Hockey Schtick: Derivation of the entire 33°C greenhouse effect without radiative forcing from greenhouse gases

Posted: November 24, 2014 by tallbloke in Analysis, atmosphere, innovation, radiative theory, Thermodynamics

Over at the Hockey Schtick, Michael has an interesting new angle on determining planetary surface temperature from pressure and gravity – a subject covered extensively here at the Talkshop over the last three years. Here’s an extract. Of particular interest here is his new method of using the centre of mass of the atmosphere as a reference point. Head on over to read the full post.

Step 2: Determine the height at the center of mass of the atmosphere

We are determining the temperature gradient within the mass of the atmosphere and the equilibrium temperature is thus at the center of mass. The “effective radiating level” or ERL of planetary atmospheres is located at the approximate center of mass of the atmosphere where the temperature is equal to the equilibrium temperature with the Sun. The equilibrium temperature of Earth with the Sun is commonly assumed to be 255K or -18C as calculated here. As a rough approximation, this height is where the pressure is ~50% of the surface pressure. It is also located at the approximate half-point of the troposphere temperature profile set by the adiabatic lapse rate, since to conserve energy in the troposphere, the increase in temperature from the ERL to the surface is offset by the temperature decrease from the ERL to the tropopause.

Fig 1. From Robinson & Catling, Nature, 2014 with added notations in red showing at the center of mass of Earth's atmosphere at ~0.5 bar the temperature is ~255K, which is equal to the equilibrium temperature with the Sun. Robinson & Catling also demonstrated that the height of the tropopause is at 0.1 bar for all the planets in our solar system with thick atmospheres, as also shown by this figure, and that convection dominates over radiative-convective equilibrium in the troposphere to produce the troposphere lapse rates of each of these planets as shown above. R&C also show the lapse rates of each of these planets are remarkably similar despite very large differences in greenhouse gas composition and equilibrium temperatures with the Sun, once again proving pressure, not radiative forcing from greenhouse gases, determines tropospheric temperatures.

Fig 1. From Robinson & Catling, Nature, 2014 with added notations in red showing at the center of mass of Earth’s atmosphere at ~0.5 bar the temperature is ~255K, which is equal to the equilibrium temperature with the Sun. Robinson & Catling also demonstrated that the height of the tropopause is at 0.1 bar for all the planets in our solar system with thick atmospheres, as also shown by this figure, and that convection dominates over radiative-convective equilibrium in the troposphere to produce the troposphere lapse rates of each of these planets as shown above. R&C also show the lapse rates of each of these planets are remarkably similar despite very large differences in greenhouse gas composition and equilibrium temperatures with the Sun, once again proving pressure, not radiative forcing from greenhouse gases, determines tropospheric temperatures.

Step 3: Determine the surface temperature

For Earth, surface pressure is 1 bar, so the ERL is located where the pressure ~0.5 bar, which is near the middle of the ~10 km high troposphere at ~5km. The average lapse rate on Earth is 6.5 km, intermediate between the 10C/km dry adiabatic lapse rate and the 5C/km wet adiabatic lapse rate, since the atmosphere on average is intermediate between dry and saturated with water vapor.

Plugging the average 6.5C/km lapse rate and 5km height of the ERL into our equation (6) above gives

T = -18 – (6.5 × (h – 5))

Using this equation we can perfectly reproduce the temperature at any height in the troposphere as shown in Fig 1. At the surface, h = 0, thus temperature at the surface Ts is calculated as

Ts = -18 – (6.5 × (0 – 5))

Ts = -18 + 32.5

Ts = 14.5°C or 288°K

which is the same as determined by satellite observations and is ~33C above the equilibrium temperature with the Sun.

Thus, we have determined the entire 33C greenhouse effect, the surface temperature, and the temperature of the troposphere at any height, entirely on the basis of the 1st law of thermodynamics and ideal gas law, without use of radiative forcing from greenhouse gases, nor the concentrations of greenhouse gases, nor the emission/absorption spectra of greenhouse gases at any point in this derivation, demonstrating that the entire 33C greenhouse effect is dependent upon atmospheric mass/pressure/gravity, rather than radiative forcing from greenhouse gases.

Comments
  1. On a related note, in my post A scientist’s guide to greenhouse warming. I show that the “greenhouse effect” is related to surface emissivity of the earth and atmospheric temperature. In other words, it is the temperature of the atmosphere that drives the “greenhouse effect”.

    This seems to fit with this article which is saying “the greenhouse effect is equal to the atmospheric temperature”.

  2. Lance Wallace says:

    Error in Figure 1? The tic mark looks to me like 0.4 bar, not 0.5. Which would mess up the perfect match with 255K, more like 260 or a bit more.

  3. It is truly encouraging that people are turning to numerical analysis as practiced by folks like Robinson & Catling. They can explain temperature gradients in troposphers and stratospheres with impressive precision.

    However I disagree with the “Hockey Schtick” when it declares the greenhouse effect for planet Earth is 33 K. Given that Earth’s average temperatture is 288 K, that would imply an average temperature of 255 K if atmospheric warming did not exist.

    The 255 K figure is based on good mathematics coupled with a poor understanding of the thermal properties of the Earth and the Moon. Vasavada, Tim Channon, “br” and this camel have demonstrated that the Moon’s average temperature of 197 K can be explained in terms of physical models:
    https://tallbloke.wordpress.com/2014/04/18/a-new-lunar-thermal-model-based-on-finite-element-analysis-of-regolith-physical-properties/

    Given that the physical models for the Moon are so precise it seems reasonable to use them to calculate the likely temperature of an airless Earth:
    https://tallbloke.wordpress.com/2014/08/27/extending-a-new-lunar-thermal-model-part-ii-modelling-an-airless-earth/

    It seems likely that Earth’s GHE is at least 54 K rather than the 33 K claimed by respectable climate scientists such as Scott Denning, Monfort Professor of Climate Science, Colorado State University :

    I applaud the “Hockey Schtick” comments on the absurdity of the 1896 Arrhenius theory:
    http://hockeyschtick.blogspot.com/2010/06/greenhouse-theory-disproven-in-1909.html

    In spite of the absurdity of the Arrhenius theory people like Roy Spencer, Judith Curry and Richard Lindzen solemnly discuss the concept of a sensitivity coefficient per doubling of CO2 concentration. When will these “Gurus” wake up and declare that the Arrhenius theory is flat out wrong?
    http://diggingintheclay.wordpress.com/2013/05/04/the-dog-that-did-not-bark/

  4. Konrad. says:

    gallopingcamel says:
    November 25, 2014 at 3:49 am
    ////////////////////////////////////////////////
    I also disagree with the “Hockey Schtick”, for three reasons. First there is no such thing as an ERL, the hight of emission from the atmosphere is constantly fluctuating as is the strength of emission, with the strongest emissions from ever changing clouds. Secondly the old 255K assumption is back in play, which is provably false. Neither our atmosphere or surface radiates as a “near blackbody”. Thirdly, this analysis indicates the same temperature profile with or without radiative gases, however our atmosphere would super heat without radiative cooling at altitude.

    However I would also have to disagree with the notion that an atmospheric GHE is warming the surface of our ocean planet by 54K. 71% of our planet’s surface is quite unlike the moon, the oceans being an extreme SW selective surface. Without atmospheric cooling, the sun alone has the power to drive our oceans to a far higher temperature than a theoretical blackbody. 335K is my conservative estimate for average ocean surface temps without atmospheric cooling. For our atmosphere to be able to cool the oceans it needs some way to cool in turn. This is the role of radiative gases.

  5. Trick says:

    Make it 3for3 disagreements. Decent visitor avg. in this ball park.

    Ref. HS site:

    T – T° = -g/C(p) × (h – h°) (6)

    Given that h of the surface = 0, g, Cp constants, there are 3 unknowns (T,T°, h°) in this eqn. (6) which is of the form y=mx+b (where m=slope and b= intercept).

    HS somehow changes -g/Cp to the standard atm. LR 6.5. Yet g and Cp are known for earth and their ratio is not 6.5. Huh? Ok, well 6.5 is now the given constant for m=slope.

    HS gets the 255K from radiative balance citation “as calculated here”. 1 unknown down (T°), 2 to go. Or as stated could get T° as measured from satellites.

