A simple logical argument about global warming

Posted: September 21, 2012 by Rog Tallbloke in climate, Clouds

Skeptic commenter Jimbo provides a neat summary of the AGW argument:

Co2 is a greenhouse gas.

The world has warmed.

Man’s co2 has had a part in that warming.

But hang on a minute Jimbo:

The ocean heat content rose
The surface air temperature rose (UHI caveat on amount)
The troposphere temp rose

and

Outgoing longwave radiation increased.

CO2 and water vapour can’t create energy.

Therefore extra energy entered the system from outside via diminished cloud cover.

Therefore any extra heat from additional ‘greenhouse gases’ ‘trapping’ energy’ can only be a secondary factor, otherwise Outgoing longwave radiation would have decreased.

Therefore the majority of the warming has been caused by other, natural factors.

QED

Discuss.

;-)

Comments
  1. Stephen Wilde says:

    i) CO2 is supposed to cool the stratosphere whilst the troposphere warms because it reduces energy loss upwards.

    However the stratosphere stopped cooling around 2000 whilst CO2 amounts continued to rise.

    ii) CO2 was supposed to be the cause of widening equatorial air masses pushing the jetsreams poleward and forcing them into more zonal west to east tracks.

    However since 2000 the jets have been meandering about meridionally much more than previously whilst CO2 amounts continued to rise.

    iii) Co2 is supposed to amplify warming at both poles but in fact the two poles vary in antiphase leaving global sea ice pretty stable.

    Lots more inconsistencies exist. It isn’t much if anything to do with CO2.

  2. Green Sand says:

    How do we know how many square metres there are at the top of atmosphere? How do we account for expansion/contraction? How much is expansion/contraction affected by the amount of energy within “the system”?

    Genuine, albeit naive, questions, not criticism

  3. tallbloke says:

    Stephen, yes. Regarding i) maybe the increased cloud from 2000 has stabilised the stratospheric temp. Proximity of more cloud tops?

  4. tallbloke says:

    GS: No problem. All things have to be considered. Still, OLR is OLR.
    GHG’s might reposition energy, but they don’t create it. Cloud is more powerful otherwise extra co2 would have made OLR diminish, whatever contraction/expansion took place.

  5. Green Sand says:

    Thanks TB, I agree OLR is OLR.. So should not the metric be total OLR leaving the system not OLR per sq m? Not questioning the premise of cloud/CO2 just the metric of how we understand/measure the amount of energy leaving/enetering the system?

  6. Trick says:

    TB asserts: “…the majority of the warming has been caused by other, natural factors. QED.”

    At least some simple logical eqn.s, please. Otherwise I get lost. Quickly.

    Restating & enhancing Jimbo:

    CO2 is an infrared active gas.
    Human activities have added CO2 to atm.
    Earth’s atm. emissivity (e) is increased.
    Earth’s surface has warmed.

    ——————————————

    Sure albedo is variable; net solar forcing is variable. Small but apparently measurable variations. Some “simple logical argument about GW” eqn.s so I don’t get lost, numbers ~ NASA:

    Compute net solar irradiance S from total solar radiant energy So: S = So*(1-albedo)/4

    Earth avg. orbit radius has 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 = 0.0 for no infrared-active atm. gases (i.e. no-GHG), compute Teq for Earth = 255K
    set e = 0.8 for actual infrared-active gases ppm in Earth atm. to get Teq = 288K

    Earth surface Teq warms/cools according to this very simplified model and basic theory & assumptions; e surely is up (Mauna Loa), albedo anomaly looks down since 1985 but mostly positive.

    Now exactly where do you get the “majority” of the warming is natural from these or similar radiative balance eqn.s? I don’t think you can; I submit your QED’d assertion is just speculation.

    Discuss.

  7. Entropic man says:

    Your graph of outgoing radiation has a short term variability, and likely 95% confidence limits, of about +/- 4W/M2. With all three moving averages showing much smaller changes I fail to see how you can claim with any statistical significance what trend the the outgoing radiation is showing.

  8. tallbloke says:

    The Units are just a convention that the observations are converted to at a notional point called the TOA (top of atmosphere).

    Don’t ask me precisely how the electric signals the satellite sensor receives are processed though, it’s late, and I don’t know all the details.:)

  9. tallbloke says:

    Trick, My argument pivots around the sign of the OLR variation, it’s about logic, not the specific numbers. I could make my logic symbolic, but why bother when it would reduce the number of people following the argument by 90% ?

    Additional co2 is supposed to make the atmosphere more opaque, thus increasing the ‘effective altitude of radiation’ to a colder place, which then forces the surface to get warmer in order to raise the T of the colder higher place so it can radiate 240W/m^2.

    But if the OLR has increased, then where did the energy come from to raise the T? It Wasn’t all ‘trapped’ by additional co2 or OLR would have dropped. So the enhanced greenhouse is a second order effect so far as I can see. And the empirical cloud data backs me up too. Seems to me the ‘higher colder place’ already got prewarmed by the Sun via the ocean due to reduced cloud, with sufficient excess heat to increase OLR as well as warm the surface.

