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New Science 8: Applying the Stefan-Boltzmann Law to Earth

Earth, Greenhouse gas, emissions, wavelength, altitude, graphic

Energy is emitted to space from many different heights in the atmosphere, depending on the wavelength (not to scale, suggestive only).

One more quick post of mostly uncontroversial foundation for the math-and-physics-heads among us. But it’s a must for anyone who wants to talk Stefan-Boltzmann and follow the details of the next posts. My intro here, just has the gist without the equations.

Mostly the IPCC will agree with this post, but they might be a bit snooty that David thinks their “effective temperature” is too much of an approximation conceptually, and the slightly more complicated idea of a “radiating temperature” is needed. Strictly, the effective temperature idea treats Earth like it is a black-body at infrared, which it isn’t really. Earth is almost a black-body, but not quite.

There is no single layer that radiates to space, instead emissions come from many different heights, depending on the wavelength. We could average the emissions into “one layer”, but doing that would lose detail that matters when computing sensitivity to increasing CO2.

Technically the Stefan-Boltzmann law is not supposed to be applied to Earth, because there is no single physical radiating surface to which to apply it. So this is where David introduces and defines the concept of  “radiating temperature”, so it can effectively be applied.

As David says: “This linearizes the otherwise highly non-linear Stefan-Boltzmann law, giving us a simple result: the increase in radiating temperature is equal to λSB times the increase in OLR, where λSB is the slope of the Stefan-Boltzmann curve where the Earth is.”

– Jo

 

8. Applying the Stefan-Boltzmann Law to Earth

Dr David Evans, 2 October 2015, David Evans’ Basic Climate Models Home, Intro, Previous, Next, Nomenclature.

Before discussing the third error in the conventional basic climate model (next post), we will review the application of the Stefan-Boltzmann law to Earth. This is the last of the foundational posts, predominately reviews to ensure readers can get up to speed on background topics.

It’s not quite straightforward, because the Stefan-Boltzmann law applies to the emissions of a body with a single surface for all wavelengths, whereas the Earth’s outgoing longwave radiation (OLR) comes from multiple emission layers (see post 6).

The Stefan-Boltzmann Law

The Stefan-Boltzmann law applies to a body with a surface radiating into space, and is

The emissivity is the ratio of energy radiated by the body to the energy radiated by a black body (one that reflects no radiation) with the same temperature. Emissivity is equal to absorptivity, and incoming energy is either reflected or absorbed — so emissivity is zero for a perfectly reflective body, while it is one for a black body, and in between zero and one for all other bodies.

The Earth’s Total Emissions

The Earth radiates all its heat to space as OLR. Thus the E in Eq. (1) is the Earth’s OLR R, for whose value we use the all-sky average OLR of 239 W m−2 from Trenberth et. al 2009 [1].

The Earth’s Emissivity

Hard numbers on the Earth’s emissivity are scarce in the climate literature.

The broadband emissivities of land and ice-snow are ~0.95 and ~0.99 respectively by Fig.s 3, 6, and 7 of Jin & Liang, 2006 [2]. For water it is 0.9907 according to Appendix B of Wilber, Kratz, & Gupta, 1999 [3], though the emissivity drops quickly as wavelength increases (see their Fig. 1), and though quoted as broadband it does not seem to use data greater than 14 μm. From older data from Miriam Sidran, across a wide broadband range (1–100 μm), the average emissivity is 0.96 for water temperatures from 0 to 30°C (Science of Doom 2010). The emissivity of the Earth’s surface is taken here as ~0.96.

However, of the 239 W m−2 of OLR emitted by the Earth, all but 90 to 100 W m−2 comes from greenhouse gases — principally water vapor, CO2, methane, and ozone. These gases do not reflect infrared, so their emissivity is one. 40 to 50 W m−2 comes from the surface or the water vapor continuum near the surface — the emissivity of the water vapor is one and the emissivity of the surface is ~0.96. The remaining 40 to 50 W m−2 comes from cloud tops, whose emissivity is one when the cloud is sufficiently bulky (Chylek & Ramaswamy, 1982 [4]) and are otherwise somewhat transparent to the surface.

The emissivity of the Earth is taken here to be ~0.995.

This says that the Earth is almost a black body at the infrared wavelengths at which it radiates OLR, though of course it is not a blackbody at visible wavelengths (because we can see it — it is in fact quite reflective, with an albedo of about 30%).

The Earth’s Radiating Temperature

The Stefan-Boltzmann law cannot be literally applied to Earth because there is no single physical radiating surface to which to apply it. Also that law, like the underlying Planck’s law, relates radiation to the temperature of the layer that emits it, so it cannot be applied to a layer that does not physically emit. We must tread carefully.


We define the quantity TR such that

This being the Stefan-Boltzmann equation applied to Earth, TR may be thought of as a temperature — which we call the “radiating temperature” of the Earth. In so much as the Earth has a temperature at which it radiates, this is it. By defining TR as the quantity which makes Eq. (2) true for a given R, we have effectively applied the Stefan-Boltzmann law to Earth — though at the cost of introducing a notional temperature TR that is some mixture of the temperatures of the physical emission layers.

TR is numerically similar to the Earth’s effective (radiating) temperature Te, the temperature of a black body that emits the same OLR as the Earth:

While the numerical difference between TR and Te is insignificant, here we are concerned with OLR from the real Earth so it is more natural to use radiating temperature (and technically incorrect to use Te, at least conceptually).

Application of the Stefan-Boltzmann Law to Earth

The average value of the Earth’s radiating temperature, by Eq (2), is

(A brief note on what TR is not. If the Earth’s OLR was all emitted from a single surface, the average height of that surface would be between 5 km and 6 km because that is where the temperature is 255 K. But TR is not a temperature that can be measured with thermometers at some fixed surface in the atmosphere. Given the temperature gradient in the troposphere, there is always a height whose temperature is numerically equal to TR; but that height may change and is of no direct significance to TR because TR changes when one of the physical emission layers warms or cools, such as when the water vapor emissions layer or the cloud tops descend or ascend (average heights), so changes in TR  may occur that are not connected with warming at any particular height around 5 to 6 km.)

The Stefan-Boltzmann Sensitivity

The Stefan-Boltzmann sensitivity (SBS) is defined as the slope of the TR curve as a function of R, where the Earth is, which we find by differentiating in Eq. (2) to be

It is the ratio of ΔTR to the corresponding ΔR, in all circumstances (quite unlike the Planck constant, which problematically requires holding everything except R and the surface temperature constant).