    HS announces the 255K occurs at ~5km (h°) by looking up US 1976 standard atm. chart. 2 unknowns down, 1 unknown to go.

    Use eqn. (6 ) to get the 3rd unknown. So all unknowns are now known.

    Note it took radiative balance (or satellites) to get one of the unknowns (in this case T° i.e. b in y=mx+b) which will always be the case. Whether one uses radiative balance to calculate 288K or 255K, that step to get b intercept from radiative balance (or satellites) at a height is always necessary (see R&C grey IR d(optical depth) eqn. S12). Despite the HS incorrectly claimed “without use of radiative forcing from greenhouse gases”.

  6. Anything is possible says:

    @ Galloping Camel

    It is possible for you or Tim to run another version of your lunar thermal model based your MOON1 output, but adjusting for the difference in axial tilt between the Earth and the Moon?

    If so, I would be very interested to see if it comes up with what I believe to be the “right” answer.

  7. tallbloke says:

    Lance: Only 7 tick marks between 1.0 and 0.1. Oops, something’s not right for sure. Have a look at how the ticks are arranged on the logarithmic pressure axis in this paper fig 1 http://www.atmos-chem-phys.net/14/4843/2014/acp-14-4843-2014.pdf

    GC: Nikolov and Zeller showed that the misapplication of Stefan Boltzmann to a ‘disc’ of double Earth diameter is wrong. They provided the correct method for the integration of incident sunlight on a sunlit hemisphere.
    https://tallbloke.wordpress.com/2012/01/17/nikolov-and-zeller-reply-to-comments-on-the-utc-part-1/ Which produces the 197K result. They have updated this with additional equations for factoring in the heat capacity of the regolith, the galactic background etc. (Private comms)

    Konrad: Michael isn’t claiming anything for the efficacy of the ERL in radiative terms. He notes that it is coincident with the height which is the ‘centre of mass’ of the atmosphere (in the vertical profile).

  8. Lance: R&C left off the tick mark for 1.0 and that’s exactly what I did count back from what I thought was 1.0 but is apparently 0.9 instead. Thanks for pointing that out, but Fig 1 from R&C is very low resolution graph anyway to show all of the planets with thick atmospheres on a single graph.

    Not to worry, the US Standard Atmosphere Calculator

    http://www.digitaldutch.com/atmoscalc/

    Shows at 5.1km the temperature is 255K and P=533 millibars = 0.53bar

    Thus, almost precisely what I showed in the post:

    P ≈ 0.5 bar and T = 255K at ≈ 5km.

    Trick : 6.5C/km is the average observed lapse rate, which is intermediate between the derived dry adiabatic lapse rate of ~10C/km (9.8C/km) and the derived saturated adiabatic rate of ~5C/km. We are obviously dealing with global averages here, so that’s why I used the observed average LR. Neither g or Cp are dependent upon radiative forcing, so I don’t know why you have a problem with using the observations.

    Same goes for calculation of Te, once again no dependence upon RF from GHGs, so why not use the observations? Same for US Std Atmosphere pressures at altitude, based upon observations, not RF from GHGs.

    Tallbloke: I just updated the post with the same center of atmospheric mass assumption for Titan and found that the equilibrium temperature Te with the Sun is located at the approximate center of mass of Titan’s atmosphere, thus this assumption appears valid for Earth and Titan as well.

    FYI, I made an error on my Venus Te calculation on twitter that we discussed yesterday and am working to see if the CoM assumption can be applied to Venus’ odd atmosphere. Even if it cannot, the Venus atmosphere is clearly explained by pressure dominating radiative forcing nonetheless and also validates the mass/gravity/pressure GHE theory.

    Thanks for posting this here for comments.

  9. markstoval says:

    I think the most important take-away from the Hockey Schtick post is that there is no “back radiation” from that magic molecule CO2 needed to account for the warming of this planet above what it would be if there was no atmosphere. While we might disagree on some of the details, I think most here would agree that the delusion of CO2 driving the temperature of Earth is just plain wrong.

    This post by HS is a good starting point for talking with a certain science teacher I know and I will ask her what she thinks about it as soon as our Thanksgiving holiday is over. She believes in the 33º number like many Christians believe in Jesus.

  10. […] Hockey Schtick: Derivation of the entire 33°C greenhouse effect without radiative forcing from gree… […]

  11. Roger Clague says:

    Saying adiabatic lapse assumes the cause. I suggest you simply say lapse rate.
    You use 1st law of thermo and 3rd law of motion, not 1st law of thermo and Ideal Gas Law, IGL. IGL not used, I am glad to see.
    We are determining the temperature gradient within the mass of the atmosphere using a linear function of atmospheric mass (the lapse rate),
    LR = gravity/specific heat
    LR is a function of gravity not mass. Gravity is not the same as mass Mass is not a fundamental concept.
    Mass = density (d) x volume (v)
    Both d and v depend only on length and are more fundamental then mass.
    Equilibrium temp of Earth with sun is not at centre of mass
    It is at the lowest temp. of the atmos. That is the tropopause temp.
    Earth 220K, Venus 260K

  12. Trick says:

    HS 11:09am: The problem with using the observations is they include the natural radiative effects of the constituent gases as shown in R&C eqn. S12. So in using observations (6.5 ELR, 255K, 5km) to compute surface 288K you HAVE included all the natural effects of “radiative forcing from greenhouse gases”.

    Those radiative effects are necessary to get the correct intercept b. The slope m can be from -g/Cp (DALR) or 6.5 standard ELR (includes radiation effects of water vapor, aerosols, liquid water, dust et. al.)

  13. Thanks for the post and comments. As a result of reading some of the links I written up some thoughts on my website: Some thoughts on greenhouse warming

    I think what I’m saying is that if like the Penn you use a model of an atmosphere without greenhouse gases 🙂 you end up with the model of adiabatically heated earth. But a more realistic atmosphere is a semi-transparent one where the adiabatic temperature and thermal cycling control the temperature in the dominant troposphere where H20 plays the dominant role setting the temperature. (But that’s not explicit in what I said)

  14. Roger: The “effective temperature” or “equilibrium temperature” with the Sun is “well accepted” to be 255K, not 220K, so please show your work

    “a linear function of the atmosphere in a gravity field” sound better?

    I tried to keep the derivation of LR a simple as possible to improve readability, but here it is including all steps including the full gas law

    http://atmos.nmsu.edu/education_and_outreach/encyclopedia/adiabatic_lapse_rate.htm

    Trick: As shown, T is function of P, and radiance/emission spectra a function of T, not the other way around.

  15. Or “a linear function of atmospheric heat capacity in a gravity field”

  16. tallbloke says:

    HS: Roger C is talking about tropopause T not the mythical 255K ‘no GHG surface temperature’ or ‘ERL height ‘ temperature

    Tropopause T for Earth averages around -55C or 218K

  17. Trick says:

    HS 5:56pm: Check the weekly day by day temperature (degreesC or F) and pressure (mb) traces at the weather station of your choice. Sometimes temperature goes up and pressure goes down; sometimes temperature goes up and pressure goes up. Please note the lack of any obvious function relation between pressure and temperature. Measured proof T is not a function of P UNLESS one adds a constraint e.g.: air density goes up as temperature goes down provided that pressure is constant.

  18. Roger said “Equilibrium temp of Earth with sun is not at centre of mass. It is at the lowest temp. of the atmos. That is the tropopause temp. Earth 220K”

    Tropopause T is 220K, surface T is 288K, midpoint between them is equilibrium temperature with the Sun, 255K, which just so happens to be located at 0.5 bar, one-half the surface pressure. Coincidence?

    Coincidence this also holds essentially perfectly for Titan as well? I think not.

    As Joe Postma said in comment today at my site:

    Great article.

    It’s mathematical law…beyond physics law. The average of a sequential distribution is necessarily found around the middle of that distribution, not at either extremity, and thus, in the case of the atmosphere, the bottom must be warmer than the average – middle -, etc, and this arises without any concern or reference to “greenhouse gases” at all, although the “GHG” water vapour makes it cooler, not warmer. The entire basic premises of climate science are wrong, and misattributed.