  10. Trick says:

    TB: Q: “..if the OLR has increased, then where did the energy come from to raise the T?”

    A: See the eqn.s – the energy could come from increased variable So. Then albedo affects the net S. The slowing of the energy flow out is in the e variable. (e.g. maybe would be 287K if e reduced a bit by taking out some infrared active gas.)

  11. tallbloke says:

    And since the Sun went quiet and cloud increased:

    OHC fell slightly from 2004 (until the ARGO data got ‘adjusted’ again last novenmber)
    Surface air temp has fallen since 2005
    Tropospheric temp at cloud level has increased, as the departing OLR heads for Alpha Centauri
    OLR has carried on increasing, as the oceans give up their stash of energy

    Where’s our extra co2 comfort blanket when we need it?
    Doesn’t seem to be doing it’s job, does it?

  12. tallbloke says:

    Trick: “The slowing of the energy flow out is in the e variable.”

    Yeah, that’s the theory. It isn’t keeping up with cloud changes though. And the energy flow hasn’t slowed, it has carried on increasing. That’s my point. Extra Co2 is a second order effect. Therefore the majority of the warming was down to cloud change not extra co2.

    QED

  13. tallbloke says:

    Andy G: welcome. Indeed, TSI has fallen. Small in W/m^2 terms, but may be linked to and amplified by cloud change. Don’t need to get into complex discussion on that for the purpose of my logical argument though.

  14. tallbloke says:

    Entropic man, what is sauce for the goose, is sauce for the gander.

    When will Kevin Trenberth stop regaling us with certainty about ‘missing heat’?

    (must be around here somewhere) :)

  15. Trick says:

    TB: (e) “Isn’t keeping up with cloud changes though.”

    Cloud changes would be in the albedo first forcing eqn., e would vary with water vapor in the clouds and CO2 et. al. in second Teq response eqn. – both are first order effects in the simple logical GW system. You haven’t shown precisely the “majority” of warming provenance (human vs. natural)…yet.

    Sure all these things you mention vary; science however just cannot pick out the natural vs. human activity component in albedo and/or e precisely enough independently of each other & “So” to earn your top post QED yet that I have read. Maybe you can precisely show that & earn your QED?

  16. Tallbloke says OLR is OLR but OLR is a mathematical construct. If some of the assumptions do not fully apply then the supposed measurements (none are direct measurements) are likely to have errors.
    This may interest you http://physicsworld.com/cws/article/news/2012/sep/14/plancks-law-violated-at-the-nanoscale . In the article it states ” Planck assumed that all radiation striking a black body will be absorbed at the surface of that body, which implies that the surface is also a perfect emitter” Please note the word surface which is also in the definition of black and gray bodies. The S-B equation applies to black and gray surfaces in a vacuum. When there is an atmosphere as with the sun and earth, firstly the atmosphere has no surface so the S-B equation does not strictly apply, and secondly other energy transfer mechanisms take place. One can pretend by mathematical manipulation that certain forms are equivalent but that does not mean the answer is correct or can physically take place.

  17. tallbloke says:

    Trick: Yes, but cloud has been increasing again, according to three different methods of measuring it (weather satellites, ground obs, and Earthlight reflected onto the moon), and the Earth is at it’s warmest for a long time (either since the 40’s or the medieval warm period?). So humidity should have increased, which should have warmed us further according to the AGW theorists, given that they also believe cloud feedback is positive.

    That should have reduced OLR, but it hasn’t happened. So even if Entropic Man is correct about the uncertainty on the absolute trend (and I’m sure he is), we should have seen a noticeable inflection in the OLR curve. But all we observe is a couple of dips consistent with effects from Pinatubo and the ’98 El Nino, and a pretty flat line otherwise.

    To me, that seems to be fairly good evidence that the additional opacity of the atmosphere is compensated for by some other feedback in the system. The most likely candidate is negative cloud feedback, as quantified by Roy Spencer and Danny Braswell.

    Incidentally, the ISSCP/Earthshine graph is one I adapted from SkS, and they’ve diddled with the left hand axis scale. The W/m^2 scale on the inset Earthshine graph is nearer to the truth. I emailed Cook about his incorrect Y axis %anomaly calibration a few times when we were on speaking terms, but he never corrected it.

  18. vukcevic says:

    Hi everyone
    I can’t claim to fully understand CO2, but since AndyG55 mentioned TSI, there is something to it, if not the TSI then the solar magnetic cycles which drive TSI. Recently the ‘solar knowledge supremo’ lost his cool and blue his top off over the TSI as you can see here
    http://wattsupwiththat.com/2012/09/15/f10-7-flux-sea-level-and-the-holocene/#comment-1080963
    and beyond

  19. Jimbo says:

    Please note I am NOT a Warmist. I’ve just added the following on WUWT quoting the IPCC. It’s meant for newbies who have just arrived on WUWT via PBS mentions of A. Watts.

