The role of gravity in the greenhouse effect

There could be no planetary atmosphere without gravity, but gravity also plays a fundamental role in the greenhouse effect thereby determining surface temperatures. To see why this is the case lets imagine that gravity has somehow been switched off and the atmosphere is held in place on the earth by an infinitely thin membrane at height d. Let’s also assume that the atmosphere is 100% composed of CO2 absorbing IR in the 15 micron band.

Fig 1: Zero gravity CO2 atmosphere held in place by thin membrane over surface at temperature Ts

Fig 1: Zero gravity CO2 atmosphere held in place by thin membrane over surface at temperature Ts

The atmosphere will behave as a perfect gas of temperature Ts. The pressure will be P = RTs/d and CO2 will absorb all 15 micron IR from the surface while emitting exactly the same amount to space at the membrane. Viewed from afar the IR spectrum will appear to be a perfect black body at temperature Ts. There is no greenhouse effect at all. Effectively the atmosphere can be viewed as part of the surface. There would be no net  difference if the gas was replaced by Argon.

Conclusion: There can be no greenhouse effect without a gravitational field. CO2 has no greenhouse effect parallel to a gravitational field.

Now switch on gravity and remove the membrane. The atmosphere expands and a density/pressure gradient is setup as it quickly reaches hydrostatic equilibrium and the atmosphere extends upwards. The surface pressure equals the weight of the atmosphere per unit area – 15 psi or 101000 pascal falling exponentially with height approximately  as

P = P_0 \exp{-\frac{Mgz}{RT_s}}

which assumes constant T, which as we will see is not exactly what occurs.

Gravity generates an exponential pressure gradient

Fig 2: Gravity generates an exponential pressure gradient

The density of CO2 molecules now diminishes exponentially with height. Therefore the IR radiative flux emitted by CO2 is no longer homogenous because gravity has broken the symmetry. Each layer has a different emissivity that depends on the density of CO2 molecules in that layer. Despite this  radiative emission within a thin horizontal layer is still homogeneous in 2 dimensions and we call this ‘local thermodynamic equilibrium’ LTE for a given height h. However each height has a different emissivity ( or absorption) for 15 micron photons.

The net flux of radiation through the atmosphere from the surface at height h is then the integral of the (emission – absorption)  from all lower levels  minus the integral of the (emission – absorption) from all higher levels. There is no longer vertical thermodynamic equilibrium and temperature can vary with height.

Figure 1: Model schematic of radiation transfer from surface at 288K through 100m wide slices of atmosphere. Each slice is a grey  body absorbing and emitting IR. A lapse rate of 6.5K/km and a hydrostatic scale height of 8.6km is assumed.

Figure 3: Model schematic of radiation transfer from surface at 288K through 100m wide slices of atmosphere. Each slice is a grey body absorbing and emitting IR. A lapse rate of 6.5K/km and a hydrostatic scale height of 8.6km is assumed.

How does the flow of radiative energy through the atmosphere change the energy balance? Since density falls exponentially there exists an effective emission height for each wavelength above which >50% of IR photons escape to space.  I calculated this height for the 15 micron CO2 band using HITRAN cross-section data for 2 different concentrations of CO2 on earth..

Fig 5b: The CO2 emission height profile for 300ppm and for 600ppm smoothed with a resolution of 20 lines.

Fig 4: The CO2 emission height profile for 300ppm and for 600ppm smoothed with a resolution of 20 lines.

Without convection the atmosphere would reach a radiative equilibrium whereby at all heights below this an equal flux of radiation would flow. This can only be achieved by the surface warming up significantly. Well before this can happen convection starts and stabilizes the temperature profile of the troposphere at the adiabatic lapse rate.

\frac{DT}{DZ} = - \frac{g}{C_p}

Here again gravity plays the crucial role because at the adiabatic lapse rate there is a perfect balance matching  buoyancy against  gravity. Such stable atmospheric condition are  rare and this is what drives weather systems. Convection and the lapse rate both halt where the radiative transfer to thin upper layers stops and IR photons escape directly to space. This is  the tropopause.  Note that it is radiative transfer by GHGs through the troposphere that  drives convection towards the lapse rate. The energy to power this atmospheric heat engine comes from the sun radiating energy directly onto the surface.

Conclusion: You need greenhouse gasses to generate a lapse rate. You  need a lapse rate  for greenhouse effect to work because radiation to space from higher altitudes reduces net upwelling IR. Gravity sets the scale of the lapse rate.  (thanks tallbloke)

Blogger HockeySchtick and others (Stephen Wilde etc.) propose a purely gravitational/Mass theory of the atmospheric greenhouse effect seemingly independent of GHG. HockeySchtick writes  :

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.

He then  derives a formula for planetary temperature which works really quite well. However they all assume a pre-existing lapse rate generated only by gravity even in the absence of any greenhouse gasses. This is wrong because you need the sun’s energy plus both gravity and greenhouse gasses to power the convective heat engine maintaining the lapse rate. Radiative transfer of surface heat through the atmosphere tries to steepen the lapse rate towards radiative equilibrium. This instability drives convection (and evaporation on earth) resulting in the approximately observed adiabatic lapse rate. Gravity just defines the thermodynamic scale.

The centre of Mass of the atmosphere corresponds to a height with a pressure of half that of the surface pressure. This is also exactly where the number of CO2 molecules below and above are equal. Therefore you would expect this to approximately coincide with the effective emission height – but for a different reason. It is not the  gravitational energy that is ‘warming’  lower levels due to compression – like in a bicycle pump . It is because above this level the IR ‘fog’ clears and photons can escape freely to space. Greenhouse warming is a subtle effect ’caused’  both by gravity and GHGs  choking surface warming directly to space. You need both. A pure argon atmosphere would have no greenhouse effect and no real lapse rate.

How much warming results from  CO2 on earth and how does that change with increased concentration? I previously calculated these emission spectra for different CO2 concentrations.

Fig 2. Change in outgoing IR  spectra for a range of CO2 concentrations. Each increasing spectra has been offset by 5 mmW/m2sr-1cm-1 to better visualise the differences.

Fig 5. Change in outgoing IR spectra for a range of CO2 concentrations. Each increasing spectra has been offset by 5 mmW/m2sr-1cm-1 to better visualise the differences.

Resulting in a CO2 surface warming effect as follows

Fig 3: Surface temperature change induced by a gradual increase in CO2 concentrations from a starting temperature of 284K

Fig 6: Surface temperature change induced by a gradual increase in CO2 concentrations from a starting temperature of 284K

You can see how the surface temperature follows a T_{lim} \times (1 - \exp{CO_2}) . Direct CO2 forcing converges on a limiting GHE temperature at 100% concentration of about 11C for the 15 micron band. This is because the central  lines saturate , and it is only the smaller side lines that continue to grow with concentration increase. So called ‘runaway greenhouse effects’ are not caused by CO2 but depend on assumptions about H2O feedbacks for hotter climates like that on Venus due to higher solar radiation.

The way the greenhouse effect on earth works is not obvious.

Conclusions:

  1. There can be no greenhouse effect without gravity.
  2. Atmospheric pressure gradient is caused by gravity.
  3. The lapse rate scale is defined by gravity but is generated by convection.
  4. Convection is induced by Radiative transfer of heat through the atmosphere
  5. Radiative transfer is due to greenhouse gasses.
  6. There can be no greenhouse effect without greenhouse gases. Gravity alone will not work.
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70 Responses to The role of gravity in the greenhouse effect

  1. Bryan says:

    Hockey Stick and the link below show that radiative gases have nothing to do with the lapse rate.
    The well known Barometric Formulas are derived with no reference to greenhouse gases.
    Even scienceofdoom agrees that greenhouse gases do not determine the adiabatic lapse rate.

    http://arxiv.org/pdf/1003.1508.pdf

    • Clive Best says:

      Absolutely right! Greenhouse gasses do not directly determine the dry adiabatic lapse rate on a planet. Indirectly the constituents of the atmosphere change slightly the Cp specific heat.

      However that is not my point. You need heat energy to maintain a lapse rate throughout 10km or more of the troposphere. If the atmosphere were transparent to IR photons that heat energy would radiate directly to space . There would be just conduction from the surface and convection would be a damp squid.

  2. tallbloke says:

    radiation to space from higher altitudes reduces net outgoing IR

    Errm. Come again?

    The lapse rate scale is defined by gravity but is generated by convection.

    What is the density of air at 288K under 1bar of pressure compared to the density of air at 220 under 0.2bar of pressure in kg/m^3?

    • Clive Best says:

      Yes indeed – very badly expressed. Should read net ‘upwelling’ radiation !

      The stratosphere is where surface heat/radiative effects essentially vanish.

      If gravity alone determines the lapse rate why does it not reach up to the top of the atmosphere ?

      • tallbloke says:

        Well according to Nikolov and Zeller the relation breaks down at around 150mb regardless of atmospheric composition – though all the atmospheres they looked at had radiative gases in them.

  3. Clive, >99% of the convection in our >99% non-GHG atmosphere is thus non-GHGs

    Please look up the coefficient of convection for N2, O2, Argon and prove using the formulas for convection that pure non-GHGs do not convect.

    Are you claiming a pure N2 tube with a heating element on the bottom wouldn’t convect?

    Also, the Cp of CO2 is < that of N2 and O2, so N2 and O2 affect the LR in addition to WV.

    The dry ALR is double the wet, proving WV is a strong cooling agent ~25C just by the LR change alone.

    • Clive Best says:

      Yes that is right. >99% of convection is due to N2 and O2. The reason for that is that they are thermalized with CO2 and H2O molecules. Each level is in thermodynamic equilibrium.

      Essentially YES. I am claiming that a 10 km high tube of pure N2 with a bottom surface kept at 288K cannot generate a lapse rate through convection. It will slowly convect heat upwards through conduction until eventually the temperature of the full column reaches 288K.

  4. millennia97 says:

    Completely ridiculous to state that there would be no convection without greenhouse gases, really not difficult to disprove in a lab experiment using only inert gases. Surely to God it is determined by relative density under heating, and how do you explain convection in the mantle – dissolved greenhouse gases causing plate tectonics now?

    One of the Venus probes recorded a temperature of 66C at 1000HPa on it’s descent, that is completely conducive with Venus’ position from the Sun, pretty much disproving that CO2 being a major constituent of the atmosphere is the driver of it’s surface temperature.

    I think you’d find Venus would be 400C+ with ANY gas sitting there at 90 atmosphere at that distance from the Sun.

    • Clive Best says:

      Sorry I need to be more precise.

      There would initially be convection and conduction through inert gases until the atmosphere reached thermal equilibrium. This would basically equal the initial surface temperature. Gravity maintains for ever a pressure gradient but it cannot maintain a temperature gradient indefinitely. Otherwise where would the heat escape to space?

      • That’s why a 100% N2 atmosphere would be warmer. The surface would have less ability to cool from radiation from greenhouse gases within the atmosphere and would have to radiate direct from the surface to space. GHGs increase radiative surface area and convection to decrease the lapse rate and cause cooling.

        Maxwell said that gravity/pressure do indeed maintain a temperature gradient forever:

        http://hockeyschtick.blogspot.com/2014/05/maxwell-established-that-gravity.html

        • Clive Best says:

          Yes – but only because the atmosphere is not in thermal equilibrium. It is approximately convective equilibrium. That is the lapse rate which is indeed determined by gravity. All planetary atmospheres contain greenhouse gases. If instead they were pure N2 then the surface temperature would be Teff because that would be the only way to balance energy with incoming solar.

          • Well, Maxwell described the entire GHE thermal gradient on the basis of T being a function of the Poisson relation of Cp/Cv and starting and ending pressures. And with no discussion of GHG RF, since that silly concept of cold bodies making hot bodies much much hotter didn’t come about until 25 years later when Maxwell was long dead (unfortunately).