The SBS is the slope of the Stefan-Boltzmann curve at the Earth’s current state. It may be regarded as a constant because the Earth does not stray far from this point — the effect of a change in λSB is second-order in the models here.

The Stefan-Boltzmann curve is approximately linear over a 10 degree range.

Figure 1: The Stefan-Boltzmann curve is approximately linear over a 10 degree range, so its slope (λSB) is approximately constant: ΔTR equals λSB* ΔR.

The Stefan-Boltzmann curve is still roughly linear over a 100 degree range.

Figure 2: The Stefan-Boltzmann curve is still roughly linear over a 100 degree range.

 

References

[1^] Trenberth, K. E., Fasullo, J. T., & Kiehl, J. (2009). Earth’s Global Energy Budget. Bulletin of the American Meteorological Society, March, p. 311.

[2^] Jin, M., & Liang, S. (2006). An Improved Land Surface Emissivity Parameter for Land Surface Models Using Global Remote Sensing Observations. American Meteorological Society, 2867 – 2881.

[3^] Wilber, A. C., Kratz, D. P., & Gupta, S. K. (1999). Surface Emissivity Maps for Use in Satellite Retrievals of Longwave Radiation. Langely Research Center, Hampton, Virginia: NASA.

[4^] Chylek, P., & Ramaswamy, V. (1982). Simple Approximation for Infrared Emissivity of Water Clouds. J.Stmospheric Sciences, 171-177.

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214 comments to New Science 8: Applying the Stefan-Boltzmann Law to Earth

  • #

    “a black body (one that reflects no radiation)”

    The Earth reflects significant amounts of radiation.

    A black body has no heat capacity.

    The Earth has significant heat capacity.

    Moreover, most of its surface (ocean) is mobile, and due to the overturning continually occurring, has an ‘effective’ emmissivity considerably lower than 0.99, nearer to 0.67.

    This makes applying SB to Earth problematic, to say the least, once you attempt to model a more realistic scenario of a rotating body illuminated from a point source providing over a kilowatt at zenith TOA, rather than an average constant illumination.

    1520

    • #

      Roger, that’s why we tread carefully. The “radiating temperature” is defined here as the temperature that satisfies the Stefan Boltzmann equation applied to Earth as seen from space, that is, with the OLR and emissivity of Earth.

      Yes, at visible wavelengths the Earth is quite reflective — it reflects about 30% of incoming solar radiation. At the infrared wavelengths of Earth’s OLR, however, the situation is quite different — the Earth is very nearly a black body. The OLR is mostly emitted by greenhouses gases, which are non-reflective and thus have an emissivity of one.

      The emissivity of 0.995 is for radiation to space, not radiation from the surface.

      200

      • #
        bobl

        However David, you said before that a considerable amount of energy is broadband IR from the surface through the atmoapheric window, given that the earths surface can be imaged cleatly in the infrared is it correct to suggest that nearly all IR is emitted from greenhouse gasses.

        35

        • #

          bobl, About 20% of OLR is emitted by the surface (including the water vapor continuum near the surface, which probably accounts for the majority of “surface” OLR — doesn’t make much difference to anything here though, because it is roughly at the surface temperature). This all goes thru the atmospheric window. About 20% of OLR comes from cloud tops, also through the atmospheric window. The other ~60% is from GHGs. We’ll be looking over these figures in a later post.

          101

          • #
            Konrad

            ”About 20% of OLR comes from cloud tops”

            David I would suggest checking that figure. I frequently measure the difference between clouds and sky background using an infrared bolometer. Cloud bases are far hotter than sky background, often by over 50C. Their tops can be hotter again, especially during the formation of cumulus. Given that radiation is proportional to the fourth power of temperature, clouds are the strongest source of LWIR emission from the atmosphere.

            A second point, “cloud tops” smells suspiciously like climate modelling with layers again. No, no, no. The atmosphere is increasing the 2D radiative cooling ability of the surface by adding a conductively and evaporatively coupled 3D LWIR radiator.

            512

            • #

              ”About 20% of OLR comes from cloud tops”

              Actually this is quite close for the exceptional fantasy of some EMR exitance from Earth’s surface proportional to surface T^4, that never ever happens. The CO2 at the isothermal tropopause can have its immovable 15% EMR exitance to space. Never changes!!
              Almost all (90%) the Earth actual surface radiative exitance becomes part of cloud bottom variable power and immovable temperature. From cloud (water condensate) tops with less than 2 meter optical depth from 0.9 microns to 100 microns wavelength. The visible clouds do account for 50 W/m^2 radiative exitance to space. The other 65% of exitance is powered by invisible atmospheric WV condensing at higher temperature exiting with no decrease in temperature, whatever it has to space in the WV continuum spectrum.
              All the best! -will-

              110

            • #

              The 20% is for OLR from cloud tops — so it is only that portion of cloud emissions in the atmospheric window that makes it to space, the bulk of the upward emissions from clouds being blocked by CO2, WV, ozone, etc.

              30

      • #

        Thanks David. I agree that for outgoing radiation, there is less of a problem, but there is still a problem. That is the issue of heat capacity. A blackbody which SB can apply to has no heat capacity. The reason the moist air radiating above the ocean that radiates through the atmospheric window at night-time is as warm as it is, is due to the overturning ocean surface putting energy into it throughout the night. And that is due to the oceanic mobility and heat capacity which blackbodies don’t have.

        This is why atmosphere led climate science doesn’t work. The atmospheric tail does not wag the oceanic dog. Follow the heat capacity.

        1118

        • #

          Roger, I am going to dodge around that fair complaint in the best tradition of climate analysis as follows :)

          The basic models, which apply the “basic physics” and are the subject of this series of blog posts, are for transitions of the Earth from one steady state to another. They are the only context where I am going to employ this application of the SB law. Furthermore, all the quantities involved are averaged over the whole Earth and over at least a year. Finally, we are only interested in OLR (which, in steady state, is equal to ASR), and use changes in OLR to find out what the changes in OLR from the surface are and thus the surface warming.

          Somehow in all those assumptions and conditions the heat capacity issue seemed to disappear. Howzat?

          Seriously though, modeling the thermal inertia of the Earth is going to be addressed later in the series for the alternative model and the notch-delay model. However, by considering only steady states and averaged variables it disappears — in steady state with variables that are averages, there are no changes and hence no thermal momentum or heat capacity to consider. We just know the initial and final steady states, without considering the dynamics of how we moved between them.

