Effective emission height

Posted: March 11, 2014 by tallbloke in solar system dynamics

.

Some useful discussion in comments below Anders post. Pekka says:

“The radiative height is determined directly by the GHG concentrations and effects of clouds, tropopause height is not sensitive to GHG concentrations and depends more on thermodynamics of air and convection.”

...and Then There's Physics

I should start by saying that this post was partly motivated by an intersting comment from Pekke Pirila on another thread. Also, Eli already has a post that mostly cover this, so this is more from completeness, than anything else.

In a number of my recent posts, I’ve been referring to an effective emission height in the atmosphere that is set by the greenhouse gas concentration. Given that the tropospheric temperature gradient (lapse rate) is largely set by convection, if you know the temperature at some height in the atmosphere, then one can work back down the lapse to the surface in order to determine the surface warming due to greenhouse effect. I haven’t, however, really defined this effective emission height. In equilibrium, the Earth radiates as much energy back into space per unit time as it receives from the Sun. If you determine the average amount of energy…

View original post 566 more words

Comments
  1. wayne says:

    GC, thanks for the reply. R&C is a definitely a breath of fresh air without a doubt and you and R&C are way ahead of what I have been working on and that is why I so like your approach as I read your articles, so many similarities. Just take what I said as input. One note, the inversion I was speaking of was not near-surface temp inversions but the profile inversions above the tropopause as also laid out in RC’s paper. Thanks for the their pdf, that make the paper more understandable.

    I’m definitely not trying to steal the fire from anyone in this area for this look at ‘all atmospheres’ has been long ignored. If I read you right, I also take Hansen’s ‘radiative only’ graph on page 35 with a grain of salt for by the time you would reach 4096 times the co2 there would be very little state-change gases present as seen on Venus… this will take a while for me to look into what is being said in the equations presented but I do like the approach. Hansen seem to be ignoring how much solar energy is reaching the surface without a likewise increase in P0 pressure to match the increase in surface temperature. Something seems amiss there.

    It seems I have been taking a different tack a bit with my adherence to looking at only what is happening to the heat capacity as the profiles of the different planets and moons are looked at against pressures, not altitudes, even though lapse rates can easily be derived by then applying the body’s scale heights. Guess what I am saying is I sure enjoy the new look at this topic and look forward to the months ahead.

    Good to hear from you.

  2. suricat says:

    wayne says: April 28, 2014 at 8:30 am

    “Any of that make some sense?”

    Yes, but it seems a bit garbled in places.

    If you take a “cp of zero” scenario, you need to account, elsewhere, for a ‘phase change’ probability/possibility within the scenario’s calculations. Notwithstanding a representation of ‘spectral bandwidth modification’ for the radiative constituents by the same pressure change.

    Does that make sense?

    Best regards, Ray.

  3. Kristian says:

    Ben Wouters says, April 27, 2014 at 8:33 pm:

    Ben, you are a strange character. And completely impossible to have a conversation/discussion with. So I won’t. I have better things to do …

  4. gallopingcamel says:

    Wayne,

    The amazing thing about Robinson & Catling is that they have made their work accessible to the general public. This should always happen given that we (the great unwashed) are paying for most of what is called “Climate Science” via our federal taxes.

    Most “Climate Scientists” like Michael Mann, Phil Jones and Thomas F. Stocker who defy “Freedom of Information Acts” and the Aarhus convention. They “Lawyer Up” whenever anyone questions their work. People like Steve McIntyre and Ross McKittrick have been battling with these folks for years but the stonewalling continues.

    In a better world Michael Mann and his “Hockey Team” would have lost their funding years ago and folks like R&C would have got their funding.

    David Catling is very busy right now (grading papers is exhausting as the academic year comes to a close). I have the same problem. In about a month I will contact him again in the hope that we can empower dozens of amateurs to apply the fine work that he and Tyler Robinson have done.

    I have no idea where this will go. Currently I am convinced that the Arrhenius (1896) theory is nonsense but R&C may convince me otherwise.

  5. gallopingcamel says:

    Wayne,

    QUOTE
    I also take Hansen’s ‘radiative only’ graph on page 35 with a grain of salt for by the time you would reach 4096 times the co2 there would be very little state-change gases present as seen on Venus…
    UNQUOTE

    I would love to see Hansen’s “Slide 35” published in a “Pal Reviewed” paper.

    One of the parameters in the R&C model is “Ttoa”. This is the temperature at the “Top of the Atmosphere” (aka cloud tops). It is not under the modeler’s control as on Earth it is defined by the physical properties of water. On Venus it is defined by the properties of sulphuric acid and on Titan by the properties of methane.

    At the cloud tops it is possible to calculate a radiation balance. This radiation balance is not sensitive to the amount of CO2 present. What matters is the physical properties of water vapor or sulphuric acid or methane in the case of Titan.

