under a point source of energy that provokes convection.

    You cannot achive an isothermal outcome in conditions where heating and cooling is anything less than perfectly even throughout the system.

  87. Clive Best says:

    You are correct. If the environmental lapse rate is exactly equal to the dry adiabatic lapse rate then heat is neither transfered up or down by air movement. This is an idealised quasi-stable situation but any tiny perturbation from it will start up the heat engine again. Net heat is transfered down to the surface without any need for so-called “back-radiation”.

  88. Stephen Wilde says:

    “This led me to the possibility that to get the DALR in practice, one needs unsteady heat sources.”

    I prefer the term uneven to unsteady.

    As before, perfectly even heating and cooling in all directions could theoretically give an isothermal outcome.

    If you have unevennness then the system is never going to be isothermal but it isn’t going to match the DALR anywhere either.

    The DALR is just a theoretical construct being the average of all the lapse rates that are present in practice.

    It will always be set at whatever number is necessary for energy in to equal energy out.

    That number is derived from atmospheric mass, pressure at the surface and insolation and the circulations within the atmosphere will always reconfigure to observe it.

  89. Stephen Wilde says:

    “Net heat is transfered down to the surface without any need for so-called “back-radiation”.”

    Quite so.

    Thus the so called back radiation is merely the temperature of the molecules at the surface and not a downward flux at all.

  90. Clive Best says:

    I agree. In the real world there is differential heating between the equator and the poles, which together with the Earth’s rotation causes bulk air movement transporting heat. However if the atmosphere itself could not radiate to space – if it were in a vacuum thermos flask – would there be a lapse rate ? I think this is the crucial point.

  91. Bryan says:

    Clive says;

    “The best derivation of the resultant dry adiabatic lapse rate I have found is given by Nasa”

    The derivation is good and you will notice that convection is not assumed.

    In fact the term convection when properly used refers to an unbalanced force acting on
    the air parcel (see bottom of page 13 of link).

    On page 31 (of link) we find that at nightime a typical situation has the near neutral residual
    layer.

    http://www-as.harvard.edu/education/brasseur_jacob/ch2_brasseurjacob_Jan11.pdf

    As ttjfolkerts says above a lot of the atmospheric structure theory is based on idealised conditions.

    The Carnot cycle applied to the atmosphere as you say contains useful concepts.
    Heat is moved from the Earth surface to the tropopause where it is radiated to space.

    Work is done in the process to make up for losses which inevitably happen in the non idealised real atmosphere.

  92. Stephen Wilde says:

    “if the atmosphere itself could not radiate to space – if it were in a vacuum thermos flask – would there be a lapse rate ? I think this is the crucial point”

    Don’t involve a vacuum flask because that is a forcibly closed system which is not comparable to the real world.

    Instead, envisage a GHG free atmosphere of say just oxygen and nitrogen with negligible radiative abilities.

    In that situation the surface would have to do all the radiating and the atmosphere would have to configure itself so as to return energy back to the surface for it to be radiated out to space at such a rate that energy in would still equal energy out.

    Lots of wind and turbulence would be required because you would still have uneven heating on the day side with lots of convection and parcels of air expanding and cooling as it rises.

    Meanwhile on the night side there would be lots of parcels of air contracting and warming as they descend and the net energy value of rising and descending on both day and night sides taken together will be zero.

    So, on the night side you would have energy redelivered to the surface by the descending contracting air so as to warm the surface to achieve the necessary radiation to space from the surface to offset the excess energy delivered to the surface on the day side.

    Lots of vertical and horizontal air movement to maintain system equilibrium.

    And through it all you still have the lapse rate as set by surface pressure, atmospheric mass and insolation.

    Neat isn’t it ?

  93. Trick says:

    tchannon 5:21pm: “Maybe I should keep away from the subject.”

    LOL. Me too. Maybe it helps to be from the poster of few words. dept. such as yourself.

    Poster Clive Best 4:12pm is struggling (e.g.“…the circular argument again – The lapse rate is caused by adiabatic expansion…”) in deriving a non-isothermal constant lapse rate g/Cp = 9.8K/km yet discussing an isothermal tropospheric atmosphere (constant T(z) no lapse).

    As many have previously, Clive has missed that the math linked from NASA just assumes a constant T(z) throughout an isothermal troposphere to allow integration to easily proceed to get approx. DALR = g/Cp ~ 9.8K/km. This is a good approximation – off only a few degrees for small z.

    That is the whole reason the approx. logic seems circular. It IS circular but easy & close enough to exact for government work.

    Now, the real earth troposphere does not have constant T(z) with earth environment lapse being not constant ~ 6.5K/km avg. and why that exists is far more interesting. The exact theory integration using non-constant T(z) showing non-isothermal trop. atmosphere with exact non-constant ideal lapse, (T(p)/To = (P(z)/Po)^R/Cp) as discussed here earlier, is way more applicable to understanding earth’s environment trop. lapse ~ 6.5K/km. No circular logic therein.

    Note the NASA link shows Venus approx. ideal lapse with the circular logic g/Cp ~ 10.5K/km and the various probes indicate Venus exact troposphere environmental lapse ~ 8.5K/km. This Earth environmental lapse delta below g/Cp and Venus environmental lapse delta below g/Cp are VERY similar even though Venus atm. is 94% CO2. Very interesting to discuss if you ask me.

  94. Clive Best says:

    “Don’t involve a vacuum flask because that is a forcibly closed system which is not comparable to the real world. Instead, envisage a GHG free atmosphere of say just oxygen and nitrogen with negligible radiative abilities.
    In that situation the surface would have to do all the radiating and the atmosphere would have to configure itself so as to return energy back to the surface for it to be radiated out to space at such a rate that energy in would still equal energy out.”

    I was thinking of exactly that case. The vacuum of space allows no heat loss except through radiation. So energy has to balance. Without any atmosphere and an albedo of 0.3 the surface reaches 255 K on average to balance incoming solar radiation. There will still be large temperature differences between equator/poles and day/night temperatures – exactly like on the moon. Now we hypothetically add just N2 and O2 but no greenhouse gases at all. The thermal heating of the atmosphere near the surface is then due only to conduction. This will surely induce vertical convection and thermal N-S winds diverted by coriolis forces. Such a scenario will surely act to disperse heat from hot regions to cold regions following the second law of thermodynamics. However, does it generate a lapse rate and will this then increase the average surface temperature ? I am not 100% sure but I think not. I am would be happy to be convinced otherwise.

    Viewed from 1 million miles in outer space the net IR radiation from Earth cannot change in the medium term as it must balance the absorbed incident energy from the sun. If the only source of radiation is the Earth’s surface I can’t see how the surface temperature can change. However, once we now add 70% surface coverage of Oceans then we have a radically different picture. Evaporation of water vapour not only allows IR to radiate upwards through the atmosphere to space, but also dampens summer/winter and night/day temperature swings through its heat capacity. Other greenhouse gases like CO2 and methane may come and go but the oceans must be the key to Earth’s remarkably stable temperatures over the last 3 billion years.

    Water vapour alone would maintain the lapse rate, without recourse to other greenhouse gases..

  95. Trick says:

    Clive Best 8:48pm: “ Now we hypothetically add (to the thermos) just N2 and O2 but no greenhouse gases at all. The thermal heating of the atmosphere near the surface is then due only to conduction.”

    At long term equilibrium in a g field, exact theory shows a non-constant lapse rate develops in the thermos as I posted (for T(p)/To) 8:25pm. The avg. temperature of the N2 O2 remains constant in the perfect, rigid thermos after it is filled & closed, no more heating is needed just no heat loss.

    The approx. theory also applies in equilibrium as a quick estimate because a constant approx. g/Cp lapse ~ 9.8K/km will develop in equilibrium if the thermos is at rest in Earth’s g field.

    The two solutions will be close – different by ~25K out of ~300K for earth’s troposphere z height.
    If the perfect insulated, rigid thermos is in space with 0g, theory shows the O2 N2 will be isothermal at the original avg. T given the assumption of no heat loss.

  96. Stephen Wilde says:

    Well I think you would get a lapse rate with no GHGs at all simply because the depth of any atmosphere spreads out the transition distance between surface temperature and the cold of space.

    However if you do have GHGs and especially water with the thermal power of its phase changes then it is a whole lot easier for the atmosphere to match energy in with energy out (radiation out can occur above the surface) so the circulation doesn’t need to be anything like as vigorous as an atmosphere bereft of GHGs.

    So, if one increases GHGs one would increase the height of the atmosphere but not the surface temperature because the more GHGs you have the further above the surface the effective radiating height can be for the same system temperature.

    More energy radiating out from above the surface from GHGs means that the surface doesn’t need to radiate out as much as if there were no GHGs and so the surface itself is cooler on the night side (the GHGs do some of the radiating) but likely hotter on the day side (the insulating effect of a GHG rich atmosphere) with a zero net effect on surface temperature overall.

    And the oceans alter the situation greatly because their internal movements can result in an irregular release of energy to the air but that is another story.

  97. Trick says:

    Stephen Wilde 9:27pm: “Well I think you would get a lapse rate with no GHGs at all simply because the depth of any atmosphere spreads out the transition distance between surface temperature and the cold of space.”

    This could be part of Earth’s environmental lapse 6.5K/km but the theory for the approx. 9.8K/km and exact lapse with no infrared active gases do not consider earth’s surface temperature and cold of space other than for initial conditions causing hydrostatic equilibrium which IS used.

    The hydrostatic p in g field and Cp info. is all that theory needs to determine an approx. lapse rate from constant T in equilibrium for Earth or Venus which is only a few degrees K from measured environmental lapse rates in the respective troposphere.

    The exact ideal theory non-constant T(p) is closer but still not there – a non-ideal empirical correction factor is needed to get real environmental lapse rates.

  98. Stephen Wilde says:

    “a non-ideal empirical correction factor is needed to get real environmental lapse rates.”

    Of course.

    But that correction factor will be determined by the characteristics of the atmosphere in so far as it does interfere with energy in and energy out and even a non GHG atmosphere does that to some extent due to conduction and some basic interaction between the mass and incoming solar radiation.

    It isn’t quite zero interaction even for oxygen and nitrogen and both those gases will conduct freely to and from a dry surface.

    So yes, I was only considering initial conditions for the purpose of that post.

  99. Trick says:

    Stephen Wilde 10:09pm – Agreed. Interesting to list/discuss reasons for the empirical lapse correction needed from the exact lapse ideal theory (or the approx. g/Cp theory) and their possible magnitude. For instance:

    a) Infrared active atm. gases – Venus CO2 at 94% and Earth just a trace CO2 – probably small or the approx. to smaller measured lapse Venus v. Earth difference would be much larger.

    b) Earth surface To to cold of space delta much less than Venus due to orbital distance – maybe large.

    c) Earth surface Po much less due to higher weight of gas on Venus – maybe large
    d) g and Cp different – probably small
    e) Convective processes – maybe large due to power of atm. in motion on Venus
    f) Measurement difficulty at Venus – some +/- maybe cancel so small
    g) Oceans, topography, surface composition, albedo, clouds, et. al. – no guess.
    h) Radiation – no guess
    i) ?

  100. Nick Stokes says:

    Clive Best
    “The best derivation of the resultant dry adiabatic lapse rate…”

    Here’s a simpler one. At the DALR no work is required to move a mass of air m up or down. The change of internal energy moving m up by dz (adiabatically) is
    m g dz + m cp dT which must be zero:
    dT/dz = -g/cp

    “However this does not explain why does convection occur anyway? It seemingly only occurs because there is a lapse rate and warmer air rises because it is less dense than colder air. “

    As you say elsewhere, convection is forced by surface temp variations. Any wind moves air up and down. If below the lapse rate, it pumps heat down, increasing the gradient. If above the lapse rate, instability produces natural convection which carries heat up, decreasing the gradient.

    “However, does it generate a lapse rate and will this then increase the average surface temperature ?”

    As you said in the preceding, there are winds – that’s all (+g) you need to push toward the DALR. But a lapse rate is a differential – it doesn’t alter the surface temperature, which is set by radiation balance. The lapse rate goes down from there. The N/O atmosphere isn’t involved in heat loss to space.

  101. Stephen Wilde says:

    “The N/O atmosphere isn’t involved in heat loss to space.”

    But it is involved as an energy store whilst heat loss to space occurs from the surface.

    That store of energy having been acquired by conduction from the surface plus convection and that energy is constantly recycled up and down.and laterally.

    The recycling has a zero net effect in the absence of ANY radiative capability but that store of energy in the air and the air being under pressure at the surface is what gives a higher surface temperature than the S-B equation would predict.

    So it is indeed atmospheric MASS that counts and NOT composition.

    If one then introduces GHGs then they simply make it easier for the system to radiate out from locations above the surface.

    Since the surface temperature is set by atmospheric mass (plus pressure and insolation) and not by atmospheric composition the surface temperature stays the same but because radiation is being allowed out from points above the surface the air circulation can be less vigorous.

    I think that pretty much squares the circle.

  102. Nick Stokes says:

    Oops:
    “If below the lapse rate…if above…”
    I mean if lapse rate below DALR

  103. Nick Stokes says:

    SW
    “The recycling has a zero net effect in the absence of ANY radiative capability but that store of energy in the air and the air being under pressure at the surface is what gives a higher surface temperature than the S-B equation would predict.”

    The no-GHG air will redistribute heat and make a slightly more even surface temperature distribution. Equator cooler, poles warmer. But the integrated radiation, as given locally by S-B, goes straight through the atmosphere.

  104. Stephen Wilde says:

    “But the integrated radiation, as given locally by S-B, goes straight through the atmosphere”

    So ?

    Any planet with an atmosphere with any mass at all has a surface warmer than predicted by S-B which applies only to an irradiated body floating in a vacuum. The composition of the atmosphere appears to be irrelevant.

    The non GHG atmosphere doesn’t just redistribute energy. It acquires energy, holds onto it and recycles it indefinitely as long as irradiation and gravity remain present.

  105. Ray C says:

    It says here ; http://www.windows2universe.org/earth/Atmosphere/aerosol_cloud_nucleation_dimming.html
    “Aerosols play a critical role in the formation of clouds. Clouds form as parcels of air cool and the water vapor in them condenses, forming small liquid droplets of water. However, under normal circumstances, these droplets form only where there is some “disturbance” in the otherwise “pure” air. In general, aerosol particles provide this “disturbance”. The particles around which cloud droplets coalesce are called cloud condensation nuclei (CCN) or sometimes “cloud seeds”. Amazingly, in the absence of CCN, air containing water vapor needs to be “supersaturated” to a humidity of about 400% before droplets spontaneously form! So, in almost all circumstances, aerosols play a vital role in the formation of clouds.”