          • chapprg1 says:

            In your figure 4. I don’t see the saturation effect on the 15 u peak nor do I see a reduction in spectral broadening with reduced pressure with altitude

      • Hockey Schtick says: ”and would have to radiate direct from the surface to space”

        Mr, Hockey, time to change to different aprouch!.

        Heat is NOT ”radiated” from surface to out of space!!! The cold vacuum penetrates trough the atmosphere and NEUTRALIZES all the heat! No heat can be detected escaping out of the stratosphere! THE TRUTH :https://globalwarmingdenier.wordpress.com/2014/07/12/cooling-earth/

    • millennia97 says: ”I think you’d find Venus would be 400C+ with ANY gas sitting there at 90 atmosphere at that distance from the Sun”

      Spot on!!! density of the atmosphere makes the biggest difference.

      2] because of the proximity to the sun – 53% of Venus is under permanent sunlight / 47% is not – that’s 6% more. on the earth is 50/50

      3] on Venus both polar caps are under PERMANENT sunlight – because of proximity to the sun – simple geometry.
      .

      • Clive Best says:

        On Venus 90% of solar energy is absorbed by the atmosphere and not by the surface. There are thick sulphuric acid clouds. However the very dense atmosphere means that the tropopause is very high above the surface. That is why the GHE is large. The surface heats up until it can convect heat right up through the clouds to the TOA where it can then radiates to space. There are violent winds on Venus.

  5. tallbloke says:

    “The pressure of the atmosphere produces an effect of the same kind: but an effect, which, in the present state of the theory, and from want of observations compared with each other, cannot be exactly defined. Whatever it may be, we cannot doubt that the effect which should be attributed to the impression of the solar rays upon a solid body of very large dimensions, by far surpasses that which would be observed in exposing a common thermometer to the same rays”

    Baron Fourier 1824

  6. DrO says:

    Dear Mr Best:

    It was good of you to illustrate some of issues in this topic, and which are often omitted from a reasonable “critical mass” of details/facts required for a sensible discourse.

    Unfortunately, we haven’t quite reached the critical mass, and some of the suggestions and “conclusions” are false or may only apply in isolation and in pure idealised settings rather far away from reality.

    I offer only a few of the possible remarks, in no particular order:

    1) There are multiple heat sources.
    2) You do not need gravity to have GHG, under some definitions.
    3) It’s not “equilibrium”, it’s “steady state” … a subtle, but crucial difference.
    4) The crucial role of saturation, particular in a “mixed gas” environment.
    5) The trap of “top of the atmosphere” models.
    6) The virtually complete (and fatal) omission of water vapour.
    7) Volcanoes, yes again.
    8) Be careful with HighTran et al (just because it “looks good”, it may not be good)

    1) It is incorrect to assume that the only “heat in” (to the surface) is from the Sun for the CC discussion. There is heat from trillions of tons of molten rock and metal a few kilometres below your feet (somewhere around 7,000 degrees “hot”). It is certainly a lower flux compared to that of the Sun. Nevertheless, it is crucial to this discussion since many CC fanatics soil their trousers over a radiative forcing of 2 – 5 W/m^2, and at those low flux differences, the heat from the planet’s core is significant. That is, the bulk of the GHG hysteria is over small differences in the “heat in – heat out” balance (e.g. the difference and extra 50 – 100 ppm of CO2 may cause), and those small differences are almost surely on a scale comparable to the planet’s source.

    Crucially, the manner in which the core’s heat reaches the surface is non-stationary in time and space, further complicating the story.

    Since these effects cannot be, for all practical purposes, measured/calculated to any reasonable accuracy, the entire heat balance strategy to CC and modelling is, well, “toast”.

    Of course, the entire CC modelling matter is completely and utterly “toast” anyway for a long list of other fundamental reasons, as discussed in Notes 1 – 3 here (http://www.thebajors.com/climategames.htm). Quite simply put, the fundamental properties of cosmos obviate the possibility of CC modelling to the extent the IPCC et al would like to insist.

    … and thus, if you can’t predict, you can’t set (sensible) policy.

    2) I cannot be certain what exactly your definition of “GHG effect” is. It is certainly possible to consider one definition of GHG where your statements are flatly wrong. You certainly DO NOT NEED gravity to have GHG, at least under some definitions.

    For example, if the definition of a GHG effect is anything in the atmosphere that has a significant infra-red cross-section leading to an “insulating” effect partially seen as increase of temperature, then gravity is not required. If you put any insulator between a high temp and low temp, then the heat flux is reduced, leading (in a pure idealised single phase setting) to an increase in temperature. As always, from the laws of Thermodynamics:

    Heat In – Heat Out + Sink/Sources = d/dt of contents = accumulation/depletion.

    If the Heat Out is reduced by the introduction of some insulator, ceteris paribus, temperature will increase to a new “equilibrium” level as measured by the accumulation of heat (the d/dt term).

    If you put on a T-shirt made of cotton, you will warm up a bit. If you put on a T-shirt made of, say, titanium, you will warm less. If you put on a parka, you will warm much more.

    If you put anything in to the atmosphere that “insulates” (and has not been saturated, see below), it will cause an accumulation of heat for a while (until steady stat is reached … not equilibrium, see below), and which may in part be seen as higher temperatures (it could be seen also as increased humidity, and many other types of changes that accumulate/store heat. see below).

    As such, by this definition of “GHG effect”, gravity is not required.

    The presence of gravity certainly increases the complexity of the process. In addition to vertical transport that you cite, there are many other convection patterns/forces such as the Coriolis effect, jet-streams, etc. The patterns are further complicated by winds and the interaction of wind with land masses, etc etc Indeed, the existence of gravity, and especially its manifestations on this planet, almost surely cause changes in the “In – Out” to come to steady state (not equilibrium, see below) much faster compared to without gravity.

    3) Although it may sound at first picayune, there is a subtle but crucial difference between equilibrium and steady state. Dynamical systems cannot, usually, achieve equilibrium. Typically, the most one can hope for is steady state. For example, a half full sealed beaker of water in you laboratory at constant temperature will achieve an equilibrium internally (eventually) in terms of the amount of water vapour in the top half of the beaker.

    By contrast, if you place a small infra-red lamp (putting out constant rate of heat) in your refrigerator, then the flow of refrigerant in the heat exchanger on the back of your refrigerator may be able to compensate and take exactly that amount of heat per unit time. The temperature in the refrigerator “stabilises”. If that happens, you have reached a steady state, not an equilibrium.

    In the context of the planet’s climate, it is (more or less) meaningless to speak of equilibria.

    This is more than semantics. There are your amount of blogs etc where attempts to cite some idealised laboratory process (which may well achieve equilibrium) as an explanation of climate issues, where in the real climate (for the most part) no equilibria are possible.

    This is a deadly trap. The laboratory bits may very well be as described, but the “leap of faith” that the idealised laboratory (or theoretical) process is what is happening in the (real) atmosphere is highly suspect, and in many case flatly wrong (even when the “lab explanation” is provided correctly, though even that is often not the case).

    Moreover, the mathematical modelling of “equilibria” process is generally very different from that of steady state process. Amongst other things, the steady processes can exhibit much more complex mechanisms, and which often have a fundamental unstable character to them. Unstable problems are quite often intractable, and hence the models (and thus the predictions) are meaningless in those cases.

    In short, relying on an incomplete collection of factors based on pure idealised laboratory or theoretical considerations is very easily abused by those with a non-science agenda, and easily confound those with good intentions.

    4) It was good of you to (at least) cite the notion of spectral saturation in your considerations. Unfortunately, in the context of CC fanaticism, this point is generally NOT covered with sufficient depth or reality, and it is CRUCIAL to this story.

    This issue is crucial not only in the context of an idealised single gas atmosphere, but also particularly crucial in the context of mixed-gas atmospheres.

    First: pure idealised saturation. For simplicity, assume you are in satellite above a planet with a pure CO2 atmosphere. Assume further that CO2 has just one absorption at 14 – 16 um (what you refer to as 15 um, and this is quite a good assumption for a variety of reasons I can explain another time, or see around page 46 of Note 2 here http://www.thebajors.com/climategames.htm). Assume the Sun is the only and constant source of heat. Then, there will be finite and constant amount of energy radiated by the planet in the 14 – 16 um range. If there is a certain special minimum level of CO2 density that allows capture of all that (finite) amount of energy leaving the planet in the 14-16 um range, then the satellite’s spectral analysis will show no energy leaving the planet seen as a portion of the spectral band as a complete “blank” in the energy spectra at 14 – 16 um. This is saturation.

    A bit like the partial saturation in your charts.

    This special minimum level of CO2 will require a sufficient number of CO2 molecules to capture all (or nearly all) the (finite) 14 – 16 um energy.

    CRUCIALLY, at this point, it makes no difference whatsoever to the planet’s GHG concerns if more CO2 is added to the atmosphere. For example, if saturation occurs at the equivalent of 400 ppm, then increasing CO2 to 600 ppm will make NO difference to the GHG effect.

    What will actually happen is that finite amount of radiated energy in the 14 – 16 um range will simply be distributed over a larger number of molecules. There is only a FINITE amount of energy, and once all of that is absorbed, adding more CO2 makes no difference whatsoever (in GHG temperature terms).

    This is ensured by the most basic laws of physics/thermodynamics.

    … if it did make a difference, you would have created a perpetual motion machine, and immediately solved the planet’s energy needs forever.

    As such, performing “impressive looking” theoretical calculations at 600 ppm or 800 ppm etc etc is meaningless if saturation, or very nearly, has already been achieved.

    If we actually look at REAL data (not some theoretical construct), such as from satellite spectral analysis, what we see is that the 14 – 16 um band is around 98% saturated. Forty or so years ago, the satellite data showed perhaps 96-97% saturation. So, yes, this is evidence for the possibility of “some” (see water vapour below) GHG effect.. However, it is a very small effect, and is very nearly saturated so not much more can happen here (see around page 46 of Note 2 here http://www.thebajors.com/climategames.htm).

    All the main-stream rhetoric about 600 ppm or CO2 doubling fear mongering is just that. Indeed, the fear mongering is further dealt a death blow when the real world mixed gas atmosphere is considered.

    Second: mixed gas atmosphere. Take the same assumptions as above, but now the planet’s atmosphere is composed of CO2 and water vapour (WV). CRUCIALLY, the absorption bands for WV give it an infra-red cross-section about 15 times bigger compared to CO2’s. That is, molecule for molecule, WV is capable of absorbing 15 times more energy.

    Even MORE crucial to the CC hysteria is that WV’s absorption bands overlap with CO2’s. For example, WV has an absorption band around the 14 – 16 um range.

    Thus, for example, sitting in your satellite, if the 14 – 16 um band is completely or nearly saturated, is it because of CO2, or because of WV, or some combination? Almost surely it is the combination, but then how do we decouple the individual effects?

    NOTICE that now saturation of the 14 – 16 um range can occur purely due to an increase in WV, even if there is CO2 around. Thus, is the apparent GHG effect in the satellite data cited above could be dominated by WV effects, rather than CO2 effects …. without further information, it is irresponsible to point to CO2 and CO2 alone.

    While we know CO2 concentration has been on the rise, we also know that WV has been on the rise ALSO (from real data, not theoretical/laboratory constructs).

    As such, without further information, we CANNOT say that CO2 is the ONLY or for that matter main culprit.

    Of course, the UN/IPCC must insist that it’s CO2 and CO2 alone, since that is the only way they can pretend that the rich countries are at fault, and so must pay up.

    Bizarrely, even the IPCC reports admit (in tiny print, hidden amongst the jumble) that WV’s contribution to GHG warming is on the order 4 times more important compared to CO2’s contribution … HOW COME THAT DOESN’T MAKE THE HEADLINES?

    Even by the IPCC’s “own interpretation”, if CO2 increases by about 15%, while during the same period WV increase by about 10%, a “back of the envelope order of magnitude” calculation implies that (even with the IPCC’s low-balled values) the planet’s warming in this period was proportional to 4*10% from WV vs. 1*15% from CO2.