    The two most abundant gases in the atmosphere, nitrogen (comprising 78% of the dry atmosphere) and oxygen (comprising 21%), exert almost no greenhouse effect. Instead, the greenhouse effect comes from molecules that are more complex and much less common. Water vapour is the most important greenhouse gas, and carbon dioxide (CO2) is the second-most important one.
    http://www.ipcc.ch/publications_and_data/ar4/wg1/en/faq-1-3.html

  20. Entropic man says:

    “Entropic man, what is sauce for the goose, is sauce for the gander.”

    Agreed. The problem of correctly interpreting uncertainty in data bedevills the whole climate change debate. I’ve repeatedly seen people at both ends of the spectrum building predictive mountains out of data molehills, whether forecasting imminent disaster or projecting reassurance that the status quo will continue.

  21. Entropic man says:

    Over the last 50 years we have measured an approximate global temperature increase of approximately 0.7C, thats about 0.014C/year. If you accept the figure that a 1C change in surface temperature requires extra surface heat input around 4W/M^2, then a warming rate of 0.014C/year require an imbalance between TSI and OLR of 0.056W/M^2.
    That is about 1 part in 25,000. With out present instrumentation I doubt we can detect an imbalance that small.

  22. Andrew MCKILLOP says:

    All I want to say (and ask) is this:

    Mars has an atmosphere of about 95.3% CO2 or 953 000 parts per million
    What is the average temperature of Mars and the nighttime temperature of Mars ?

    OK, Mars also has almost no atmosphere at all compared with Earth, but the simplistic argument that CO2 increase in the atmosphere only leads to rising temps is easy to question

  23. Entropic man says:

    Mars has a much thinner atmosphere, but it is mostly CO2. The TSI is 44% of Earth’s and 42% reaches the surface, giving a surface illumination about 16% of Earth’s.
    Back radiation from the CO2 gives a warming effect of somewhat less than 10C. With only traces of water vapour, there is hardly any secondary forcing.
    Surface temperatures vary between 20C and -140C, with the average well below 0C.

    Just for fun!

    http://www.msnbc.msn.com/id/6908408/ns/technology_and_science-space/t/greenhouse-effect-could-make-mars-livable/

  24. tallbloke says:

    Jimbo, apologies, I should have made it clear you were stating the party line, not your own position. I’ll fix that.

    Entropic: 11.39: Agreed, though natural variation remains the null hypothesis, and your 12.01 temperature data doesn’t look very alarming in a broader context anyway. You need to divide TOA TSI by 4 to get the correct input to the hemisphere, but also take into account the amplification via cloud cover prof. Shaviv found of x5 to x8 or so. Mars atmospheric mass is also a consideration for its surface temperature as well as composition.

  25. Trick says:

    tallbloke- “…but cloud has been increasing again…”

    The theme here is simple & logical. I’ve shown 2 eqn.s with 3 variables and fixed one of them (e) to obtain naturally meaningful Teq solutions. Here’s a 3rd simple & logical independent eqn. but it comes with two variables:

    e(total) = e(human activity) + e(natural)

    The goal is to solve these 3 eqn.s w/4 variables for Teq “since the 40′s or the medieval warm period”. So need a 4th independent eqn.

    If you can find (theory or empirical) an OLR eqn. as a function of only the 4 variables then you can earn your QED by setting e(human activity) = 0 as you assert and solve for Teq. – if find it follows thermometer measured earth Tavg. within decent error bands. Is it not so?

    ———————–

    Andrew: You can solve the eqn.s with e=0 to get Mars Teq! All you need is the data on this NASA page:

    http://pds-atmospheres.nmsu.edu/education_and_outreach/encyclopedia/heat_balance.htm

    You can then find Mars “e” for the measured Tavg (212 -215K or so).

  26. Entropic man says:

    My problem with natural variation is its vagueness. To convince the professionals you would neeed to quantify the energy flows associated with the various cycles to much higher levels of accuracy than you’ve managed so far, and show that they explain the changes seen over the last century better than CO2 primary and secondary forcing.
    Within the sceptic community your discussions of cloud cover, gravity induced lapse rates etc are accepted, but in the wider academic community you have conspicuously failed to make your case.

  27. tallbloke says:

    Trick: You are correct, but I see a value in qualitative description and interpretation as well as quantification according to theory. Especially with datasets whose error terms makes them essentially useless for deciding the issue.

  28. Green Sand says, September 21, 2012 at 11:31 pm: How do we know how many square metres there are at the top of atmosphere? How do we account for expansion/contraction? How much is expansion/contraction affected by the amount of energy within “the system”? Genuine, albeit naive, questions, not criticism.

    Answers came there none, so here goes…

    1. The ‘top-of-the atmosphere’ in this context means the top of the troposphere. This varies between about 8km at the poles to 16km at the equator. So on average let’s say its height is 12km.

    2. The surface area of the Earth is 511,186,000 sq km and its radius is 6378km. A lot of people think that an atmospheric column which is 1 sq m at the surface would expand out significantly by the time you reach the top of the troposphere because of the Earth’s curvature. But in fact the expansion is completely negligible because the troposphere is such an incredily thin veneer on top of the mighty Earth.In fact the upper surface area of a 12km high troposphere would be 513,111,369 sq km which is only 0.38% larger than the Earth’s surface area.