    In an atmosphere devoid of aerosols what would happen to water vapour? Is the ELR on Earth dependent on the presence of aerosols and water in all its‘ phases? But specifically are aerosols essential? I think they are and they have a significant role in slowing the rate of energy loss to space.
    At an atomic level is it like pumpkins floating in peas, where the peas are nitrogen and oxygen and the pumpkins are molecular compounds equivalent to thousands/ millions of atoms clustered together? ( I am a gardener not a scientist). There are thousands to millions of aerosol in one cubic centimeter of air so do these little lumps of stuff constantly alter the way energy moves in the atmosphere?

    http://www.agu.org/pubs/crossref/2012/2012GL051851.shtml

  106. Bryan says:

    Nick Stokes says:

    “But the integrated radiation, as given locally by S-B, goes straight through the atmosphere.”

    Thats the interesting thing about DALR conditions – no mention of radiation!

    Its perfectly obvious that CO2 and the 30 times more numerous H2O gases are still radiating as usual.

    The radiative effects are included naturally in the bulk thermodynamic quantity Cp.
    Adjacent volumes of air mutually cancel the radiative effects.

    Only near or at the tropopause is there a significant leakage of radiation to space.

    What is a puzzle to me is when the radiative effects are dealt with separately as is common in climate science what value do they use for Cp.
    Cp without the radiative effects or what?

    I cannot think of an experiment to find a value for Cp that could exclude the radiative contribution.

  107. Clive Best says:

    @Nick Stokes… “At the DALR no work is required to move a mass of air m up or down. The change of internal energy moving m up by dz (adiabatically) is
    m g dz + m cp dT which must be zero:
    dT/dz = -g/cp ”

    This says that at the DALR the loss in kinetic energy of rising air exactly balances the gain in gravitational potential energy. – very nice !

    So an atmosphere without greenhouse gases can have a lapse rate but it is driven by differential N/S and day/night differential. However in this case would not the tropopause be much lower ?

    @RayC: The presence of aerosols in a pure N/O2 atmosphere could perhaps take over the role of greenhouse gases now allowing IR radiation absorbed from the surface to escape to space again from the atmosphere. This would increase surface temperatures and drive the lapse rate.

  108. Stephen Wilde says:

    “However in this case would not the tropopause be much lower ?”

    Good point.

    The available options are:

    i) A vigorous circulation with a low tropopause in the absence of GHGs or aerosols.

    ii) A slacker circulation with a higher tropopause in the presence of GHGs or aerosols.

    The more GHGs and / or aerosols the bigger and ‘lazier’ the atmosphere can afford to become without upsetting the energy in equals energy out ratio.

    That helps us with the issue of raising the atmospheric heights too. When the atmosphere expands all the temperature heights increase so outgoing longwave increases to offset the decrease in energy flows through the system caused by the presence of aerosols and GHGs.

    If that is right then GHGs do not raise the temperature of the system but only raise the temperature of the new upper region now incorporated into the atmosphere when it expands.

    And even at the new radiating height the temperature will be just the same as at the old radiating height.

  109. Ray C says:

    Clive Best says: September 1, 2012 at 12:21 pm
    @RayC: The presence of aerosols in a pure N/O2 atmosphere could perhaps take over the role of greenhouse gases now allowing IR radiation absorbed from the surface to escape to space again from the atmosphere. This would increase surface temperatures and drive the lapse rate.

    http://carnegiescience.edu/news/climate_change_black_carbon_depends_altitude

    @Clive Best, I imagine there are dark coloured aerosol, either silt or brown/black carbon present at all levels in the atmosphere. The above link says that, yes, if they are near Earths surface they contribute to near surface warming and so would as you say drive the lapse rate. Are they not absorbing short wave radiation direct from the Sun? Conversely if they are aloft they can effectively heat the upper atmosphere due to diabatic heating and cause cooling to the lower atmosphere. My question is, because there are so many aerosol present in our atmosphere do they play a far more significant role in moving energy about and that their presence needs to be considered when discussing the way energy moves up, down or sideways in the atmosphere. Not by IR absorbed from the surface but direct heating in the atmosphere? There are many types and colours but the dark ones would seem to predominate over land.
    The Northern Hemisphere has an increasing amount of dark coloured aerosol added to it from various activities. These have the ability to heat the upper atmosphere when they are at these higher altitudes. Could this direct, diabatic, heating cause the troposphere to bulge upwards, expanding due to the extra energy? Could this depressurise the jet stream and cause it to meander under the bulge?
    Oh! Does anybody now, What would happen to atmospheric water vapour if there were no aerosol present for it to condense onto? Would it float off into space or just hang around absorbing IR! With no way back to the surface would Earth just get warmer? Sorry if OT, don’t really know if I was on topic in the first place!! Just curious!

  110. Trick says:

    Stephen Wilde 9:44am: “The composition of the atmosphere appears to be irrelevant.”

    There is still the need for an empirical correction to the planetary 1) approx. constant -g/Cp lapse rate and 2) exact theory variable ideal lapse rate to get the 3) real environmental lapse rate. Infrared-active gas physics operate on the z thermal energy flow so operate on 3) T lapse rate but not operate on 1) or 2).

    The composition of the atmosphere modifies relevant thermal energy flow physics.

    ——————————–

    Nick Stokes 5:49am: “The change of internal energy moving m up by dz (adiabatically) is
    m g dz + m cp dT which must be zero: dT/dz = -g/cp”

    Good demonstration of Clive’s top post conundrum circular logic: over the interval dz the T lapses –g/cp but T is assumed adiabatic in dz so no lapse.

    Clive’s original Q – how can T lapse but not lapse in the interval dz? – is not answered by this. This shows –g/cp is just an approximation assuming small dz parcel isothermal but large z parcel non-isothermal at same time. This assumption of adiabatic T for small dz IS close enough for government work in the planetary troposphere and helps understand forced convection and the neutral atmosphere.

  111. Clive Best says:

    @ RayC The IPCC narrative for aerosols is that their net effect is overall cooling because they reflect solar energy – negative forcing. This is why Hansen et al. explain why their GCM models for AGW over-predict the observed warming. see for example – http://data.giss.nasa.gov/modelforce/efficacy_fig28.gif

    Black carbon particles however absorb both solar radiation and IR radiation from the surface, and therefore directly warm the atmosphere (from below and above). I think the effect of aerosoles and GHG must “drive” the lapse rate. Lets take CO2.

    Suppose we have an IR detector sensitive only to emissions from CO2 molecules. and move it upwards through the atmosphere. Above some nominal height (1000 m ?) there will be more upward radiation from CO2 below the detector than downwards from CO2 above the detector. This is despite the lower atmosphere being opaque to IR. So the presence of greenhouse gases moves radiative heat upwards in the atmosphere thereby acting to reduce the lapse rate. This induces more convection.

    If we now double the amount of CO2 the reduction effect of the lapse rate will increases further. If the resultant environmental lapse rate itself changes due to the doubling of CO2 and the tropopause increases in height, then this will increase the temperature of the effective radiative level to space. – a negative feedback.

    ( P.S. I got seriously flamed on SoD for suggesting just this)

  112. Trick says:

    Clive Best 3:50pm:” So the presence of greenhouse gases moves radiative heat upwards in the atmosphere thereby acting to reduce the lapse rate.”

    So with 94% CO2 Venus environmental lapse rate would reduce below its approx. –g/Cp rate even more than earth’s, right? (there may be a minus sign here muddying the communication logic water).

    From your NASA link:

    Venus = -10.468 K/km from –g/Cp
    Venus = -8.5 K/km for measured real environmental lapse (from various probes) & 10.48 * .81 = 8.5

    Earth = -9.76 K/km from –g/Cp
    Earth = -6.5K/km for measured real Standard Atm. environmental lapse & 9.76 * .67 = 6.5

    Thus Earth’s real environmental lapse rate falls off MORE (.67) from approx. ideal than Venus real environmental lapse rate(.81 give or take) implying infrared-active gas is acting to increase Venus environmental lapse rate over that of Earth (admittedly mixed in with other relevant atm. physics).

  113. Stephen Wilde says:

    “The composition of the atmosphere modifies relevant thermal energy flow physics.”

    Agreed that composition affects the amount of correction needed to arrive at the locally observed environmental lapse rate.

    However the sum total of all the environmental lapse rates must average out to the DALR to ensure that energy out equals energy in and composition is irrelevant to that baseline DALR. It only affects the local environmental lapse rates.

  114. Trick says:

    Stephen 5:29pm “..the sum total of all the environmental lapse rates must average out to the DALR to ensure that energy out equals energy in and composition is irrelevant to that baseline DALR.”

    Very good point, worth discussing. The baseline 1) DALR = -g/Cp would be affected by the composition imposing differences in Cp, a minor issue.

    The big deal would be in 2) the idealized exact solution lapse rate and 3) the real environmental lapse rate. The idealized version does not know the tropopause exists, it just continues on course lapsing to p=0. The 3) real environmental lapse then is affected by the tropopause change to isothermal lapse up around 200hPa. It would have to compensate for energy balance – thus another difference from ideal exact theory needs proper accounting.

    The 2) ideal exact theory lapse within the troposphere would have to start at higher T at surface (=302K) then cross over the 3) environmental lapse (start T=287K at surface) about halfway in p up thru troposphere to maintain constant integrated potential temperature as the environment. The composition of the actual atmosphere being different than ideal forces this.

    Cool point, thx. Replace the ? with this as item i) on my list of differences ideal vs. real at 8/31 11:42pm.

  115. Stephen Wilde says:

    As I recall, the vertical temperature profile of the whole atmosphere is the shape of a ‘W’ on its side with discontinuities along the way from surface to space.

    There is an inversion at the tropopause and also at the mesopause.

    Those inversions are differently caused but are related to composition.

    However, in the end the average slope from surface to space must match the baseline DALR for energy out to equal energy in.

    In practice there is never an equilibrium so the volume of the atmosphere constantly changes in order to maintain balance and all the heights vary as necessary with consequent circulation changes.

    The most disruptive influence on the vertical temperature profile seems to be spectral and particle variations from the sun, especially ultra violet acting on ozone, Apparently uv amounts can change by up to 20% as a result of solar variability which is way beyond TSI variations of about 0.1% and uv acts on the ozone destruction / creation balance whilst ozone is known to be responsible for the stratospheric temperature inversion which is critical to tropopause height.

    The whole atmosphere is constantly expanding or contracting in response to changes in solar behaviour and the circulation at the surface shifts accordingly.

    Hence the climate zone shifts from MWP to LIA to date.

  116. Trick says:

    Stephen: “…the average slope from surface to space must match the baseline DALR for energy out to equal energy in.”

    Certainly the average of the variable environmental lapse rate from surface to space will result in energy out to = equal energy in at equilibrium. Earth Standard Atm. varying environment lapse starts out about -6.5K/km avg. to tropopause then is close to 0 until the last maybe 50hPa where it becomes positive. Thus total avg. environment lapse only slightly different than -6.5K/km.

    There is no theory I can see for the baseline DALR average slope from surface to space to have to equal that same avg. environmental lapse. The DALR is constant –g/Cp = -9.8K/km from energy balance assuming adiabatic which is only true for small dz not large z.

    If say -9.8K/km DALR from 1000hPa to 200hPa then -0K/km from 200hPa to 50hPa then +10K/km to 0hPa maybe the math works to obtain about -6.5K/km. Haven’t seen that done nor tried it.

  117. Stephen Wilde says:

    I assumed that logically the average slope for all the varied evironmental lapse rates from surface to space would need to match the theoretical DALR but if it isn’t necessary then I’m ok with that but I would need it to be demonstrated..

    It just seemed to me that if the slope diverged from DALR in one direction on the way up then that would have to be compensated for by a divergence in the other direction on the way up.

    In any event both DALR and the net outcome for the actual environmental lapse rates need to result in energy out equalling energy in.

  118. tallbloke says:

    Hi Stephen. I think you need to bear in mind that Ned and Karl say that the relationship only hold down to a pressure around that of Mars’ surface pressure. So once you’re above the Earth’s tropopause things are no longer going to conform to their equations.

    Additionally, Ned told us that the ‘W on it’s side’ has to be viewed with caution as the temperature below the tropopause is measured from the bulk gas whereas out in the thermosphere etc it is the temperature of individual molecules and atoms.

  119. Roger Clague says:

    Tallbloke says
    “temperature below the tropopause is measured from the bulk gas whereas out in the thermosphere etc it is the temperature of individual molecules and atoms.”

    http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper.html

    Temperature is defined as average tranlational kinetic energy.

    Temperature is a bulk property, there cannot be an average for a single molecule.

    How do you calculate the temperature of a single atom or molecule?

  120. tallbloke says:

    Hi Roger C: I don’t claim to be an expert in this matter, I’m just reporting what Ned Nikolov told us.

    I think the issue is the radiating temperature of particles as opposed to the bulk properties of a volume which is too sparsely occupied by matter to be considered as a homogenous ‘gas’.

  121. tjfolkerts says:

    Stephen says: “Any planet with an atmosphere with any mass at all has a surface warmer than predicted by S-B which applies only to an irradiated body floating in a vacuum. The composition of the atmosphere appears to be irrelevant.

    No, every planet in our solar system with an atmosphere has a warmer surface than the simple S-B prediction. And every planet in our solar system has significant amounts of GHGs.

    So no conclusion can be drawn (based only on these two observations) about whether GHGs are relevant or not.

  122. tjfolkerts says:

    Stephen: “…the average slope from surface to space must match the baseline DALR for energy out to equal energy in.”

    Not only is there no reason this must be true, but it is not true! The observed ELR is typically smaller than the DALR. For one thing, there is water vapor in the atmosphere. I know you are a big fan of considering enthalpy with respect to evaporation at the surface; now consider condensation in the atmosphere. Also, the atmosphere is clearly not truly adiabatic. There is conduction and (probably much more important) radiation which transfer energy into and out of parcels.

    So both theory and observation belie your claim above.

  123. Roger Clague says:

    Clive Best says

    “This would increase surface temperatures and drive the lapse rate.”

    19th century thermodynamics of gases tells us that it is the lapse rate that sets the surface temperaure.

    You are using modern radiative convective theory, which is wrong.

    Here is Richard Lindzen’s analysis of the greenhouse effect.

    ftp://texmex.mit.edu/pub/emanuel/PAPERS/greenhouse.pdf

  124. Stephen Wilde says:

    “The observed ELR is typically smaller than the DALR”

    How about the inversions in the stratosphere and thermosphere ?.

    You have to consider the entire vertical temperature profile but I suspect that you are only considering the troposphere because there is very little water vapour above the tropopause.

  125. Stephen Wilde says:

    “every planet in our solar system has significant amounts of GHGs.”

    So what ?

    Every planet in our solar system has significant amounts of mass.

  126. tjfolkerts says:

    TIm>> “every planet in our solar system has significant amounts of GHGs.”

    Stephen> “So what ? Every planet in our solar system has significant amounts of mass. ”

    Exactly! Every atmosphere has both GHGs and mass. So there is no way to conclude that mass (rather than GHG’s) are responsible for the elevated surface temperatures. Your conclusion “the composition of the atmosphere appears to be irrelevant” is unsupported. You would need to find a planet with an atmosphere WITHOUT GHG’s but WITH an enhanced surface temperature in order to make your claim.