    I also added the money quote from Robinson & Catling’s paper, and 3 reasons why the ERL can’t be explained by GHG radiative forcing to the post:

    http://hockeyschtick.blogspot.com/2014/11/derivation-of-entire-33c-greenhouse.html

    Thanks for everyone’s input!

  19. Kristian says:

    Tallbloke, Roger Clague, Hockey Schtick,

    The global mean tropopause height is surely no lower than 12 km:

    What you continually refer to is the American standard atmosphere of north temperate latitudes. That is not equal to the global average.

    6.5 K/km * 12 km = 78K

    288 – 78 = 210K, the global mean tropopause temperature.

    Same with mean global tropopause atmospheric pressure, NOT 0.1 bar, that’s only in the tropics. It’s 0.3 bar or higher at temperate and polar latitudes. So the global average is most likely close to 0.2 bar. The difference in height between 0.1 and 0.2 bar is almost 4 km.

  20. Kristian says:

    BTW, the Venusian atmospheric layer with a physical temperature more or less equal to the planetary radiating temperature in space is NOT found anywhere near its centre of mass. It is located at or high above the tropopause, depending on whether you choose to believe the 0.75 or the 0.9 albedo figure. I would agree that the latter one sounds remarkably high, almost suspiciously so. I have, however, seen no reliable sources providing a global Bond albedo value below the former one. That gives a net (absorbed) solar flux from the ToA down on Venus at 165 W/m^2. Compare this to Earth’s 240 W/m^2. The 240 W/m^2 flux IN/OUT through the ToA is in turn used to calculate our planet’s BB emission temperature in space, which is 255K. If we did the same with Venus, its equivalent temperature (its radiative equilibrium temp with the Sun) would be 232K. This layer is to be found in the vicinity of the tropopause, in the upper part of the main cloud deck, at about 65 km or … about 0.1 bar:

    So on Venus, the actual tropopause (main cloud deck) appears to correlate directly with the theoretical planetary BB emission height, NOT with the atmospheric centre of mass. On Earth, it’s the other way around … On Mars, it’s different again. There, the theoretical planetary BB emission height seems to correlate best with the solid surface itself.

  21. wayne says:

    Interesting, there is the same 7.7 K/km that I found to be true at least per the latest Vega proble data. Kristian, might I ask where you found that graphic? A paper and is it available online? I find such detailed data hard to come by and nearly devoid for Titan.

  22. Kristian says:

    wayne,

    If you look through this one, you’ll find it. Good luck.
    http://theoilconundrum.blogspot.no/2013/03/standard-atmosphere-model-and.html

  23. wayne says:

    Muchas gracias! That’s a new one for me and is talking right in the area I’ve been digging into.

  24. Kristian says:

    I know. Noticed the g/1.5cp …

  25. wayne says:

    Kristian… crap…that is nearly an identical trek I have spent many month’s digging out through the data. Wish I had known that article existed. The only place I see he and I come up with a noticeable different value is on Jupiter and his f is 3.5 where mine fit tightly to right at 3.0 for the adiabatic index. “Adiabatic index”, a new term for me and I’ll definitely use it and there I have been terming it degrees of freedom!

  26. Kristian: We are dealing with global averages, obviously not claiming the global average values I used apply to every specific location from the equator to poles, since Te/solar insolation, heat capacity, and pressures of each coordinate vary tremendously and constantly.

    However, unless you completely reject R&C’s paper explaining why in general the tropopause height varies with pressure, then the same general principles can be applied that the tropopause height is determined by pressure, and starting from where P=0.1 bar down to the surface using the lapse rate & Cp at that location, the surface temperature can be determined.

    WR Pratt has confirmed that for a few specific locations he eyeballed today that the radiosonde data backs this up for specific locations, but if you have any other examples with observations for specific locations refuting this, please do let me know.

    http://hockeyschtick.blogspot.com/2014/11/derivation-of-entire-33c-greenhouse.html?showComment=1416951311833#c2853473179666741759

    Re Venus atmosphere is a solar system outlier with opaque TOA that heats from the top via conduction and the bottom via lapse rate/pressure. I’ve asked Claes Johnson for his opinion on Venus and the center of mass concept and he said he’ll look into it. I’ll post his comments when received.

  27. Konrad, November 25, 2014 at 4:24 am

    The ERH provoked one of the largest debates on Tallbloke:
    https://tallbloke.wordpress.com/2014/03/11/effective-emission-height/
    https://tallbloke.wordpress.com/2014/07/13/the-so-called-effective-height-of-emission-vs-the-actual-height-of-emission-which-is-more-informative/

    The ERH is no longer a useful idea given that Robinson & Catling’s equations provide more precision. I am using FEA (Finite Element Anaysis) to verify R&C’s analysis. If this is successful, it will be relatively simple to add a cloud layer for any planet with 100% cloud cover (e.g. Venus). The next step will be to model multiple cloud layers as on Earth, Jupiter and Saturn.

    With regard to the 54 K GHE, it does assume that an airless Earth would be covered with ice except for a few puddles of water on the equator. If the ice were to be covered with basalt regolith (unlikely) the GHE would be 79 Kelvin.
    https://tallbloke.wordpress.com/2014/08/27/extending-a-new-lunar-thermal-model-part-ii-modelling-an-airless-earth/

  28. Anything is possible November 25, 2014 at 6:20 am
    “It is possible for you or Tim to run another version of your lunar thermal model based your MOON1 output, but adjusting for the difference in axial tilt between the Earth and the Moon? If so, I would be very interested to see if it comes up with what I believe to be the “right” answer.”

    For myself, I am sure my analyis is wrong (Tim Channon may disagree with me). All I am saying is that my analysis is nearer the truth than the 255 K figure quoted by “Respectable Climate Scientists”.

    Tim was the first to state the effect of rotation rate on the average temperature of the Moon would be small. My analysis confirmed that. Now you ask about axial tilt which seems likely to be an even smaller effect but the effect can be reproduced using Finite Element Analysis. It seems likely that Tim’s methods will work just as well.

    Right now I am trying to get my Venus model ready for a meeting with Tyler Robinson in two weeks and things are not going well.

  29. tallbloke, November 25, 2014 at 9:37 am

    “GC: Nikolov and Zeller showed that the misapplication of Stefan Boltzmann to a ‘disc’ of double Earth diameter is wrong. They provided the correct method for the integration of incident sunlight on a sunlit hemisphere.
    https://tallbloke.wordpress.com/2012/01/17/nikolov-and-zeller-reply-to-comments-on-the-utc-part-1/ Which produces the 197K result. They have updated this with additional equations for factoring in the heat capacity of the regolith, the galactic background etc. (Private comms)”

    I agree that N&K showed that the 255 K average global temperature calculation for Earth was wrong. They claimed that the correct fihure was 154.3 K as here:

    Click to access unified_theory_of_climate_poster_nikolov_zeller.pdf

    The N&K analysis was wrong for the same reasons that Scott Denning’s calculations were wrong. N&K made unrealistic assumptions about the Moon’s surface properties. They predicted that an airless Earth would have a temperature of 154.3 K based on the unlikely theory that an airless Earth would have a surface similar to the Moon. Given the abundance of water on Earth, this makes no sense:

    N&K corrected themselves in that link you quoted so their revised average temperature for the Moon is 206 K at the equator which is quite close to the Diviner LRE observations (212 K) and my model (213 K).

  30. Konrad. says:

    gallopingcamel says:
    November 26, 2014 at 4:45 am
    //////////////////////////////////////////////////
    The “ice except for puddles at the equator” is a dangerous assumption. Where is the “snow line” in the solar system? 3 AU… .What happened to the ice exposed by the Phoenix lander on Mars even though temperatures only got above -20 C (vacuum sublimation temp for water) on one day?

    Ice, just like liquid water is a SW selective surface, not a near blackbody.

    As I have asked in the past, please try your FEA model on this –

    Constant 1000 w/m2 of LWIR and both target blocks reach the same near equilibrium temperature. Constant 1000 w/m2 of SW for the same time and block A runs 20C hotter. There is a world of difference between near blackbody and SW selective surface. And no, it doesn’t matter if SW absorptivity is close to IR emissivity, what causes the differential is depth of SW absorption. (although it does make things catastrophically worse for AGW when the true hemispherical effective (not apparent, measured within atmospheric Hohlrumn) emissivity is below 0.7 for water.)