    3. If you increased the energy flowing through the Earth’s atmosphere sufficiently to cause a surface temperature rise of 1 degC from its present average value of 15 degC, you would increase its volume by about 0.35%. Since the atmosphere can only expand upwards this would increase its average height by 0.35% or 42 metres.

    So I hope you now see that the geometry of the Earth and its atmosphere is pretty well damn fixed! (The average surface pressure is completely fixed by the mass of the atmosphere above, and this average does not vary at all on human timescales).

    Actually, the debate in this thread is not about atmospheric expansion but about atmospheric composition and whether that makes any difference to surface temperature. In particular, does changing the proportion of CO2 in the atmosphere change the surface atmospheric temperature significantly? TB is arguing that empirical facts support the proposition that the observed increase in temperature from 1970 to 2000 is due to increasing energy from the Sun. Consequently this logically relegates CO2 to a minor and probably negligible role.

  29. cementafriend says, September 22, 2012 at 3:22 am: Tallbloke says OLR is OLR but OLR is a mathematical construct.

    Sorry, OLR is not a mathematical construct. It is a physical reality.

    Yes the method of measuring it may be fraught with uncertainty but that is a different issue altogether.

    Likewise, although I agree completely with you that atmospheric gas is nowhere near being a black body, and much nonsense has been generated from assuming that it is, that has no bearing on the reality of OLR as a measurable physical entity.

  30. Stephen Wilde says:

    Entropic,

    Just turn that around.

    There is insufficient evidence that the effect of CO2 is significant in the face of natural changes such as cloudiness variations affecting global albedo and the amount of solar energy able to enter the oceans.

    To convince the professionals that CO2 is a significant factor you ought to need to quantify the changes in energy flows associated with CO2 to much higher levels of accuracy than you’ve managed so far, and show that they can explain the changes seen over the last century better than natural forcings.

    If we compare the scale of natural air circulation changes from MWP to LIA and LIA to date with the air circulation changes to be reasonably expected from a little more CO2 it is perfectly apparent that the effect of CO2 is miniscule in comparison.

    The burden of proof is on the alarmists and they have conspicuously failed to discharge it.

  31. Bart says:

    I have been toying with a model for a few months which I believe suggests that added CO2 would actually tend to decrease temperatures. Someday, I may sit down and thoroughly flesh it out, but I will toss out what I have here and let others think it through.

    The thing is, a GHG tends to warm a planet up to the point at which the gases start to radiate significantly. Once the overall outward flux equlibrates with the incoming, you reach an equlibrium. We can thus consider a linearized differential equation for the surface temperature to read something like this:

    dT/dt = a*(T1 – T)

    where “T” is temperature anomaly from where absolute temperature would be without the GHG, “a” is a coupling constant, and “T1″ is the temperature anomaly to which the GHG drives the system. An increase in the amount of the GHG changes both “a” and “T1″, but “a” increases more or less linearly, whereas “T1″ is logarithmic, with decreasing sensitivity as more of the GHG is added. Thus, adding more GHG creates more or less proportionately more rapid convergence, but only modestly increasing equilibrium temperature. The equilibirum is reached when dT/dt = 0, or T = T1.

    None of this is particularly controversial, I think. But, where it gets interesting is when you have more than one significantly radiating GHG. In our atmosphere, we have water vapor, CO2, and CH4 as significant GHG radiators. We’ll neglect the H2O for now just to make the point. Assuming two significant radiators, the differential equation should be something like

    dT/dt = a*(T1 – T) + b*(T2 – T)

    Assume “a” is the coupling constant for CO2 and “b” for CH4. It follows that T2 is greater than T1. The equilibrium temperature is attained when dT/dt = 0, or

    T = (a*T1 + b*T2) / (a + b)

    If we assume that T1 and T2 are relatively insensitive to changes in concentration, then the sensitivity to increased CO2 is approximately the partial derivative

    dT/da = b*(T1 – T2) / (a+b)^2

    Since T2 is greater than T1, the sensitivity is negative, and adding CO2 would actually decrease the equilibrium temperature.

    I have sometimes made the analogy to a dam with floodgates. The area and height of the floodgates is analogous to the concentration. With one row of floodgates, increasing the height tends to increase the steady state depth of the water behind the dam. But, now suppose you have two sets of floodgates, one at middling height, and one at higher level. At steady state, there is water flowing out of both sets of floodgates, with the lower level completely submerged. You now increase the height and area of the lower floodgates. But, with these floodgates already submerged, the major effect is from the increase in area, which draws more water out. Thus, the overall level of water behind the dam decreases. The area of the floodgates is analogous to the coupling constant, which dictates how fast water can drain, while the height of the floodgates is analogous to the equilibirum temperature level.

    Now, surely, the climate modelers have meticuously considered these dynamics, and reached the conclusion that, for the current relative mix of GHGs, the sensitivity to increased CO2 is actually positive, right? Well, given the quality of the “science” these clowns have been pushing, I have significant doubts that such a conclusion is warranted. We already know they are wrong on two counts:

    1) relentlessly increasing CO2 in the last decade has not produced the expected rise in temperature, hence the AGW hypothesis has been falsified

    2) CO2 is accumulating in the atmosphere due to temperature changes, not to human inputs

    I’d bet it is more-or-less a shoe-in that they have not even correctly calculated the sign of the sensitivity.