  127. tjfolkerts says:

    TIM >> “The observed ELR is typically smaller than the DALR”
    Stephen: > “How about the inversions in the stratosphere and thermosphere ? … I suspect that you are only considering the troposphere”

    I’m not sure what your point is. The lapse rate in these regions is smaller than the DALR (inversions are negative lapse rates, which is definitely less than +10 K/km”

    If your point is that there is (practically) no water there, that is certainly true. There is still radiation there to lower the lapse rate below the DALR.

    So, no, I was not considering only the troposphere. My comments about both theory and observations belying your statement are true throughout the atmosphere all the way up to the thermosphere.

  128. tallbloke says:

    tjfolkerts says:
    September 3, 2012 at 4:01 am (Edit)
    TIm>> “every planet in our solar system has significant amounts of GHGs.”

    Stephen> “So what ? Every planet in our solar system has significant amounts of mass. ”

    Exactly! Every atmosphere has both GHGs and mass. So there is no way to conclude that mass (rather than GHG’s) are responsible for the elevated surface temperatures. Your conclusion “the composition of the atmosphere appears to be irrelevant” is unsupported. You would need to find a planet with an atmosphere WITHOUT GHG’s but WITH an enhanced surface temperature in order to make your claim.

    I think the similarity in the lapse rate on Earth and Venus despite their very different compositions is strong evidence that Stephen is right. The depth and weight of Venus’ atmosphere is the main factor in its surface temperature, not its composition.

    The mass/pressure theorists have a much better model which conforms more closely to reality than the radiative theorists IMO.

  129. tjfolkerts says:

    Tallbloke says: “The mass/pressure theorists have a much better model …”

    I understand your argument — mass of the atmosphere DOES play an important role. The amount of atmosphere helps determine the thickness, which (along with the lapse rate) helps determine the temperature difference between the TOA and the surface.

    But you STILL need to determine the TOA, which is determined by the radiation leaving the planet, which in turn is affected by the radiation of GHG’s.

    Determining exactly how much effect GHGs have vs mass of atmosphere would be a challenge, but I can’t see any way to leave out GHG’s

  130. tallbloke says:

    Tim F obfuscates:
    I understand your argument — mass of the atmosphere DOES play an important role. The amount of atmosphere helps determine the thickness

    No Tim. I know you do understand the argument (although you don’t agree with it), and optical thickness has nothing to do with it, apart from a minor effect on insolation at the surface. You are just trying to muddy the waters (or in this case, the atmosphere). Shame on you.

    The primary effect is the effect of atmospheric mass on sea level pressure. Along with insolation, this is what limits the evaporation rate, thus forcing the ocean to rise above the grey body temperature in order to lose energy as fast as it gains it. That’s why the ‘greenhouse effect’ is stronger in the ocean than the atmosphere. Additionally, if you think long wave has a tough time getting through air, check out how short a distance it is able to travel in water before re-absorption.

  131. Trick says:

    tjfolkerts 2:11pm – “I can’t see any way to leave out GHG’s…”

    No infrared-active gases in the DALR theory lapsing faster than reality so that is one way.

    tallbloke 2:39pm “Shame on you.” Geez TB, watch out for the mod.s – LOL.

    Slipping OT: another way to leave out infrared-active gas is that simple model of a 1m^2 atmospheric column in an open at top, adiabatic rigid container from surface up to near the tropopause (~264hPa) filled with the Standard Atm. initial conditions and another theoretical closed, rigid adiabatic column filled with no infrared-active gas (non-GHG) clean air which can be exactly solved for troposphere T profile.

    Both columns having same integrated potential temperature, same mass. The Standard Atmosphere column having very slightly less entropy so maybe not quite at same equilibrium but close enough for blog work.

    Thermo theory shows non-infrared active clean air closed column intersecting lower in z tropopause (~10% higher p) and about a 5% warmer surface T than Standard Earth atm.

    Going into the non-GHG theory column then & slowly replacing clean air w/dirty air and adding in standard amount of infrared-active gases (replacing equiv. N2,O2 mass) to get to standard atm. (and open the closed container on top to do work on air column above) would then serve to increase tropopause height and lower surface T at new equilibrium.

    Adding infrared-active gas (among other things) lowers! surface T 5%. But there is much written & unwritten in this & that is a whole ‘nother thread as y’all know.

  132. tjfolkerts says:

    TB says: “No Tim. I know you do understand the argument (although you don’t agree with it), and optical thickness has nothing to do with it…”

    I was talking about PHYSICAL thickness, not OPTICAL thickness. If the lapse rate is 10 K/km, then the more kilometers of atmosphere you have, the more temperature difference there will be from the top to the bottom. And you can get more thickness by adding more mass.

    PS It gets tough as these discussions progress to keep the discussion focused. When some people are trying to focus on a specific issue (eg DALR = the topic of the top post) others want to include other ideas (eg evaporation, GHGs, and mass). While these issues are ALSO important, it is tough to stay focused when the issues are heading several different directions. I have been trying (but perhaps not succeeding) to stay focused on DALR and its implications, without getting too much into the side issues.

  133. tallbloke says:

    Great! I didn’t realise we’ d made a convert of you :)

  134. tjfolkerts says:

    Or maybe I will still make a convert out of you. ;-)

    Where we differ, i think, is in deciding what temperature to make the bottom of the atmosphere.
    * If the atmosphere was basically “perfectly opaque” to IR, then the TOP of the atmosphere would be at the “effective blackbody temperature” (-18 C) because all the outgoing IR would be from the top of the atmosphere. The surface would be WARMER than -18 (by an amount given by the lapse rate and physical thickness of the atmosphere).
    * If the atmosphere was basically “perfectly transparent” to IR, then the BOTTOM of the atmosphere would be at the “effective blackbody temperature” (-18 C) because all the outgoing IR is coming from the surface. The atmosphere would be COOLER than -18 C (by an amount given by the lapse rate).
    *For earth, with an atmosphere that is partially opaque/partially transparent to IR, the temperature is -18 C somewhere inbetween the top and the bottom. The surface is then somewhat warmer than -18 C.

    The surface is only warmed above the effective BB temperature (ie there is only a GHE) if the planet has BOTH
    1) IR absorptive properties in the atmosphere, and
    2) some physical thickness to the atmosphere to allow a temperature difference (related to the the DALR).

  135. Bryan says:

    tjfolkerts

    I’m surprised that you try to defend the 33K greenhouse effect theory.

    As G&T convincingly proved, the 33K is a meaningless number wrongly calculated.
    The logic that supports the 33K number is thinner than interstellar space.

  136. tjfolkerts says:

    Bryan says: “I’m surprised that you try to defend the 33K greenhouse effect theory.”

    I’m surprised that you thought I was defending the 33K greenhouse effect theory. :-)

    1) I never mentioned 33K as the warming observed on earth.
    2) I was very careful to use the term “effective blackbody temperature”. I don’t think anyone seriously argues against the conclusion that, under current albedo conditions, the “effective blackbody temperature” is indeed ~ -18C. That is all that I had claimed.

    That said, I don’t think the 33 K number is really all that bad — the average surface temperature is not that far from + 15 C. Stll, there are definite short-comings to attributing +33 C to GHGs, including:
    1) You can’t remove all the GHGs without removing water, which gets rid of clouds, which changes the albedo. To maintain the current albedo without clouds, you would have to lighten the earth some otehr way (like painting some of the surface white).
    2) “Effective temperature” is not equal to “average temperature”. It is easy to prove that the average temperature will always be less than the effective temperature (uness the temperature is the same everywhere, in which case they are equal).
    3) Average temperature is tough to measure accurately.

  137. tallbloke says:

    4) You lose the ocean too, which spreads heat towards the poles and retains it better at night than land. So much so, that it doesn’t cool down by the next day, unless until it rises in temperature sufficiently to be able to lose heat as fast as it gains it on average. Without an ocean and cloud, Earth’s “effective blackbody temperature” will be similar to the Moon’s, about 212K, nothwithstanding a small difference due to faster rotation and inclined axis.

    5) Logic tells me that since the ocean surface is 2C warmer than the near surface air, and downwelling longwave can’t penetrate seawater by more than it’s own wavelength, that temperature is ~289K. Therefore co2 is redundant as a heating agent for the Earth’s main bulk heat retention medium, apart from keeping the air over land a bit warmer – a minor effect.

  138. tjfolkerts says:

    TB says: ” Without an ocean and cloud, Earth’s “effective blackbody temperature” will be similar to the Moon’s, about 212K, nothwithstanding a small difference due to faster rotation and inclined axis.”

    I don’t think you understand the standard way that the term “effective blackbody temperature” is used.

    The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation.
    Wikipedia

    Rotation or oceans or tipped axes or GHGs make absolutely no difference when finding the effective temperature (other than the secondary effect of possibly affecting the albedo). If you know the incoming radiation and the albedo, then you know the effective temperature. As I alluded to above, this is not going to be the same as the average temperature at the ground or at the top of the atmosphere or any other particular surface.

    The moon, having a lower albedo than the earth (ie it is less reflective) has a HIGHER effective temperature than the earth, NOT a LOWER effective temperature. http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html

    You don’t have to like this definition, but if you are going to talk with others, you should use the same standard terminology.

  139. Trick says:

    Tim F.: “*For earth….The surface is then somewhat warmer than (BB) -18 C….the average surface temperature is not that far from + 15 C…. It is easy to prove that the average temperature will always be less than the effective temperature (uness the temperature is the same everywhere, in which case they are equal).”

    Why is my head spinning around?

    This was on DALR but I do get that surface T is important too, the start of whatever lapse rate you want to discuss.

    If Earth albedo measured = .30 so that 240W/m^2 net solar irradiance spread around entire surface then it is easier to just think about setting the emissivity of Earth atm. avg. over spectrum = 0 to get the equivalent blackbody surface Te = -18C (255K).*

    With the emissivity of Earth atm. avg. over spectrum set = 1**, then Te = 30C (303K).

    Since we get told incessantly about the increasing Earth Tavg. ~ 16C (~288K) by MSM then set atm. emissivity ~ 0.8 to compute Te = 16C (288K) (=Tavg.!). Then discuss DALR or env. lapse above z=0 from there.

    As atmosphere emissivity is increased above 0.8 by adding infrared-active gases, I can then see the Tavg. surface warming issue easier, and, hoo wow, my head spins less.

    Also, Tim F. is right about Tavg. being of limited usefulness, DO NOT go outside in Kapuskasing, Canada dressed simply by looking at MSM Tavg. on a given day – you could perish.

    —————————————————

    *This has a conundrum like the one in top post for DALR: atm. emissivity = 0 implies no radiative property gases. Oh well, albedo still = 0.30 somehow as Tim F. points out (painting the surface works).

    *Te from e=emissivity eqn. (Te)^4 = 240/[(S-B const.)*(1-e/2)] considering earth & atm. as radiating slabs in a vacuum which is an analogue that serves a fine but limited purpose (reduced head spinning).

    **Can emissivity ever be > 1? (If read this far, I ask since TB now looking for 2nd million hits).

  140. Trick says:

    TB 10:12pm: “Without an ocean and cloud, Earth’s “effective blackbody temperature” will be…”

    Here you vary both albedo and atm. emissivity independently in the simple analogue slab setup which makes my head spin too much (some affects might cancel).

    TB continues: “Therefore co2 is redundant as a heating agent…”

    I’m sending the thermo police to look into your towers to root this thinking right out. Or maybe this is why bottles of Coke might explode?

    ———————————————-

    Tim F.: “Rotation or oceans or tipped axes or GHGs make absolutely no difference when finding the effective temperature (other than the secondary effect of possibly affecting the albedo).”

    I don’t think planetary/moon rotation usually affects a planet or moon Te, the rest do. Because albedo is measured avg. over the rotation I would think.

    Also, you wrote about standard terms and using the term “black body” can be misleading – for one they don’t exist in nature; it is more accurate to think of natural matter being in radiative equilibrium at Te.

  141. Bryan says:

    tjfolkerts

    Having your cake and eating it springs to mind!
    These comments are from your two most recent posts.
    …………………………………………………….

    Bryan says: “I’m surprised that you try to defend the 33K greenhouse effect theory.”

    That said, I don’t think the 33 K number is really all that bad

    I’m surprised that you thought I was defending the 33K greenhouse effect theory.

    1) You can’t remove all the GHGs without removing water, which gets rid of clouds, which changes the albedo.

    From second post….(other than the secondary effect of possibly affecting the albedo).

    To maintain the current albedo without clouds, you would have to lighten the earth some otehr way (like painting some of the surface white).
    2) “Effective temperature” is not equal to “average temperature”. It is easy to prove that the average temperature will always be less than the effective temperature (uness the temperature is the same everywhere, in which case they are equal).
    3) Average temperature is tough to measure accurately.
    …………………………………………………………..

    As I said above “G&T convincingly proved, the 33K is a meaningless number wrongly calculated.”

    You would/would not agree?

  142. tjfolkerts says:

    As I said above “G&T convincingly proved, the 33K is a meaningless number wrongly calculated.”

    The 33K temperature difference is indeed fraught with difficulties, since lots of inter-related factors affect local and global temperatures.

    But I do firmly believe:
    1) The average temperature of the surface is well above -18C no matter how you want to calculate “average temperature”.
    2) a significant portion of that difference must be attributed to GHGs.
    3) G&T have enough errors in their analysis that they have not “convincingly proven” anything to me or to most of the scientific community.

    http://www.physicsforums.com/showthread.php?s=0fb1b1cba361c7961b87aa9b8d5605d5&p=2127073#post2127073

    http://www.worldscientific.com/doi/abs/10.1142/S021797921005555X

    http://scienceofdoom.com/2010/04/05/on-the-miseducation-of-the-uninformed-by-gerlich-and-scheuschner-2009/

  143. suricat says:

    tjfolkerts.

    Apologies for absenting myself from this thread for so long, but I’ve been so enthused by posters comments here that I just had to cogitate.

    “tjfolkerts says:

    August 31, 2012 at 12:15 pm

    Suricat says: “IMHO we need to observe the ‘ELR’ (environmental lapse rate) to distinguish/demarcate convective activity.”

    We need knowledge of both. The ALR gives the maximum stable lapse rate. The ELR gives the actual lapse rate. When ELR > ALR, the air becomes unstable. This is basic meteorology. Googling “unstable air” gives lots of simple explanations, starting with this one:
    http://www.weatherquestions.com/What_is_an_unstable_air_mass.htm

    Well yes, but the DALR (as defined by meteorologists) isn’t ‘dry’ for all altitudes of the atmosphere and this confuses climatologists, together with ‘Joe public’ trying to get a handle on things. :)

    The meteorological definition of a ‘dry parcel of air’ includes water vapour that ‘doesn’t’ condense! This is because meteorological data ‘doesn’t’ need to model a ‘parcel of air’ for more than a few days, but climatology tries to model for vastly longer periods where any water vapour in the parcel ‘shall’ condense, many times, as the parcel falls and ascends within the atmosphere during the accepted 30 year period that demarcates ‘climate’ from ‘weather’. This may look like an ‘aside’, but it’s pertinent to the accepted use of the DALR.