          Of course GCMs are dynamic models and they cannot hide behind steady state and averaging, but I don’t address these aspects of GCMs in this series. The GCM builders don’t use the SB law, AFAIK.

          140

          • #

            Thanks again David.
            I’ll sit back and wait to see where you’re driving with this. From previous discussions of ‘the notch’ I know you’re already aware of heat capacity and thermal inertia issues. What’s less well understood is the ‘effective’ emissivity of oceans under a massive troposphere, and that is key to understanding the reason the surface temperature is higher than your radiating temperature.

            80

            • #

              “Thanks again David.
              I’ll sit back and wait to see where you’re driving with this.”

              I concur that waiting to see is best.
              For me ’tis hard to accept this blind acceptance of CAGW clown nonsense here at joannova. It would be nice if we could have hints of some useful result of this series. Will this connect to the notch delay, or something else. So far only obvious deliberate falsehoods, from incompetence. Where is evidence of deliberate intent to harm, for profit!

              1017

          • #
            Konrad

            David,
            Tallbloke is correct, the key to understanding why the earth’s surface is hotter than the theoretical blackbody temperature of an object in vacuum illuminated by a constant 240 w/m2 is to understand the surface properties of the planet.

            Running away to discuss radiative properties of the atmosphere is to miss the simplest disproof of all of the AGW hypothesis. To know what the net effect of our radiatively cooled atmosphere on surface temperatures is you only need to do one thing -correctly calculate the average “surface without radiative atmosphere” temperature. Is it higher or lower than our current average of 288K?

            This is where the critical mistake in the very foundation of the AGW hypothesis lays. Climate scientists didn’t just use the S-B equation to calculate LWIR flux between surface and atmosphere or atmosphere to space, they used it to calculate the effect of SW illumination of the surface!. This is where their 255K surface without radiative atmosphere figure comes from. But empirical experiment clearly shows that figure is out by around 80K for 71% of our planet’s surface. The oceans are an extreme SW selective surface, but the use of the S-B equation treated them as SW opaque, constantly illuminated and without convection. The surface of this ocean planet would average around 312K were it not for cooling by our radiatively cooled atmosphere.

            David, I know you have put a lot of time into your modelling, and like Rog I am interested in where it if going, but I fear you are going to end up in exactly the same place as the climastrologists :ie believing that adding radiative gases to our radiatively cooled atmosphere reduces its ability to cool the solar heated surface of our planet. You could avoid that dead end by just running this simple experiment (the bigger you build it, the better it works).

            The two samples have equal ability to absorb SW, emit LWIR and equal conductive and evaporative cooling ability. The only difference is depth of SW absorption. When equally illuminated by solar SW, both water samples rise in temperature, but there is a marked difference between them. When you understand the physics behind this you will find out -
            Why the S-B equation cannot determine “surface without radiative atmosphere”
            Why 255K for “surface without radiative atmosphere” is completely wrong.
            Why linear equations cannot solve for climate and CFD or empirical experiment is needed.
            Why AGW due to CO2 is a physical impossibility.
            What the most likely “notch” mechanism is.

            1212

            • #
              David Cosserat

              Konrad, my old friend and sparring partner, you really do know how to put down us mere mortals, don’t you?

              Running away to discuss radiative properties… David Evans is not ‘running away’ anywhere. On the contrary, he has developed a series of interesting and challenging articles much of the content necessarily involving discussion of the ‘standard’ theory, right or wrong.

              …you only need to do one thing – correctly calculate the average “surface without radiative atmosphere” temperature. Is it higher or lower than our current average of 288K?” Wow, how ignorant of us all. And think of the time and effort David Evans could have saved if he had only consulted you first.

              The surface of this ocean planet would average around 312K were it not for cooling by our radiatively cooled atmosphere. 312K huh? So that’s it – an announcement from the sage. No need to doubt you are correct. No need for an explanation.

              David, I know you have put a lot of time into your modelling…but I fear you are going to end up in exactly the same place as the climastrologists… . You could avoid that dead end by just running this simple experiment (the bigger you build it, the better it works). Well, dang! Why didn’t we all think of that. Maybe you should look up the word ‘condescension’ in the dictionary.

              Konrad, I find it impossible to know where you are coming from in your writings other than that you are a climate sceptic like me (and, I suspect, like the majority of commentators here). The word ‘troll’ comes unfairly to mind. More ‘obfuscator’ perhaps.

              I suggest you also look up the word ‘didactic’ and try to be more so.

              But, nevertheless, all the very best, David C

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          • #
            Rick Will

            For this series to have relevance to climate modellers and their believers it needs to look inside GCMs and identify their core failures and/or weaknesses. I cannot see any point introducing new basic models.

            It is now apparent to most climate observers that GCMs and coupled GCMs produce poor results as far as CO2 sensitivity is concerned. The question is why? If you do not know what is inside GCMs and how they work how can you identify their specific faults.

            10

            • #

              Read post 1 on why the basic model is important (there is only one, essentially).

              The “why” of poor GCM performance will be answered in upcoming posts, because they share the same faulty architecture as the basic model. Stick around!

              01

        • #
          bobl

          Not only that Roj, in the overturning oceans, overturning is largely powered by gravitation and momentum (the interplay of the moons gravity and the earths rotation).

          I’ve always wondered how climate scientists explain that ocean kinetic wave energy can be 100 times the average insolation, and how friction from there has magically zero effect on temperature!

          Beats me… simple minds, simple models.

          50

        • #
          Bob Fernley-Jones

          Rog and David,
          Is there not also a significant complexity that some 40% of unfiltered sunlight reaching the ocean is longwave and is absorbed mostly in the skin of the water, the far-red penetration being measured in only nanometres? From there the thermodynamics become rather complicated including; surface cooling by evaporation (varying with wind speed etcetera) resulting in latent heat transfer during condensation at varying heights above/ water turbulence and conductive heat transfer downwards/ because IR absorption is in the skin, convective (more so at night) conductive and radiative heat transfers to the air is an immediate consideration/ everything influenced by temperature differences between the skin and air, further affected by varying humidity; great differences between tropics and poles, day and night; and in a particular region e.g. the English Channel, major seasonal and daily variations and…….

          No worries; we can model the average result eh?

          Oh let’s make it easy and assume the ocean surface is perfectly flat and smooth everywhere.