  32. David Socrates, you are correct OLR exists and is a physical reality but it can not be measured directly. It is a mathematical construct making assumptions of energy from the sun, reflections of the suns energy, absorption on the earths surface, heat exchange at the earths surface, absorption by the atmosphere (including clouds), and chemical changes in the atmosphere and at the earths surface. (Stephen Wilde I hope I have not left something out, maybe I should add any other unknown factor) The supposed accuracy of OLR calculations is nonsense, particularly on a global scale considering difference at the poles and at the equator.

  33. Entropic man,

    There are a bunch of things (more than two) that stick-out like dogs balls that the modelled assumptions for CO2 importance/feedbacks are rather suspect.

    One that I find very headshaking is that the most recent warming phase, (which has ended recently, arguably since 1998 if you embrace the 1999/2000 La Nina “correction” or smoothing), is remarkably similar to that from ~1910 to ~1940 before CO2 increase really got going. True there have been some assertions from alarmists as to why, but they are speculative with no empirical data in support and in my view are really dodgy.

    Yep, it’s hard to nail-down the natural variations wot are complicated, but they sure are there!

  34. Geoff Cruickshank says:

    You should also consider the possibility of warmer water originating in the tropics or from ocean overturning making it to the arctic, where it has a better opportunity of getting out to space. As the OLR from 70-90 N (the ocean area of the arctic) has increased OLR of maybe as high as 6w/m2 since about 2005, I think this is a likely scenario. Noting that more open water there at this time of year also facilitates that.

  35. Geoff Cruickshank

    Yep, that’s a good point but various authorities outside of the NSIDC and its somewhat colourful director Mark Serreze; have pointed out that because the arctic sea-ice is largely floating free, (as distinct from with the huge continent of Antarctica), it is more strongly influenced by wind patterns. Back in 2007 a division of NASA declared that the big melt then was caused by unusually strong north winds pushing the ice into warmer waters, and earlier this year there was a big storm which reportedly caused “damage” to the floating ice aggregation and its comparative measurement.

    I’m paraphrasing from memory but could find some references if anyone is interested

  36. tallbloke says:

    Bart says:
    Assuming two significant radiators, the differential equation should be something like

    dT/dt = a*(T1 – T) + b*(T2 – T)

    Assume “a” is the coupling constant for CO2 and “b” for CH4. It follows that T2 is greater than T1. The equilibrium temperature is attained when dT/dt = 0, or

    T = (a*T1 + b*T2) / (a + b)

    If we assume that T1 and T2 are relatively insensitive to changes in concentration, then the sensitivity to increased CO2 is approximately the partial derivative

    dT/da = b*(T1 – T2) / (a+b)^2

    Since T2 is greater than T1, the sensitivity is negative, and adding CO2 would actually decrease the equilibrium temperature.

    OK, that’s a bit too densely constructed for me to follow. Are you saying it follows that T2 is greater than T1 because CH4 is more absorptive than CO2 i.e. because the coupling factor is bigger ?

  37. Geoff Cruickshank says:

    Bob Fernley Jones

    I think I saw the NASA report on that event and have no reason to disbelieve them.
    Playing with numbers here
    http://climexp.knmi.nl/get_index.cgi
    it seems to me that the the rise in OLR is much more pronounced from 45-90N than it is from 0-45N.
    Thus my speculation is that this is not so much less cloud in the tropics as from warm water redistributed northwards finally emitting its heat to space. As it really steps up about 2004, perhaps it is even the after effects of 1998. The further north the area considered the more dramatic the effect. I presume this is because of the greater atmospheric window in the water vapour spectrum as you approach the arctis.
    But as I said, a speculation only.

  38. Geoff Cruickshank says:

    And I should have added, that if you happen to have a look at that site, it produces three graphs, and the anomaly graph is where the change is most easily seen.

  39. tallbloke says:

    Geoff, which group is OLR under on KNMI? Monthly re-analysis? or where?

  40. tallbloke says:

    Lower Troposphere anomaly split in to north and south hemispheres:

    Why the difference if warming is mostly due to CO2?

  41. Tallbloke, CH4 is not more absorptive than CO2 in fact very much less (maybe one tenth, you might also look at section 5 of Perry’s Chemical Engineering Handbook which has actual values of various gases -CH4 is very little with respect to CO2 which in turn is very much less than H2O maybe 1/10th) -look at the post about CH4 on my blog.
    I must get around to putting up some more post, particularly the S-B equation which is being misused by the so-called climate scientists..

  42. tallbloke says:

    Lower Troposphere anomaly: Tropics 15N – 15S

    Where’s the ‘Tropical tropospheric hotspot’?

  43. tallbloke says:

    Thanks CF. I’ve probably misunderstood Bart. I’ll await his reply.

  44. Trick says:

    Bart – “I will toss out what I have here and let others think it through.”