    Clearly WV is much more important in every important respect.

    … and we don’t even know how much of that CO2 increase was man-made vs. natural, etc. etc.

    … and in any case, those bands are either fully or nearly saturated, so adding more makes (almost) no difference to this aspect of the story.

    5) The trap of “top of the atmosphere” models: It is understandable why so many are attempting to contort the climate problem into a “top of the atmosphere” (ToA) model. That is, a model that some how reduces the massive complexity of the atmosphere and its dynamics to a model where we can somehow imagine there is finite, more or less homogenous, layer/skin, and all the radiation leaving the planet happens at that ToA altitude/skin boundary.

    Indeed, if we could come up with “model” that treats the atmosphere like a “continuously stirred tank reactor” (a common concept used to create energy balances in engineering), then we would have a (very) much simpler model, and perhaps one that we could even solve.

    Of course, whatever model that would be would have very little to do with the real world, since it requires so many simplifying assumptions as to have thrown out a huge number of critical influences.

    Crucially, some of those influences are fundamentally unstable phenomenon, which quite often do not have the possibility of any practical solution.

    Moreover, the huge number of “fiddles” in ToA models allow all manner of abuses to allow anyone to “prove anything”.

    For example, some ToA’s take an altitude around 50k – 70k feet (say 20 – 25 km). At those altitudes, density is low, and (depending on the exact altitude, see below) temperatures can be quite low. Some then argue that WV cannot exist to any appreciable extent at the ToA, and thus CO2 controls planet’s radiation.

    This is NOT science, it is purely a fiddle to come up with (dare I say it) a plausible sounding proposition backing the CO2 story, and generally used by the IPCC/UN’ types to further an ideological agenda (not science).

    In fact even a small change to the “fiddles” in those suggestions/stories substantially alters the ToA and its implications.

    Other fiddles can put the ToA much lower, where there is substantial WV, very much defeating the “CO2 and CO2 alone” ToA fiddle.

    MOREOVER, although somewhat counterintuitive, while temperature does drop with altitude (at least initially), it does so in a complex manner. Between 30 km and 50 km the temperature can be as low as the -50’s, but in some special places massively warmer at around +10’s. Yes, it is very cold outside your jet airliner at 10km, but go up another 20 + km, and it might be +10 outside (see page 54 of Note 2 here http://www.thebajors.com/climategames.htm).

    Just this one item is critical in the ability to manipulate ToA stories. For example, since radiative heat transfer is proportional to temperature to the power of 3 – 4 (i.e. T^3 to T^4 depending the grey body/black body etc), a tiny change in temperature results with a massive change in the heat flux. Thus, if a ToA story manipulates the facts to imply a ToA where temperature is -50, while another ToA story insists on an altitude where the temperature is +10, those two “models” will produce massively different results (and likely both are wrong).

    Though, of course, ToA approaches lend themselves well to those who don’t mind manipulating science for their agenda.

    As such, any discussions where any of the steps rely on things similar to ToA arguments are highly suspect. At the very least, all the many caveats of attempting to shoehorn the massively complex climate system into a near trivially simple “climate model” should be screamed at the audience.

    6) The virtually complete (and fatal) omission of water vapour.

    A man is wearing a T-shirt underneath a parka, and is complaining he is too hot. However, all the details of his complaints seem to revolve around the T-shirt. Surely, some considerations should be given to the parka. So it is with GHG’s. WV is the parka, CO2 is the T-shirt.

    The earlier data and discussion already (in part 4) above) demonstrated the absolutely crucial and dominant role of WV in spectral/GHG considerations, and that it is massively more important to the contribution of warming of the planet compared to CO2. Moreover, even though it is difficult to decompose the near-saturation of the bands, the bands are nearly saturated so an increase in WV or CO2 (or methane, etc) or both (all), will not have much affect.

    However, the role WV contributes very considerably greater complexity to the issues at hand. For example, the real world data shows WV has been steadily increasing. Roughly speaking, this means that the hydrological cycle is in imbalance. That is, more water is evaporating compared to the amount precipitating. The latent heat of evaporation of water is roughly 1,000 times greater compared to the energy required to change the temperature of water by 1 degree. Put differently, huge amounts of energy are required to evaporate water compared to heating water. Energy used for evaporating water is not used for heating water. When WV precipitates it “gives back” that latent heat (more or less). Thus, if the amount evaporating is about the same as that precipitating, then the net energy in the hydrological cycle is close to zero. Since WV is on the rise, it implies an imbalance in the cycle, and thus implies an energy imbalance with increasing energy stored in the increasing amounts of WV.

    As such, if there is an energy imbalance of the planet, it is possible to accumulate energy without seeing any (or much) temperature change. As usual, we write:

    Heat In – Heat Out + sink/source = d/dt of contents (change in temp).

    If the In energy, say from the Sun, is greater compared to the Out (say from radiation), that would imply a change (i.e. non-zero d/dt) and would imply an increase in temperature. However, if the Sink/Source represents energy consumed, say, to evaporate water, then even if In > Out, we can have d/dt = 0 (or nearly) if the Sink (e.g. evaporation) is consuming the In – Out difference.

    Your putting more money into your bank account compared to what you withdraw, so you would expect your balance to increase. However, if the bank takes fees (a Sink), your balance could be flat or even go down, in spite of your efforts to save.

    As such, the omission of WV from the story and modelling is a fatal flaw, and its omission must necessarily create fatally flawed models.

    Of course, these effect of WV and other factors are just too complicated to include faithfully in the models. In any case, they are often fundamentally unstable, so even if you managed to include these in your models, you could NOT make any practical use of the models.

    In addition, and for good science, one must establish the “embedding dimension” and factors affecting the process. The “Coffee vs. Health” study discussion around page 62 of Note 2 here http://www.thebajors.com/climategames.htm) demonstrates how one can “prove” utter rubbish by ignoring the dimensionality of the problem. In particular, ignoring the role (dimension) of smoking in the coffee study is like ignoring WV in climate science.

    It is hard to see how any reasonable consideration of the effect of gravity on the climate could omit the hydrological cycle and various other phenomenon.

    7) Volcanoes, yes again.

    I have already shown that anyone, even those without any mathematical training, can use the volcanoes with the IPCC’s own data to prove conclusively the utter and necessary impossibility of any practical climate modelling (see Note 2 here http://www.thebajors.com/climategames.htm)

    However, in the context of this “gravity” discussion, can we omit volcanoes from the story. For example, the last 100 years saw only about 4 medium sized volcanoes (and many smaller ones). By contrast, the 1800’s saw two large volcanoes (and many smaller ones). The temperature records show that for years at the time (following large volcanoes) the planet was effectively an ice-ball (e.g. snow/frost in Aug in NY and Florida etc, for years).

    As such, whatever absorption GHG effects we consider, surely the frequency and intensity of volcanoes must figure into the equations.

    Would we be having any of these discussions had there been a Tambora type volcano, say, in the 1990’s?

    8) Be careful with HighTran et al. One of the potentially biggest problems in climate matters is the “impressive looking” calculations one can perform with ease. Unfortunately, that can work against the greater good of science. What one must really ask is what do those calculations mean?

    The case of HighTran and many other models/calculators/databases are in a sense the worse case scenario for “truth”, since they aim to encompass a very high degree of detail and complexity, but may not do a particular good job in terms of the reliability/usefulness of the results, as impressive looking as they are.

    The calculation of spectral absorptions is a very tricky matter. A few points to illustrate some difficulties:

    a) The actual mathematics for the “core” calculation do not resolve to closed form solutions, and so generally, computational methods are required (basically we need to integrate one or more equations by approximations). Unfortunately, due to idiosyncratic nature of these integrations, small changes in parameters of computational settings (e.g. discretisation choices etc), can make a substantial difference to the answer.

    In general, even to get to the “right ball park” answer, the integrations must be on a high resolution requiring massive computational effort (many hours on supercomputers etc.).

    Remember, since the entire “sky is falling” GHG discussion revolves around very small differences in the net “In – Out” (e.g. 2 – 5 W/m^2), the errors in the spectral integrations can be sufficiently large to compete with those scales.

    At the very least, some idea of the scale of those errors (or possibility of those errors) should be included somewhere (a bit like error bars).

    b) In addition, the integrations rely on large databases and other methods in an attempt to parameterise many inputs. For example, absorption properties of the calculation depended on concentrations of different compounds, temperature, pressures, etc. Those parameterisations have non-linearities and often are incomplete. As such, even many many hours on a supercomputer running super high resolution integrations may result in unreliable answers due to such “missing physics” issues.

    In short, it is all well good to download an impressive calculator and drive it around the block a few times, but very great care is required in assessing the true meaning/reliability of the results.

    … and of course that is aside from the bigger picture issues of a world with mixed gas saturated spectra, imbalances in the hydrological cycle, volcanoes, …. the list goes on.

    • Clive Best says:

      “It’s not “equilibrium”, it’s “steady state” … a subtle, but crucial difference.” I agree with that statement.

      “6) The virtually complete (and fatal) omission of water vapour.” I deliberately wanted to avoid the complications on earth of water vapour. H2O is the main driver of earth’s climate. Latent Heat transport is more important than convection of earth – especially in the tropics.

      Plate tectonics and volcanoes recycle carbon and minerals like phosphorus buried 10s of millions of years ago. Life would run out of the raw materials for photosynthesis without plate tectonics. So yes its role is fundamental to earth’s long term climate.

      2) I define GHE as the increase of average surface temperature above Teff. So on earth it is about 33 C. On Mars it is about 5C. However for the purpose of this discussion I wanted to concentrate just on the radiative effects of CO2.

      3) I agree with your statement on steady states. The climate is not in equilibrium and can change to a new steady state if any component changes.

      4) Your discussion here is very interest. Untangling H2O from CO2 is fraught with difficulty. Of course IPCC will argue that H2O is a feedback to CO2 even though it has 5-10 times the effect. The saturation argument depends on the height at which CO2 15 micron photons escape to space. The central line is already saturated up into the stratosphere. An increase in CO2 for this line will actually warming the planet. The ‘warming’ effect depends on the side lines of the 15 micron band whose emission height in the atmosphere is low – 1000m or so. However these lines have a very low cross-section so there increase is very weak. This results in a logarithmic dependence. If you ignore H2O then even increasing the CO2 content on earth to 100% would only warm the surface by about 5C !

      5) Tend to agree with you.

      6) Yes the surface loses 4 times more energy through evaporation than through convection. In the tropics vast convection clouds and thunderstorms dump energy up to the top of the troposphere where it radiates to space by H2O and to a much lesser extent CO2. Hadley cells move energy polewards cooling all the time by radiation to space.

      7) Volcanoes and aerosols in general ( natural and anthropogenic) are fine tuned by climate models to fit the past data – hindcasting. So for example we have heard one excuse for the pause in warming as being due to pollution in China – coal is to blame. I agree with your other points.

      8) Radiative transfer calculations are a bit of a bootstrap process. To get an answer you have to assume a standard atmospheric temperature profile. Standard American Atmosphere or something. This has a built in lapse rate. You then run the calculation to quantify how much radiative energy moves from one level to another. If you now increase the concentration of CO2 or H2O you get a new result which you interpret as an increase in forcing. However this new configuration would also change the temperature profile and this is ignored. If the lapse rate decreases then you over-estimate the radiative forcing.

      More H2O should produce more clouds which decrease albedo and offset forcing etc. etc.

      It is immensely complicated !

      • Kristian says:

        Clive Best says, December 1, 2014 at 11:05 am:

        “2) I define GHE as the increase of average surface temperature above Teff. So on earth it is about 33 C. On Mars it is about 5C. However for the purpose of this discussion I wanted to concentrate just on the radiative effects of CO2.”