    Our radiatively cooled atmosphere is conductively and evaporatively cooling our SW selective ocean surface. It truly is that simple.

  31. Hockey Schtick November 25, 2014 at 11:09 am:

    Like you I am impressed by the work of Robinson & Catling. Their calculations are in good agreement with observations on all seven bodies in the solar system that have significant atmospheres. Given the dismal performance of the IPCC’s climate models it is refreshing to find that the scientific method has not been entirely abandoned by all “Climate Scientists”.

    The link below involved a spirited exchange of emails with David Catling who was quite offended when I compared his work to the pressure based theories of Nikolov & Zeller:
    http://diggingintheclay.wordpress.com/2014/04/27/robinson-and-catling-model-closely-matches-data-for-titans-atmosphere/

  32. Konrad. November 26, 2014 at 5:35 am

    That problem you pose is well suited to Finite Element Analysis. Right now I am trying to solve another problem in order to be ready for a meeting with Tyler Robinson, namely temperature vs. altitude on Venus. Please be patient!

  33. Anything is possible says:

    gallopingcamel says:
    November 26, 2014 at 4:56 am

    “Tim was the first to state the effect of rotation rate on the average temperature of the Moon would be small. My analysis confirmed that. Now you ask about axial tilt which seems likely to be an even smaller effect but the effect can be reproduced using Finite Element Analysis. It seems likely that Tim’s methods will work just as well.

    Right now I am trying to get my Venus model ready for a meeting with Tyler Robinson in two weeks and things are not going well.”

    =================================================

    I’m not sure that the effect of axial tilt would actually be that small, because the increase in insolation at the lunar poles could well raise temperatures to a greater extent than the decrease in insolation would cause lower temperatures in the equatorial regions. So I think it would be worth confirming at some stage.

    Clearly not now, though. Your work for Tyler Robinson is far more important, and I wish you the best of British luck with it.

  34. Kristian, November 25, 2014 at 9:26 pm
    Thanks for an excellent plot of the temperature gradient in the Venusian atmosphere showing a lapse rate of -7.72 K/km.

    Back in 1967 Carl Sagan correctly predicted the surface temperature of Venus when he published a correction to earlier papers which ignored the effect of pressure on the Cp (specific heat at constant pressure) of CO2. Sagan estimated the lapse rate as -7.9 K/km which is remarkably close to the modern estimate

    Sagan did not know whether the Venusian atmosphere was primarily Nitrogen or CO2 but he opined that it would not make much difference given that the specific heats of these gases were similar:

    Click to access nph-iarticle_query

  35. Kristian says:

    Hockey Schtick says, November 25, 2014 at 11:28 pm:

    “Kristian: We are dealing with global averages, obviously not claiming the global average values I used apply to every specific location from the equator to poles, since Te/solar insolation, heat capacity, and pressures of each coordinate vary tremendously and constantly.”

    Yes, and the global average for Earth is NOT a 0.1 bar tropopause, but closer to a 0.2 tropopause. If R&C want to argue that only Earth’s tropical tropopause really matters, then fine, I haven’t heard any justification for that. But if you look at this plot:

    you will notice how the thermal tropopause height from 90-30/35 degrees of latitude is at about 8-12 km at the equinoxes, a mean of ~10 km (correlating with the midlatitude American Standard Atmosphere height). This is not a 0.1 bar pressure level.

    The only true and consistent tropospheric convective upthrust on Earth, though, occurs in the tropics (the Hadley-Walker Cell), where the tropopause is pushed by deep moist convection up to 0.15 bar and beyond.

    I do not reject R&C’s paper at all. I find it very interesting, and to some degree compelling. But it doesn’t explain the whole process. Tropopause pressure and convective uplift are both important.

    The whole ‘effective emission height’ (EEH) thing, however, is a different matter altogether. Here I agree completely with Konrad. It is a chimaera, a ridiculous mathematical construct that has no bearing on reality whatsoever. Any planetary flux to space is simply the one that balances the (absorbed) incoming flux from the Sun, and this final flux is the one that goes through the ToA to space, not the S-B one computed from some ‘centre of mass’ EEH temperature. This is pure rGHE/AGW nonsense.

  36. Konrad. says:

    gallopingcamel says:
    November 26, 2014 at 5:42 am
    //////////////////////////////////////////////////
    “That problem you pose is well suited to Finite Element Analysis.”

    Indeed, but I have others best suited for CFD –

    As to my patience? Well, I actually take the time to build and run before publishing build diagrams for others –


    – always remember, empirical experiments raise questions you didn’t know to ask…Maths is a dodge. Maths can model the physical, but it can also model the non-physical. Waiting for you to catch up…

    Remember how they calibrated the instruments for Diviner pre-launch? Imagine doing that for 71% of our planet’s surface? Might look something like this –

    *sniggers*

  37. tallbloke says:

    Kristian: You may have already considered this, but don’t forget the atmosphere bulges at the equator, so the pressure at 8-12km further away from the equator will be lower than it is at the equator.

  38. tallbloke says:

    GC:”Back in 1967 Carl Sagan correctly predicted the surface temperature of Venus when he published a correction to earlier papers which ignored the effect of pressure on the Cp (specific heat at constant pressure) of CO2.”

    I published it recently:
    https://tallbloke.wordpress.com/2014/06/28/venus-surface-temp-correctly-predicted-from-lapse-rate-in-1967-but-is-it-the-whole-story/

    But wasn’t Sagan already convinced that the surface temperature of Venus was due to a runaway greenhouse effect? He had earlier posited that steam in the atmosphere produced the high surface T in around 1960. Did he inflate the sensitivity in order to get the co2 atmospheric greenhouse effect to match the -g/Cp calculation?

    http://www.aip.org/history/climate/Venus.htm#N_13_

  39. Bryan says:

    Good article

    Comment has been made that the results above do not apply very well to Mars and Venus.

    This is only to be expected.

    The Barometric Equations and the Perfect Gas Laws are only true if the Specific Heat Capacity stays constant while the temperature changes.

    This is true for our atmosphere mainly N2 and O2.
    It is not true for Mars and Venus where CO2 forms a major part of the atmosphere.

    http://www.engineeringtoolbox.com/carbon-dioxide-d_974.html

  40. Roger Clague says:

    Kristian says:
    November 25, 2014 at 9:26 pm

    The 240 W/m^2 flux IN/OUT through the ToA is in turn used to calculate our planet’s BB emission temperature in space, which is 255K. If we did the same with Venus, its equivalent temperature (its radiative equilibrium temp with the Sun) would be 232K

    A bb has one surface and one temperature, such as a piece of metal, as used by Kirchhoff who invented the concept.
    The Earth emits from its whole volume which is at many different temperatures, e.g. poles, equator, day and night, and at different altitudes.
    Earth is not a black body radiator (bb) Sun is a bb radiator

    It is better to look at measured temp. Not calculated using a wrong equation (S-B ).
    The tropopause temp is the radiative equilibrium temp (RET) with the sun.
    The temps are higher lower down caused by gravitational enhancement.

    How does Earth at 220K emit the same as a bb at 255K?
    It is by extra emissions due gravitationally enhancement temps
    .
    Albedo is reflected light. It is part of total emission which causes the radiative equilibrium temp. It does not determine the total or affect radiative equilibrium temp. temp

    Earth tropopause temp 218K is near the ave temp of atmosphere lacking moon at 212K

  41. To the dismay of many I believe there is a GHG effect but it is the result of the climate not the cause.

  42. Skeptical Arguments that Don’t Hold Water April 25th, 2014

    http://www.drroyspencer.com/2014/04/skeptical-arguments-that-dont-hold-water/

    I am with him on all points other then point 7.

    I DON’T BUY THE COUNTER ARGUMENT THAT THERE IS NO GREENHOUSE EFFECT.

    That said the GHG effect is in response to climate not the cause and there is no man made global warming due to increases in CO2.

    [Reply] Salvatore: please provide links rather than huge cut/pastes. Thanks – TB.