    Some limited thinking through:

    1) Your dT/dt = 0 math condition may be a local min. as well as max. You need to prove it is a local max. and then this max. is not only local max. but the one & only ultimate max. at each point on the surface. Even then I am not sure what that means b/c….

    2) The equilibrium condition being reached when “overall outward flux equilibrates with the incoming” so that dT/dt = 0 satisfies the 1st law but says nothing about 2nd law equilibrium.

    3) The application of the 2nd law requires an isolated system. Your system is not isolated.

    That oughta’ hold your interest for awhile. Implementing 2nd law properly is why theorists consider the tall isolated columns of air. The practical folks are still struggling with that implementation.

    My suggestion would be to start from the T profile theory solutions already obtained w/o infrared active gas in the clean air columns (emissivity e =0, surf. Tavg. = 255K for Earth). Add infrared active gas (radiation or e .NE. 0) to the air column variational problem – see what happens to T profile from there – let some photons with squiggly lines rattle around in the gravity field being emitted/absorbed & reflected. That would be new AFAIK.

  45. Bart says:

    tallbloke says:
    September 23, 2012 at 8:55 am

    “Are you saying it follows that T2 is greater than T1 because CH4 is more absorptive than CO2 i.e. because the coupling factor is bigger ?”

    It has to do with the emissions spectrum of the surface. In order to get the CH4 to radiate significantly, the temperature has to move up higher than it does for CO2. There is a positive feedback involved due to backradiation, which is resisted by the increase in total outward radiation which provides a counteracting negative feedback. Since the CH4 radiates at higher energy, it is trying to pull the temperature higher.

    cementafriend says:
    September 23, 2012 at 11:49 am

    However, the energy per photon at the CH4 level is much higher than that at the CO2 level, so there is an avenue for elevated sensitivity.

    Trick says:
    September 23, 2012 at 1:54 pm

    “Your dT/dt = 0 math condition may be a local min. as well as max. You need to prove it is a local max. and then this max. is not only local max. but the one & only ultimate max. at each point on the surface.”

    Local stability should be sufficient. And, stability is built into the way I have expressed the equations, with “T” providing negative feedback. Am I justified in doing that? Yes, because in the full set of nonlinear equations, the very powerful T^4, where “T” is here absolute temperature, negative feedback of outward radiation will always stabilize the termperature somewhere.

    What I have presented is by no means proof. I have made implicit assumptions regarding the strength of various terms and dropped them from the linearized equations. My point was not to prove anything, but to explain why I have misgivings about what I suspect is merely an assumption on the part of the climate modelers that more GHG always means more heat being retained. I suspect it is likely that the sensitivity is actually negative for a couple of reasons:

    1) GHGs are actually heat sinks – they allow energy to flee the system when they start radiating. I believe my dam-floodgate analogy is appropriate.

    2) As I discussed here, because of the positive correlation between temperature and CO2, a positive forcing from CO2 to temperature would create a positive feedback, which would tend to destabilize the climate, and there is no evidence for this.

  46. tallbloke says:

    Thanks Bart, I’m clearer on this now. That’s a good point about destabilising feedback too. Roger A thinks he may have constrained the anthropogenic contribution to the increase in co2 to somewhere between 25 and 60%. You said somehwere between 5 and 10% if I recall correctly. I wonder if we can bring anything else to bear on the issue to tighten it down any further.

  47. Entropic man says:

    Dont H2O and CO2 have different effects?
    H2O absorbs its infrared wavelenghts from the surface and warms, increasing the air temperature and ultimately generating a wide band OLR output .
    CO2 absorbs and immediately reradiates part of the surface radiation around 15 micrometres without warming the air significantly. Depending on CO2 concentration a proportion ultimately goes outwards as part of the OLR, the rest warms the surface again.

  48. Trick says:

    Bart says: “GHGs are actually heat sinks – they allow energy to flee the system when they start radiating.”

    Infrared active gas (commonly GHG) molecules absorb a photon of thermal energy and re-emit the equivalent photon of thermal energy – they are individually neither thermal energy source nor sink.

    See the simple logical atm. with emissivity e = 0 energy balance eqn. above 9/22 at 12:30am.

    Setting e=0 means the earth surface would be radiating OLR at Tavg. = 255K directly thru the atm. to deep space, meaning the e=0 atm. does not emit so it does not absorb radiation (an idealization – not physical – since really all matter >0K emits & absorbs thermal energy).

    Now add only infrared-active gas properties to the atm. in the balance eqn.s with emissivity e = 0.8 so that the atm. can emit and therefore absorb radiation – see TB’s OLR chart above, raising the Earth surface Tavg. = 288K which is physical & measured with thermometers, give or take.

    This simple logical physically basic assumption start to the simple logical OLR argument shows infrared-active gas properties slow the radiation to deep space by emitting & absorbing radiation so the resultant energy balance at LTE (law 1) is higher Earth surface Tavg.

    This means infrared-active gases (your GHGs) are not heat sinks and do not allow energy to flee the system; they do interact with the OLR & ISR energy balance fundamentals causing Earth’s surface Tavg. to be higher (288K) than it otherwise would be (255K) without your GHGs.

    I think I earned a QED in there, see what you think.