        This is a veeery general definition. I think everyone and anyone would agree that having an atmosphere on top of a solar-heated planetary surface would tend to increase the mean temperature of that surface above its pure radiative equilibrium temperature with its heat source. That the atmosphere simply INSULATES the surface. It is hard to deny such an effect. All you need to do is compare the Moon and the Earth.

        But wouldn’t you then agree that there is nothing in this definition itself that points out any particular MECHANISM through which the atmosphere forces the mean temp of the solar-heated planetary surface to rise above the planet’s BB emission temp in space. And that the effect as such should simply be called ‘The Atmospheric Effect’ (or, a bit more specific, ‘The Atmospheric Insulating Effect’).

        It is but ONE suggestion that this ‘Atmospheric Insulating Effect’ has anything to do with the atmospheric content of radiatively active gases (so-called ‘GHGs’).

        Another suggestion is that the atmosphere simply acts like regular (conductive/evaporative/convective) insulation, by slowing down the transfer of heat from the solar-heated surface to the top of the atmosphere (basically the tropopause) and out of the system through its MASS ‘being in the way’ (the atmosphere being massive means it has a ‘heat capacity’, it is able to warm (space isn’t), hence a finite (sub-max) temperature gradient for the movement of energy away from the solar-heated surface is set up; it also means it gains a ‘weight’ (total mass times the gravitational pull), thus providing the air that is to be lifted with a certain ‘heaviness’ (‘slowness’), plus it makes it exert a certain pressure on the surface (space doesn’t), a downward force that suppresses evaporation at a certain temperature).

        In this perspective, the radiatively active gases aid in the heat’s both entering and leaving the atmosphere, while it is the sludginess of convection (the movement of air) that creates the delay, that is actually doing the insulation. The radiation is doing its utmost at all times to get the energy up and away from the surface and out to space, by heating the surface and cooling aloft, thus inceasing the temperature gradient, provoking convective cooling.

  7. Kristian says:

    Clive, you say:

    “Radiative transfer of surface heat through the atmosphere tries to steepen the lapse rate towards radiative equilibrium. This instability drives convection (and evaporation on earth) resulting in the approximately observed adiabatic lapse rate.”

    and

    “Convection is induced by Radiative transfer of heat through the atmosphere”

    This is the classic AGW way of seeing things. Not how reality works.

    Energy is transferred as heat from the surface air layer to the tropopause and from the tropics to the poles – that is, inside the troposphere – by way of bulk air movement (convection/advection), not by radiative (or conductive) transfer. Radiation and conduction both transfer surface energy as heat to the lowermost layers of the troposphere, but from the point of absorption, convection takes over. Yes, there is both radiation and conduction going on inside the troposphere as well. But these two mechanisms are not themselves able to generate separate internal ‘transfers’ of energy as heat. The energy is moved and distributed (from the heating end to the cooling end) with the air.

    The radiative-convective equilibrium establishing the observed (environmental) lapse rate to correlate with the quasi-adiabatic one (on the continuum between dry and saturated) is rather accomplished thus:

    – The Sun heats the surface by incoming radiation.
    – The radiatively active gases in the atmosphere (the so-called ‘GHGs’) cool the air masses aloft to space by outgoing radiation.

    THESE continuous radiative processes are what tries to steepen the ELR beyond the ALR, so that convection is initiated to bring it back down.

    Radiative processes do not move heat inside the troposphere, thus inducing convection. Convection is what moves the heat inside the troposphere. The radiative processes rather operate at each end (heating down low (or equatorward), cooling up high (or poleward)). In between, the energy is moved by mass transfer (convection).

    The main role of the so-called ‘GHGs’ in the atmosphere is to let the energy transferred from the solar-heated surface into the massive atmosphere above escape back out to space, thus letting it cool radiatively.

    • Clive Best says:

      Energy is transferred as heat from the surface air layer to the tropopause and from the tropics to the poles – that is, inside the troposphere – by way of bulk air movement (convection/advection), not by radiative (or conductive) transfer.

      That is correct, but this only can occur because the heat can radiateto space high up ion the troposphere. The Hadley cells move tropical heat polewards high up in the troposphere where they cool by mainly by H2O and CO2 molecules radiating directly to space. If somehow you could switch convection off then the lapse rate would be much steeper. One way to do that would be to consider a neutron star with such a high g-force that convection is impossible. The star radiates to space.

  8. millennia97 says:

    Seconded – that was never typed in real time 😉

  9. wayne says:

    Clive, aren’t you just saying that over time that convection would stall if there no l.w. loss at the top end? That is an isopycnal atmosphere that you never hear mentioned, equal density from the top to the bottom even though the pressure and temperature would still have small gradients.

    I very generally agree with your conclusions but the exact wording is so critical to prevent some pretty wild ideas to sproat wings that always cloud understanding.

    Point (4) needs some addtions. Add slow conduction, especially at the surface in direct contact with atmosphere. And what of any state changes like on Earth (water), Venus (sulfur compounds), Titan (methane)? Those also add heat that causes further convection (density differences).

    • Clive Best says:

      Yes exactly. Convection would stall if energy was not being radiated from the top end to space. That is exactly what happens in large thunderstorms forming anvil clouds at the tropopause. The convection stalls and the cloud spreads out horizontally. Cirrus clouds are the wispy remains of thunderstorms.

      I agree that on Venus the atmosphere itself absorbs energy from the sun complicating matters.

  10. Bryan says:

    I think you exaggerate the effect of the radiative properties of CO2 in sustaining convection.

    We agree that the Sun heats the Earth surface.

    The actual temperature of the surface reached at any local area at any particular time depends on several things principally:

    1. The nature of the surface for example water can evaporate and so on
    2. The intensity of Sun’s radiation at the local area
    3. The reflective nature of the local area
    4. The heat capacity of the surface layer
    5 The temperature of the air above the local area

    A land sea interface is a good example of local wind production quite independent of CO2.
    So local winds and regional winds are set up which constantly mix the atmosphere.

    Polar wind masses have recently brought sub zero temperatures to every state in the USA.
    While recently Britain has comparatively mild weather because of warm winds from the south

    Maxwell put it like this

    “The extreme slowness of the conduction of heat in air, compared with the rapidity with which large masses of air are carried from one height to another by the winds, causes the temperature of the different strata of the atmosphere to depend far more on this condition of convective equilibrium than on true thermal equilibrium.”

    Air increases in pressure as the altitude decreases.
    Air is compressible and so forces an increase in density.
    Earth surface is generally warmer than the air above it particularly during daytime
    Warmer air from contact with surface will naturally rise up from buoyancy considerations.
    The CO2 fraction of the air will thermalise certain radiation of suitable wavelengths but this process must be a minor effect .
    As higher altitudes more radiation will escape to space and this cooling effect is the real contribution CO2 makes to our atmosphere

    • Clive Best says:

      The CO2 fraction of the air will thermalise certain radiation of suitable wavelengths but this process must be a minor effect .

      It is a minor effect in the lower atmosphere because the surface cools much more efficiently through convection and latent heat.

      As higher altitudes more radiation will escape to space and this cooling effect is the real contribution CO2 makes to our atmosphere

      This is the key point. Convection is a heat engine powered by the difference in temperature between the hot surface and the cold tropopause. It is maintained by radiative heat loss from the top. It is a bit like a cooling tower at a power station except that radiation is emitted and not steam.

      • millennia97 says:

        “It is maintained by radiative heat loss from the top. It is a bit like a cooling tower at a power station except that radiation is emitted and not steam.”

        God I hate being pedantic but it’s a pet hate of mine. All that comes out of a cooling tower, or any other chimney, is water vapour, not steam. Steam is a colourless gas in excess of 100C and I know of no atmospheric process that can allow it to exist at the normal range of temperatures – even a surface at 90C will just be throwing off water vapour.

        Anyway, I know it’s become a figure of speech but I wish in topics as important as this one that such a fundamental misuse of a word wasn’t made at all.

        • Clive Best says:

          I thought it was that dangerous CO2 stuff being emitted from cooling towers ! At least that’s what Roger Harrabin and the Guardian tell me .

        • Tony Price says:

          Water vapour is the invisible gaseous form of water, alternately referred to as steam. In common parlance, the mist of condensed water vapour which IS visible is referred to as steam. Clive was right in the use of the term. If you can see it it ain’t water vapour.

  11. New post explains and calculates why a 100% N2 atmosphere would convect, have almost the same and probably higher lapse rate (thus warmer at surface), and almost the same height at the center of mass where Te=255K is located and sets the lapse rate.

    http://hockeyschtick.blogspot.com/2014/11/why-greenhouse-gases-dont-affect.html

    The reason why N2 atmosphere would be warmer is WV increases Cp, which lowers LR to cause cooling on Earth.

    • Kristian says:

      The tropospheric lapse rate constitutes the temperature gradient away from the solar-heated surface. The steeper such a gradient, the more effective the convective cooling of the surface. And vice versa. Therefore, if you somehow force the gradient to become less steep, you will hamper convective uplift and thus force the surface to warm to restore balance. Suppress convective cooling and you get warming. Just look at how a solar pond works. Or a greenhouse.

      • Kristian says:

        The so-called ‘GHGs’ in the atmosphere do not work toward reducing the environmental lapse rate (ELR). They work toward increasing it. Convection is the mechanism working towards reducing it – in bringing it (the ELR) back down to the gravity-based ALR.

        Convection is the mechanism that brings the surface heat through mass transfer from down low to up high, thus reducing the temp gradient. Radiation simply heats low (solar surface heating) and cools high (‘GHG’ radiative cooling of air masses to space).

      • “the steeper the gradient, the more effective the cooling of the surface”

        The greenhouse gas water vapor does have a very large negative-feedback cooling effect on the surface and atmospheric temperature by reducing the lapse rate by half from the 10C/km dry rate to the 5C/km wet rate. Increased water vapor increases the heat capacity of the atmosphere Cp, which is inversely related to temperature by the lapse rate equation above:

        dT/dh = -g/Cp

        Using formula for Ts = Te + -g/C(p) × (h – h°) where h=0 at surface, h° = height at center of mass/ERL/where T=Te=-18 at ~5.1km

        Ts = -18 – (10 × (0 – 5.1)) = 33C using dry adiabatic lapse rate

        Ts = -18 – (5 × (0 – 5.1)) = 7.5C using wet adiabatic lapse rate [fully saturated]

        showing a cooling effect of up to 25.5C just from changes in the lapse rate from water vapor. Water vapor also cools the planet via evaporation and clouds, and which is confirmed by observations. Water vapor is thus proven by observations and theory to be a strong negative-feedback cooling agent, not a positive-feedback warming agent as assumed by the overheated climate models to amplify warming projections by a factor of 3-5 times.

        • Kristian says:

          Hockey Schtick says, December 1, 2014 at 6:46 pm:

          “The greenhouse gas water vapor does have a very large negative-feedback cooling effect on the surface and atmospheric temperature by reducing the lapse rate by half from the 10C/km dry rate to the 5C/km wet rate.”

          No, because this assumes that the surface is lapse-rate heated from above. This is pure rGHE/AGW nonsense. Don’t buy into it. It turns reality exactly on its head. So you want to fix the ERL altitude/temperature and extrapolate a water-reduced lapse rate DOWN to the surface from this level to get cooling. I’m sorry, nature doesn’t operate like that.

          The surface temperature is the baseline for the tropospheric temperature profile. You need to know the surface temperature FIRST and then the lapse rate to define the temperature of each layer of atmosphere up to the tropopause. The lapse rate, the temperature profile, climbs UP from the surface temperature, not DOWN from some mathematically derived BB surface temp.

          I wish people started to open their eyes to this basic and very simple fact.

          The temperature of a planetary surface is set by the final compromise of the incoming flux from its star and the difficulties with which the absorbed energy is able to escape back out again. The heavier the atmosphere, the harder time it will have, and the higher the steady state temperature will have to be, for the surface to maintain balance between heat IN and OUT.