  43. tallbloke says:

    Thanks Salvatore, I followed the link in Roy’s post back to his critique of Ned Nikolov and Karl Zeller’s theory and laughed my way through the mishmash of confused concepts. This bit at the end was great though. Roy obviously believes in the Loschmidt effect, so there we have it, he accepts a gravito-thermal effect.

    “When an air parcel is raised adiabatically, it’s loss of thermal energy is balanced by an equal gain in potential energy due to its altitude. The ‘dry static energy’ of the parcel thus remains the same, which equals cpT + gZ, where cp is the specific heat capacity, T is temperature in Kelvin, g is the gravitational acceleration, and Z is height in meters.”

  44. tallbloke, November 26, 2014 at 9:25 am
    ” But wasn’t Sagan already convinced that the surface temperature of Venus was due to a runaway greenhouse effect? He had earlier posited that steam in the atmosphere produced the high surface T in around 1960. Did he inflate the sensitivity in order to get the co2 atmospheric greenhouse effect to match the -g/Cp calculation?”

    My impression is that Sagan was a little embarrassed becuase his crude calculations in 1967 produced values for the surface temperature of Venus that were close to the 735 K observed by Russian probes.

    The 1967 correction you published shows a lower value of lapse rate and therefore a lower surface temperature than in Sagan’s earlier papers. I had assumed this was because he realized that the Cp of CO2 falls when the pressure exceeds one bar. It seems to me that he deflated the lapse rate to get closer to the right answer.

  45. tallbloke says:

    GC: Thanks. Can you link any of Sagan’s earlier papers or summaries of them?

  46. Roger Clague says:

    HS says:
    November 25, 2014 at 5:56 pm
    Roger: The “effective temperature” or “equilibrium temperature” with the Sun is “well accepted” to be 255K, not 220K, so please show your work
    Earth tropopause temp = 220K is an observation not a calculation The radiative equilibrium temp. Lower than the 255 bb temp. because of emission from the atmos and surface.
    “a linear function of the atmosphere in a gravity field” sound better?
    And
    Or “a linear function of atmospheric heat capacity in a gravity field”
    Heat capacity = mass x specific heat
    LR is not a function of atmospheric mass LR is a function of the gravity field
    g varies x 0.003 up to tropopause. g at 16km is 0.997 x g at sea-level

  47. Roger Clague says:

    Kristian says:
    November 25, 2014 at 9:05 pm

    6.5 K/km * 12 km = 78K
    288 – 78 = 210K, the global mean tropopause temperature

    That is Trop temp + ( LR x ave. Trop. height ) = surface temp
    210K + 6.5K/km x 12km = 210K + 78K = 288K
    Radiative equilibrium temp + GHE = surface temp

  48. Kristian says:

    Roger Clague says, November 27, 2014 at 12:30 pm:

    “Earth tropopause temp = 220K is an observation not a calculation”

    No, it’s a flawed estimation. The real global mean tropopause temp is ~210K. The 220K value is for midlatitude tropopause (American Standard Atmosphere), NOT for the global average.

    “LR is not a function of atmospheric mass LR is a function of the gravity field”

    Mass is of course also important. No mass, gravity pulls at nothing. And no energy is ever absorbed; no heat capacity.

  49. Kristian says:

    tallbloke says, November 26, 2014 at 7:54 pm:

    ““When an air parcel is raised adiabatically, it’s loss of thermal energy is balanced by an equal gain in potential energy due to its altitude. The ‘dry static energy’ of the parcel thus remains the same, which equals cpT + gZ, where cp is the specific heat capacity, T is temperature in Kelvin, g is the gravitational acceleration, and Z is height in meters.””

    This is mixing two separate processes and pretending they’re one and the same. Lifting air is NOT an adiabatic process. It’s a Newtonian (mechanical) process. In such a process, mechanical kinetic energy is progressively replaced by potential energy as the air moves higher. This change, however, does not in the least affect the TEMPERATURE of the air. You don’t cool something by simply lifting it up.

    Lifting air does not cool because it’s lifted. It cools because it EXPANDS as it lifts, the external pressure weakening as it gets higher. The EXPANSION is why the air cools. THIS is the adiabatic process, a distinct THERMODYNAMIC process. Air undergoing expansion LOSES energy to its surroundings by doing WORK on it (expanding into it, forcing it to the sides). That’s how it cools. When the air subsides again, it contracts, or, rather, it is compressed by the higher external pressure. The surroundings thus in turn do work on IT. The air GAINS energy and warms. This is how adiabatic cooling and heating come about.

  50. @Talbloke,
    My links to those Sagan papers don’t work any more. Fortunately I had saved some of the papers in my “Sagan” folder so I tried to send them to you as email attachments.

    When that did not work I sent them to Tim Channon.

  51. Christopher says:

    Kristian says:
    November 27, 2014 at 3:18 pm

    “Lifting air does not cool because it’s lifted. It cools because it EXPANDS as it lifts, the external pressure weakening as it gets higher. The EXPANSION is why the air cools. THIS is the adiabatic process, a distinct THERMODYNAMIC process. Air undergoing expansion LOSES energy to its surroundings by doing WORK on it (expanding into it, forcing it to the sides). That’s how it cools. When the air subsides again, it contracts, or, rather, it is compressed by the higher external pressure. The surroundings thus in turn do work on IT. The air GAINS energy and warms. This is how adiabatic cooling and heating come about.”

    I thought this was obvious, but it seems not to be. Therefore it may be worth while adding some more explanation. 🙂

    The reason why the temperature changes as described by Kristian is the change in density of the air. Each individual molecule may well keep its kinetic energy when the density changes. However, since the number of molecules in a unit volume changes, the average distance between each molecule changes and consequently the temperature will also change. This since the temperature is given by the average kinetic energy of the molecules in a unit volume of air.

  52. oldbrew says:

    Christopher says: ‘The reason why the temperature changes as described by Kristian is the change in density of the air’

    Hence the altitude graphs of pressure and density are identical.

    http://www.digitaldutch.com/atmoscalc/graphs.htm

  53. wayne says:

    Kristian, expansion itself does not imply cooling. If exapanded against a vacuum, temperature does not change. See free expansion.

    Christopher, a mere change of density with an expanded volume even with the same mean v does not imply cooling. See free expansion.

    Here we go again! (but I must now go for some turkey!)

  54. Kristian says:

    tallbloke says, November 26, 2014 at 9:21 am:

    “Kristian: You may have already considered this, but don’t forget the atmosphere bulges at the equator, so the pressure at 8-12km further away from the equator will be lower than it is at the equator.”

    It bulges, yes, but I can’t see this as being particularly significant. It’s not like the 0.1 bar level is at 16 km in the equatorial region and at 10 km in the temperate regions. Also, those ‘pressure/altitude’-diagrams are mostly based on the Standard Atmosphere, which is a midlatitude one, humidity and temperature for the most part ignored:

    As you can see: 10 km equals 270 mbar, while the 100 mbar level correlates with an altitude of ~16.5 km.

    The global mean tropopause altitude is ~12 km. That’s pretty close to 200 mbar.

    There’s no question a 0.1 bar tropopause ONLY exists in the tropics. However, that doesn’t mean R&C are wrong; they just most likely haven’t accounted properly for the momentum of convective uplift. The 0.1 bar level might simply be an upper tropopause limit of some sort (but don’t take my word for it) and this – on Earth – can only be reached in the tropics, where surface heating and evaporation rates are high enough. The upward extent of the troposphere simply isn’t able to reach its full potential outside the tropical Hadley cells, because there the convective processes aren’t strong enough. Just an idea …

  55. Christopher says:

    wayne says:
    November 27, 2014 at 6:48 pm

    “Kristian, expansion itself does not imply cooling. If exapanded against a vacuum, temperature does not change. See free expansion.

    Christopher, a mere change of density with an expanded volume even with the same mean v does not imply cooling. See free expansion.”

    This applies to an ideal gas. A real gas, such as air, will experience cooling even for free expansion against vacuum.

  56. wayne says:

    I’m back, a good Thanksgiving here!

    Christopher, on the extreme margins that is true (Joules-Thomson) but calculate our air’s difference from an ideal gas, it is insignificant especially at the low pressures and the slow speed of any changes that you find occurring in an atmosphere.