  49. Bart says:

    Trick says:
    September 24, 2012 at 12:30 am

    “Setting e=0 means the earth surface would be radiating OLR at Tavg. = 255K directly thru the atm. to deep space, meaning the e=0 atm. does not emit so it does not absorb radiation (an idealization – not physical – since really all matter >0K emits & absorbs thermal energy).”

    The key phrase in that is “an idealization – not physical.” What happens when a real gas re-radiates incident radiation it has absorbed from the surface? Some of it goes back to be re-absorbed and emitted again by the surface. This raises the temperature, creating more outward emissions. Which causes the gas to re-radiate more of that back. Which causes the temperature to rise some more. It is a positive feedback cycle, but embedded within the larger negative feedback loop created by energy loss proportional to nearly T^4 over all other frequencies, so it does not lead to instability.

    In any case, every gas will do this, at least theoretically, because every gas radiates at some energy level, and the tail of the Planck distribution for surface emissions, though it approaches zero asymptotically, is never actually zero. Every gas pulls the temperature up at least a little. How significantly it does so is a question I have not yet answered to my own satisfaction.

    I think until I have something more substantial, I will refrain from pushing this idea further. All I have right now is a vague sense of unease on my part as to whether everything has been properly accounted for, and there appears to be at least a potential for negative sensitivity. More, I cannot say at the present time. Talk of a “shoe-in” and so forth on my part is merely hyperbole reflecting the cynicism I have developed watching all the counter-hyperbole fly from the other side. But, it would hardly be surprising for them to have gotten even this basic element wrong, given the fiasco unfolding before us.

  50. Trick says:

    Bart – Fair enough.

    Setting the e = 0 for idealized energy balance eliminates all the issues you mention. You are right that setting the e = 0.8 encompasses a whole range of processes that cannot yet be separated out – hence in the top post I don’t think TB earns his QED for reasons such as you discuss.

  51. Geoff Cruickshank @ September 23, 2012 at 10:55 am & 10:53 am

    That all sounds plausibly interesting but your link won’t help me by only presenting this unanswerable message: “Please select a field”

  52. Geoff Cruickshank says:

    September 23, 2012 at 10:55 am & 10:53 am

    That all sounds plausibly interesting but your link won’t work for me by only presenting this unanswerable message: “Please select a field”

  53. Entropic man @ September 23, 2012 at 11:22 pm

    I’m not sure what your point is but all GHG’s radiate predominantly laterally (much more so than up and down) so that at least in the conceptual Local Thermal Equilibrium (LTE) that means that nothing happens from that substantial portion of radiation. In a broader consideration, elemental layers of air also respond in the same way to a degree.

    See: http://tallbloke.wordpress.com/2012/02/08/bob-fernley-jones-trenberth-trouble-the-radiative-question/

  54. Geoff Cruickshank says:

    Apologies for my non working link.
    http://climexp.knmi.nl/select.cgi?id=someone@somewhere&field=noaa_olr
    That should find it.

  55. Entropic man says:

    There is no preferred direction for reradiation from individual CO2 molecules. All directions are equally probable.
    However, different directions can have different consequences.
    Most reradiated 15 micrometre wavelength photons, especially those radiated sideways will probably be absorbed by another CO2 molecule and reradiated in another direction.
    A photon reradiated downwards near the ground may reach the ground and be absorbed, warming it slightly.
    A photon reradiated upwards higher in the atmosphere may escape outwards and become part of the Outward Longwave Radiation.
    The result is a drop in the Outward Longwave Radiation spectrum at 15 micrometres and a peak in the 1/ radiance spectrum at 15 micrometres looking up.
    Both are most clearly visible in spectra taken in, or looking down on,areas under low humidity conditions, such as deserts or icecaps..
    Under humid conditions the more complex interactions of infrared radiation with water vapour and clouds tend to dominate , making the effect of CO2 harder to separate out.

    http://www.google.co.uk/imgres?imgurl=http://wattsupwiththat.files.wordpress.com/2011/03/gw-spectrum-tropical-pacific.jpg&imgrefurl=http://wattsupwiththat.com/2011/03/10/visualizing-the-greenhouse-effect-emission-spectra/&h=1133&w=1521&sz=229&tbnid=yxci5WKVU_3ZmM:&tbnh=90&tbnw=121&prev=/search%3Fq%3Dearth%2Bthermal%2Bemission%2Bspectrum%26tbm%3Disch%26tbo%3Du&zoom=1&q=earth+thermal+emission+spectrum&usg=__WtKhiRZzlbs097XgGkNCn-eBkhA=&docid=IRWq7_ORGx9idM&sa=X&ei=jndgULf5EcLb0QWz1IDoDg&ved=0CE8Q9QEwCQ&dur=29782

  56. Out of the Box says:

    Is there any evidence that the planet is releasing more energy from within?

  57. Entropic man says:

    Out of the box, there is a small amount of energy release, as the Earth continues its long, slow cooling, mostly from volcanos and hot springs. On the scale of the energy flows resulting from incoming solar radiation it is not significant beyond the immediate locality. The effect of volcanos on climate is mainly through cooling due to sulphur and ash release reducing the incoming energy reaching the surface.