          This is all a matter of atmospheric mass and gravity, yes. But it has to do with how much of a physical hindrance the atmosphere turns out to be for the energy escaping the surface after absorption. As much energy needs to leave the surface per unit of time as comes in for the surface to stay in dynamic equilibrium. The energy moves away from the surface by way of convective/evaporative uplift. The mass/weight/density of the atmosphere put constraints on the speed of this moving away process … at a particular mean temperature. This mean temperature thus has to go up (by accumulation of incoming solar energy – cannot escape as fast as it comes in during warming) until the balance point is reached.

  12. “No, because this assumes that the surface is lapse-rate heated from above.”

    Does not make such an assumption. Of course convection of warm air drives the lapse rate, but an equal and opposite amount of cold air has to descend/compress/heat up along the exact same lapse rate, which reflects the balance between the rising/expanding/cooling air packets and the falling/compressing/heating air packets.

    This continuous rising/expanding/cooling process has to balance with the falling/compressing/warming process and both of these balanced processes together set the same lapse rate up and down – i.e. the T rises on the way down and vice versa (at a given time/location, but global ave 6.5K/km up AND down).

    So, you think it’s just a complete coincidence that the temperature at the center of mass of both Earth and Titan is located exactly at the equilibrium temperature with the Sun, right? And you think increased GHGs have changed that exact point over the past 39 years since the 1976 Standard Atmosphere database, correct? And thus you think my equation that calculates the 1976 Standard Atmosphere database at every meter from 0-12000 based only on the center of mass at Patm/2 pressure and Te exclusively, without any GHG forcing whatsoever, is just one big coincidence, right?

  13. Clive Best commented on stefanthedenier: ”There are violent winds on Venus”

    Clive, that’s very interesting. Because 3 factors say that ”shouldn’t be any strong winds on Venus”

    1] the day is 4 months long, so is night – no constant change of temp as on earth, to create winds
    2] no oceans / land; to have different speed of warming / cooling, to create winds
    3] polar caps there are permanently illuminated -> less difference in temp with the equator – on the earth, when air extra cools on a polar cap -> shrinks and earth’s centrifugal force puls it to warmer climates and creates strong winds / not on Venus.

    Is it possible that: everything is rigged on Venus – to fit the occasion? In Wikipedia everything is rigged, where CO2 or ”greenhouse” is mentioned.
    I’m trying for last two months to contact a person that was part of sending satellites to Venus in 80’s from Russia, to get the truth from him. At that time politics was propaganda, because of the cold war, but science was science – now science is pure propaganda…
    Clive, thanks for informing me!

  14. Kristian says:

    Hockey Schtick says. December 2, 2014 at 5:16 am:

    “So, you think it’s just a complete coincidence that the temperature at the center of mass of both Earth and Titan is located exactly at the equilibrium temperature with the Sun, right?”

    Why wouldn’t it be? It only (sort of) works on Earth and Titan, two planets that happen to have atmospheres of similar weight. And only sort of. There is no exact match. The ‘match’ is approximate. The centre of atmospheric mass on Earth is at 5.7 km, not at 5.1. That is 4 degrees off an exact match. On Titan, the centre of atmospheric mass is at 13 km, the ERL (which doesn’t exist as a single temperature layer, which is only a mathematical construct, a chimaera, HS!) is at 11.25 km (84K) or 14.72 km (80.6K).

    I’m afraid you can get nowhere with this as long as you accept the ridiculous rGHE/AGW concept of the ERL plus the equally ridiculous rGHE/AGW notion that the lapse rate somehow warms the surface from such an imaginary layer DOWN.

    The world doesn’t work this way. It should be blindingly obvious.

    “And you think increased GHGs have changed that exact point over the past 39 years since the 1976 Standard Atmosphere database, correct?”

    I believe no such thing. There is no such ‘point’. The Earth system gives off a final LW flux to space to balance the absorbed incoming flux from the Sun. This outgoing flux doesn’t come from ONE specific temperature layer. The temperature of any layer inside the Earth system has no connection whatsoever with this total flux. It is accumulated from ALL layers, from the surface to the ToA. There is no connection. The ERL is only a mathematical construct based on that total flux (239 W/m^2). If you put that flux into the Stefan-Boltzmann equation and assume that it is emitted from one solid BB surface, then that surface would be at 255K. That’s it. There exists no such surface in the real world.

    “This continuous rising/expanding/cooling process has to balance with the falling/compressing/warming process and both of these balanced processes together set the same lapse rate up and down – i.e. the T rises on the way down and vice versa (at a given time/location, but global ave 6.5K/km up AND down).”

    No heat is brought either up or down the atmospheric column by the expansion and compression of rising/sinking air. That’s just the adiabatic process. The heat is only brought up, originally transferred through conduction, radiation and evaporation from the surface to the surface air layers, then brought up by convection, and finally radiated to space aloft in the troposphere, mostly by H2O (WV + clouds).

  15. Bryan says:

    Clive says

    “There would initially be convection and conduction through inert gases until the atmosphere reached thermal equilibrium. This would basically equal the initial surface temperature. Gravity maintains for ever a pressure gradient but it cannot maintain a temperature gradient indefinitely. Otherwise where would the heat escape to space?”

    Stop and think for a moment

    The speculation that in the absence of IR active gases the atmosphere would be isothermal is just an assertion.

    The surface would still radiate directly to space keeping the Earth cool.

    Lets see what your non radiating atmosphere does now?

    Let the isothermal atmosphere be 30C (say) or you can supply your own figure.

    3. The Suns radiation will now be more intense at the surface (without a radiative absorbing atmosphere reducing Suns inward rays) so the surface is now like the Moon.

    Now the Moons Sun facing equator reaches 120C and the night time surface approaches -270C.

    What you are saying is the atmosphere will stick at 30C at all heights and latitudes seemingly ignoring the cosine falloff from equator to poles !

    The atmosphere is in contact with the surface and conduction and the boundary atmosphere will take on the characteristic temperature after collision with the surface.
    There is still a massive buoyancy effect causing convective turbulence on a local ,regional and continental scale.

    The Barometric Equations uses The Ideal Gas Laws and the Laws of Thermodynamics to determine the lapse rate.

    No involvement of IR gases is necessary.

    All that is required is an energy source(the Sun) to supply the thermal energy.
    If there is no Sun then there will be no atmosphere

    Gravity does not create any thermal energy rather it sets up the hydrostatic equilibrium conditions that set up the density and pressure patten.
    But with the Sun and Gravity we will have the usual -g/Cp adiabatic lapse rate for a non IR active atmosphere.

    • Clive Best says:

      I was talking hypothetically about the average surface temperature.

      Yes you are right there would be differential warming of the surface with latitude and diurnal heating. There could be no oceans as otherwise the atmosphere would contain H2O. This would create temperature sharp gradients at the surface which would indeed cause convection cells and strong winds moving heat from hot to cold. During the day there would be strong net heating of the surface followed by strong radiative cooling causing violent day/night temperature swings. However the atmosphere would just move heat around the surface. The temperature averaged over lat,lon and day/night would still have to be Teff.

      The adiabatic lapse rate is a thermodynamic property of all atmospheres on all planets -g/Cp It represents a perfect balance between buoancy and gravity. If the atmosphere contains greenhouse gases then heat escapes to space from the top of the atmosphere and a lapse rate can be maintained indefinitely. Without greenhouse gases I suspect the following would happen:

      After sunrise there would be strong convection as the surface heats up quickly. This generates a lapse rate. After midday the insolation falls and convection stops. Towards evening upper air starts descending downwards inverting the lapse rate as the surface cools rapidly. By nightfall there is a strong temperature inversion which keeps the surface warmer than on the moon. By 2am the atmosphere becomes isothermal again. The whole process then repeats itself daily.

  16. Pierre-Normand says:

    Hi Clive,

    I posted a couple more comments regarding your brain tease at Climate Etc.

  17. Frank says:

    Clive: I prefer to examine the GHE using the Schwarzschild eqn, written for a single wavelength and explicitly showing which variables vary with altitude (z).

    dI(z)/dz = n(z) * o * [ B{lamba,T(z)} – I(z) ]

    The GHE can be qualitatively understood by examining this equation (but it must be numerically integrated over a path from the surface to space and over all wavelengths to produce quantitative information). The intensity of upward radiation will increase with altitude when B{lamba,T(z)} – I(z) is greater than zero and decrease with altitude when B{lamba,T(z)} – I(z) is less than zero. In an atmosphere where temperature decreases with altitude, B{lamba,T(z)} – I(z) is usually less than zero, so outward radiation will decrease with altitude. In the latter case, increasing n(z), the density of GHGs at altitude z, will magnify this decrease – producing what is commonly called the GHE: More GHE = less OLR (instantaneously) = warming until radiative equilibrium is restored.

    From this perspective, the existence of a GHE depends primarily on the presence of a [negative] TEMPERATURE GRADIENT. Such a temperature gradient is USUALLY produced by gravity and the Ideal Gas Law. However, there are cases where the expected negative temperature gradient doesn’t exist in a gravitational field – our stratosphere for example. There is an “anti-GHE” in the stratosphere that is overwhelmed by the normal GHE in the troposphere. I see no reason why one couldn’t “design” an atmosphere where other SWR-absorbing gases could produce a temperature rise with altitude and an anti-GHE. Therefore, at a fundamental level, it may be better to say that the GHE is caused by the temperature gradient, not the gravitational field.

    • clivebest says:

      Frank,

      I can’t fault your logic!

      In fact for the central spectral lines in the 15 micron CO2 absorption band an anti-GHE does operate.

      gravity sets the barymetric pressure gradient and the the equilibrium lapse rate for a convective atmosphere.

  18. DrO says:

    Dear Mr Best:

    Please forgive the EMPHATIC nature of this submission … and allow me to make a request.

    I am not sure, but it seems there is a SERIOUS misunderstanding about what climate models mean/are, and certainly a SERIOUS misunderstanding about IPCC style climate modelling.

    Climate modelling a la IPCC style methods are UTTERLY MEANINGLESS in the context they are used. This is not “opinion”, but rather a fundamental property of the space-time continuum, see below and the cited Notes.

    The Billions of dollars spent on such are all well and good to provide a luxurious welfare state for math geeks … but otherwise a near complete waste of money. Worse, the “results” (such as they are) are used/manipulated to imply that we can actually make forecasts, and hence set policy, when in fact THIS CANNOT POSSIBLY BE TRUE.

    I have tried to provide some insight into this subject, but apparently I may not have done a very good job.

    … in this light, I ASK for your, and for your fellow bloggers’ assistance to let me know which part of FATAL errors I have raised in the IPCC-style methods can be made more clear.

    For instance, how could Note 1 here (http://www.thebajors.com/climategames.htm) be improved to finally put an end to all this climate modelling/prediction rubbish?

    For example, your comment earlier to the effect:

    “7) Volcanoes and aerosols in general ( natural and anthropogenic) are fine tuned by climate models to fit the past data – hindcasting.”

    Forgive me, but this is the type of MEANINGLESS remark that may be interpreted by some to suggest that their models have done “something good”, and as such a step in the wrong direction, since the remark is “promoting” rubbish.

    To illustrate, a statement like that is meaningless for at least two reasons:

    1) You CANT have “hindcasting” (what the rest of the universe calls back-testing), and “fine tuning” at the same time. It is one or the other.

    Back-testing shows whether your model can predict some known data. If it cannot, then your model is buggered, and it’s back to the drawing board.

    “Fine tuning”, in the IPCC sense, is simply another word for curve fitting (or more appropriately, parameter estimation). Here, the idea is to adjust the parameters of (more or less) the SAME model to get it to “fit the curve”, which in this case is historical data.

    ASIDE: … there are some subtleties here, since some parameter estimation can be preformed in conjunction with back testing, BUT NOT for important/fundamental forces/mechanisms underlying the process.