          20

        • #
          jim2

          Hi Tallbloke.

          There is no variable for heat capacity in the SB law. Given a blackbody with heat capacity C, heated to a temperature T at an instant in time t, the blackbody would still radiate in accordance with the SB law at that very instant of tme, would it not?

          Heat capacity would determine how quickly the body cooled OVER TIME via action of SB, but would not determine the frequency distribution of that radiation at any particular instant of time.

          What am I missing.

          50

        • #
          Franktoo (Frank)

          Rog: The ocean obviously has heat capacity, so either the ocean isn’t a blackbody or blackbodies can have heat capacity. In my ignorance, the last statement seems OK. Do you have a reference?

          20

      • #
        Leonard Lane

        David, what do you use to represent the physical shape and dimensions of the near black body OLR?
        Homogeneous lamina or disk subject to continuous sunlight?
        Or do you use a sphere which is rotating and thus heating and cooling through diurnal cycles and yearly cycles?
        Radiation on the dark side cannot equal radiation on the side receiving sunlight. And for the side sunlight, the incoming radiation must be distributed according to the angle of incidence and the speed of rotation.
        I am sure you are aware of all this, but just what assumptions are made about the earth, its shape, and its rotation and orbit around the sun? I have never seen this explained anywhere when talking about the radiation balance of the earth.

        61

        • #

          Leonard, all those factors are ignored, because these basic models are 0-D, with variables that are averages over more than a year, used to describe transitions between steady states.

          21

      • #
        Patrick Espy

        I read with interest your article. However, I think the statement that “The OLR is mostly emitted by greenhouses gases…) is a bit misleading. Unlike the surface, greenhouse gases absorb little visible radiation. Thus, they derive little heat from the Sun directly. The energy that is ultimately emitted to space has come from the infrared blackbody emission of the Earth’s surface. Some of this energy is directly emitted to space. However, at some wavelengths greenhouse gases repeatedly absorb and re-emit a portion of that energy (at the local temperature of the gas) in all directions. The portion of this emitted and re-absorbed IR energy that “diffuses” downward to the surface is reabsorbed by the surface, warming it. The energy that “diffuses” upward in the atmosphere is continuously re-absorbed and re-emitted by the greenhouse gases in the atmosphere. However, at higher altitudes the density of greenhouse gas is so low that the energy emitted upward does not encounter a sufficient density of greenhouse gas to be re-absorbed. This energy escapes to space and is characterised by the temperature of the gas that last emitted it. Since the air temperature falls with altitude, this temperature is lower than the surface temperature, and thus the radiation to space is less than that directly emitted from the surface to space. The difference between the Earth’s directly emitted OLR and that emitted in narrow bands by greenhouse gases is energy that has gone into heating the greenhouse gas and the Earth’s surface.

        Thus, the OLR is a combination of the earth’s direct IR blackbody radiation, plus a portion of that blackbody energy that has been absorbed and re-emitted to space by greenhouse gases in the atmosphere. A spectrum of OLR shows the direct surface blackbody contribution, characterized by the temperature of the surface, and a lower amount of radiation in the absorption bands of the greenhouse gases, characterised by the temperature of the atmosphere at which they escaped to space. The difference in these two is the portion of the Earth’s surface OLR that has remained in the Earth-atmosphere system.

        00

        • #

          Patrick, the statement “The OLR is mostly emitted by greenhouses gases…” is literally true.

          Later in the series (post 14) we investigate how much OLR comes from various sources: about 48 + 79 + 14 + 5 or 146 W/m2 of OLR comes from CO2, water vapor, ozone and methane, out of a total of 239 W/m2 of OLR. In addition, anther 20 W/m2 or so of OLR attributed to “the surface” actually comes from the water vapor continuum near the surface. So about 70% of OLR comes from greenhouse gases. Note the emission spectrum of the Earth from a Nimbus satellite in figure 2 of post 14.

          While what you write seems to be mainly or wholly true, note that the atmospheric window is too narrow (wavelength-wise) for even half of the radiation emitted by the surface to make it directly to space.

          Note also that “OLR” means “outgoing longwave radiation” — it is the radiation that actually escapes to space. So “the portion of the Earth’s surface OLR that has remained in the Earth-atmosphere system” is technically zero, which is probably not what you meant.

          00

        • #
          gai

          “…However, at some wavelengths greenhouse gases repeatedly absorb and re-emit a portion of that energy (at the local temperature of the gas) in all directions. The portion of this emitted and re-absorbed IR energy that “diffuses” downward to the surface is reabsorbed by the surface, warming it….”

          ****

          Actually this is also incorrect. I had this same visualization until I went to a lecture by Dr Happer that was backed up by information from Dr. Brown. (Both physicists.)

          In the troposphere the energy absorbed by CO2 from the earth’s surface is not radiated at all near the surface. Instead it is handed of via collusion to the rest of the atmosphere until the atmosphere is thin enough, about 47 kn above the surface, so the time to re-radiate is the same or faster than the time to the next collision. The time to radiate being about ten times slower than the time to the next collision in the troposphere near the surface. This means near the surface CO2 is contributing a slight bit to convection. With 400 ppm CO2 you have 0.04% or 4 molecules adding a bit of warming to the other 96 molecules.

          Dr Happer’s presentation on this. link

          And a graph:

          http://www2.sunysuffolk.edu/mandias/global_warming/images/stratospheric_cooling.jpg

          00

          • #

            gai
            October 29, 2015 at 11:33 pm

            (“…However, at some wavelengths greenhouse gases repeatedly absorb and re-emit a portion of that energy (at the local temperature of the gas) in all directions. The portion of this emitted and re-absorbed IR energy that “diffuses” downward to the surface is reabsorbed by the surface, warming it….”)

            ****

            “Actually this is also incorrect. I had this same visualization until I went to a lecture by Dr Happer that was backed up by information from Dr. Brown. (Both physicists.)”

            Do you think that either ‘physicist’ has any clue to EMR?
            It seems that they are divided between “photons” and “heat”
            Neither has any relevance to EMR power transfer requiring no mass nor any energy. The EMR power requires no accumulation of power into mass and sensible heat as defined by specific heat of mass as a function of temperature. This is even a more bizarre concept than the meteorological concept of air parcel! Has your Dr. Brown or your Dr. Happer ever considered how their microwave oven can and does heat coffee or boil water?
            All the best! -will-

            02

        • #
          David Cosserat

          star comment
          Patrick,

          Gai’s response to you is correct. Allow me to add a few facts:

          INCOMING RADIATION FROM THE SUN ABSORBED BY THE ATMOSPHERE
          1. You are not correct when you say: “…Unlike the surface, greenhouse gases absorb little visible radiation. Thus, they derive little heat from the Sun directly.”