  58. Out of the Box says:

    Is it true that more heat leaves our oceans than comes into them? If so what would be the source of the excess output of energy?

  59. tallbloke says:

    OOTB: Welcome. I’m not sure of the context of your question. At the moment, the oceans may be cooling slightly (pre ARGO data ‘adjustment’). If so, this suggests that solar and geothermal input is less than their energy output by several cooling processes of conduction, convection and radiation.

  60. Out of the Box says:

    Tallbloke: All of the data I’ve seen would lean towards the oceans warming (glacial melting, ocean rising and the like). If the ocean temperature is rising while the oceanic energy output is greater than its input, then would that suggest a geothermal energy increase?

  61. tallbloke says:

    Over what period? Which data?

  62. Out of the Box says:

    Over the past century according to this National Geographic article http://ocean.nationalgeographic.com/ocean/critical-issues-sea-temperature-rise/

  63. tallbloke says:

    “Global warming caused by human activities that emit heat-trapping carbon dioxide has raised the average global temperature by about 1°F (0.6°C) over the past century.”

    That’s not data, it’s propaganda.

    But assuming the figure is about right, what makes you think its output was greater than the input? If the ocean warmed, then clearly it gained more energy than it lost. In my opinion, that was due to increased solar activity and reduced cloud cover. You opinion probably differs. However, I can back up my opinions with data and reasoned argument whereas you don’t seem to be offering any.

    Geothermal output into the oceans is a big unknown, but I don’t think it would vary enough to cause the kind of changes in ocean energy content we have seen.

  64. Out of the Box says:

    I agree it’s a lot of propaganda and I am just seeking answers. I do not believe our oceans are heating up due to AGW but I do believe they are heating. What data and reasoned argument could you supply that would support the increased solar activity and reduced cloud cover philosophy? I am in agreement with you, the more data the better. There is very little data available to support my thinking but I may be able to make a well reasoned argument.

  65. Out of the Box says:

    Thanks. This explains your thinking on how solar activity has increased over time, but what about the cause of reduced cloud cover. Would not cloud cover increase with ocean temperature increase due to evaporation increase.

  66. Stephen Wilde says:

    “Would not cloud cover increase with ocean temperature increase due to evaporation increase.”

    One would think so but the data says otherwise.

    In fact the oceans warm when clouds decrease and cool when clouds increase and it is that observation which gives us the direction of causation.

    Given that the cloudiness changes PRECEDE ocean temperature changes we have to look elsewhere for the cause of the cloudiness changes.

    The correlation between changes in the behaviour of the jet streams and changes in the level of solar activity looks good to me.

    An active sun draws the climate zones poleward, increases jet stream meridionality and reduces global cloudiness to ‘open the window blinds’ and allow more solar energy into the oceans.

    The reverse when the sun is inactive.

  67. tallbloke says:

    I don’t know what caused the reduction in cloud cover. Svensmark effect, Stephen Wilde’s hypothesis on shifting jet streams, take your pick. But I do know there was a reduction in cloud cover from ~1960 accordng to Spanish and Chinese datasets. And from 1979 to 1998 according to weather satellites.
    Also, a reduction in cloud cover linked to solar activity levels is a logical deduction from proxy records and from Nir Shaviv’s theoretical work on using the oceans as a calorimeter.

    Your turn, what is your geothermal argument and where are your data?

  68. Bart says:

    Out of the Box says:
    September 25, 2012 at 5:11 pm

    “Over the past century according to this National Geographic article…”

    Two things:

    1) We really have no good grasp of ocean temperatures pre-ARGO, which has only been around for roughly a decade. Prior to that, we only have measurements with poor quality control over shipping lanes.

    2) We can only measure ocean temperatures accurately in the upper 700 m or so of ocean. ARGO reports at depths down to 2000 m, but those measurements become increasingly uncertain with depth.

    You do not need a constant input source to get warming and cooling of surface waters, which are only a small part of the entire ocean. It’s like measuring the voltage at a particular node in an LRC circuit. There are oscillations triggered by abrupt shifts in the input, whose reverberations can last for quite some time after the initial excitation, and the components of the signal which represent the response to the smooth part of the input are generally delayed by the phase characteristics of the circuit.

  69. Out of the Box says:

    I came across this report by accident but it talks about core related hot spots that oscillate periodically (kind of like sun spots) that could transfer heat to our oceans. http://www.gsaaj.org/articles/TempPaperv1n22007.pdf

  70. tallbloke says:

    I have seen that paper a few years ago. For sure there are interesting correlations between geomagnetic data and climate indicators.

    There are several proposals for mechanisms. I’d suggest reading some of Brian Tinsley’s work. Keep an eye on Vukcevic’s stuff too. Geothermal seems a bit slow acting and changes too small in magnitude. Having said that, there’s a lot we don’t know about underwater volcanos and vents.

    http://www.vukcevic.talktalk.net/NFC1.htm

  71. Brian H says:

    Green Sand;
    TOA doesn’t exist. It is an imaginary layer which would be equivalent in its output to the entire atmosphere. If it existed. But it doesn’t.