    I thought you agreed on that other thread that it is the work against the surroundings that causes the cooling and that portion is adiabatic and reversible. Rising packet cools expending work against the much larger surroundings, the surroundings warm slightly receiving the identical amount work from the expanding smaller packet but the volumes of the two are hugely different. Same thing but in reverse if the packet is denser and is subsiding. Gravity is a conserving force and perfectly reversible and so is that adiabatic portion.

    But none of that above has to do with the original energy that warmed the air that expanded and lowered the density causing the convective buoyancy in the first place. That is separate.

    I must have severely misread you during that last thread.

  57. New post mathematically derives the height of the ERL to be at the center of mass of the atmosphere:

    http://hockeyschtick.blogspot.com/2014/11/derivation-of-effective-radiating.html

    Please let me know what you think Tallbloke and denziens

    (I know about the controversies of “ERL”, global temperature/pressure/mass averages, etc. but it is necessary to use these concepts as a framework for a mathematical derivation, so no need to tell me why there’s no ERL etc.)

    Thanks all for taking a look and helpful suggestions.

  58. Hockey Schtick says: November 28, 2014 at 2:56 am

    “New post mathematically derives the height of the ERL to be at the center of mass of the atmosphere:
    http://hockeyschtick.blogspot.com/2014/11/derivation-of-effective-radiating.html
    Please let me know what you think Tallbloke and denziens”
    “(I know about the controversies of “ERL”, global temperature/pressure/mass averages, etc. but it is necessary to use these concepts as a framework for a mathematical derivation, so no need to tell me why there’s no ERL etc.)”

    Why do you need a mathematical derivation of a fantasy? Every WV molecule radiates energy to space at every altitude! ERL is but another fantasy to justify the fantasy of 255 Kelvin! In no two directions does this planet have a the same temperature. It is the diversity, not mean, that makes this planet work.

  59. Trick says:

    Ref. HS site step 3:

    dP = -(MPg/RT)dh

    ∫dP/P = -(Mg/RT) ∫dh (the first integral is from 1 to P, second from 0 to h)

    HS 2:56am – Two things at least:

    1) In step 3 by taking T outside the dh integral, you assume T is constant over dh. Hence you are assuming an isothermal atmosphere on earth. So you really have computed surface T=255K for a non-GHG transparent atm. in step 3. NOT surface 288K. And yes, 255K is from planetary albedo and insolation not GHG. The non-transparent optical depth of the real GHG atm. causes the surface measured Tmedian increase to 288K. To find the ERL (sometimes referred as Chapman layer), just look in a good relevant textbook. Most of the outgoing radiation comes from a level 1 optical thickness unit below the TOA.

    In step 4, you turn this isothermal atm. assumption into non-isothermal atm. somehow.

    2) Computing the mass of m^2 of atm. column, you use the entire atm. to get 10.5*10^ 3kg yet the troposphere where -g/Cp ~holds is ~7.63*10^3 kg.

    You never really define center of gravity of the atm. either. If earth atm. is heated: its internal energy increases AND its center of gravity (Zavg.) rises. Zavg. = PE/Ma*g where the total mass of the atm. Ma (per unit area) is fixed (at least over time scales of tens of thousands of years). This increase in Zavg. has been observed during the day.

    [Zavg. = (integral 0 to infinity rho*g*z dz)/(integral 0 to infinity rho*g dz)]

  60. Christopher says:

    wayne says:
    November 28, 2014 at 1:18 am

    “I must have severely misread you during that last thread.”

    Or maybe I have missed an important point somewhere. I think I have to revisit the basic stuff in detail here. There is a couple of things that at the moment not fit together for me … 🙂

  61. Christopher says:

    Christopher says:
    November 27, 2014 at 4:33 pm
    “The reason why the temperature changes as described by Kristian is the change in density of the air. Each individual molecule may well keep its kinetic energy when the density changes. However, since the number of molecules in a unit volume changes, the average distance between each molecule changes and consequently the temperature will also change. This since the temperature is given by the average kinetic energy of the molecules in a unit volume of air.”

    Thanks to wayne (wayne says: November 28, 2014 at 1:18 am). I did a brush-up of the basics of temperature and kinetic gas theory as given by Richard Feynman (http://www.feynmanlectures.caltech.edu/I_39.html)

    It is NOT correct that the temperature changes because the average distance between the molecules changes as I said above. Temperature is DEFINED by the average kinetic energy of the molecules, not the average kinetic energy of the molecules per unit volume as I mistakenly postulated.

    Now things fit better together … 🙂

  62. wayne says:

    Thank you very much Christopher. As a good scientist you self-corrected, nice. Didn’t think you meant that. That little correction will help to keep some pretty far-fetched ideas that constantly spawn here from getting wings… yet again.

    I have nothing against meteorology but for some reason those here that have a meteorological base, and there are many, for some reason, that most seem to view this very topic with a sense that doesn’t align with what actually happens when dealing with the vertical movement of energy within an atmosphere; there gravity is involved. Horizontally, density differences do *not* impart some immediate force (buoyancy) from gravity and since meteorologists mainly deal with horizontal effects in a 2d plane near the surface maybe that is where this misunderstanding always pops up. Horizontally it is pressure that is the fore-front force and in meteorological texts it mainly speaks everywhere of pressure, high pressure, low pressure and that is correct horizontally. Maybe that is why you rarely hear the term ‘density‘ used but by never considering this term very important term of density vertically, they get things wrong conceptually.

    Wish everyone here could get on the same page on such simple topics so we could then move into deeper matters that have to do the incorrect AGW radiative-only concept of atmospheres and energy flows.

  63. Hi all,

    Please let me know what you think about my new post ‘the greenhouse equation’

    http://hockeyschtick.blogspot.com/2014/11/the-greenhouse-equation.html

    The “Greenhouse Equation” calculates temperature (T) at any location from the surface to the top of the troposphere as a function of atmospheric mass/gravity/pressure and radiative forcing from the Sun only, and without any radiative forcing from greenhouse gases. Note the pressure (P) divided by 2 in the greenhouse equation is the pressure at the center of mass of the atmosphere (after density correction), where the temperature and height are equal to the equilibrium temperature with the Sun and ERL respectively.

    Calculation of T at surface where s=0:

  64. wayne says:

    ” Please let me know what you think about my new post ‘the greenhouse equation’ “

    When I see log(e) as a one parameter and an exponent that solves to zero because T is zero I have to stop and first ask; This is some sort of mathematical parody on climate ‘science’, right? Please tell me that is so.

  65. Trick says:

    HS site ref.: “..temperature does not appear on the right side of the equation..”

    HS 2:49am: Temperature appears on right side of the eqn. solution.

    Also the assumption of isothermal atm. is embedded in HS theory but the eqn. for T varies with s: non-isothermal. Needs some work.

    Also HS might want to rethink this line after using g=9.8 in the solution:

    g = the Newtonian gravitational constant = 6.673×10−11 N·(m/kg)2

  66. Hockey Schtick says: November 29, 2014 at 2:49 am Hi all,

    “Please let me know what you think about my new post ‘the greenhouse equation’”

    You are almost as funny as Doug Cotton, or Joel Shore!

  67. Konrad. says:

    Hockey Schtick says:
    November 29, 2014 at 2:49 am
    ///////////////////////////////////////////////
    HS,
    I’m sorry but I’m with Will on this one. Radiative gases, particularly WV, play a critical role in governing atmospheric temperature.

    The correct approach* to modelling atmospheric temperatures is CFD (computational fluid dynamics). There are no solutions with direct linear equations for a moving gas atmosphere. Currently not even the best GCMs have the power to run CFD in the vertical dimension. This is of course the most critical dimension as we need to determine energy flow from below the surface of our SW translucent oceans to space.

    Let’s just quickly review the first critical mistake, averaging solar insolation. The temperature of the bulk of a SW transparent non-radiative atmosphere would be driven by surface Tmax not Tav. Remember – there are no planets or moons in our solar system that have managed to retain an atmosphere without radiative gases.

    Sorry HS, what you are attempting here is little better than the climastrologists. You can’t do it this way, as Sir George Simpson pointed out back in 1938. Wrong way, go back. No radiative gases = atmospheric super heating = everyone’s breathing privileges revoked.