    I could fit a Fourier series to the 20th centuries climate data, and have a beautiful curve … but is that a “climate model” … NO! It is at best a “data model” for that, and ONLY that, interval. One would have no reasonable expectation of that particular Fourier series having anything to do with what may happen in the 21st century.

    If you “fine tune/curve fit”, even if the results look good, your parameters are ONLY VALID for the period of the known data. That is, your model is ONLY VALID for that interval, and may be even a good tool for interpolation. HOWEVER, your model, particularly with highly non-linear/aperiodic process such as the climate is almost surely UTTERLY MEANINGLESS for FORECASTING.

    Yet, the IPCC use their interval curve fit to predict also. That is, they simultaneously curve fit/back-test and present that as a “verification” of their model … .THAT is VERBOTEN, and UTTERLY MEANINGLESS, and indeed DISHONEST.

    Curve fitting volcanoes, as just one example, is surely an utterly meaningless matter in the context of forecasting. There is not a single math geek at any one of the 34 entire armies of math geeks used by the IPCC who would say to your that they can forecast volcanoes … and yet by the time the IPCC publishes, a miraculous transformation has taken place, and one which necessarily implies that they can forecast volcanoes … that’s a LIE, and cannot be an honest mistake.

    One of many trivially simple illustrations of this is the existence of volcanoes. During the 20th century just the four medium sized volcanoes (there were no big ones in that period) caused an effective cooling of about 2.7C while during the same period the planet’s entire net warming was only 0.7C. That is, getting volcanoes even a little wrong has a massive impact on the outcome. Since nobody can forecast volcanoes, no amount of “fine tuning” to the 20th century data will help you, say, with forecasting for the 21st century, since your “fine tuned” model is only applicable to the 20th century..

    2) Even if you were to perform PROPER hindcasting/back-testing, and even if that arrived at “good looking” results, the entirely unpredictable and highly aperiodic nature of the climate (volcanoes, tectonics, Sun cycles, etc etc) would still mean that ANY forecasting is UTTERLY MEANINGLESS, and particular when the IPCC is using the “predictions” to insist on a complete upheaval for the entire human population.

    You will note that, as far as I know, they haven’t even bothered to gauge the degree of aperiodicity in the climate, and hence what the basic model equations should even look like (yes it is all well and good to jot down a system of PDE’s representing some heat/mass/momentum transport, but that is MEANINGLESS if applied blindly). Much worse, it is DISHONEST, if then one pretends to have the “answer”.

    So if these and other absolutely fatal blows to IPCC style climate modelling and (laughably) “predictions” could be better expressed to finally put an end to all the modelling/prediction rubbish, I welcome your comments, which can be sent to me at droli@thebajors.com.

    … I will do my best to create a better presentation of these issues.

    PS, you may have misunderstood the key point of my plate-tectonics remarks. Since the plates move and change, the amount of heat coming up from the core as a function of time/space also changes. Thus, since the total heat to the surface is Sun+Core, if Core changes, then the surface can warm or cool, and may have nothing or little to do with GHG’s etc. Since there is virtually no possibility of modelling the Core’s impact and non-stationary effects on the climate, climate modelling and GHG hysteria are necessarily fundamentally incomplete, for this reason also.

    PPS, there is so much discussion on lapse rate this, and convection that, and much of it based on pure theoretical/laboratory “thinking”. The reality is much more complex, and to a large extent unknown. For example, weather patterns, jet-streams, etc make a mockery of any pure idealised lapse rate discussion.

    However, one of the most important bits of “reality impact” that I have been searching for is “altitude based spectrometry”. That is, in addition to the planet’s emissions from satellite measurements, why not do also something like this: Grab a 747 stuffed with instrumentations. Have it circle for a while over a single point at, say, 3 km, and obtain the planet’s spectral emissions (at that point, altitude, and time, along with all the other vitals (temp, press, WV, CO2, etc etc). Move to 6km and repeat, and so on in intervals, to 50+km. Then repeat the whole thing several times in that location, for good measure. Then repeat all of the above at various locations on the planet, and on various dates, times of day etc.

    … this may very well end all varied speculation as to what/how the energy leaving the planet is doing as it interacts with the atmosphere on its way to that 3K in deep dark space.

    … I’ve been looking for data that provides this type of information, but no joy. If anyone knows of such, please advise.

    … according to the data I have seen, there is on the order of 5 – 10 BILLION, spent on climate change research ANNUALLY buy Gov’s, IPCC, et al, you’d think they could spare one of NASA’s 747’s for a short while.

  19. clivebest says:

    Dr O,

    Your comments on Volcanoes are spot on.

    – IPCC models claim to describe the observed global temperature dependence since 1900 once the cooling effects of actual Volcanic erruptions (Pinatubu etc) are ‘included’.

    – Without the negative forcing from these volcanoes these same models would have predicted a net warming of 2C since 1900. Therefore the models exaggerated actual warming by 1.3C or nearly 200%.

    – Now to predict future warming of 3C by 2100 is likewise wrong because no-one can know or predict future Volcanic erruptions. The best the IPCC can do is to assume a simliar rate of volcanic erruptions in the future. This means that 3C warming should be reduced to 1± 1C of warming. This fact should be better known.

    – It is inherently impossible to improve on these future predictions.

    Clive

    • Clive Best says:

      This isn’t really quite true because volcanoes are a transient phenomenon.

      Aerosols emitted by volcanoes cool the planet by refecting sunlight. This is interpreted in models as “negative” forcing. This leads to a drop in global temperatures of up to 1C for a medium size volcano. However after a few years the aerosols eventually disperse and the original forcing recovers. The climate responds by slowly warming back to the temperature it would have been before. Of course the climate never is in balance as many things are changing continuously.

      So I don’t think you can simply add up all the cooling shifts from volcanoes over the last 100 years together.

      • DrO says:

        To say that volcanoes are a “transient” effect seems to completely defy basic physics of the planet’s energy content.

        In – out + (sink or source) = d/dt of the contents … there can be no arguing with this.

        Suppose every month you put GBP 100 into your piggy-bank, and every month you take out 90. Your “balance” accumulates at the rate of 10/month.

        If there is a net energy imbalance for the planet, the same kind of accumulation/depletion occurs in the planet’s energy content/balance (in reality we must account for sinks/sources, but will omit that for simplicity for this point).

        If then something “transient” happens, say your house burns down, the fire is put out in very quickly, so the fire is “transient”. Now you have to raid your piggy-bank and empty it so that you can buy a new house.

        … what happens to the “balance” in the piggy-bank? It goes to nothing.

        The effect on the balance, although happening instantaneously, and appearing to be “transient”, is in fact a long term cumulative impact on the balance (heat content).

        Now, the process starts again, 100/month in less 90/month out, and the balance starts to grow again.

        … then you have another fire or whatever, and again the piggy-bank is empty.

        Each fire is a “transient” event, and there is a “spike” in your “balance”.

        However, had you not had any one or more of those “fires”, your balance would be that much greater at any time.

        … the effects of “local transients” on the balance are CUMULATIVE.

        When volcanoes throw masses of particulates into the atmosphere, which act like tiny mirrors, it causes a sudden and massive drop in the IN flow of energy from the sun. Thus, for that period, you are only making “large withdrawals”, and the (planet’s energy) balance plummets, as can be seen by the “spikes” on every single medium or major volcanic date, see for example Note 1 here (http://www.thebajors.com/climategames.htm), where the images are taken from the IPCC AR4 Chapter 8 (but almost the exact same information is presented in AR5 Chapter 9).

        … what would the planet’s temperature be in the year 2000 if those 20th century volcanoes had not occurred? It would be much higher, since the planet would not have reflected huge amounts of energy when the volcanoes were “having their way”. That is, the total cumulative energy that would have been received by the planet would have been much bigger (since there would have been much more “In”). The exact answer is a bit complicated since there are many factors and non-linearities,

        but still … much higher, and cumulative.

        • DrO says:

          Clive

          Have expanded Note 1 here (http://www.thebajors.com/climategames.htm) with a new Appendix providing a pedestrian explanation of why/how physics/energy balances demonstrate that volcanoes do in fact have a long term cumulative effect, in spite of their ephemeral nature.

          I use the sort of “bank balance” metaphor as above, but with a bit more background for those without math/physics.

          I would be pleased to receive comments, corrections, etc

        • Clive Best says:

          Dr O,

          I like your 3 ‘notes’ although I don’t agree with everything. I wonder if they could not eventually be combined into a book !

          Regarding Volcanoes – correct me if I am wrong.

          Your hypothesis is that there is a huge heat content stored within the earth with different timescales. That heat is increased by solar radiation and reduced by radiation to space.

          There are 3 main reserves of heat.

          Land
          Oceans
          Earth’s core

          Every now and again energy loss from the earth’s core disrupts energy balance. Volcanoes reduce heat input and the earth cools. This removes heat from the land and rather slower from the oceans.

          The total reserve of heat falls until the dust clouds finally settle and energy balance is eventually restored. The net total energy is less than it was before equal to the volcanic energy released.

          CO2 levels and H2O levels may rise and fall increasing or decreasing very slightly the heat loss (spending) from the surface.

          In short term human scales there may be changes in temperature both up and down as the different systems re-balance over different timescales.

          In the long term temperatures are way out of human control. Predicting future temperatures is also highly uncertain.

          My current position is that there is has been a small net reduction in OLR due to human activity. The earth responds to this energy deficit like any other external perturbation.

          • DrO says:

            Dear Clive

            I think you may have completely misunderstood my entire volcano story, and perhaps entirely misunderstood what I mean by heat/energy balances. So I begin with a short review of what a heat balance is, and the return to the volcano matter after.

            … HOWEVER, the response I composed would be more difficult to read in these increasingly narrow/indented reply slots … so for clarity I have posted my response in new comment slot below with the subtitle

            Heat Balance of a Hollow Sphere

            As for Note 3, many thanks for your kind words. I would be interested to know which part you disagree with, if that is not too onerous.

            As for a book, yes, I am thinking about it. At the moment I am working on Note 5, which aims to explain about mathematical modelling of dynamical systems for those without math’s (a bit similar in flavour to my Hollow Sphere response provided below.

            Also, some of my Notes are “explanatory” notes, while others are really just a collection “debunkings” of highly objectionable material in the large. I will have to figure out a way to interleave those formats into a cohesive structure before I can begin a book.

  20. Clive Best says:

    Plate Tectonics also plays a fundamental role to maintain life on earth.

    1. Current levels of photosynthesis on earth would deplete all CO2 in the atmosphere in just 9 years.

    2. Photosynthesis in the Oceans depletes all available phosphorous needed by aquatic plants and algae in just 86 years.

    Most of the CO2 absorbed by plants is soon liberated to the atmosphere when they die or are eaten by animals, while only a tiny amount of carbon is buried in sediments. Even by including this recycling effect we still find CO2 depletion of the atmosphere takes a mere 13,000 years while phosphorous depletion takes only 29,000 years.

    The incredible story is that these trapped sediments are not lost from the environment for ever because plate tectonics recycles material over very long timescales today. Subduction, mountain building and sea level change continuously re-exposes the raw materials for life through weathering.

    Plate tectonics is essential to re-cycle the raw materials for life on earth !

    Clearly it also determines the climate on earth at leasyt in the long trem. If Antarctica was not sitting on top of the south pole the earth would be far warmer.

  21. DrO says:

    Dear Clive – on the Heat Balance of a Hollow Sphere, and response to your comments above.

    I think you may have completely misunderstood my entire volcano story, and perhaps entirely misunderstood what I mean by heat/energy balances. So I begin with a short review of what a heat balance is, and the return to the volcano matter after.

    Heat Balance of a Hollow Sphere

    If there is only one thing you are permitted to know in all this climate change business, then it should be:

    In – Out +Sinks/Sources = d/dt of the contents

    … everyone should have this tattooed on their forehead’s etc.

    The simplest physical explanation of climate change begins with the simplest explanation of the planet’s heat/energy balance.