          According to Kiehl & Trenberth (2009) (you can Google “Trenberth diagram” and check my figures) the incoming absorbed energy from the Sun is 239W/m^2. Of this, 78W/m^2 is absorbed by the atmosphere and 161W/m^2 is absorbed by the surface. So about 33% of the Sun’s incoming radiation is absorbed by the atmosphere and about 67% is absorbed by the surface. I hope you will agree that 33% is not just a ‘little’ contribution!

          OUTGOING RADIATION FROM THE EARTH’S SURFACE
          2. Regarding what happens to the LW radiation emitted from the earth’s surface, you say that some of this energy is directly emitted to space and that the rest is absorbed by greenhouse gases in the atmosphere. That is correct. But you then assert that the atmospheric GHGs re-radiate the energy in all directions and that some of it returns to the ground where it “is re-absorbed by the surface, thus warming it”.That is NOT correct physics!

          Again using the Kiehl & Trenberth figures for ease of explanation…At the surface-atmosphere interface:

          (1) the surface exerts an upward potential flux of 396W/m^2
          (2) the atmosphere exerts a downward potential flux of 333W/m^2

          But neither of these potential fluxes are actual flows of thermal energy (although they may be considered as photon flows if you invoke quantum theory). The actual flow of thermal energy is simply calculated as the difference between them, namely 23W/m^2, travelling upwards from the warmer surface to the cooler atmosphere, in full conformance with the second law of thermodynamics.

          Now 23W/m^2 is a tiny atmospheric heating effect. So this raises a question: if the earth’s surface is only radiating 23W/m^2 to the atmosphere (and a similarly insignificant 40W/m^2 is going directly to space) how does the rest of the surface’s 161W/m^2 absorbed energy received from the Sun get transferred to the atmosphere? The answer is: 17W/m^2 travels by conduction/convection (“thermals”) and 80W/m^2 travels by water evaporation, a total of 97W/m^2 of non-radiative energy transfer.

          CONCLUSIONS
          So from all the above figure it turns out that the atmosphere is heated as follows:

          78W/m^2 by radiation directly from the Sun
          23W/m^2 by radiation from the surface
          97W/m^2 by thermal (i.e. non-radiative) transfer from the surface

          In ALL THREE CASES the energy is anihilated (‘thermalised), ending up as kinetic energy in the molecules, which constantly collide with one another thereby maintaining local thermal equilibrium. The GHG molecules in the bulk of the atmosphere typically collide with other molecules (99.9% of which are non-GHGs) and give up their energy long before they can emit radiation. And even in the cases where they do radiate, the radiation is typiclly absorbed very quickly by other GHGs.

          So GHGs in the bulk of the atmosphere only have a minor effect on the rate of transmission of energy upwards, most of it taking place by convection. Only towards the top where the air gets thinner, does the balance of probability slowly change in favour of emission of radiation to space rather than exchange of energy by collision. Thus GHGs should be regarded essentially as cooling agents towards the top of the atmosphere. Increasing their concentration means that they become less efficient at their job of cooling, hence the surface has to warm to a higher temperature to ensure that sufficient energy still flows to space to maintain the energy balance.

          12

          • #
            David Cosserat

            A small but important correction: I said: “In ALL THREE CASES the energy is annihilated (‘thermalised). Of course I should have said that In THE FIRST TWO CASES the radiative energy is annihilated, being replaced by thermal energy. In the third (non-radiative) case it is already thermal energy and simply transfers upwards from one regime (the surface) to the other (the atmosphere).

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      bobl

      Also conceptually wrong, at the height of the layer that is 255 degrees there is air that has molecules with kinetic energy that only AVERAGES 255 degrees, it is plausible that no actual molecule has energy equal to 255 degrees. There is a statistical mix of molecules from stationary (-273 deg) to some maximum. In all of the layers below and most above there are also molecules with this 255 degree KE. So unlike a surface where all molecules are at a common temperature gasses are a statistical mix, they do not represent a surface to radiate from full stop. I dont see that you can treat a layer where 1/2 the gas does not have sufficient energy to radiate at Tr as a surface. You need to take account that there is a band of emission temperatures, emanating from a spherical shell 40 km deep…. one average too far I think.

      Secondly the weather bureau routinely images the earth in the infrared and produces images with significant contrast particularly clouds, the fact that this can be done does not bode well for the idea that IR absorbtion is 99.95

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        bobl, As explained in the post, air around 5 or 6 km that happens to be at 255 K is of little or no interest here. There is no emission layer there on average (except on a very narrow range of wavelengths for CO2, out in the wings as the EL descends to the ground with wavelength, as CO2 is increasingly unlikely to absorb). This is not where any appreciable amount of OLR is coming from. The single-layer emitter concept is too simple to compute sensitivity to CO2, unrealistic, and we are not using it.

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          bobl

          Yes David, and you are correct, far too simple. Again, not criticizing you, just the model, just trying to point out that the atmosphere is not a surface with a common temperature but a statistical mix (normal distribution?) of molecules at many different temperatures and ionisation states. Therefore the temperature of a gas has a totally different meaning to the temperature of a solid, and applying SB to it is not particularly sensible.

          I’m not sure how I would how I would model this particular problem but I can be pretty certain that the integral of eneegy in a spherical shell 10000km deep with turbulent flows, with several temperature gradients and actually ionised through 1000 km of it’s depth with energy mediated by at least three separate forces is NOT going to be accurately represented by a simple 2D emission surface at a certain height.

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            bobl: “applying SB to it is not particularly sensible”

            Exactly. That’s why the “radiating temperature” is defined here as the temperature that satisfies the Stefan Boltzmann equation applied to Earth as seen from space, that is, with the OLR and emissivity of Earth.

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              Konrad

              The S-B equation [alone] is applicable to no factor in earth’s climate system. All that can be said is that for the planet’s temperature to be in equilibrium, OLR should match UV/SW/SWIR absorbed.

              Our measurement of OLR is too poor to confirm your modelling. All we know is that OLR drops as the planet cools and increases as the planet warms. (enough to disprove AGW as OLR should have dropped as the planet warmed if the unproven hypothesis was correct).