    TBH, ‘adiabatic expansion’ was introduced as a method to educate engineers on the machinations of steam engines and internal combustion engines. Notwithstanding that post its introduction, internal losses within the system’s insulating boundaries needed to be addressed (steam condensation within the boundary by ‘tail gasses’ and molecular dissociation before combustion, respectively, are singular examples for each system [this ignores ‘boundary transgressions’]).

    Does this ‘ring a bell’? The only ‘true adiabat’ is a ‘perfect gas’! Thus, how can ‘ALR’ (adiabatic lapse rate) relate to ELR when Earth’s atmosphere’s constitution is one of a ‘mixed gas’ and doesn’t conform to an adiabatic model? You’ve got me stumped. :)

    Again, sorry for my absence here recently. :(

    Best regards, Ray Dart.

  144. br1 says:

    Update from my side: I’ve rewritten and debugged the core code for my molecules sim in C++. This improves sim speed by well over a factor of 100, so I’m checking what I can get with that. No graphics yet (I hate C!), but the numerics look like they work. Of course the general result is the same – an isothermal profile under gravity, but maybe I’ll get more of a stream flow rather than a diffusive flow when I put in the heat differentials.

  145. br1 says:

    Well this is fun, I could basically copy-paste the code from Visual C++ on the PC into Xcode on the MacPro, and got another improvement in speed (better specs on the Mac for a start). Is noticeably clunky at 10,000 molecules, which is not that large a number, but could be useful for something. Doesn’t crash anyway, but doubt I’ll get up to 20,000 molecules (without having to run the sim over the weekend or something like that – not impossible but becomes impractical at some stage). I might have another algorithm time saver, so will try that, but must get back to trying to simulate the DALR soon…

  146. Clive Best says:

    Monte Carlo simulations of an ensemble of molecules look like a good way to go. I would be interested in the code. If you could include cross-sections for IR absorption, gravity, density etc. maybe it could end up being an alternative to GCMs !

  147. suricat says:

    “Clive Best says: September 10, 2012 at 10:30 pm”

    I’m sure you realise that a molecular ensemble is no substitute for a General Circulation Model Clive! :)

    GCMs are usually written in FORTRAN 98 language, with lots of compilers and translators that enable the programme to run using the machine code for the resident CPU on a UNIX based beast. I dare say that there are other methods, but for speed and complexity considerations, machine code is needed to actually ‘run’ the GCM programme.

    I’ve lost the link I had to the old ‘Model E’ coupled GCM (I wasn’t impressed with it anyhow), but here’s something of interest:

    http://mitgcm.org/

    Though I’ve only glimpsed at the site, the M.I.T. GCM looks, at first impressions, to be suited to a LINUX o/s, but it may also be FORTRAN based (the two systems have their similarities).

    Nevertheless, I’m sure br1 can find ample places within a GCM for the application of his/her ‘ensemble’, which ‘isn’t’ of a ‘Monte Carlo simulation’ type. As I understand, it’s a ‘fluid parcel’ model that replicates behaviour on a small scale and doesn’t second guess anything.

    Best regards, Ray.

  148. suricat says:

    It’s such a pain in the a–e to page down for access to this thread that I’ve ‘bookmarked’ a link here. Hopefully, the bookmark will be useful.

    Best regards, Ray.

  149. clivebest says:

    Hi Ray,
    I actually have been running a GCM on my Mac (GISS Model II ). I wrote some posts about what I learned: see for example Thermal inertia and climate feedbacks and Getting to grips with GISS GCM plus those in between.

    Yes GCMs are rather sophisticated numerical for momentum and energy conservation equations, fluid dynamics + Coriolis effects, and models for solar heating, evaporation etc. on a 3-d grid. They are macro scale solutions solving partial differential equations with some extra macro-model assumptions. What they don’t tell you what is happening at the molecular level. So I think there is still room for molecular simulations to understand basic processes.

    The main reason you need super-computers to run GCMs today is because the grid size is getting smaller and the computer time scales with the cube of the grid dimensions. However the original models from 10 years ago runs just fine on a desktop and the overall results have not changed dramatically – just moderated a bit the warming !

  150. suricat says:

    Hi Clive,
    I took a quick squiz at your links and whilst I concur with most of your post here, I have some problems with your links. “Thermal inertia and climate feedbacks”??? To a semi-retired engineer, “thermal inertia” isn’t the process that’s described there. It’s ‘thermal capacity’ (Cp), just another descriptor that Climate Science has messed with.

    A school experiment for “thermal inertia” consists of a silver rod heated at the tip of one end, while the change in temp along its length (by conduction) is observed. The heat source is then removed and the hot end cooled by a source of water, whilst the change in temp along its length continues to be observed. The point of the experiment is to show that the ‘cool’ end of the silver rod continues to increase in temperature when the ‘heated’ end has now been cooled to a lower temp than the ‘cool’ end.

    Before you say that this is an introduction to thermal capacity, it isn’t. It’s an introduction to a dynamical quality of ‘thermal conduction/thermal capacity’. Because Earth’s systems are mostly ‘insulating’, I can’t understand why the use of “thermal inertia” is inserted for a ‘thermal capacity’ quality. :)

    Enough of nomenclature (and what could develop into a rant). GCMs tend to ‘parametrise’ (use fixed quanta for a variable) objects within the programme to expedite the time taken during an iteration. If the final outcome is garbage the ‘parametrisation’ is altered, but if a ‘Monty Carlo’ check of the validity of the parametrisation is made, the programme can be made to halt at that iteration and save computer time from running a duff scenario.

    IMHO, programmers should concentrate more on excluding parametrisations and introducing them as ‘programmed variables’ than ‘validating’ them as parametrisations. This may be where br1 can help. :)

    Best regards, Ray.

  151. Clive Best says:

    “Thermal inertia” is a term that Hansen’s group use to describe what they say is pent up warming already in the system. So if we overnight returned CO2 levels to 280 ppm they claim the climate would still continue warming for another 50 years or so , due to the enormous heat capacity of the Oceans. I was just trying to quantify this using their model and at the same time fit the results to hadcrut3 temperature data. The end result is climate sensitivity of 2.2 degrees to a doubling of CO2 which is not catastrophic at all !

  152. tallbloke says:

    Clive, no physical mechanism I know of enables back radiation to heat the oceans to any measurable degree. Long wave is absorbed and re-emitted from the top millimetre, it can’t penetrate the surface much beyond its own wavelength. Unlike short wave from the Sun, which penetrates up to 100m.

  153. Roger Clague says:

    Clive,

    Returning to the subject of your post ” understanding lapse rate”.

    The radiative-convective and the pure thermodynamic theories both consider lapse rate and convection to be important, but disagree about their relationship.

    To help me understand your position, Which of the following do you agree with

    1. convection causes lapse rate

    2. lapse rate causes convection

    3. Both convection and lapse rate have another cause which is
    (a) the same for both
    (b) different for each

    If you agree with 3.(a) or 3.(b), what do you think cause lapse rate and convection?

    Others are also invited to answer this simple multi-choice question about the relationship between 2 important concepts in atmospheric physics.Please justify your choice.

    The IPCC talk of “water vapour-lapse rate feedback”, Thus they say that they are less important than CO2 and they don’t discuss the relationship between them.

    My answer is 2.
    Because (a) Theory tell me that gravity causes lapse rate and
    (b) Observation shows me that hot air rises

  154. tallbloke says:

    Roger, yes, 2 for me too. -g/cp works.

  155. clivebest says:

    I think 2 is almost correct but you still need some external energy source. The dry adiabatic lapse for a planet depends only on its gravity and the type of molecules (diatomic, triatomic + mass) in the atmosphere (cp). A completely still atmosphere is in practice impossible due to day/night, seasonal/latitudinal solar heating variations. Any movement in the atmosphere will result in a lapse rate. The dry adiabatic lapse rate is exactly the rate at which gravitational potential energy gain/loss is equal to internal kinetic energy loss/gain.

    I initially thought that a perfectly still non radiating atmosphere in a gravitational field sitting on an infinite “hot plate” held at a fixed temperature would also achieve a dry adiabatic lapse rate for ever. I now think that after millions of years heat conduction from the surface would eventually equalise temperatures, assuming that no energy loss to space. In practice such a hypothetical situation never occurs and all planets have a lapse rate. Whether the lapse rate causes convection is like asking which came first the egg or the chicken. The equilibrium lapse rate exists independent of convection.

    I don’t believe the energy source needs to originate from the surface either. On Venus 90% of solar radiation is absorbed in the thick clouds some 50-60 km above the surface. Only a tiny 17 watts/m2 actually reaches the surface. I thick it is high atmospheric winds ( like Hadley cells) that circulate and mix the atmosphere. This is the primary cause of the 700K surface temperatures – not a “run-away” greenhouse effect as such.

  156. Stephen Wilde says:

    3a

    Gravity and atmospheric mass cause the lapse rate which then governs the rate at which convection occurs for a given level of solar input.

  157. Stephen Wilde says:

    2 would be correct if one starts with the lapse rate alone but the more complete picture is that gravity and atmospheric mass cause the lapse rate and the lapse rate then allows convection related to the level of solar input.

    There is also another way of looking at it because without solar input there is no atmosphere, lapse rate or convection. In that case the materials of the atmosphere just congeal on the surface.

    So you could say that insolation is the single cause of both lapse rate and convection because insolation is what lifts the atmospheric constituents off the ground in the first place.

    Once insolation has created a gaseous atmosphere the combination of gravity and atmospheric mass directly dictate the slope of the lapse rate and indirectly (via the lapse rate) dictate the rate of convection for any given level of solar irradiation.

    That is why one cannot increase system energy content other than by changing atmospheric mass, the strength of the gravitational field or the level of insolation.

    If one simply changes atmospheric composition without a significant change in atmospheric mass all that happens is a change in atmospheric volume as per the gas laws which cancels the effect of the change in composition.

    So all that more GHGs achieve is a change in the height of the atmosphere and a shift in the atmospheric circulation for zero change in system energy content.

  158. Stephen Wilde says:

    Note that liquid oceans are a separate issue altogether such that the energy content of the oceans is set by pressure at the surface plus solar input as I explained in some detail elsewhere.

    And the oceans on Earth control the atmospheric temperature which is another reason why GHGs can have little effect other than a miniscule shift in the air circulation. That miniscule shift is needed to arrange that atmospheric temperatures continue to follow sea surface temperatures.

    So I think human CO2 emissions might shift the climate zones a tiny fraction, perhaps less than a mile, compared to 1000 miles from natural solar influences such as from MWP to LIA and LIA to date.

    All fits doesn’t it ?

  159. clivebest says:

    “So all that more GHGs achieve is a change in the height of the atmosphere”

    I have been trying to understand exactly what determines the height of the troposphere on any given planet X. The tropopause is defined as the level where the lapse rate ( or convection) stops. On Earth the troposphere is 10-15 km above the surface. On Mars it is at about 45 km high, while on Venus it is about 65 km high. Mars has 0.008 of the Earth’s atmosphere mass while Venus has 100 times more mass than Earth’s atmosphere. The theoretical lapse rates (g,cp) for each planet vary by only a factor 2. On Venus and Mars the atmosphere is mostly composed of CO2 while on Earth it is mostly N2,O2 and H2O. Greenhouse effects vary enormously- on Mars is < 5 degrees, on Venus ~ 500 degrees, and on Earth ~ 30 degrees

    Why ?

  160. Stephen Wilde says:

    Clive:

    I referred to atmosphere, not troposphere.

    The structure of each planet’s atmosphere is very different because compositions vary greatly.

    Ozone layers in Earth’s stratosphere dictate the height of the tropopause by creating a temperature inversion which puts a cap on upward convection.

    However, if one takes the atmosphere as a whole it will still expand and contract as necessary to ensure that overall energy out equals energy in. That is what keeps system energy content stable. All that changes is the rate of throughput and that is reflected in climate zone positioning.

    Any temperature inversion will put a cap on convection but will be compensated for higher up in the atmosphere so that the lapse rate set by atmospheric mass and gravity will be maintained overall.

    The composition is relevant to the vertical temperature profile but that can be any shape at all. In every case the lapse rate is maintained from surface to top of atmosphere.

    If it were not so maintained then either the atmospheric constituents would be frozen to the surface or they would be boiled off to space.

    In practice, every planet with an atmosphere has, by virtue of a gaseous atmosphere being present, reached a balance that is sustainable indefinitely as long as there is a gravitational field strong enough to hold onto it and enough insolation to lift the atmosphere off the surface.

    That balance is achieved in every case by the air circulation throughout the atmosphere reconfiguring to offset any imbalances arising in the vertical structure as a result of compositional variations.

    In essence any change in composition that does not significantly affect total mass will simply result in a reconfiguration of the air circulation with consequent climate zone shifting.

    But the climate zone shifting on Earth from solar and oceanic variability is magnitudes greater than any similar effect that may result from human emissions.

    Mind you, it does seem that the human emissions are rapidly sequestered locally in any event (see the AIRS data) for little or no climate effect.

  161. tallbloke says:

    The composition is relevant to the vertical temperature profile but that can be any shape at all. In every case the lapse rate is maintained from surface to top of atmosphere.

    This seems contradictory. If the lapse rate is maintained then it determines the vertical temperature profile.

    That balance is achieved in every case by the air circulation throughout the atmosphere reconfiguring to offset any imbalances arising in the vertical structure as a result of compositional variations.

    And in comparing planets we also need to consider rate of rotation, surface features (oceans, landmass) and obliquity.

  162. Stephen Wilde says:

    “If the lapse rate is maintained then it determines the vertical temperature profile”

    I should have said ‘on average’.

    Thus an inversion at one level must be offset by a steeper slope or a deeper layer at another level.

    The basic shape of Earth’s atmosphere is that of a ‘W’ on its side. Others will be different.

    “And in comparing planets we also need to consider rate of rotation, surface features (oceans, landmass) and obliquity”

    Agreed..

    All such factors that might upset the lapse rate set by gravity and atmospheric mass must be offset by a change in the atmospheric circulation.

    Otherwise, no atmosphere.

  163. clivebest says:

    If you look at the lapse rates on Venus and Earth in the troposphere they are rather similar. Mars is shallower because it has less gravity. What I don’t understand is what precisely determines how high the lapse rate extends and why convection ends there. There must be some simple principal here, but I don’t know what it is. On Earth Ozone in the stratosphere absorbs solar UV heating the very thin upper atmosphere reversing the temperature trend but this is a different effect.

  164. Stephen Wilde says:

    The interesting feature of Earth as compared to Venus is that the temperature within the atmosphere is much the same at the same atmospheric pressure when adjusted for distance from the sun, as you say.

    Harry Dale Huffman drew attention to that some time ago.

    Within a warmer layer such as Earth’s stratosphere the consequent expansion would affect pressure at any given height so it might well be the contraction and expansion of the atmospheres of different planets at different temperatures and at different heights that equalises the pressure / temperature relationship.

    As for your specific question convection does not end where the lapse rate ends.