    Imagine the planet was a hollow sphere, without its hot core, without an atmosphere, no water, etc. Then, the planet’s surface is heated by just one source: the Sun. Assume the Sun’s heat flux is constant.

    Since the planet’s surface temperature is above absolute zero, it radiates energy out to the deep dark cold of space.

    Assume there are no Sinks or Sources, for now.

    The determinant of the planet’s surface temperature is dependent on the difference between the in flow of energy from the Sun, less the out flow of energy being radiated by the surface of the sphere (planet).

    The amount of heat radiated out by the planet is proportional to temperature. The hotter the surface, the (much) faster the planet can radiate (dissipate) heat (e.g. as coming in from the Sun, or wherever).

    In fact, the planet’s radiative (out) flux is proportion to something between T^3 or T^4, which are respectively the “grey body” and “black body” radiative proportionalities (and where T is in degrees Kelvin). For those interested, you may wish to look up Boltzmann’s equations.

    I don’t wish to get too technical here, but crudely speaking, the simple Out rate would have an expression of the form

    d/dr A u (T^3)

    where d/dr is outward vector/differential orthogonal to the planet’s surface, A represents a term for cross sectional area, u represents a term for a variety of properties required for radiation/spectral issues, and T is temperature.

    For the moment, the important thing is that even a small increase in the planet’s surface temperature can produce a large increase in the rate at which the planet can “throw-off” energy to space.

    So, enter the classic standard energy/heat balance as derived from thermodynamics. Since energy/heat cannot be created or destroyed (only moved/transformed), there exist the so-called “conservation principle”. That is, all the energy coming in, less all the energy going must equate to the energy being accumulated.

    This works EXACTLY like your bank account. The rate of deposits, less the rate of withdrawals determines the balance (or the change in the balance).

    In its simplest form:

    Rate In – Rate Out = d/dt of the contents.

    So

    Rate of Sun energy In – Rate of surface radiated energy Out = d/dt of the planet’s accumulation of energy

    where -accumulation = depletion, and d/dt is differentiation with respect to time (wrt) (i.e. that is how we write things that change with time)

    If the rate In = rate Out, then the d/dt contents = 0, i.e. there is no accumulation or depletion. This is also called the “steady state”.

    In order to have Climate Change (for simplicity Global Warming (GW)) in this simple model, there must be an IMBALANCE in the In and the Out, otherwise there would be no change in the content, and thus no change in temperature.

    In a super simple model such as a hollow sphere (no water, no atmosphere, etc), the heat content of the sphere is described as:

    Heat Content = p * Cp * V * T

    where p = density, Cp is heat capacity, V is volume, and T is temperature. p, Cp, and V are, for this simplest example, constant.

    ASIDE: by now you should be able to see the beginnings of a partial differential equation. Assume the Sun’s heat flow is a constant S, then:

    S – d/dr A u d/dr(T^3) = d/dt p * Cp * V * T
    In – Out = change in the contents

    In fact, the simplest radiative models of the planet take this form … though I am omitting a lot of minutia and technicalities to avoid diluting the main point of this “volcano story”.

    ASIDE: When you spoke earlier about using HighTran, that is part of the process to determine the Out.

    ASIDE: in principle, this is exactly the type of derivation provided in Chapter 2 of Note 2: Climate Science and Telephone Polls, under the heading of “Fluid Mechanics for 7-year Olds”, see here (http://www.thebajors.com/climategames.htm). Some people may find it easier to follow these ideas expressed in terms of “water flowing” compared to heat radiating.

    Thus when In = Out, Heat content is at steady state/constant, and the usual proxy for this is seen as a constant temperature (in such simple cases).

    If In > Out, then some energy must accumulate and d/dt contents > 0.

    In this simple model, density (p), heat capacity (Cp), and volume (V) are taken to be constants. Therefore, the only thing that can change on RHS of this equation is T. Thus, if In > Out, the immediate result is that T starts to increase.

    However, notice that the Out radiation is proportional to T^3 or something like that. Thus, as the In – Out imbalance is causing the surface temperature to increase, it is also increasing the rate/intensity at which the planet “glows” (i.e. increasing the rate at which the planet “dumps” heat to space).

    This increases the Out rate as T increases, and will continue to increase the Out rate until the Out rate matches the In rate, whence we arrive at a new steady state (InNew = OutNew) with a new steady state temperature.

    Introducing an imbalance between In and Out will create a “transient” (which is special word in differential equations land, not the same use as you had made wrt to volcanoes). Crudely speaking, an imbalance causes a non-zero d/dt on the RHS, and the forces of nature go to work until a new steady state is reached.

    More complex settings may not permit simple steady states, but that’s for another day.

    Again, this is exactly like your bank balance. Suppose your salary increases, and so do your deposits, and your balance starts to rise. However, now that you are richer, you spend more. If at some point the (new) in flow matches the (new) out flow, your bank balance will level off at its new steady state balance.

    Notice it does not matter what specifically is causing the imbalance, from the perspective of accumulation. For example, suppose we let the system sit for a long while and achieve steady state. Now, we can cause an imbalance by either altering the In (the Sun), or altering the Out, or both.

    The classical GHG hysteria is based on exactly this notion: It is basically the proposition that an insulator (GHG’s) is/are wrapped around the sphere causing the Out to decrease. Since the In has not changed, In > Out, so the RHS must also be > 0, and now the heat content starts to rise, seen as an increase in temperature only (in this ridiculously simple hollow sphere model). The Out will start to increase as the surface temperature increases, and eventually, we achieve a new steady state temperature for the “insulated” planet/sphere.

    If you start mucking around with the insulator(s) in small increments (e.g. increasing/decreasing etc), then the planet may be in a constant meta-stable (PDE) transient state. That is, the steady state will not be a flat line, but some wobbly thing. If you muck around enough, there can be no steady state.

    … though even a quick glance at the last few million years’ temperature reconstruction shows clearly that the planet is very happily wobbling about in a clearly defined (mostly) periodic meta-stable bounded by a very stable “trough” or “band”.

    Now, back to the volcano story. When certain types of medium/large volcanoes erupt, they throw huge amounts of particulates high into the atmosphere. Those tiny particulates act like (many) tiny mirrors, and thus block much of the Sun’s energy.

    Thus, the In flow of energy to the surface is reduced considerably. However, the planet continues to radiate at about the same rate, since the particulates are mostly transparent to outbound infra-red. So suddenly, In < Out, and thus d/dt Out, and for a while the sphere warms until the “normal” steady state/temperature is reached again.

    So, if there was only one volcano ever, then yes there would be what you call a “transient” and which would not have a major impact over the (very) long run.

    HOWEVER, that is NOT the reality. Volcanoes are fairly frequent, albeit aperiodic, and the scale, nature, and composition is also aperiodic, and have a massive impact on the Sun’s In flow.

    CRUCIALLY, the CONCERNS as presented by the IPCC et al, are over very short time periods (e.g. 100 years).

    So let us consider two scenarios combining some of the bits from above.

    1) The sudden appearance of “insulation”, but no volcanoes: So the sphere/planet was at steady state, you wave your magic wand, and instantaneously there appears a layer of insulation on the sphere. Now, suddenly, the In > Out, since the insulation is retarding some of the Out flow. Hence, d/dt of contents > 0, and the sphere starts warming (i.e. accumulates energy, seen as an increase in T, in this simple hollow sphere model).

    Eventually, the increase in surface temperature (under the insulation) causes the Out flow to increase sufficiently to again match/balance the (Sun’s) In flow of heat/energy.

    If you graphed the solution to these equations, you would see an asymptotic increase in temperature over time to the new steady state with No volcanoes, TN. For practical purposes, most of us can’t wait around to reach the asymptote, so we could consider some percentage of the asymptote to arrive at a “usable” time period required to reach (approximately) the new steady state; call this Z.

    Put differently, in this simple setting, the PDE’s can be solved reliably to predict TN will occur in approximate Z years.

    2) The sudden appearance of “insulation”, with periodic volcanoes: Start with the magic wand insulation setting above, but introduce “volcano effects” with some periodicity. For simplicity, assume all of the volcanic effects occur on an exact period, and each of them have an identical impact. That is, each of them have the same degree and duration of and effectiveness of “Sun blocking”.

    Of course, the exact period and exact degree of blocking would have to be specified, but for simplicity, perform just an “order of magnitude” analysis.

    Remember, the FIRST KEY OBJECTIVE is to predict T by the date Z.

    It is reasonable to begin with the scenario that there will be many volcanoes prior to Z. However, if there were even just one, how would that impact the prediction of the sphere’s temperature by date Z?

    SURELY, TV (i.e. the temperature with Volcanoes achieved by date Z) must be < compared to TN (the temperature achieved with No volcanoes by date Z) since the planet would have received cumulatively less energy. That is, the total amount of energy accumulated by the In rate without "blocking" must be greater compared to the total amount of cumulative In with "blocking".

    If you are filling your bucket with a hose, your bucket will accumulate more water (for a given period) if you do not periodically turn off the tap.

    It just like your bank account. If, periodically, your wife takes away your credit cards, cheque-book etc, then for those intervals the bank balance will accumulate, since there is "spending blocking". This has a cumulative effect. Conversely, if you are routinely fined for transgressions, ceteris paribus, your bank balance will be lower, cumulatively. In each case, the "blocking" is "transient", but cumulative nevertheless.

    In short, the total accumulation is the total accumulation of all the imbalances experienced along the way.

    Now all this volcano blocking, while certainly correct to say it is cumulative, is IMPORTANT for two primary reasons:

    a) The shear scale of the effect: The four medium sized volcanoes during the 20th century each cooled the planet by about 0.3 – 0.5 C. That is, they prevented a huge amount of energy reaching the surface, that would have otherwise arrived and warmed the planet.

    When the entire planetary warming for the 20th century was about 0.7C, getting even one of those medium sized volcanoes wrong is a BIG PROBLEM. Then, imagine the impact of large volcanoes, like Tambora which quite literally "froze the planet" for several years (e.g. snow/frost in NY and Florida in August).

    If the 20th century had also one or two large Tambora like volcanoes, like the 19th century, the planet's 20th century 100 year temperature experience might have been a cooling by -2 or -3C rather than a warming of +0.7C.

    If the forecast for the year 2,100 was a cooling of -3C (instead of an IPCC warming of +5-6C), how much "global warming" hysteria would we see?

    b) Volcanoes are unpredictable: We don't know when, what, how much etc etc. However, we do know with certainty that they occur. So any prediction to date Z that ignores all volcanoes must, almost surely, over estimate T by the date Z, and likely by a huge amount.

    So what is the FIRST OBJECTIVE? To predict T by date Z. Any interruption of the heat flow In, even if ephemeral, causes a cumulative reduction in the planet's accumulated energy, and by implication temperature (though it's rather more complex in the real world with atmospheres, water, 7,000 degree core temp, Sun cycles, creation of life, etc etc)

    In short, volcanoes necessarily produce large and cumulative reductions in the planet's/surface etc heat content, and by implication temperature. Omitting these from predictions is a fatal error, and necessarily has a profound impact on the reliability of the forecast.

    The OBJECTIVE must also accommodate "context". This is particularly important when the "context" is the UN et al's insistence that the entire population of the planet must undertake a colossal upheaval in costs and disruptions, and potential destroy the economies of developed nations.

    BTW, the prediction problem for temperature is already infinitely impossible, but the prediction problem for whether it is good or bad for mankind is an uncountable infinitely impossible problem.

    … and yes, you may explain to your wife that your bank account is empty because of volcanoes 🙂

  22. Clive Best says:

    Dr. O

    Your decsription above is a very clear explanation of clmate responses to energy imbalances from both incoming SW and outgoing IR. In some sense human activity is just another natural event like volcanoes but without a strong reduction in SW. Volcanoes too also emit CO2.

    There is just a difference in recovery lifetimes which are both tiny on geological timescales.