              As to the “emissivity [and absorptivity] of earth”, as I demonstrate through empirical experiment all the standard assumptions are incorrect. Clouds, not un-condensed water vapour, are the strongest source of atmospheric LWIR emission and the surface of our planet is an extreme SW selective surface.

              To model climate in any meaningful way is beyond “rocket surgery”. This is just a toe dipped into spacecraft thermal control (check page 53 for surface properties). You would need to know all that and more to effectively model climate on our planet. Go with assumptions? Then your “Jade” lunar rover will pack it up and die from thermal stress.

              Right now I am working on solar access through trafficable glass for new underground train stations for Sydney. The glass is 39mm thick and has 4 layers of glass and 3 PVB interlayers stopping and thermalising varying amounts of UV and SW at varying depths. Diurnal thermal loading? Compared to our planet’s thermal response to solar radiation, quite a simple problem. But no linear equations give the answer. Given the materials are non convecting, FEA can be used. But if they were fluid, CFD would be needed.

              You appear to have chosen the wrong approach David. Yes, eliminate unknowns or incalculables from the model. But you should have eliminated the atmosphere [excepting surface pressure], not surface properties.

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                I must disagree! The surface and Oceans take lifetimes to vary a wee bit.
                This atmosphere however, never even considered different from gas. Can and does kick the **** out of anything ‘right now, right here’ in its way. The rest of us hide behind bushes, eating berries and peering out from!!!!
                Please give us your learned description of this atmosphere
                [Expletive deleted] Fly

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      KinkyKeith

      Rog

      There have been many winters when I have been happy to have lived within 2 kilometres of the ocean. Keeps us warm at night.

      Up the valley temps can be low enough to freeze the water in your pipes.

      So many factors left out of the classic models and as I have written on here many times previously: a model must prove itself.

      The Classic models don’t work and are nothing more than fantasy computer simulations of someones scientifically untrained mind.

      At one level the models do work; they help bring in lots of money to spread around the followers of CAGW.

      KK

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      Konrad

      Rog,
      Just a note – the high level of red thumbing on this thread is because it was linked via Andrew Bolt’s blog, the most read political blog in Australia. A significant number of AGW believers read his blog and will red-thumb here if a thread is linked. You can safely ignore any red-thumber that can’t type a scientific rebuttal.

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        Sometimes a ‘whatever’ thumb comes from the posted handle.
        Sometimes from one skimming and instinct.
        Sometimes but very rarely from one that can read and ‘get’ a concept!
        Just which is your intended audience? If you get more greens, you are preaching to the choir!
        All the best! -will-

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        Bob Fernley-Jones

        @ Konrad,
        That’s an interesting comment given some high counts here of thumbs-down on some topics that are worthy of discussion even if controversial or complicated alternatives.
        At my Comment #15 I’ve had a thumbs-down but no comment from him/her to suggest that the basic science stated on omnidirectional radiation in the atmosphere is false in any way. The elementary geometry of it undeniably means that radiation is predominantly tending towards the horizontal where its net local thermal effect is zero. (Versus hemispherically uniform radiation in S & B)

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    Den Volokin

    In regard to the physical meaning of the radiating temperature (Te or TR) of Earth or any other planetary body, please read this recent paper published in the open-access journal SpringerPlus:

    On the average temperature of airless spherical bodies and the magnitude of Earth’s atmospheric thermal effect

    The effective radiating temperature of a spherical body is a non-physical (unmeasurable) abstract mathematical quantity. Hence, any comparison of that temperature (e.g. 255 K) with any physical (measurable) temperatures is conceptually meaningless! Consequently, there is no effective radiating height in reality….

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    Richard

    Instead of the Stefan-Boltzmann law have you guys tried applying the Ideal Gas Law to Earth and the other planets such as Venus and Mars? If you take mean molecular mass, atmospheric density and pressure, and input them into the Ideal Gas Law equation you get the precise temperature of the planet without using the Stefan-Boltzmann law. It’s interesting.

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      Richard if the planet was out near Pluto would this equation come up with the same temperature?

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        Richard

        I have no idea. All I know is that applying the Ideal Gas Law to planets with sufficiently large atmospheres and to the planets we have sufficient data for gives us the exact temperature of the planet. The equation accurately predicts the surface temperature of Earth, Venus and Mars and also accurately predicts the temperature of planets at 1 bar such as Jupiter, Saturn, Uranus and Neptune.

        Venus comes out as the most striking to me. Assuming an atmospheric pressure of 92000 mb, a density of 67 kg/m^3 and a mean molecular mass of 43.45 (see NASA’s ‘Fact Sheet Venus’) we get a temperature of T = PV/nR = 92000/(67000/43.45*0.082) = 727K for Venus when the actual surface temperature according to NASA is 737K. This works for all atmospheric planets we have enough data for.

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          “I have no idea. All I know is that applying the Ideal Gas Law to planets with sufficiently large atmospheres and to the planets we have sufficient data for gives us the exact temperature of the planet.”

          Interesting! With the Ideal Gas Law you only have number of molecules with no mass. Please, how can this concept ever apply to a gas atmosphere wholly constrained only by ‘gravity’ which can only interact with mass? Your dimensionality reduced ideal gas law can only be applied to gas molecular motion orthogonal to a gravitational force vector.
          All the best! -will-

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          The ideal gas law can’t be applied to Venus, because the pressure is too high.

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        GeeANGRY

        or at an infinite distance from the sun or within the orbit of mercury. Simple thought experiments dismiss nonsense.

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      Leonard Weinstein

      Richard,
      Where did you think the level of the density for a given pressure came from? It is not a specific value for all cases of given pressure and average gas composition. Giving the pressure (mass of gas over the surface), average chemical composition, and gas density together defines what the temperature had to be. If you had the pressure, composition and temperature, this defines what the density would have to be. If all you knew was pressure and average gas composition you could not determine temperature.

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        “If all you knew was pressure and average gas composition you could not determine temperature.”

        Indeed! in this Earth’s atmosphere, in every direction molecular temperature is not some ‘energy’ dependent on mass but only related by transient molecular noise ‘power’ alway instantaneously equal to kT/t. This is the definition of gas molecular ‘temperature’. Temperature gradients are easy. Temperature itself remains unknown to any of the current and easily replaceable Earth’s top predators. Grinn ;-)

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        Richard

        I don’t know, all I’m saying is that you can use that method above to accurately calculate the temperature of planets. See here.