    The lapse rate extends from surface to top of atmosphere but convection from the surface ends wherever it hits an inversion strong enough to prevent further rising of air that has been warmed at the surface.

    The vertical temperature profile of any planet depends on how the composition of the atmosphere varies with height because each planet’s atmospheric composition reacts differently to incoming solar energy.

    Overall one cannot have energy out failing to match energy in otherwise over time the atmosphere would freeze to the surface or boil off into space.

    The only mechanism available for the necessary adjustments to avoid loss of atmosphere is air circulation.

    Air circulation is what creates climate zones and jet streams.

    The fact is that whatever the atmospheric composition may be and whatever effect that has on the vertical temperature profile the atmospheric circulation will always reconfigure to match energy in with energy out.

    If the circulation changes fail to achieve that then the atmosphere will be lost.

    More GHGs simply change the air circulation. They cannot change system energy content.

  165. suricat says:

    Well said Stephen, I concur with almost all that you’ve described, so clearly, but I think more needs to be said for rotational properties. :)

    Yes, planetary rotation gives ‘climate cells’ ~in the troposphere (greater altitudes are not so ‘influenced’ by planetary rotation). Polar cells from the planar centrifuge configuration at the poles and Hadley cells from the radial centrifuge configuration at the equator, with the ‘idler’ configuration of the Ferrel cells in each hemisphere (in-between the centrifuges). An offset of the insolation focus from an equatorial centre causes bias to these geostrophic winds, by way of upwards convection into the gravitational gradient towards the poles that originates from rotation ‘per se’.

    Even using a perfect gas with this scenario the DALR is both complex and varying as we observe varying latitudes.

    Now, let’s hypothesise a non-destructive halt to rotation of this planet with an atmosphere.

    The first thing to be observed is that the climate cells just ‘disappear’! All that would be left is the ‘single’ insolation cell that convects the atmosphere from the centre of insolation towards the ‘dark side’ (cold side) of the planet. From this initial state the outcome should be quite obvious. The atmosphere is constantly moved to the cold side of the planet where it condenses into the ‘crust’. The final outcome? A planet without an atmosphere, but has the potential to have one (if only it revolved on an axis not parallel to the insolation vector)!

    This post is likely to generate questions about Uranus, of which I know next to nothing, but, what the hey! :)

    Best regards, Ray.

  166. tjfolkerts says:

    I vote for “3. Both convection and lapse rate have another cause.”

    That cause is differential heating of the top and bottom of a column of air. Consider a few thought experiments.

    1) A 1 km tall column of air with a cross-section 10m x 10 m that is completely insulated from the surroundings.
    At equilibrium there should be uniform temperature (as confirmed by various models described in this thread and by statistical mechanics and by the zeroth law of thermodynamics). If you disagree, then you may as well stop reading now.

    2) Now add a heater at the bottom of Q = 0.0024 W (= 24 μW/m^2) and a cooler at the top of -2.4 mW.
    The thermal conductivity of air is 0.024 W/m*K (http://www.engineeringtoolbox.com/thermal-conductivity-d_429.html). This incredibly weak heater/cooler combo will set up a gradient
    dT/dy = Q/A*k = 0.001 K/m = 1 K/km. This is a stable situation, and no convection will occur.

    3) Increase the heater/cooler by a factor of 10 –> Q = 0.024 W/m^2.
    Now the gradient established by conduction will be 10 K/km. This is right at the edge of instability, and right at the edge of the onset of convection.

    4) Increase the heater/cooler by a ANOTHER factor of 10 –> Q = 0.24 W/m^2.
    Now the gradient established by conduction would be 100 K/km. This is highly unstable. Convection will start. Convection will transport some of the energy energy from the bottom. This reduces the energy transported by conduction and reduces the gradient. Convection will not reduce the gradient below the adiabatic lapse rate, but it will get close.

    If you continue increasing the differential heating/cooling, you will increase convection, but hardly raise the lapse rate. Convection LIMITS the lapse rate, it does not CREATE the lapse rate.

    *****************************************************************

    This is the simplified version. When you add in rotation or IR radiation within the gas or water vapor or any number of other factors, the analysis will get more complicated. But as long as you have cooling at the top of the atmosphere (by IR radiation in the case of Earth) and heating at the bottom (from sunlight), then you will get a lapse rate CREATED by differential heating and LIMITED by convection.

  167. tallbloke says:

    Clive says:
    What I don’t understand is what precisely determines how high the lapse rate extends and why convection ends there.

    Nikolov and Zeller say it’s where the pressure drops to a certain level.

  168. tallbloke says:

    Tim F, interesting numbers, thanks.
    So what happens to your calcs when gravity is introduced and causes the density (and thus the specific heat capacity) of the medium to vary from high at the bottom to low at the top?

  169. Clive Best says:

    @Steven Wilde: What you write sounds correct for Earth. The presence of O2 leads to Ozone production in the high atmosphere absorbing UV and heating the stratosphere. So this could be the reason the Earth’s troposphere is capped off at 10-15 km through a temperature inversion. The troposphere on Venus and Mars without any oxygen reaches 45-65 km, as would presumably the Earth without life. As Lovelock would say – the Earth’s climate is governed by the presence of life.

    tjfolkerts says: “Convection LIMITS the lapse rate, it does not CREATE the lapse rate.” I fully agree with this statement and your analysis.

    Once we add greenhouse gases in : H2o and Co2 the atmosphere itself becomes active in overall energy balance. Water provides another heat loss for the surface through evaporation. Active heat flow (IR + latent heat) through the atmosphere reduces the lapse rate. In the tropics this indeed raises the troposphere.

  170. Stephen Wilde says:

    “Active heat flow (IR + latent heat) through the atmosphere reduces the lapse rate. In the tropics this indeed raises the troposphere.”

    Careful, you are mixing up the two types of lapse rate.

    Firstly we have the theoretical lapse rate from surface to top of atmosphere as set by gravity, and atmospheric mass.

    Secondly we have the actual observed lapse rate or lapse rates that can vary greatly at different heights though ultimately they must all net out to the theoretical lapse rate otherwise the atmosphere would be lost.

    Tim is describing the effect of convection below the tropopause which as stated does indeed alter the height of the tropopause as part of the stabilisation process. There is hardly any convection above the tropopause but noneheless the atmospheric heights can rise and fall with atmospheric expansion and contraction.

    Once gravity and atmospheric mass have set the theoretical lapse rate the layers of the atmosphere and the horizontal pressure distribution will adjust as necessary to net out all the other actual lapse rates to match the theoretical one set by gravity and mass.

    Every planet with a gaseous atmosphere must be following the same rule in its own way and it is composition differences that lead to different solutions within the internal structure of any given atmosphere.

    Change the composition and the only effect is a change in the circulation not a change in system energy content.

    Meanwhile, variations in sun and oceans cause huge air circulation changes many magnitudes larger than we could cause with our emissions.

  171. Trick says:

    Tim F. 3:12am: If your #1 does have uniform initial condition temperature everywhere after the 1km perfectly insulated, rigidly enclosed column is filled at LTE then w/constant volume, uniform density there can be no pressure gradient and therefore no gravity field
    .
    Simply P = density*k*T = constant everywhere in the 1km shows no gravity.

  172. tallbloke says:

    Clive Best says:
    Active heat flow (IR + latent heat) through the atmosphere reduces the lapse rate. In the tropics this indeed raises the troposphere.

    How much does the centrifugal force of spinning round at a thousand miles and hour affect the height of the troposphere at the equator relative to its height at the poles?

  173. suricat says:

    Hi TB,

    I made that calculation some time ago, but used imperial dimensions. This is a gravity counterpoise property of the latitude observed. Thus, spring type weighing machines need to be calibrated for the latitude in which they are to be employed.

    IIRC. At the equator a counterpoise of a little more than 3 inches/sec^2 is felt. Thus, 384 – 3 = 381 inches/sec^2 (~31.75 ft/sec^2) substitutes for 1G. Because, due to Earth’s rotation, the gravitational constant at the equatorial surface exerts only ~0.992 of Earth’s normal gravity, the atmosphere (in rotation) there extends to more elevated altitudes.

    However, this is an approximation from memory and leads on to discussion of the Coriolis Effect, also, there are other laws that help to produce a tropospheric equatorial bulge and they all alter the ‘ELR’ Environmental Lapse Rate.

    Anyone want to make a more accurate comment in metric? Be my guest. :)

    Best regards, Ray.

  174. tallbloke says:

    Thanks Ray. I think it should also be considered that there are a large number of billions of tons of water up there, and a disproportionate number of them are above the temperate latitudes and tropics, rather than the polar regions. This water vapour absorbs some 16% of the incoming solar energy and this, along with obliquity effects causes the tropical atmosphere to be a lot warmer than the high lattudes. These things need to be factored in before we decide how much of the extra height of the troposphere in the tropics to attribute to the greenhouse effect.

  175. tjfolkerts says:

    TB asks: “So what happens to your calcs when gravity is introduced and causes the density (and thus the specific heat capacity) of the medium to vary from high at the bottom to low at the top??”

    The gravity is ALREADY included in the theory of DALR, so there is no need to “introduce” it to my thought experiments. Hydrostatic equilibrium is assumed, with a drop in density as altitude increases. http://en.wikipedia.org/wiki/Lapse_rate#Dry_adiabatic_lapse_rate

  176. tallbloke says:

    Tim F says:
    1) A 1 km tall column of air with a cross-section 10m x 10 m that is completely insulated from the surroundings.
    At equilibrium there should be uniform temperature (as confirmed by various models described in this thread and by statistical mechanics and by the zeroth law of thermodynamics). If you disagree, then you may as well stop reading now.

    1) Completely insulated from surroundings means no gravity.
    2) The zeroth law does not exclude the possibility of a temperature gradient at equilibrium.

  177. tjfolkerts says:

    “1) Completely insulated from surroundings means no gravity.”

    No, completely insulated simple meant completely *thermally* insulated from the surroundings. Since there is no way to “insulate” from gravity, I was not trying to imply removing gravity. And since it was implied we were on earth, then gravity was assumed to be present.

  178. suricat says:

    tallbloke says: September 15, 2012 at 4:49 pm

    “These things need to be factored in before we decide how much of the extra height of the troposphere in the tropics to attribute to the greenhouse effect.”

    I concur. A higher temp at the equator than at the poles means that whilst the RH is fairly constant, the SH is much greater at the elevated equatorial temp. Thus, a lighter air parcel at equatorial latitudes (WV is lighter than dry air). ;)

    Take care on using property icons, ‘Cp’ (~taken as specific heat capacity) actually refers to a ‘mass’. That’s why engineers use the term ‘Cp’ for gasses, as it requires ‘constant pressure’ and is a ‘mass for mass’ term. When a volume of gas expands, the ‘original mass’ is reduced within the ‘original volume’ causing calculation error and should be avoided. I’ve used this term here before, but I’m not sure everyone understands its full meaning.

    ‘Cv’ can be taken as a term if any density change can be properly accounted for, but generally speaking, for a ‘constant’ ‘specific heat capacity’, the quality of ‘Cm’ (specific heat capacity for a mass) must be justified within any calculation involving specific heat capacity.

    Gasses are difficult in that, on a macroscopic scale, their divergence from ‘STP’ (Standard Temperature and Pressure) needs to be addressed and accounted for within any calculation for the above. I don’t want to be a bore, but…… :)

    Best regards, Ray.

  179. Trick says:

    Tim F. 11:16pm: “…gravity was assumed to be present.”

    Then there is a pressure gradient in your column. And hence a T lapse rate. Thus temperature can’t be uniform in your closed column with g field as you wrote at 3:12am: “At equilibrium there should be uniform temperature…”

    Tim F. 6:45pm: “gravity is ALREADY included in the theory of DALR…”

    At equilibrium there can’t be a uniform temp. and DALR in the same column conditions for goodness sakes. Obtain a DALR with g field, obtain uniform T with no g field.

    The theory shows if your closed, insulated, rigid column in earth’s gravity field is filled with non-GHG (emissivity =0) clean air then the exact lapse is T(p)/To = (P(z)/Po)^(R/Cp).

    If you fill your 1km tall column with earth’s actual standard atmosphere in equilibrium then the approx. hydrostatic lapse is –g/Cp = -9.8K and the measured actual avg. environmental lapse (including all the GHGs, heat source/sink & aerosols) would be -6.5K.

    Then from there can properly discuss free and/or forced convection by mod.s to the initial column.

  180. tallbloke says:

    suricat says:
    September 16, 2012 at 12:35 am
    Take care on using property icons, ‘Cp’ (~taken as specific heat capacity) actually refers to a ‘mass’. That’s why engineers use the term ‘Cp’ for gasses, as it requires ‘constant pressure’ and is a ‘mass for mass’ term. When a volume of gas expands, the ‘original mass’ is reduced within the ‘original volume’ causing calculation error and should be avoided. I’ve used this term here before, but I’m not sure everyone understands its full meaning.

    ‘Cv’ can be taken as a term if any density change can be properly accounted for, but generally speaking, for a ‘constant’ ‘specific heat capacity’, the quality of ‘Cm’ (specific heat capacity for a mass) must be justified within any calculation involving specific heat capacity.

    Gasses are difficult in that, on a macroscopic scale, their divergence from ‘STP’ (Standard Temperature and Pressure) needs to be addressed and accounted for within any calculation for the above. I don’t want to be a bore, but……

    On the contrary Ray, this may be one of the most important comments here in months. Loschmidt originally formulated his hypothesis that a gravity affected gas column would not be isothermal but would exhibit a gradient as -g/Cv

    It was Andreas Tripp who reformulated it as -g/Cp

    I’d appreciate it if You and Trick could put your heads together round that and see what evolves.
    See the Loschmidt thread:

    http://tallbloke.wordpress.com/2012/01/04/the-loschmidt-gravito-thermal-effect-old-controversy-new-relevance/

  181. Stephen Wilde says:

    “When a volume of gas expands, the ‘original mass’ is reduced within the ‘original volume’ “.

    That is indeed a very important point and refers back to a comment I made on the N & Z thread.

    If there is less mass within the original volume then there will be a reduced thermal response to any insolation passing through that original volume.

    Thus less density at the surface will produce a lower surface temperature for the same level of insolation.

    I made the point that that is why an expansion of the atmosphere negates the thermal effect at the surface of whatever causes that expansion.

    Thus more GHGs hold onto more energy in the air and the atmosphere expands.

    That reduces surface density proportionately to offset the warming at the surface that would have occurred if surface density had remained the same.

  182. tallbloke says:

    Yes, the linked subjects of lapse rate, natural co2 emission rate, and olr/greenhouse seem to be cross fertilising ideas nicely.

    Another good summary, thanks Stephen.

  183. Clive Best says:

    TB asks : “How much does the centrifugal force of spinning round at a thousand miles and hour affect the height of the troposphere at the equator relative to its height at the poles?”

    g at the equator becomes g’ = g – v^2/2 with v= 465 m/s and R=6378 km

    so g is reduced by only 0.034 m/s^2 . I estimate the atmosphere rises also by about a similar 0.35% over the equator – so about 50m for the troposphere.