    Just imagine what Hansen’s “Slide 35” would look like if the temperature at the cloud tops was constant as it has to be. The sensitivity of surface temperature to the amount of CO2 present would be close to zero.

  6. wayne says:

    Peter, I’m understanding what you are saying and am in agreement. My track has been more via potential temperature but I come up with the same conclusion, temperature changes so small at 2x it is immeasurable, at 2500x (dry and nearly pure co2 atm) I get a +16°C increase at the surface using my method described above, constant T at the TOA, where Hansen is coming up with +70°C in that slide. Any change would be that at very high co2 concentrations both R (specific) and the specific heat would change altering that R/cp ratio used in the exponent. Like if 225 mb is the TOA and co2 saturated:
    T = 216.6 K / (22500/101325 Pa) ^ (R=(8.314/0.044) / cp=840) = 304 K

  7. gallopingcamel says:

    Hansen is a shameless charlatan. He sold the idea of “Catastrophic Anthropogenic Global Warming” but failed to provide a valid mathematical justification.

    His “Slide 35” is nonsense just like his “Runaway Greenhouse Effect” on Venus. Thankfully there are still some honest “Climate Scientists” who are not afraid to share their calculations with the general public.

  8. wayne says:

    suricat, you’re correct, how do you ever end up with a cp of zero? Sounds screwy, right?

    I am using a rather unorthodox way to study what the apparent cp is in the potential temperature as you break any known profile of any atmosphere into thin pressure bands and only if the composition is known or closely assumed. By the composition you can determine the specific gas constant R. By the potential temperature equation T = T0 (P/P0)^(R/cp) solve for cp you then extract it by the equation given in my first comment. As you approach 0.1 atm nearly all planets and moons with thick atmosphere’s profiles turn vertical (isothermal) and at this band the cp solves as zero. Hmm. As the inversion occurs and the atm gets warmer with height the cp solves as negative.

    What I see in this is without radiation or state changes occurring in a pressure level band the cp will be what you can look up in a lab charts. Our dry atmosphere with a lapse of g/cp (DALR) has a cp of about 1003 J/kg/K and a R/cp of about 0.286 in the potential temperature equation but our atmosphere is not on the average dry, the R/cp that matches the 6.5 K/km lapse is 0.1903. So to get a cp of zero there has to be 1003 J/kg/K of radiation being absorbed (or state changes in the troposphere) to counter the natural lapse that would still occur and in the opposite direction. As you go even higher above the isothermal section even more absorption is occurring and you can get a figure on how much by solving these equations or that is what I am currently doing. This all started with a question in my mind “how much absorption or how much heat from condensation numerically is occurring to cause the profile of our atmosphere to be what it is” and I’m still following this track in the manner I described but carrying this to other body’s atmospheres is quite interesting!

  9. suricat says:

    wayne says: April 29, 2014 at 9:17 am

    “suricat, you’re correct, how do you ever end up with a cp of zero? Sounds screwy, right?”

    Yes. The only equations I’ve understood during my career used ‘cp’ as a notation for the ‘mass of the gas/Mole’, with its specific heat, at a ‘constant pressure’. I’m, now, not sure what you use it as.

    ‘cp’; enables a calculation without pressure change.
    ‘cv’; enables a calculation without volume change.
    ‘ct’; enables a calculation without temperature change.
    These notate ‘basic gas law’ theory, but leave much to be desired when contemplating atmospheric physical properties.

    TBH, these are just ‘gas laws’ that only apply to a ‘gas’! They don’t relate to ‘solids’, or ‘liquids’. Thus, can’t relate, with any accuracy, to a planet’s atmosphere where ‘phase change’ is apparent. How can you suggest otherwise?

    TBH, I don’t/can’t follow your logic. Please elucidate. I’m intrigued (needless to say that this post didn’t ‘do it’ for me). 🙂

    Yours until the desert sands freeze and the camels come skating home, Ray. 🙂

  10. wayne says:

    suricat, sorry to be so long. As I hinted to GC I’m finding my time so tight I can not even read all of the comments lately. Daybreak to midnight daily, busy, no computers.

    Clearly the cp mentioned is a composite variable here since the actual heat capacity is formed from three heat flows: radiation both ways, state change both ways and convection simultaneously and also affected by gravity per Poisson’s equation. Wish I had the time to explain further and I hpe I gave enough above but I simply cannot fully engage right now but if you don’t mind it sometimes being many days between, I’d be happy to try to explain further.