    *(the cheap and dirty approach – work out the average surface temp in absence of atmospheric cooling and DWLWIR (Yes Will, I know. DWLWIR = two stream garbage…). Given we know current average surface temps (288K) and can see that 312K is a fair figure for “surface without atmosphere” for our ocean planet (think extreme SW selective surface), then the net effect of our radiatively cooled atmosphere on surface temps is clear. It’s cooling. It’s cooling for all concentrations of radiative gases above 0.0ppm.)

  68. Trick says “Temperature appears on right side of the eqn. solution”

    The simultaneous solution for T on both sides of the equation by Wolfram Alpha provides the solution I posted with no T on the right-hand side, and a unique value for that solution for T at every value of s that perfectly matches observations, thus it’s not a tautology and T is clearly a function of mass/gravity/pressure, not the other way around.

    If you’re so sure about a tautology, show me where it is.

    “Also the assumption of isothermal atm. is embedded in HS theory but the eqn. for T varies with s: non-isothermal. Needs some work.”

    No such assumption of an isothermal atmosphere is ever made, in fact, the entire purpose of the theory and equation is to prove the gravitational temperature gradient would exist even with 100% non-greenhouse gases.

    Thanks for pointing out the gravitational acceleration constant, which I’ve corrected, and which doesn’t change the numerical solutions I posted since I did use 9.8m/s^2 for all of those.

    Will says “You are almost as funny as Doug Cotton, or Joel Shore!”
    Konrad says HS, I’m sorry but I’m with Will on this one. Radiative gases, particularly WV, play a critical role in governing atmospheric temperature.

    Jeez, if this is the denzien’s idea of constructive feedback, I’m outta here. I didn’t ask anyone to post my material and I don’t spam threads like Doug Cotton, but since it was posted here by Tallbloke, do I not have the courtesy of reply without facing hostility/ad homs?

    As the greenhouse eqn shows, WV increases Cp, which is inversely related to T, thus WV is a strong negative-feedback cooling agent that decreases the LR by half to cause cooling.

    It’s a pretty amazing coincidence is it not if the use of global averages for multiple constants and variables in that big equation essentially perfectly reproduces temperatures from the surface to troposphere?

  69. Wayne says:”When I see log(e) as a one parameter and an exponent that solves to zero because T is zero I have to stop and first ask; This is some sort of mathematical parody on climate ‘science’, right? Please tell me that is so.”

    log(e) = 0.4342944819… i.e. not zero
    T is never zero, why would you possibly believe that?

    yes that big equation that just so happens to reproduce the temperature everywhere in the troposphere is just one amazing coincidence and parody that Wolfram Alpha and I have managed to pull off.

  70. meant to say “…reproduces temperatures from the surface to tropopause?”

  71. Oh and BTW, my “parody” equation also explains the troposphere temperatures from the surface to ERL to tropopause on Titan too, the only other Earth atmosphere analog in the solar system.

    I thought it would be tough enough coming up with this “parody” equation to try an infinite number of combinations and permutations of variables and constants to make it match the entire earth troposphere, and a whole ‘nother planet as well, but turns out it only took a few minutes to find the perfect combination of variables and constants for both planets. Such luck!

  72. wayne says:

    Hockey Schtick, I haven’t seen ‘log’ being used as the Briggsian logarithm in a long time. Also each course I have taken recently always uses ‘log’ as the natural log. You should clarify and use log10(e) since evidentaly was what you intentioned. But the log10 of the natural log base ?? You sure threw me there, so why was that included, physically what is it? And excuse me, that was ‘s’ and not ‘T’ you set to zero that zeroed out that entire exponent on the right of your solution and there still is a ‘T’ unexplained in that exponent also so how did that math package even solve the equation? Sorry, still looks suspicious to me.

    To get anyone to take their precious time to look seriously at this you should first explain why each term exists, what they are to you and what they may physically represent.

  73. @Hockey Schtick,
    “Climate Science” needs equations and numerical analysis to replace the ridiculous Arrhenius theory that claims a logarithmic relationship between surface temperature and the concentration of CO2 in the atmosphere. Therefore I applaud your efforts and your appreciation of Robinson & Catling.

    It will take me more time than I can spare right now to undertake a critical review of your equations, so here is a comment on one of your assumptions:
    “ε = emissivity = 1 assuming Sun and Earth are blackbodies”

    In my analysis of the Moon, emissivity was of critical importance. The value had to be ~0.95 to ensure a good match between the model and observations:
    https://tallbloke.wordpress.com/2014/04/18/a-new-lunar-thermal-model-based-on-finite-element-analysis-of-regolith-physical-properties/

    Currently I am modeling Venus which has 100% cloud cover. The surface emissivity is irrelevant. What matters is the emissivity of the cloud tops.

  74. phi says:

    Hockey Schtick (November 29, 2014 at 7:05 am),

    “…the entire purpose of the theory and equation is to prove the gravitational temperature gradient would exist even with 100% non-greenhouse gases.”

    Let’s say you’re right. We can imagine the following experiment : a closed cylinder fully insulated, height 300 m, filled with dry air.
    A control system allows you to set the pressure at the base and the temperature profile.
    Forced values: p base 1000 hPa, isothermal 20 °C.
    Regulation is cut.
    Now what ? How ? Why ?

  75. tchannon says:

    HS, apologies, I didn’t see your comments before putting up a new article, kind of a crossover.

    Commenting on Google sites is tricky, why I rarely comment on your site. Try to link up and snoop, hits blocking, impasse.

    Willis grief, I think the 1983 Essex papers are critical, the earth is not and may not be reduced to a static system as is done with disc world.
    Maybe choosing a mean of some kind as you seem to have done approximates around this.

    There again what do I know.

  76. Konrad. says:

    phi says:
    November 29, 2014 at 11:02 am
    ///////////////////////////////////////////////////
    Gas columns?

    That one is easy….
    No cooling at altitude –
    https://tallbloke.wordpress.com/2014/10/20/stefan-rahmsdorf-goes-all-naomi-oreskes-publishes-futureshock-fantasy/comment-page-1/#comment-91313
    – and “Trick” gets their posterior handed to them on a platter 😉

  77. phi says:

    Konrad,
    This fable of the gravitational temperature gradient comes from neophlogistics. It pleases to many people. Too bad, since without it the IPCC is naked.

  78. Kristian says:

    phi says, November 29, 2014 at 11:59 am:

    “This fable of the gravitational temperature gradient comes from neophlogistics. It pleases to many people. Too bad, since without it the IPCC is naked.”

    Strange, because no one claims the troposperic temperature profile is set by gravity. The ADIABATIC LAPSE RATE is set by gravity (and air ‘heat capacity’). Everyone agrees the temperature profile, the ENVIRONMENTAL LAPSE RATE, is set by a radiative-convective equilibrium, where radiation always tries to steepen the gradient and convection always brings it back down.

  79. phi says:

    Kristian,

    “no one claims the troposperic temperature profile is set by gravity”

    It is not exactly the profile but the gradient.

    Many players here think the gradient is fixed only by gravity. Neophlogistics, by introducing the notion of forcing and assuming that only convection sets the gradient, make the same mistake.

    “The ADIABATIC LAPSE RATE is set by gravity (and air ‘heat capacity’).”
    Yes.

    “Everyone agrees the temperature profile, the ENVIRONMENTAL LAPSE RATE, is set by a radiative-convective equilibrium, where radiation always tries to steepen the gradient and convection always brings it back down.”

    Again, this is not the official position which admits that only convection determines the gradient, GHGs acting only through the translation of the temperature profile.

  80. Kristian says:

    phi says, November 29, 2014 at 1:25 pm:

    “Again, this is not the official position which admits that only convection determines the gradient, GHGs acting only through the translation of the temperature profile.”

    Yes, that MIGHT be true. That would, however, only be the case because they do not want to admit that radiative cooling of air masses aloft contributes significantly to keep the overall circulation running in a stable fashion and keeping the mean temperatures steady. Seems to me they only care to include solar heating (of surface and air masses) as the radiative player in their r/c equilibrium, and that, like you say, the so-called ‘GHGs’ are only there to determine the ‘intercept’ (‘the translation of the temperature profile’). This is a pretty devious approach …

  81. Trick says:

    HS 7:05am: “If you’re so sure about a tautology, show me where it is.”