  184. tallbloke says:

    Thanks Clive. Another factor I forgot to add to the list is the atmospheric equatorial elongation due to Lunar and Solar gravitational pull. Any thoughts on how to calculate those?

    Maybe that’s a much bigger factor, given that Earth is around 44km bigger in diameter across the equator than the poles? Or is that because it’s a better coupled centrifugal effect? I’d guess it’s the latter.

    There will be stronger entrainment at the equator up to the mid latitudes too, I would have thought.

    Tim Ball thinks the height difference is down to temperature

    http://drtimball.com/2012/static-climate-models-in-a-virtually-unknown-dynamic-atmosphere/

    I think we need to subtract out other calculable factors and see what’s left. New thread coming on this.

  185. […] Comments tallbloke on Clive Best: Understanding the …Clive Best on Clive Best: Understanding the …tallbloke on Ian Wilson: LOD, Precip, […]

  186. Clive Best says:

    For sure the moon does have an effect on climate. The most important effect is to stabilise the Earth’s axis of rotation, giving stable seasons. Tidal forces fall off as 1/R^3 which explains why why the moon has a larger tidal effect than the sun. The inclination of the moon also varies with an 18.6 year cycle, so the position and strengths of tidal bulge vary with this and the earth’s orbit. Some studies claim to have observed an 18.6 year cycle in droughts for large continents (China and US). Atmospheric tides are dominated by solar insolation effects rather than gravitational tides. I think that gravitational tides though at the poles especially in winter could be significant. Tides work more by dragging fluids tangentially perpendicular to gravity rather than directly against gravity. So I don’t think gravitational tides really effect much the height of the atmosphere.

    I wrote up some of the moon’s climate effects 3 years ago here

  187. tallbloke says:

    Thanks again Clive. Please post this comment in the new thread as well. I read recently on Erl Happs site that the 18.6 year cycle causes a shift in some of the main circulations. If it can do that by changing declination a small number of degrees, I think the tidal effect might be larger than thought. I’ll take a look at your article.

  188. tjfolkerts says:

    There are so many (incorrect) hypotheses presented as facts! I don’t have time (or inclinatation) to address ALL the issues here, but here are a few comments …

    Trick say: September 16, 2012 at 4:43 am “Thus temperature can’t be uniform in your closed column with g field as you wrote at 3:12am”
    The temperature CAN be uniform!
    * BR1 has done extensive modeling that shows there is no temperature gradient.
    * The 0th law of thermodynamics requires a uniform temperature at equilibrium — this is the DEFINITION of thermal equilibrium.
    * the 2nd law of thermodynamics requires a uniform temperature — otherwise you could set up two columns with different gases and get different lapse rates and then run a perpetual motion machine off the perpetual temperature difference at the top.

    The only serious claim to the contrary that I have seen is Graeff’s work. While he seems to be a very competent engineer, I am not ready to discard fundamental physics yet based on a series of unreplicated experiments.

    If you have any evidence to the contrary for your claims, I would love to hear them.

    Clive says: “g at the equator becomes g’ = g – v^2/2 with v= 465 m/s and R=6378 km“
    Officially what you are calling ” g’ ” is actually “g”. The strict definition of “g” is the observed acceleration of objects near the earth, which INCLUDES the centripetal forces due to rotation.

    http://en.wikipedia.org/wiki/Standard_gravitational_acceleration

    (Even physics textbooks tend to be sloppy about this, glossing over the small but measurable effect of rotation.)

    Ray says: “That’s why engineers use the term ‘Cp’ for gasses..”
    Hopefully engineers say what they mean and mean what they say. When they mean “Cp” they should use “Cp” and when they mean “Cv” they should use “Cv”. For gases heated in a sealed container (as might be common for steam), then Cv is appropriate. For gases heated in a flexible container surrounded by the atmosphere (in a balloon or a cylinder with a moveable piston), then Cp is appropriate.

    BOTH of these are for a fixed mass (or number of moles) — the constant mass is assumed. (In principle, you could also have some sort of “Cpv” = heat capacity at constant volume and pressure, but changing mass.)

    For most calculations in the atmosphere, pressure is kept constant, not volume, so Cp is appropriate.

    “When a volume of gas expands, the ‘original mass’ is reduced within the ‘original volume’ causing calculation error and should be avoided.”
    I’m not quite sure what your point is (although TB seems to think it is rather profound). Certainly you cannot heat a gas while keeping mass AND volume AND pressure all constant. You can only pick any two to keep constant. In the atmosphere, the surrounding atmospheric pressure keeps things at constant pressure, so it is logical to let volume change and use Cp.

    ” ‘Cv’ can be taken as a term if any density change can be properly accounted for … “
    For Cv, by definition there can be NO density change! You are keeping the mass constant, and you are keeping the volume constant. So the ratio of the two will necessarily be constant.

  189. tallbloke says:

    tjfolkerts says:
    September 16, 2012 at 7:19 pm
    There are so many (incorrect) hypotheses presented as facts! I don’t have time (or inclinatation) to address ALL the issues here, but here are a few comments …

    Trick say: September 16, 2012 at 4:43 am “Thus temperature can’t be uniform in your closed column with g field as you wrote at 3:12am”
    The temperature CAN be uniform!
    * BR1 has done extensive modeling that shows there is no temperature gradient.
    * The 0th law of thermodynamics requires a uniform temperature at equilibrium — this is the DEFINITION of thermal equilibrium.
    * the 2nd law of thermodynamics requires a uniform temperature — otherwise you could set up two columns with different gases and get different lapse rates and then run a perpetual motion machine off the perpetual temperature difference at the top.

    I do appreciate you being around here Tim, you tell me stuff I didn’t know, like the rotation being included in gravity – thanks.

    However, the stuff I’ve quoted is all wrong. Here we go again:

    br1’s model considers the energy of individual molecules, not the total energy ensembles including the space between the molecules at different pressure as altitude increases.

    The 0th law is not violated by a gradient of temperature at equilibrium because the gradient passes through adjacent parcels which are at equilibrium where they are in contact. As Robert Brown eventually admitted.

    Your ‘perpetual motion’ machine won’t run for long, and you’ll use as much energy recharging it with freshly equilibriated gas as you got from it.

    As for the profound difference between Cp and Cv, I invite you to read the Loschmidt thread and give it some thought.

  190. Trick says:

    tallbloke 8:11am says: “Loschmidt originally formulated his hypothesis that a gravity affected gas column would not be isothermal but would exhibit a gradient as -g/Cv. Andreas Tr(u)pp who reformulated it as -g/Cp. I’d appreciate it if You and Trick could put your heads together round that and see what evolves.”

    ————————————

    All I can see evolve is the 6.4 eqn. of TB link must be intuited from solids where volume is relatively constant so use Cv when solid is heated within reason compared to ideal gas; lapse using Cp is more accurate for ideal gas. The wording in TB linked clip is confused between gas enthalpy & solid enthalpy IMO. Here’s why – solid enthalpy ignores the small work on environment term, can’t ignore that term for atm. ideal gas – it matters in these debates.

    Spinach time, many can skip this & still live a normal life but as a result incorrectly debate on some thermo blog threads.

    The basics: for closed system (control volume) solid or ideal gas, the internal energy U changes 1) when adding thermal energy Q (ok, heat flow if you will) and 2) doing work W on/from environment (i.e. dW = PdV or dW = -VdP) so delta Q=delta(U+W) from 1st law or in math:

    dQ = dU + PdV or equivalently from enthalpy H consideration, note an important minus sign:

    dQ = dH – VdP

    Hold dW=0 thru either dV = 0 or dP = 0 (meaning constant V or constant P) then change just the internal energy (dU or equiv. dH) of the solid or gas when heated; find dQ = dU or dQ=dH. N’est ce pas? (Translation: “Is it not so?”)

    Can then see if system volume is constant (dV = 0 rigid container) or the pressure is constant (dP =0 balloon container) then can measure Cv (rigid) and Cp (balloon) from this theory and turns out they are related by gas Runiversal = Cp – Cv all in J/mole-K. Or Rspecific = cp – cv all in J/kg-K.

    Runiversal = 8.3143 J/mole-K from Clive’s NASA link above along with:

    For Earth air Rspecific = 0.2871 J/gm-k, Earth air cp = 1.004 J/gm-K, Earth surface g=979.86 cm/sec^2

    get Earth air approx. hydrostatic lapse -g/Cp = -979.86/1.004 K/cm = -9.76K/Km.

    (NB1 to Tim Folkerts: see this is NOT uniform T in your 1) column as you say it should be. Can’t have a DALR within g field and be isothermal uniform in g field at same time Tim, geez. Pick a side!)

    If use Earth air cv = cp – Rspecific = 1.004 – .2871 = 0.7169 get more inaccurate higher lapse = 13.67K/Km.

    I’m not familiar with Loschmidt or with Andreas Trupp work so Trupp might have just written be sure to replace Cv from relatively constant volume solids with Cp when analyzing ideal gas for much better accuracy to experiment and real atm.

    I’ve observed many incorrectly intuit from solids what happens in ideal gas; like incorrectly applying the 0th law to one energy reservoir. The 0th says nothing about 1 reservoir; 0th does say something about 3 reservoirs. From that, I observe that basing ideal gas intuition from solids is incorrigibly hard to overcome for some.

    I am satisfied this confusion results from PdV or VdP term so close to 0 in solid state enthalpy (conservation of system energy Law 1) that it can be justifiably ignored for solids. The work term can’t be ignored for accurately using atm. ideal gas enthalpy. We moved on to put air in tires partly for these physics, not make tires of solid rubber anymore.

    As discussed (litigated?) at length, I’m also satisfied this “work on environment” term is the whole cause of the isothermal vs. non-isothermal ideal gas column debate. Allow work on environment (open container), get classic isothermal column at max. entropy; do not allow work on environment (dW = 0 closed container), get non-isothermal column at max. entropy (e.g. see exact closed, adiabatic ideal non-isothermal lapse eqn. 2.88 in the excellent Caballero on-line text).

    (NB2 to Tim Folkerts: Your 1) column is closed, assumed rigid, adiabatic so Caballero exact lapse eqn. 2.88 applies, dW=0 and find non-uniform T at equilibrium lapsing with pressure going up to 1Km so T NOT isothermal, T is exactly non-isothermal – your column with g field is not a solid so use Cp, it is only 1 reservoir so no 0th application allowed AND you can (if you want, I know you do) approximate assuming isothermal uniform T since you are off from DALR by only about +/- 5 kelvin degrees out of about 300K at top & bottom of your 1) column).

    As always, I hunted some typo.s down but still check the above for OMG typo.s before submitting to a journal….

    Q: NOW if still awake, what happens to earth standard lapse rate when infrared-active gas PPM (commonly GHG), heat sink/source, dirt aerosols are added to Tim’s 1) DALR column and are increased in the real lapse atmosphere?

    A1: I say atm. cools less rapidly than DALR with z up thru troposphere since real dry lapse only = 6.5K/km. Interesting to discuss that “warmer” lapse rate, while my finger blisters cool off.

    A2: If you add as much infrared-active gas PPM, and use same heat source/sink as Venus has, atmosphere cools little less rapidly than DALR of 10.5K/km with real Venus lapse measured around 8.5 K/km. Interesting, huh? Ratio that w/Earth. Discuss.

  191. tallbloke says:

    Trick: Many thanks, that makes sense to me. Loschmidt was also working on the idea of the gradient existing in solids, so the Cv makes sense in that context as you say. Still reading the rest of your comment, more tomorrow when I’m less tired.

  192. suricat says:

    tjfolkerts says: September 16, 2012 at 7:19 pm

    “suricat says: September 16, 2012 at 12:35 am
    ‘Cv’ can be taken as a term if any density change can be properly accounted for, but generally speaking, for a ‘constant’ ‘specific heat capacity’, the quality of ‘Cm’ (specific heat capacity for a mass) must be justified within any calculation involving specific heat capacity.”

    Full apologies for the logic slip there, but time constraints necessitate posting late in the day as the cogs begin to slow down. :( That should start with: ‘Volume’ can be taken as a term if…..

    I don’t think this is the reason for the excitement here though, I only imply that the specific heat capacity of ‘a parcel of air’, as defined by meteorologists, reduces proportionately with its expansion losses. Common knowledge, I thought. :)

    Best regards, Ray.

  193. Trick says:

    Tim F. 7:19pm: “If you (Trick) have any evidence to the contrary for your claims, I would love to hear them.”

    As does tallbloke, I appreciate the air column debate with an incorrigible-conduction-in-solids-thinking Tim F. taking the other side. I have bountifully re-learned and learned about thermo. I would learn even more taking Tim F. thru the step-by-step “evidence to the contrary” in the thermo exact theory derivation of the non-uniform non-isothermal solution to his rigid column 1) 9/15 3:12am in a gravity field.

    The excellent Caballero online text is here, just see non-isothermal soln. eqn. 2.88. Then backtrack from there to wherever/whatever text/author/paper you have access/like to understand its provenance.

    http://people.su.se/~rcaba/teaching/PhysMetLectNotes.pdf

    So far as I can tell, the other informed, critical authors 100% agree your 1) column is non-isothermal at LTE. I even went and looked up Gibbs piece & found he agrees with me, non-isothermal is no 2nd law violation!

    That’s from the 1890s, Gibbs passed away in 1903. Title of the relevant piece I didn’t write down was something like “On the Claimed Violation of the 2nd Law”. Sound familiar? Took him 2 pages to show no violation. Me, more like 170 posts.

    The classic guys were right that the column is isothermal with the non-zero “work on environment” – column open to work on air column above & below – term left in the gas enthalpy. Supporting evidence for closed column non-isothermal solution is that the standard atmosphere is WAY closer to the exact non-isothermal column curvy solution than the straight line up approx. isothermal solution. This shows the air parcels really don’t do much work up and down so adiabatic and dW=0 assumptions work more closely to reality and even the DALR.

    To add some to TB’s 8:54pm defense of my views:

    1) Tim F. is not very wrong to assume the column is isothermal. The necessary hard work of the exact integrations can be avoided by just assuming constant T. This assumption is close enough (at most 10-20% off or so) for government work. Isothermal soln. happens to be exact about halfway up the troposphere. So there’s that.

    2) br1’s computer model will be perfected when it obtains the exact solution shown in Caballero eqn. 2.88. As does Tallbloke, I have some reservations the model includes all the necessary physics but I have not the detail. For sure sim is closed, can be made adiabatic & rigid, does not have infrared-active gas, aerosols. I think br1 models Boltzmann’s constant off by about 23 orders of magnitude, but that may be ok as it is just a scaling factor for T to get into macroscopic dimensions not a physical law.

    3) 0th law does not apply to your 1) column since there is only one heat reservoir. You could apply 0th by inventing 2 more columns. Breaking the column in half doesn’t help – is just 2*1 reservoirs – 0th N.A.