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        Richard

        Not sure why my comments are suddenly “awaiting moderation” after that last submission. Guess I’m not allowed to express a different opinion here.

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          Guess I’m not allowed to express a different opinion here.

          Settle down with the censorship accusation mate. Only a few volunteers “patrol” the comments. Numerous words act as triggers which could see your comment sit in moderation until one of the few gets to it.

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      bobl

      I think that directly using the IGL is inappropriate too as it was devised for closed systems. But it does show in general that a gas at a higher pressure should be hotter.

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    Mike Flynn

    David,

    You wrote “The Earth radiates all its heat to space as OLR.”

    I invite you you to define “heat”. I suspect you can’t, but give it a try anyway.

    The Earth, quite obviously, radiates energy to space on a wide variety of wavelengths – visible, radio, infrared and so on. Any loss of energy at any wavelength, will eventually result in a lowering in what we perceive as temperature.

    Statements such as yours are ignorant and misleading at best, and mischievous at worst.

    Would you care to clarify your statement, or do you just wish to continue providing fantasy as truth?

    The Earth has cooled over the last four and a half billion years, regardless of your beliefs.

    Have you a fact or two to support your statements, or do you depend on assumptions all the way down? The warming effect of CO2 is as real as n rays, or or phlogiston. Demonstrate anything to the contrary, and I will smartly change my opinions. Of course you can’t demonstrate the existence of your fantasy, but I suppose people have a need to believe in the non existent.

    I just wish I wasn’t expected to fund this nonsense.

    Believe as you wish. Just don’t expect me to fund your fantasy!

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    • #

      Mike while I agree with you that the sky is blue, David has proven track record of correcting errors and is thus worth far more than those who will never admit mistakes.
      The mistake here could be nothing more than the choice of the word all instead nearly all.

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      Random Comment

      Mike, Not sure you’re following the logic of this series of posts. Did you start at New Science 1 and read all posts? My understanding is that at this stage of proceedings (given all that has gone before and in light of near term global politics) it is much smarter tactically to work from within the citadel than continue to attack its ever-strengthening walls of elite opinion.

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      Mike Flynn

      Science is about detail and experimental verification. Facts are facts, nonsense is nonsense. If David meant to say “nearly all”, he should have said so. I trust people to mean what they say. If a scientist is not sure, just say so.

      As a mathematician, David should be painfully aware of the difference between “all”, and “nearly all”, or “almost all”.

      David may well be an extremely talented mathematician and economist, but I’m not sure about his grasp of quantum physics, heat, energy, radiation, and their relationships. Be that as it may, four and a half billion years of CO2 heat trapping has resulted in a fall of surface temperature of some 5000K or so. Hardly a ringing endorsement for the warming power of CO2, I would think.

      CO2 is plant food, as is H2O, that other, even more dreadful, greenhouse gas. Remove all CO2 from the atmosphere, all plant life perishes. Shortly thereafter, so do we all!

      If that is what you want, leave me out of your suicidal endeavour. I tend to wanting more plant life, less deserts and so on. Just as did Svante Arrhenius, although I don’t support his odd speculations about CO2 or the need for racial cleansing and eugenics.

      Any fool can claim expertise in climatology, and many do, obviously! Bah, humbug, I say! Go back to your delusional fantasies. I’ll leave you to it.

      Cheers.

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        bobl

        Mike,
        It depends on your perspective, David is dealing with the basic physics model of what happens to the OLR emission particularly that within the stopband of CO2 and indeed pretty much all of that would go as OLR as far as the models go. David has already stated in comments for example that the earth is 30% reflective in the visible spectrum, a not insubstantial loss to space. We already have pointed out the other 100x pipes in the climate which David specifically acknowledged.

        Right now be is trying to pull apart the basic physics, but unfortunately for you or I, while he goes through the background of the classic model he restates many of the errors. It does seem like he’s gone to the dark side, no, I trust he wants to understwnd the dark side in order to strengthen the argument.

        Your agument about CO2 being the peultimate fuel for life is of course true, and trying to muck with it (in a negative direction ) is fraught with danger — you are absolutely right but it has nothing to do with radiative gas physics.
        Finally David seems to be a rather good Electrical Engineer, so rest assured he has a good handle on Physics and Chemistry as all good EEs do. Sometimes some reminding can help though.

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        David Cosserat

        Mike, You say: …four and a half billion years of CO2 heat trapping has resulted in a fall of surface temperature of some 5000K or so. Hardly a ringing endorsement for the warming power of CO2…

        Having just said the stupidest thing that I have ever read on a blog trail, you then ask to be left out of what you call David’s “suicidal endeavour” . Please do indeed walk away.

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      Eugene WR Gallun

      Mike Flynn — You say nothing worth paying attention to, much less replying to. You are a troll. — Eugene WR Gallun

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      Leonard Weinstein

      Mike,
      Heat transfer is defined as NET energy transfer. Since the average incoming solar energy is equal to the average outgoing thermal energy, the average net energy transfer is zero (but not always zero, only on average). The use here seems to be restricted to a specific portion of the energy wavelength range (IR). This is not normal use, and the statement should be net outgoing energy, not heat transfer.

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      • #

        Whatever do you mean by energy? Some accumulation of power over time, (linear time) or the power contained within some defined time interval (power per cycle)? Which type need be conserved?

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        Leonard Weinstein says, October 3, 2015 at 3:01 am:

        Heat transfer is defined as NET energy transfer. Since the average incoming solar energy is equal to the average outgoing thermal energy, the average net energy transfer is zero (but not always zero, only on average). The use here seems to be restricted to a specific portion of the energy wavelength range (IR). This is not normal use, and the statement should be net outgoing energy, not heat transfer.

        Leonard, this is among the most basic of thermodynamic principles. Earth (as a closed thermodynamic system) gains heat (Q_in) from the Sun, its hot reservoir (“heat source”), and sheds heat (Q_out) to space, its cold reservoir (“heat sink”). In other words, there are TWO heat transfers going on at the same time, not just one. So David is absolutely correct in saying that Earth sheds it “heat” to space in the form of OLR.

        The NET heat (Q_in minus Q_out) is zero in the steady state (dynamic equilibrium). However, the heat between the Earth and space (Earth’s surroundings) is NEVER zero. That’s 239 W/m^2 on average. Just as the heat between the Sun and Earth is never zero. It is also 239 W/m^2 on average. Earth’s NET heat is zero: 239 – 239 = 0 W/m^2.