    HS used the word tautology, not me. Inspection of the solution shows T on right side 2:49am (see that little T under the 9.8) where HS incorrectly claimed “..temperature does not appear on the right side of the equation..”.

    “No such assumption of an isothermal atmosphere is ever made.”

    Yes, the isothermal assumption is in HS math. HS still uses it to substitute for P in the equation 2:49am.

    As I noted 4:51am HS site shows on 11/27 top post eqn. (12) and (13):

    dP = -(MPg/RT)dh
    ∫dP/P = -(Mg/RT) ∫dh (the first integral is from 1 to P, second from 0 to h)

    Note T(h) therein assumed constant with height (isothermal) in going outside the integral. Then note the substitution for P at 2:49am. To do this substitute for P, HS invokes the isothermal assumption.

    “Thanks for pointing out the gravitational acceleration constant, which I’ve corrected..”

    Without change noted on HS site and/or attribution.

  82. Trick says:

    HS 7:05am: “…the solution I posted with no T on the right-hand side, and a unique value for that solution for T at every value of s that perfectly matches observations”

    There is T on the RHS in the HS solution after 2:49am “solve” (meaning T is actually shown function of mass, gravity, pressure AND T) but that exponent is 0 for s=0 allowing a solution. Please show a solution “perfectly matching the observations” above s=0.

  83. phi says:

    Kristian,

    “This is a pretty devious approach …”

    Indeed.

    What allows the assimilation of CO2 to a forcing : the translation of the profile is the thermal effect produced by simply increasing the heating power. This increase is supposed to be caused by backradiations to which one gives generously a reserved property of phlogistons (heat source per se). Hence neophlogitics.

  84. “Please show a solution “perfectly matching the observations” above s=0.”

    I have plotted the output from Wolfram Alpha for s= 0,1,2,3,4,5,6,7,8,9,10,11 km and it matches the standard atmosphere database within 0.28C at each of these heights. The code is in the post if you wish to use it

    http://hockeyschtick.blogspot.com/2014/11/the-greenhouse-equation-predicts.html

  85. wayne says:

    Hockey Schtick, I hate to always stand as one of the tenth men but once again, I do not understand. You have replaced ‘s’ with the height in kilometers in one place but have left the very ‘s’ that I was complaining about as zero earlier and that still makes that entire exponent to remain zero. ‘e’ to the zero power is one. Why do you not just remove that entire exponent term and leave it as the log base 10 of 1/2 ?? Does that destroy the way Wolfram Alpha solves that equation ?? I don’t believe it would, or it should not.

    What I am saying is why leave this relation so complex when it doesn’t even need to be so? Just set your core SOLAR_IRR = root(S*(1-a)/(4*eps*sig), 4) and then place SOLAR_IRR in a second equation in two places. Let your 6.5 K/km be 0.0065 K/m and toss the divide by 1000. That is, stay in base SI units. Change the log10(1/2*e^(m*g*s/(R*T))) with log10(1/2) since ‘s’ is always zero. And why the log10(e) is there as some physical entity I will never know. Is that just another way to say some scalar of ≈0.4343 and leave it as that? That is unless you *know* why it has physical meaning. I see even more simplifications but that is enough for now.

    This is why I was wondering if this was some sort of parody, or joke when first viewed. Maybe you shouldn’t just let Wolfram Alpha do your thinking in simple algebra for you.

  86. Wayne, thanks and I appreciate the constructive reply.

    I symbolic solution just uses log(P/2), and since I’m using unit atmospheres, Patm = 1 at the surface so the equation becomes log(1/2). In the numeric solution at one point substituted in the derivation of P as a function of h in the numeric solution, but that was unnecessary and complicates the equation.

    So I’ve returned the numeric soln to the same as the original symbolic solution with log(1/2) in that part of the equation and obtain e.g. thus just have to change s in one place and no T on right side of eqn.

    I cannot just change 6.5 to 0.0065K/m as you suggest since eqn is 6.5(s – x/1000) so I’m leaving the 1000 in so people can easily recognize the lapse rate and change it if they wish.

    I know I have the solar forcing in there twice, but don’t see an easy way to disentangle it as you suggested, but if you have a suggestion on how to simplify the equation, here it is:

    T = [1367 (1 – 0.3) / (4*1* (5.6704*10^-8))]^1/4 +((-6.5)*(0-[-[8.31*{[1367 (1 – 0.3) / (4*1* (5.6704*10^-8))]^(1/4)}*log(1/2)]/[9.8*0.029*log(e)]/1000]))

    the reason for the logarithms is the logarithmic change in pressure and density with h

    thanks for the constructive criticism

  87. Roger Clague says:

    phi says:
    November 29, 2014 at 1:25 pm
    Kristian,
    “no one claims the troposperic temperature profile is set by gravity”
    It is not exactly the profile but the gradient.

    I’m with phi.
    I also claim the troposperic temperature profile, lapse rate LR is set by gravity.

    LR = gravity/specific heat.
    The gravity field of Earth causes the lapse rate. That is what the equation is saying to me.
    Gravity at 16km is 0.997 times gravity at the surface.
    0.003g acting for 16km causes 30m/s2 velocity increase.
    V^2 = 2gs
    = 2 x 0.003 x 10 x 16 000
    = 960
    V = 30m/s2
    Thermal enhancement directly caused by gravity variation, not by air pressure

  88. Trick says:

    HS 3:22am: Thanks. Where would you think the “within 0.28C” error comes from? My guess is rounding. Exact US Standard Atmosphere T(s) w/0.0C error up to tropopause is from:

    T(s) = To – 6.5 * s meters/1000

  89. Peter Mander says:

    Will these results be presented at COP20, do you know?

  90. tallbloke says:

    Clive Best has joined in the gravity/pressure fun
    http://clivebest.com/blog/?p=6305

  91. Trick says:

    tallbloke 9:07pm: Thanks. Three things I note:

    1) Clive Fig. 1 doesn’t show or discuss squiggly red arrow emitted rays from light blue CO2 mass toward the gray&dotted green slash body.

    2) Clive writes HS “derives a formula for planetary temperature”. Not true, HS matches to “within 0.28C” the US Standard Atm. designed & set up by a committee using the same available information. I guess the difference is rounding but could be due different To, insolation et. al. assumptions. I see center of mass of atm. discussed & assumed but not calculations.

    3) Clive writes “A pure argon atmosphere would have no greenhouse effect and no real lapse rate.”

    Robinson&Catling 2013 Letter formulae & observations show this is not the case. The Ar atm. optical depth would be thick if at Venus surface pressure. If at Mars surface p, then thin but existent similar R&C call on Mars. The DALR would be -g/Cp: Cp of Ar .52 vs. air 1.01 (kJ/kg-K), gas constant air .287, Ar .208, Poisson eqn. kappa air=1.4, Ar = 1.667, so forth.

  92. Trick says: “Thanks. Where would you think the “within 0.28C” error comes from?”

    I tried calculating a more accurate value of the molar mass instead of using the 0.029 kg/mol that I found on the internet, came up with 0.02925 instead of 0.029 so substituted that into the equation

    T = [1367 (1 – 0.3) / (4*1* (5.6704*10^-8))]^1/4 +((-6.5)*(0-[-[8.31*{[1367 (1 – 0.3) / (4*1* (5.6704*10^-8))]^(1/4)}*log(1/2)]/[9.8*0.029258*log(e)]/1000]))

    and now get Ts = 288.137K vs. Std Atm 288.15K, a difference of only 0.02K between the equation and std atmosphere

  93. Trick says:

    HS 10:56pm – Ok, thanks, nice work. It is interesting to learn of the means US Standard Atm. comes about, the specialist papers are so out of date.

  94. tchannon says:

    The mol mass of air is given 28.97
    http://www.engineeringtoolbox.com/molecular-mass-air-d_679.html

    Reason I looked it up is AFAICR standard omits water.

  95. oldbrew says:

    ‘Here we will discuss articles on the “Hockey Schtick” climate change blog which are similar also to articles on Tallbloke’s Talkshop. Each blog site recognises that gravity plays a part, but they misunderstand the convective heat transfer process.’

    http://www.whyitsnotco2.com/HS.html