    4) The 2nd law does NOT require a uniform temperature in all cases, here’s the thing:
    The 2nd law requires system entropy to be maximized at system equilibrium and it does not (much if at all) tell about how long that may take. Gas entropy is maximized with exact isothermal solution ONLY when the air column is open to work and the dW term .NE. 0.

    First, derive the correct entropy eqn. then mathematically maximize it, this is not easy.

    Close the column to work on environment as your thought set-up so that dW=0 and the resulting entropy eqn. is maximized only with the non-isothermal solution. See some of the gory basic details in my 11:29pm post right above.

    There is no perpetual motion in your example since the columns are adiabatic, you can’t pierce the walls with any device allowing T in/out by definition. Now you can run a machine by doing the piercing on the T difference though, allowing thermal energy to flow but not forever. A proposed completely physical example is here – it is just not economic presently.

    http://en.wikipedia.org/wiki/Ocean_thermal_energy_conversion

    Again, no warranty on typo.s.

  194. suricat says:

    Trick says: September 16, 2012 at 11:29 pm

    “The basics: for closed system (control volume) solid or ideal gas, the internal energy U changes 1) when adding thermal energy Q (ok, heat flow if you will) and 2) doing work W on/from environment (i.e. dW = PdV or dW = -VdP) so delta Q=delta(U+W) from 1st law or in math:”

    In a theoretical ‘closed system’ there is no work done to, or done by, the environment. However, forces against the boundary, +ive or -ive, are permitted.

    If the closed system is a ‘controlled volume’ (constrained?) there can be no ‘dV’ (delta volume). Thus:-
    dW = PdV can only exist as dW = VdP unless the system is a theoretical ‘open system’ to volume where a variation of volume is permitted. Is this what you imply?

    I’m in real time with this site and like TB I need my zeds.

    Best regards, Ray.

  195. tjfolkerts says:

    TB,

    I appreciate that you are willing to discuss and learn. That is valuable. And I learn things from these discussions too.

    However, there are fundamental ideas in physics that cannot simply be ignored. It is possible that the laws are wrong. It is possiblethat generations of scientists smarter than you or me are wrong. But I doubt it.

    You (and others) objected to my two column counterexample. Let be be more specific.
    * There are two columns of gas that have perfect thermal insulation except for a few specific places.
    * The bottoms of the two columns are thermally connected (eg a piece of metal that joins the two sides) but is still insulated from the rest of the universe. The connection at the bottom ensures the bottoms of the columns are the same temperature.
    * The tops of the two columns have uninsulated regions that are connected to the two sides of a heat engine — maybe a sterling engine. (http://www.youtube.com/watch?v=ARD3ctp80ac) or a thermopile (http://en.wikipedia.org/wiki/Thermopile)
    * the columns are filled with gases with different specific heats.

    IF THE EQUILIBRIUM CONDITION WERE THE ADIABATIC LAPSE RATE, then the different specific heats ensure the tops of the two columns were at different temperatures — and that they would RETURN to those different temperatures if disturbed (that is what “equilibrium” means after all). The connection to a heat engine at at those two different temperatures would allow the extraction of work. The heat engine would try to decrease the temperature difference; the “equilibrium lapse rate” would try to maintain the temperature difference. The result would be a continued temperature difference somewhat less than predicted simply by the adiabatic lapse rate, but definitely more than zero. This means the heat engine could continue forever, utilizing the temperature difference and producing useful work.

    “br1′s model considers the energy of individual molecules, not the total energy ensembles including the space between the molecules at different pressure as altitude increases.”
    Empty space does not have energy (unless you want to discuss “dark energy”, but that is totally unconnected to this discussion). The sum of the energy of the particles IS the total energy of the ensemble.
    Empty space does not have pressure, either. The sum of the force from the collisions of the particles IS the pressure.

    “The 0th law is not violated by a gradient of temperature at equilibrium because the gradient passes through adjacent parcels which are at equilibrium where they are in contact. As Robert Brown eventually admitted.”
    I’d be amazed if RGB admitted that. Do you have a link to any such statement?

    “Your ‘perpetual motion’ machine won’t run for long, and you’ll use as much energy recharging it with freshly equilibriated gas as you got from it.
    The only energy I would “using” to run the machine is the energy provided by the gas itself. The gas itself “recharges” the temperature difference. As long as the gas keeps “recharging” the temperature difference, I can keep getting energy from the machine.

    Either
    1) the gas CANNOT recharge the temperature difference (and comes eventually to equilibrium at the same temperature throughout).
    or
    2) the gas CAN recharge the temperature difference, and I can use that continually recharging temperature difference to continually “recharge” my perpetual motion machine.

    “As for the profound difference between Cp and Cv, I invite you to read the Loschmidt thread and give it some thought.”
    I glanced at that thread. As near as I can tell, the original analysis made the mistake of using Cv. Even early on, it was realized that this was a mistake, and that Cp should have been used instead in the derivation of the adiabatic lapse rate. That doesn’t seem so profound to me.

  196. tjfolkerts says:

    Trick says: “The excellent Caballero online text is here, just see non-isothermal soln. eqn. 2.88. Then backtrack from there to wherever/whatever text/author/paper you have access/like to understand its provenance.

    http://people.su.se/~rcaba/teaching/PhysMetLectNotes.pdf

    Actually, you can just backtrack to the paragraphs before Eqn 2.88:

    Just like entropy, potential temperature is conserved under adiabatic, reversible transformations. It has many advantages in atmospheric applications, mostly related to its simple physical interpretation: it is the temperature a parcel of air will have if brought adiabatically to pressure p0.

    Note the supposition “if brought adiabatically to pressure p0″. This means the parcel does exchange any energy with the surroundings. In fact, the parcel is FORBIDDEN to exchange any energy because it is adiabatically isolated from the rest of the gas. If the parcel cannot exchange energy then, by definition, it can never come to thermal equilibrium with the gas around it. Each parcel will remain at its own thermodynamic equilibrium, independent of the surrounding parcels. THIS TELLS US NOTHING ABOUT THE TRUE EQUILIBRIUM CONDITION for the atmosphere as a whole.

    Now, if you DID allow the parcels to exchange energy, then they would eventually come to thermal equilibrium. As argued repeatedly above, I conclude this will be an isothermal condition. Others are free to seek other conclusions, but you are going to need STRONG evidence if you want to change the minds of generations of scientists.

  197. tjfolkerts says:

    Suricat says: “In a theoretical ‘closed system’ …”

    This seems to be a nomenclature misunderstanding. Traditionally, a “closed system” doesn’t allow particles in or out, but it could change volume. So work could be done on (or by) the system.

  198. Trick says:

    Tim F 2:50am: “In fact, the parcel is FORBIDDEN to exchange any energy because it is adiabatically isolated from the rest of the gas.”

    YES. You ARE making progress reading here. Read your clip very close. Rodrigo Caballero tells us here as you bring a parcel of air down in your column 1, the temperature will increase adiabatically (meaning parcel will not lose internal energy to environment nor do work on the environment) from smaller T above to higher To below as pressure increases P to Po at bottom.

    The gravity field causes P to increase on the way down your column & T increase process with pressure is shown exactly in eqn. 2.88, the approx. DALR is shown in 2.92.

    This non-isothermal exact soln. 2.88 exactly lines up with generations of critical, informed published thermo scientists I have now traced back to Gibbs in the 1890s. Further back the generations of scientists knew that if the parcel is allowed to come down your column adiabatically w/no heat loss to environment AND do work on the environment, then the parcel was isothermal, T(z) = To constant.

    It all just adds up nicely. Keep digging for more of the provenance of Caballero eqn. 2.88, exact non-isothermal derivation is very long & very thorough.

  199. Trick says:

    clivebest 9/14 8:04pm: “Greenhouse effects vary enormously- on Mars is < 5 degrees, on Venus ~ 500 degrees, and on Earth ~ 30 degrees. Why?”

    Here’s why: These come from relevant basic governing eqn.s derived from first principal simplifying radiative balancing atm. emissivity/absorption assumptions as given in “Fundamentals of Atmospheric Radiation” p. 33 (a remarkable coincidence of numerology).

    Compute net solar irradiance S from total solar radiant energy So: S = So*(1-albedo)/4

    Earth avg. orbit radius So ~ 1369 W per m^2, albedo ~ 0.30, find S ~ 240 W per m^2.

    Find Teq at surface spread over entire planet from: Teq ^4 = S/(c*(1-e/2))

    Where:

    c = Stefan-Boltzmann constant
    e = radiative emissivity of planetary atmosphere averaged over emission spectrum;
    set e = 0 for no infrared-active gases (commonly non-GHG), compute Teq for Earth = 255K,

    set e = 1 (i.e. add infrared-active gas) get Teq = 303K

    set e = 0.8 for actual infrared-active gases ppm in Earth atm. to get Teq = 288K

    So Clive can see why & where the Earth ~30K comes from (288K – 255K = 33K GHE)

    Venus closer sun orbit(So), albedo ~0.75, e=0 non-GHG shows 232K (~732K – 232K = 500K GHE)

    Mars further from sun orbit (So), albedo 0.25, e=0 non- GHG shows 210K (~215 – 210 = 5K GHE)

    All that is needed is empirical c, albedo, e=atm. radiative emissivity to get Teq. at long term hydrostatic equilibrium to see the atm. greenhouse effects (GHE) on the 3 planets.

    As atm. CO2 ppm goes up, increase the e, maybe change albedo, find the new Teq. Big question of course is how much each of the variable factors change. Note troposphere ideal lapse rate of each planet from –g/Cp is also different; add CO2 and the trop. DALR goes up a bit as Cp comes down when adding CO2 and vice versa.

    Confirm numbers, eqn.s in case of any typo from the NASA page, item “Heat Balance” Clive linked 8/31 1:29pm:

    http://pds-atmospheres.nmsu.edu/education_and_outreach/encyclopedia/heat_balance.htm

  200. Trick says:

    Tim F. 2:39am :* There are two columns of gas that have perfect thermal insulation except for a few specific places.”

    LOL. NO, can’t pierce the adiabatic veils anywhere, even a few specific places. The control volume then changes. All you do is draw a bigger adiabatic control volume around the pierce contraption in that case.

    No thermo laws broken, no perpetual motion free energy. If you want, pierce the adiabatic cv, build an OTEC. But still the OTEC energy flow won’t outlast the sun unfortunately. No free energy.

  201. tallbloke says:

    tjfolkerts says:
    September 17, 2012 at 2:50 am
    Trick says: “The excellent Caballero online text is here, just see non-isothermal soln. eqn. 2.88. Then backtrack from there to wherever/whatever text/author/paper you have access/like to understand its provenance.

    http://people.su.se/~rcaba/teaching/PhysMetLectNotes.pdf“

    Actually, you can just backtrack to the paragraphs before Eqn 2.88:

    Just like entropy, potential temperature is conserved under adiabatic, reversible transformations. It has many advantages in atmospheric applications, mostly related to its simple physical interpretation: it is the temperature a parcel of air will have if brought adiabatically to pressure p0.

    Note the supposition “if brought adiabatically to pressure p0″. This means the parcel does exchange any energy with the surroundings. In fact, the parcel is FORBIDDEN to exchange any energy because it is adiabatically isolated from the rest of the gas. If the parcel cannot exchange energy then, by definition, it can never come to thermal equilibrium with the gas around it

    If brought adiabatically to a different pressure, the parcels volume will change and this will cause it’s temperature to change such that it is then in thermal equilibrium with its surroundings. Remember however than if the parcel has risen, then it has gained gravitational potential energy and thus kinetic energy will form a smaller proportion of its total energy. That’s where the gradient comes from.

    Robert brown finally acknowledged my simple proof of the possibility of a gradient through contiguous parcels which didn’t violate the 0th law in one of the interminable arguments on WUWT around the N&Z and Jelbring theses. I had to pursue him with the proff through several threads before he finally buried his admission in a long rambling reply. Good luck finding it. I thnk I may have excerpted the relevant passage and reposted it here for posterity.

  202. Bryan says:

    Tallbloke says
    “This means the parcel does exchange any energy with the surroundings. In fact, the parcel is FORBIDDEN to exchange any energy because it is adiabatically isolated”

    I’m sure you meant heat rather than energy here.
    The parcel does PdV work in expanding.
    This energy is stored in the surrounding atmosphere.
    A descending parcel on the other hand has PdV work done on it by the surroundings,

  203. tallbloke says:

    Hi Bryan,

    That was Tim Folkerts who said that, I was quoting him to refute what he said.

  204. Clive Best says:

    Reading through the Loschmidt effect discussions and the various refutations of it in various blogs, I came across this paper Christian Fronsdal, Univ. California.

    He points out that there is an easy way to test it experimentally using a centrifuge. Assuming the equivalence principal that gravitational mass = inertial mass, then huge gravitational fields can be simulated using a centrifuge. A hypothetical experimental setup is shown here :

    For a gap of about 10cm between the inner and outer cylinders, a centrifuge should be able to reach T1-T2 ~ 1 degree C if Loschmidt is correct. Otherwise T1=T2 if the “consensus” is correct. This would resolve this argument once and for all.

  205. br1 says:

    Hi all,

    Sorry for not contributing the last few days, I got distracted trying to use the model to break 2LoT. Didn’t work, but worth a try!

    Anyway, here’s a contribution, I hope it adds some clarity, please see some results posted at the following link:

    Text associated with the picture is:
    “In these figures, a 2D kinetic gas simulation is run and the temperature profile of the gas vs height is plotted. The walls are entirely reflective, so the particles represent the micro-canonical ensemble. Gravity is present at ten times Earth’s gravity, molecular mass is taken as 1e-26 kg to be on the order of a typical atmospheric molecule, and molecular radius is 1 m in order that the few molecules have a reasonable chance of colliding and coming to thermal equilibrium. The container has a width of 250 m, but the height is taken as infinitely tall (g is constant vs height). The temperature profile of the lowest 5000 m is plotted. In the four top figures, the number of molecules, N, is varied, and the blue data points are compared to the theoretical value obtained by Velasco Eqn(8) in this paper: http://tallbloke.files.wordpress.com/2012/01/s-velasco.pdf . Average temperatures are slightly different in each run, as the molecules are started with random velocities around 300 K. One can see that although there is a steady-state gradient in temperature, it reduces rapdily with increasing number of molecules. By comparing to the DALR for this 2D gas in the lower figure (DALR=g/Cp=m.g/4kB), one can see that the results for larger molecule number are practically isothermal and the DALR is not reproduced. Note that in Velasco Eqn(8), the temperature drop is given by mgh/E where m is the mass of a single molecule while E is the total system energy (KE+PE) summed over all molecules. Hence the gradient becomes insignificant for large N.”

    Isothermal it is.

    Note that while I don’t say so here, there are some important deviations from Velasco Eqn(8) which I’ll come back to in a later post. I’ve already mentioned them in previous threads, but I just want to plot them up properly.

  206. br1 says:

    Because there is a temperature gradient at equilibrium, it is tempting to think that one can extract a heat flow from this. To do this I tried extracting heat from 1 in 10,000 collisions between a molecule and the ceiling or floor, by making that one collision a thermal collision. The hope was that such a small disturbance wouldn’t affect the gradient, which would re-establish itself in between disturbances.