    Today I have been here: https://royalsociety.org/events/2014/feedback-climate-system/

    Aerosols and clouds are the largest uncertainties. All modles have positive feedbacks from clouds with tempertature based on assumptions.

    The CLOUD experiment finds that biogenic aerosols were stronger before the industrial revolution. This and clouds are nature’s heat shield thermostat.

  23. DrO says:

    Dear Clive

    I am not sure if you just “don’t get it”, or if you are just having a little fun with me. So this will be my last go at this volcano point:

    1) It is NOT geological time scales of interest, but very short time scales (e.g. 100 years), since it is all the hysteria and “massive upheaval policies” in the short term that must be addressed. If the IPCC et al were only concerned about geological time scales, I doubt anyone would give a toss. If all their forecasts and “doom and gloom” were predicted for 1,000 or 10,000 years from now … how much public attention/worry would it cause? … would your blog even exist?

    They can’t even get a 15 year forecast right … so to suggest geological time scales seems to be a completely different, and in a sense unrelated, discussion.

    Moreover, once we start considering geological time scales, then we must start to think about massive additional forces currently omitted from the models etc.

    2) By far, the most important climate impact of volcanoes is PROFOUND COOLING … so forget about any CO2 etc from volcanoes … that is an unnecessary distraction in the context of the utter meaninglessness of climate forecasts … just look at any temp history of real world data.

    3) If you predict that a heat lamp will warm your sandwich by a temp diff of dT, over a period of Z (e.g. temp increase by 6C over 100 years, as the IPCC et al insist) THEN you will be WRONG and end up with a rather cold sandwich.

    The reason is that some “joker” keeps sliding a sheet of tin foil between the lamp and the sandwich, periodically. Although the tin foil is only there for a few minutes/years, each time the joker does this, your sandwich’s temp drops 0.3-1C (as clearly demonstrated by the real world data). If they do this four times in the 100 year period, what will be your sandwich’s temp? … CERTAINLY NOT what the “without tin foil” prediction was.

    CRUCIALLY, your sandwich’s ACTUAL temp at Z will be a small fraction of the “non-tin foil” dT, say increasing only by 2C, rather than 6C.

    INDEED, if the joker is particularly nasty and inserts a very thick bit of foil for a longer period of time, your sandwich could actually be colder at Z compared to where it started (i.e. global cooling, or -dT, such as in the early part of the 19th century).

    … since we have no idea what this “joker” will do in the future, any forecast of dT by Z becomes meaningless (at least in the context of setting policies to cause global upheaval for the planet’s population).

    … completely omitting any consideration that a “joker” even exist from your forecasts is decidedly dishonest.

    … “curve fitting” your models to historical data to give the appearance that they can handle volcanoes/”jokers” (e.g. pretend the models are verified) is decidedly dishonest … but bizarrely, after all that “curve fitting”, the volcanoes/”jokers” are completed omitted from the forecast … that is very dodgy indeed.

    THE POINT BEING, separate from the many other fatal problems with climate models (see my Notes), volcanoes alone introduce a sufficiently MASSIVE error into the forecast to render any such forecast utterly meaningless … at least in the IPCC “sky is falling” and “lets massively change the world’s policies and economies” context.

    Perhaps that is not the context of interest to you. Some people seem to think that a forecast of +/-100C over 100 years can be called a forecast (I didn’t make that up, this really happened). In a sense, they are correct … it is a “kind of” forecast … but utterly meaningless for making anything vaguely resembling sensible decisions for the population of the planet.

    And finally, the most important point, even if a reliable Temp forecast was possible (which it is not), one would then need to make the “higher importance” forecast of whether that would be good or bad for mankind. That “higher importance” forecast is infinitely more difficult compared to the Temp forecast (which is already known to be impossible). That the IPCC’s forecasts don’t permit even discussing the possibility that global warming is a good thing is decidedly anti-science and dishonest. The last 100 years have been the most astonishing expansion in human welfare/standard of living for the planet in recorded history … all while there was global warming.

    …. once and for all, IPCC forecasts are utterly meaningless, and really just a fiddle to insist on a particular ideological agenda …. nothing to do with science.

    • Clive Best says:

      There is no disagreement.

      Volcanoes do make IPCC model predictions inherently inaccurate. Volcanoes could even make the earth cooler by 2050. The future is inherently unpredictable.

      I learned yesterday that the modellers even know this. Models pop off random future volcanoes to stop them running too hot. Models have built in parameterizations of things like clouds, lapse rate feedbacks, carbon cycle feedbacks etc. There is perhaps a pschological tendency to “exaggerate” positive feedback terms. This causes the models to run too hot. Now there has been a pause in warming lasting 17 years in contrast to most model predictions.

      There are several excuses for this – including volcanoes.

      • bob Peckham says:

        Very nicely put Clive. So you were at the meeting of the modelers. Did you learn whether they have put the moon into their models yet ? Or do they have plans to do so ?

        • Clive Best says:

          Hi Bob,

          The main problem with the models are clouds. The grid size is still very large 50km or so. Cloud formation works on on a much smaller scale. Cloud modeling is based on random number generation with relative humidity, aerosols etc. The moon is the least of their worries.

          The moon should be included in the Met Office short range weather forecasting models.

          • DrO says:

            Dear Clive

            While I appreciate what you may be trying to say, in reality, and especially in the AR/IPCC reality, your statements are patently misleading, and in some cases patently false.

            Given the extent to which politico’s have hijacked the science, I really don’t feel comfortable allowing statements of this sort, since they can be all too easily “cherry picked” for abuse.

            1) The modellers have ALWAYS known about these problems. That is not the issue, nor the point.

            Even a 7-year old scientist knows volcanoes are not predictable (nor is solar flux, cosmic rays/cloud formation, changes in “core heating”, etc etc, each of which individual have a giant impact on the forecast, and all that is before we get to the impossibility of forecasting aperiodic systems).

            The problem is, what the modellers produce is irrelevant. The material hits the IPCC “spin factory”, and what comes out the other end is NOT what modellers would produce.

            … even if workable models could be produced, which they cannot (not in the IPCC “policy context”), it would not matter, unless those models produced the alarmist results insisted (yes, insisted) by the IPCC (over 700 IPCC scientists have resigned in disgust following attempts by the IPCC to distort and “alarmise” their work).

            2) A statement like “Models pop off random future volcanoes to stop them running too hot” is absolutely FALSE in the context of the AR’s and iPCC. To the best of my knowledge, there is NOT a SINGLE forecast anywhere in any IPCC/AR report that includes volcanoes … NOT ONE. If you find one, please let me know.

            Yes, they talk about volcanoes, and they even include volcanoes in their “pretend verification” (but which are really “curve fitting” to past data, and which are purely to fool the reader into believing that the models are “verified” (not!) … but there is not single explicit volcano in any of their forecasts.

            In fact it is worse still, if you read the AR5 you will discover not only the complete exclusion of explicit volcanic events from the future, but also they use a special kind of “scrubbing” to calibrate their atmosphere transmissivity to be virtually cleared of any remnant volcanic dust or evidence (i.e. none in the future, and none in the past).

            That is a deliberate “double whammy” manipulation, no volcanoes to cause cooling, and an artificially clear sky to maximise solar in flux.

            … what a surprise, the models are deliberately fudged to massively distort the forecast upwards, thus maximising the “alarm”.

            3) I have considerably expanded Appendix D of my Note 1 here (http://www.thebajors.com/climategames.htm) since you last saw it. I have put some little bits in from my “far from ready” Note 6, dealing with brand new and unbelievably horrible manipulations in the AR5. You may wish to have another look at that.

            4) I have been working on Note 6, to deal with at least a few of the incredulous new problems created by the IPCC spin factory. Amongst other things:

            a) They seem to shifting from conservation based models to time series models … this is a complete “own goal” and is even more fatal compared to the rubbish in their GCM’s etc. Unfortunately, a pedestrian illustration of why/how that is takes a bit of time.

            b) They have introduced a number of new “terms of art”. For example, they no longer make “predictions”, they now make “projections”. They assigned their own special proprietary definition to the world “projection”. Basically, it means that a model projection is considered valid, regardless of what the model contains.

            … the list goes on …

            Note 6 is way too rough for any general distribution at this time. However, if you would like to see an “early/rough” draft to get a sense of some of these issues, email me at droli “at” thebajors “dot” com, and I will provide a link

            ONCE AGAIN, I cannot emphasise too strongly that if this matter was simply science for the sake of science, I doubt I would bother … however, as the IPCC/UN et al are succeeding formidably in a process to cause narcissistic massive socio-economic upheaval on BS they call science, it is a matter rather disturbing to a scientist/math-geek like me.

  24. Pingback: I don’t get ‘the gravito-thermal effect’ « Okulær

  25. Hi found your content to be very interesting appreciate the good work you doing…

  26. ”Gravity” / density of the ”atmosphere” is the most important factor in the cooling process.

    Here is the completely different / radical approach that will win on the end; because only the whole truth wins always on the end. Gentlemen, please broaden your view and discussion – if you can’t find anything wrong = I’m 100% correct; because I don’t ”guess” I have the real facts, here is the challenge for all of you: ,https://globalwarmingdenier.wordpress.com/2014/07/12/cooling-earth/

  27. Nick Stokes says:

    Clive,
    Some late comments:
    “There can be no greenhouse effect without a gravitational field. “
    There is no atmosphere without a gravitational field. But your analysis misses the temperature gradient that would be crated by the passage of IR through the gas. At high opacity transmission approaches a diffusion, associated with the name of Rosseland (described here). A temperature gradient in the gas is required for the flux to pass.

    The fundamental thing is that GHG impedes radiation and efflux. It’s always going to have a warming effect, with or without gravity. The blanket analogy is not so far off.

    “You need greenhouse gasses to generate a lapse rate.”
    No. There is no mention of GHG in the lapse rate equation. I’ve described the process here and here. In an isothermal gas, any vertical motion, up or down, pumps heat downward. That takes KE from the air. It continues to do so until the DALR is reached. Then motion switches to pumping heat upward, which creates instability.

    • Clive Best says:

      Nick,
      “But your analysis misses the temperature gradient that would be crated by the passage of IR through the gas.”

      No that’s wrong because without gravity there would be no pressure gradient. The emitted IR from a slab of air would be exactly the same as that absorbed. There would be no net IR heating of a level at height h.

      There is no mention of GHG in the lapse rate equation.
      No but you need gravity to generate a lapse rate.
      You need a lapse rate to have a greenhouse effect.
      You need convective/latent heat flow through the atmosphere to maintain a lapse rate and you need greenhouse gases to radiate the heat to space.

    • Nick Stokes says:

      “The emitted IR from a slab of air would be exactly the same as that absorbed.”
      That’s true of a blanket. It’s true of your clothes. The heat flux emerging is the same as that entering. The question is whether they create a temperature differential.

      The standard example here is of a shell of material over Earth that allows sunlight in and is opaque to air, but conductive. Vacuum above and below. If 238W/m2 enters, 238 W/m2 must leave, at temp 255K. But at 255K, 238 W/m2 is also radiated downward. The Earth surface must emit 476 W/m2, and so must be much warmer. No gravity involved.

      “You need convective/latent heat flow through the atmosphere to maintain a lapse rate”
      No. You need a heat pump. Vertical motions pump the heat. All you need is temperature differentials to drive motion. Latitude alone can do that.

      • Clive Best says:

        Are but that is a shell of material with a vacuum gap to the surface.

        The zero gravity atmosphere would be isothermal with the earth’s surface at 255K. It fact it could be considered to be part of the earth’s surface. There would be no convection because air density everywhere is the same.

        OK – All the above is an idealised flat earth picture with no seasons and no differential heating.

        In the real world you are right there would be latitude temperature gradients driving winds and the earth would be rotating. However I was just trying to make a gedankin experiment to show how the greenhouse effect is more subtle that people imagine.

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