    Maybe take any radiosonde data and reverse apply as described above and look at what the actual cp is in place between any pressure/temperature segment. Where I live sometimes it may be raining from the cloud bases but the rain never reaches the ground, evaporation occurring of course. Look at how that affects the cp that determines the lapse there. In that case you will see the additional absorption of heat reflected in the cp term mainly with a small influence from a change also in the specific gas constant… that is all wrapped into the R/cp exponent term. Maybe try it on some other scenarios. Try some standard or reported atmosphere profiles. Personally I am finding this type of study illuminating when applied to different averaged atmospheres and seems in line with the Robinson paper.

  11. suricat says:

    wayne says: May 4, 2014 at 3:25 pm

    Here’s my problem. The ‘gas laws’ relating to a “cp” ‘model’ equate a gasses ‘specific heat’ without any change in ‘pressure’ (other models for vol. and temp. unchanging are also available). These models are limited to the ‘gas phase’ only!

    “Clearly the cp mentioned is a composite variable here since the actual heat capacity is formed from three heat flows: radiation both ways, state change both ways and convection simultaneously and also affected by gravity per Poisson’s equation.”

    Er, you’re describing the overall system’s ‘outcome’ here, without any explanation of ‘how it was achieved’?

    I disagree with your “radiation both ways” because radiation doesn’t possess ‘specific heat’, and “state change both ways” because ‘latent heat’ is worlds away from specific heat.

    “Where I live sometimes it may be raining from the cloud bases but the rain never reaches the ground, evaporation occurring of course. Look at how that affects the cp that determines the lapse there.”

    Yes, energy from a ‘latent source’ buggers the ELR! This has nothing to do with “cp”!

    I’m exhausted.

    Best regards, Ray.

  12. suricat says:

    wayne says: May 4, 2014 at 3:25 pm

    Let me try to explain again wayne.

    ‘cp’, ‘cv’ and ‘ct’ are different values of/for the ‘specific heat’ of a gas under different ‘static’ scenarios (a ‘constant field’ enables an ‘accurate analysis of the scenario’, but each ‘constant’ evokes a different value for the gas’s ‘specific heat’). Thus the reference to the ‘p’, ‘v’ and ‘t’ statistics for “c” (the ‘specific heat’ value)!

    Now. When we look at an ALR curve, that was generated by a profile from a ‘CP = nR T’ source, we see a ‘natural curve’ for a constant pressure. However, if we look at an ELR (natural observation) curve for the same ‘scenario’, the temp profile is all over the place!

    I don’t know how to explain this in other ‘dialogue’ wayne. ‘Latent energy’ (“Q” “q”) is both a ‘source’ of IR energy in the upper tropo and a ‘sink’ of IR energy at surface, notwithstanding its activity ‘between these levels’, ‘latent heat’ CAN’T be deduced from a ‘sensible heat’ equation. Does this make sense?

    The ‘latent’ product is what bridges the gap between the ALR and the ELR.

    Best regards, Ray.

  13. Ben Wouters says:

    @ wayne and suricat

    You both seem to use the ALR as if it has anything to say about a temperature profile for the whole atmosphere (ELR)

    Could you point me to a source on which this would be based?

    I’ve known and used something along the following lines my whole professional live:
    “The adiabatic lapse rates – which refer to the change in temperature of a parcel of air as it moves upwards (or downwards) without exchanging heat with its surroundings. The temperature change that occurs within the air parcel reflects the adjusting balance between potential energy and kinetic energy of the molecules of gas that comprise the moving air mass.”

    I do have a simple model to discuss the basic ELR if you’re interested.

  14. suricat says:

    Ben Wouters says: May 14, 2014 at 11:39 am

    “@ wayne and suricat

    You both seem to use the ALR as if it has anything to say about a temperature profile for the whole atmosphere (ELR)”

    Do you mean ‘atmospheric altitudes’ (it’s a limited profile)? If so, for my part, No! However, I can’t speak for wayne.

    The ALR is a ‘dry’ composite based on first principles which ‘don’t’ include any ‘latent heat’ properties. The ELR is an ‘observation’ which, by its nature, includes ‘latent heat’ properties. It’s difficult to bring any clear resolution between the ALR and the ELR due to the unpredictable nature of ‘latent heat/energy’, other than that ‘latent energy’ releases/absorbs ‘heat’ at a fixed/set temperature at a particular altitude. Thus, ‘latency’ becomes a ‘thermal capacitance’ in an ‘electronically described circuit’.

    Whilst wayne seems to have uncovered/learned of a method to disclose ‘latency properties’ within the more standard ‘sensible heat’ Cp/Cv equations, I’m doubtful (I’m being polite).

    “I do have a simple model to discuss the basic ELR if you’re interested.”

    If it resolves my issues with wayne’s POV, yes I am. This is a ‘talk shop’ where we can both ‘learn’ and ‘educate’, is it not? 🙂

    I’ve read several papers on the ‘fudge’ of representing latent heat with/by sensible heat and none of them come close to reality.

    Best regards, Ray.