    This does not work!

    I summed the energy entering and leaving the container (this time with a lid on top), and the long term average is zero. Furthermore, the gas becomes isothermal despite the smallness of the disturbance.

    The reason is clear – while the walls are entirely reflective, the phase space that the gas can traverse is limited by the internal energy. By exchanging energy with the surroundings, even the tiniest amount, one allows different regions of phase space to be reached. As thermodynamics doesn’t mind about time, one finds that the amount of phase space reachable with this tiny thermal interaction is exactly equal to the amount of phase space reachable when every single collision with the wall is a thermal collision. In such a case one gets the canonical ensemble, and that is isothermal under gravity.

    So no free lunches yet!

    But there is an amusing unintended consequence I realised while doing this. If such a scheme were possible, and heat could enter the ceiling and leave the floor due to the thermal gradient, then this implies momentum flow as well as heat flow. Heat in this model is only due to kinetic energy, and KE flow implies momentum flow. Hence the container would self-accelerate!

    While this doesn’t quite break Newton’s 3rd law, as the momentum would be taken up by the thermal reservoir, it does produce a rather strange image in the mind of closed containers spontaneoulsy accelerating and heading off across the universe!

  207. tjfolkerts says:

    Bryan says:
    September 17, 2012 at 9:07 am

    “Tallbloke says
    “This means the parcel does exchange any energy with the surroundings. In fact, the parcel is FORBIDDEN to exchange any energy because it is adiabatically isolated”

    Actually, I said that. And yes, i meant cannot exchange THERMAL energy with the surroundings. Work can still be done.

  208. tjfolkerts says:

    Trick says: “LOL. NO, can’t pierce the adiabatic veils anywhere”

    Yes, I can. It is a thought experiment and I can set it up however I want! In fact, how I really want to set it up is with a thermal reservoir at the bottom — say 300 K — to ensure that the bottom of each column is kept at the same temperature. This is closer the real atmosphere anyway, since the air is in thermal contact with the ground. (This also solves the canonical/microcanonical issue in the Velasco paper.)

    Then you get two temperatures at the top of the two columns — say 290 K and 292 K. You could then use that difference to run a heat engine. You would have heat continuously moving from one gas to the other at the top of the column, extracting useful work from a heat engine operating from a single heat reservoir.

    I, on the other hand, would have the same temperature at the top (300 K for both columns), and no perpetual motion machine.

  209. tjfolkerts says:

    I’m out of time, but I think BR1 is pretty much exactly on the right track.

  210. Trick says:

    Tim F. 12:12pm: “I can set it up however I want!”

    Yes of course. No need to follow the thermo laws in a thought experiment or sim. And yes you can extract work from a single reservoir especially one with thermal energy flowing in from the bottom at 300K. You are describing OTEC here as you can extract energy from your thought experiment just as OTEC will be run by the sun.

    When your 300K energy source is turned off or runs out of fuel the device will eventually cease operating as will OTEC.

    Tim continues: “I, on the other hand, would have the same temperature at the top (300 K for both columns).”

    Tim F. can, but nature will not make it so in a gravity field. This thought experiment is inconsistent with nature – Caballero eqn. 2.88 and all the prior science work he references that invoke nature’s thermo laws to get to that eqn. but as Tim F. writes “I can set it up however I want!”

  211. Tim Folkerts says:

    Trick says: “This thought experiment is inconsistent with nature … ”

    Only in the sense that ALL thought experiments are idealizations (as are all equations for that matter). But the thought experiments are all completely consistent with the (idealized) laws of thermodynamics.

    Caballero makes his assumptions too — that the atmosphere has exactly zero thermal conductivity and there is never any heating of one part of the atmosphere by another. In that world, once convection as set up a temperature gradient, then the temperature gradient would indeed remain for evermore.

    His assumptions are close to reality — the thermal conductivity of air is often so small that it can be ignored. The atmosphere often has a lapse rate approximating the DALR. But these are assumptions. And these assumptions explicitly require that the atmosphere cannot come to thermal equilibrium. If you could TRULY let the perfectly insulated columns of gas come to equilibrium by conduction (a process that would almost certainly take months if not decades) the equilibrium conditions would indeed be isothermal (or differ by nanokelvins/km in the exact microcanonical solution).

    More telling, Trick says: “And yes you can extract work from a single reservoir … “
    This EXACTLY CONTRADICTS the 2nd Law of thermodynamics. The Kelvin statement is “No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.” You are claiming the opposite — that you can absorb energy from the single reservoir at 300K and extract work from it using the heat engine at the top of the columns.

  212. Trick says:

    Tim F.: “If you could TRULY let the perfectly insulated columns of gas come to equilibrium by conduction (a process that would almost certainly take months if not decades) the equilibrium conditions would indeed be isothermal (or differ by nanokelvins/km in the exact microcanonical solution).”

    No, Tim, respectfully your 9/15 3:12am column was closed off (“completely insulated from the surroundings”) & this is where you are incorrigibly confused by conduction & enthalpy in solids. In nature, gas enthalpy and gas entropy come to different LTE conclusion: Caballero 2.88.

    Generations of scientists he references all prove your closed column is non-isothermal after gravity turns on and waiting “…months if not decades”. Your bold statement of isothermal w/gravity overrides generations of science work & requires bold proof not just statements to the contrary.

    Let’s implement past science work that you are trying to overturn (i.e. you write if turn on gravity column remains isothermal – “uniform temperature”)….

    In your 1) column, rigid, adiabatic, closed, gravity field, if the initial temperature To at z=earth surface=0 is say 288.15K and Po is 1013.25mb after being filled with earth ideal standard atmosphere then at 1km up closed off to the world and the top (Pz) = P(1km) = 898.7mb i.e. gravity & hydrostatic equilibrium.

    http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770009539_1977009539.pdf

    R=287 J/K-kg and cp = 1004 J/K-kg.

    Initially w/o gravity your column is isothermal, Po=P(1km) = 1013.25mb and To=T(1km)=288.15K.
    Now turn on gravity & wait “…months if not decades” and measure the T at the top based on a generation or two of science progress (energy conserved, entropy maximized):

    Find T(1km) exactly in column = 288.15 * (898.7/1013.25)^287/1004 = 287.44K a lapse of 0.71K/km (not nanokelvins).

    See, you are not very wrong solving w/your bold statement of column remaining isothermal after turning on gravity T(1km) = 288.15, lapse 0K/km. Just your theory is wrong according to science.

    The 1km approx. DALR is of course way off exact theory 288.15 – 278.39 = 9.76K/km lapse but closer to reality which includes the sun heat source/deep space sink, dirty air, non-equilibrium convection:

    Actual 1km environmental lapse turns out to be 288.15 – 281.65 = 6.5K/km lapse what do you know!

    So if you want to try and understand earth atm. processes based on nature in your column (convection, conduction, infrared-active gas, aerosols), start the column from the past theory of generations of scientists eqn. 2.88 or eqn. 2.92 that show lapse rates closer to reality to improve your understanding of reality.

    Trying to figure out where you et. al. fall off the track & become inconsistent with nature has been fun though a lot of work extracted from a single reservoir (me).

  213. Trick says:

    Soldiering on, I see Tim F. continues 4:43pm: : More telling, Trick says: “And yes you can extract work from a single reservoir … “ This EXACTLY CONTRADICTS the 2nd Law of thermodynamics. The Kelvin statement is “No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.” You are claiming the opposite — that you can absorb energy from the single reservoir at 300K and extract work from it using the heat engine at the top of the columns.”

    OTEC has been implemented & the system actually does extract work from a single reservoir with temperature at top hotter than bottom! Didn’t Tim F. read about OTEC? How does it do that? Magic? OMG was Kelvin/Clausius/Carnot wrong? Hint: no. Look up the definition of “complete”.

  214. Tim Folkerts says:

    Trick says: ““In your 1) column, rigid, adiabatic, closed, gravity field, if the initial temperature To at z=earth surface=0 is say 288.15K and Po is 1013.25mb after being filled with earth ideal standard atmosphere then at 1km up closed off to the world and the top (Pz) = P(1km) = 898.7mb i.e. gravity & hydrostatic equilibrium.

    http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770009539_1977009539.pdf

    You continue to confuse the properties of various different idealized atmosphere. In this case, the “US Standard Atmosphere” is an attempt to come up with an idealized model that closely approximates the actual atmosphere.

    Let me repeat — the actual atmosphere. The actual atmosphere is NOT in thermal equilibrium. The actual atmosphere is NOT adiabatically isolated from the rest of the universe. So yes, this idealized model has a lapse rate — because such a lapse rate is observed in the non-equilibrium, non-adiabatic atmosphere. The model was intentionally adjusted to be of practical use in the actual atmosphere, so it BETTER have profiles for temperature, pressure, density, etc that closely match the actual atmosphere. (And since the actual lapse rate is less than the DALR, the US Standard atmosphere ALSO has a lapse rate less than the DALR.)

    So we now agree that the ACTUAL atmosphere has a lapse rate. That actual environmental lapse rate is about 6.5 K/km (your number seems to be a factor of 10 too small). If we recreate the non-equilibrium, non-adiabatic conditions of the actual atmosphere atmosphere in my hypothetical column of gas, I would expect my 1 km column to have as lapse rate similar this this number.

    But once again, it completely fails to address the question of the lapse rate in an adiabatically-isolated, thermally-equilibrated column of air. You are no closer to disproving my conclusion than you were before posting your last post.

    I will grant you that the lapse rate in an adiabatically isolated column is of little practical importance, since it is not much at all like the real atmosphere. Pretty much any real atmosphere will be closer to the DARL than to isothermal because all real atmospheres have at least SOME small heating from the surface (either geothermal heat, sunshine, or nuclear) and some cooling from the top (from GHGs). This means that the real atmospheres will have large lapse rates.

    My suggestion to you — focus on the difference between “adiabatically isolated from the rest of the universe, but heat can flow WITHIN the gas inside the column” and “adiabatically isolated from the rest of the universe, and each ‘parcel’ is also adiabatically isolated from the other parcels in the gas”.
    * I continue to agree with you that the SECOND scenario typically does have a lapse rate approximated by the DALR. (Or put another way, the “potential temperature” is approximately constant.)
    * I continue to disagree with you that the first case will have a lapse rate approximated by the DALR — rather the lapse rate will be approximated by zero.

  215. Trick says:

    Tim F. 9/17 8:19pm: “…adiabatically isolated from the rest of the universe, but heat can flow WITHIN the gas inside the column…the lapse rate will be approximated by zero.”

    Tim F. makes a small but major concession here to now write a non-zero lapse rate for his 9/15 3:12am 1) column idealization with gravity. Book mark this TB: Tim F. comes over to non-isothermal camp: “approximated by zero” – ideal 0.71K/km lapse truly is not zero but approximated by zero.

    Tim continues: “That actual environmental lapse rate is about 6.5 K/km (your number seems to be a factor of 10 too small).”

    My environmental lapse number clipped from 7:14pm: “… 288.15 – 281.65 = 6.5K/km lapse…”

    My number, same as Tim’s, is not factor of 10 too small. Interesting that the ideal theory (0.71) is ~10 times smaller than environment (6.5) – there are some majorly important other processes. Now let’s discuss the relative importance of each of those on the real 6.5K/km lapse rate.

    NB: It was others that initially focused on your 1) idealization of a tall adiabatic column above, not me. The fun and whole point of focusing on this is to get the basic details right & agreed before moving on to more deeply discuss other much more complex systems and processes.

  216. Tim Folkerts says:

    Trick, we do seem to be getting a bit closer — always a good sign!

    Trick says: “My number, same as Tim’s, is not factor of 10 too small. “
    I was responding to “Find T(1km) exactly in column = 288.15 * (898.7/1013.25)^287/1004 = 287.44K a lapse of 0.71K/km (not nanokelvins).” which IS a factor of 10 too small. But in other places we seem to be closer together. I can easily chalk that one up to a simple misunderstanding.

    But again, this lapse rate is the observed lapse rate in the non-adiabatic, non-equilibrium actual atmosphere, so it is immaterial to the discussion of my theoretical column.

    “Tim F. makes a small but major concession here to now write a non-zero lapse rate for his 9/15 3:12am
    The only concession is that a paper by Velasco studied the exact case for a truly adiabatic (microcanonical) gas, and found that the temperature DOES drop with altitude. But this drop is a function of the number of particles. The drop is significant when you only have a handful of particles, but with moles worth of particles in the box, the drop is immeasurably small (hence the “nanokelvins” or “approximated by zero.”). (And no actual container is truly perfect insulation, so even this immeasurably small theoretical lapse rate disappears in a more applicable canonical ensemble.)

  217. suricat says:

    tjfolkerts says: September 17, 2012 at 3:02 am

    “Suricat says: “In a theoretical ‘closed system’ …”

    This seems to be a nomenclature misunderstanding. Traditionally, a “closed system” doesn’t allow particles in or out, but it could change volume. So work could be done on (or by) the system.”

    Thanks for your response of my post to Trick. I note your ‘tag’ has changed Tim. :)

    The evolution of ‘enthalpy’ (work done) is a violation of Cp (or Cv for that matter)! The system scenario just doesn’t permit the evolution of ‘work’. Enthalpy can be realised by the employment of PVT (‘nr’ should fit in there somewhere [PVnrT?]), or visually in a PVT diagram.

    It’s a long time since I used either of those methods. :)

    Best regards, Ray.

  218. Trick says:

    br1, ferd – How’s the sim progressing? Anything new?

    br1 9/17 11:31am above: “I got distracted trying to use the model to break 2LoT. Didn’t work…”

    How?

    For me, I’ve been wondering about how the sim even includes entropy. I haven’t seen y’all mention that entropy theory is coded in somehow, maybe it is. I just finished a fun book about Maxwell’s Demon and the hard working light-fingered fellow’s four deaths and reincarnations* over some 115 years. In the book, I believe I found the reasoning that seems to make sense for the sim.

    The entropy of the sim as I understand your model from a distance is exactly 0, all the time – even when it is running.

    The sim is unlike a tall column of Earth’s air modeled as ideal gas which starts out with non-zero entropy and increases entropy to the max. in equation form in a subtle way. It is possible the Akmaev paper has the details about how to add non-zero entropy to the sim. Might be interesting to discuss.

    ——————————————–

    *1) First death at age 47 in 1914, demon succumbs to heat
    *2) Demon reincarnated with intelligence, dies again in 1929 at 62, felled by measurements
    *3) Resurrected but is crushed in 1950 by the cost of information acquisition at age 83
    *4) Dug up once again but drowns in garbage in 1982 at the age of 115.

    Poor thing. But currently the demon seems to be twitching again, maybe it is not over ’till it is over.

  219. Brian H says:

    Trick;
    Your ‘trick’ description of that book is, of course, totally inaccurate. It is a description, in witty lay terminology, of just why the demon is dead as a doornail. Fail.

  220. Trick says:

    Interesting Brian. Can you be specific?