        You can never speak of “net heat” inside one single heat transfer. Then there is only “the heat”. It’s unidirectional, after all. But when two separate transfers are involved, then the term “net heat” becomes appropriate. The net of the two transfers …

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      Roy Hogue

      Not that I’m in any way qualified to speak authoritatively about thermodynamics but one thing at least is clear — one way or another, through one mechanism or another, the Earth radiates all incoming energy it receives from whatever source, back into space in some form or another. Otherwise its temperature must increase.

      This is simply too obvious a conclusion to miss. The question before us seems to be this: since we have a history of temperature variation that no one can sensibly dispute, by what mechanism does this happen? Does it happen because incoming energy increases and decreases? Does it happen because Earth’s ability to get rid of it back into space changes with time? Or is it a combination of both?

      David is concerned with the utter failure of the current, shall we say “classical” model of AGW to predict what’s really happening and then proposing his alternative theory about what controls the changes in Earth’s temperature.

      David or Jo, I’m struggling a bit with putting my thoughts into a good statement of what I’m thinking and your comments would be appreciated. Have I oversimplified? Probably. But I’m not sure exactly how.

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        Roy Hogue

        In light of what I already know about David’s theory I should say,

        …back into space in some form or another at some time or another,

        since delay seems to be the big question.

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          KinkyKeith

          Good comment Roy.

          KK

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            KK For you my special friend,
            To continue from below, Earth’s atmosphere has a huge bulge near the equator Sunward. Surface pressure is near same nightside. Surface temperature is higher. Atmospheric density is way lower at altitudes all the way to 30km. With longitude represented by ‘time of day’ (a Solar reference frame eliminating Earth rotation for clarity), easy to see but never mentioned, by CAGW priests. Why? Incompetence or hiding what they know to be true?
            The tropopause (20hPa) is at 18 km with lapse rate temperature decrease extending to such low temperature that only solid H2O can and does exist, thrown up there by equatorial Cb vertical velocity. At such temperature specific WV is zero as it also cannot exist This stratospheric ‘snow’ is invisible from the surface but never from space UEUV.
            Engineering disciplines have tables documenting this giving no theoretical reason for what is measurable. If all engineering throws up hands and shakes head sideways, how can Climate Clowns be 97% certain? Just what is an atmosphere? ;-)

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              KinkyKeith

              The DiUrnal Bulge.

              Amazing concept.

              Like a giant street sweeper that moves around the Earth vacuuming up air as it goes around every day. A big big disturbance.

              KK

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          The mechanism or the reference for the amount and location of both atmospheric water condensate and the latent heat of WV seems to be unknown! There so far is not even any agreement on how an atmosphere differs from a volumetrically limited compressible fluid. Nether effort in meteorology nor atmospheric physics has bothered to consider such. It is but forecast from the cyclic but never repeatable, or blame all on CO2, with absolutely no science or understanding required. Innumerable peer reviewed plagiarism, with attribution, is much more preferred!! :-(

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        Ross

        Roger

        I think you have it exactly right and given some of the critical comments from people, who much more of the science than I do, they need to read what you’ve said and keep it front of mind when reading what David and Jo put up each post.

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        bobl

        Um, Mo
        There is absolutely no proof that incoming electromagnetic radiation (EMR) energy leaves the earth as EMR. As I have pointed out constantly, there is a completely unknown contribution / loss from gravity, inertial and momentum of the earth – moon – solar systems motion and potential energies, changes in the chemistry of earth etc.

        Look at it this way, when we recieve incoming EMR and after reflection the remaining EMR is dumped to the surface as waste heat. In order to be dissipated that heat has to be either retained (heating the oceans and the rocks) or converted to another form, what energy transitions can happen to that energy, how can that HEAT be lost as some other energy form. After EMR (IR) emission, probably the most common conversion is TO MOTION, wind, waves, currents.

        This is the first criticism of the basis physics model I would make. The atmosphere is part of a system that is subject to kinetic energies 800 BILLION times the total annual insolation for the whole of the earth and we anticipate there will be ZERO – NADA – NO leakage from these titanic energies into the climate as waste heat! Not even 0.6 Watts per square metre.
        Until someone does a full momentum/ energy balance of the earth with respect to the solar system this is mere speculation. The most basic assumption the physics model makes incoming EMR = Outgoing EMR is just a speculation.

        This is the biggest problem in applying Sevante’s theorem to the atmosphere, in a test tube you can assure that incoming EMR = Outgoing EMR on a unconstrained earth you can’t

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          bobl

          Q. How many angels can dance on the head of a pin,
          A the question is meaningless because the existance of angels is as yet mere spculation

          Q. How many degrees does the surface rise because of the inmbalance in incoming vs outgoing energy.
          A. The question is meaningless because the balance between incoming and outgoing EMR is as yet mere speculation.

          Climate Science = Arguing about hown many angels can dance on the head of a pin … QED.

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          David Cosserat

          Bobl, You say: There is absolutely no proof that incoming electromagnetic radiation (EMR) energy leaves the earth as EMR.

          What planet are you on? Are you not aware that exiting EMR has been measured from orbiting satellites? Or do you think there is some conspiracy afoot? Or what?

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      Mike- established troll;

      “The Earth, quite obviously, radiates energy to space on a wide variety of wavelengths – visible, radio, infrared and so on. Any loss of energy at any wavelength, will eventually result in a lowering in what we perceive as temperature.”

      Thermal EMR flux is never energy of any sort, only power! Spontaneous thermal flux can only dispatch in the direction of lower radiance some rate of entropy decay, either in terms of power, flux, or the integral of flux from an isotropic radiator into 4 PI steradians!! Such has absolutely nothing to do with some insane utterances of temperature.
      All the best! -will-

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      Robk

      Could there not be an issue of the temperature “hunting” or surging up or down as a steady state tries to re-establish. The hunting of such a large system would occur over long periods. The buffering capacity of the system would need to be known.

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      The Earth, quite obviously, radiates energy to space on a wide variety of wavelengths – visible, radio, infrared and so on.

      The Earth radiating in the visible? That’s news to me. Maybe you’re confusing reflection with radiation.
      Then again, judging by your ill mannered comment, I’d say you’re just mouthing off.

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      The Earth emits infrared radiation, and CO2 absorbs it at many wavelengths. That’s really all you need to know to determine that CO2 causes warming.

      But there are also direct measurements, such as

      “Observational determination of surface radiative forcing by CO2 from 2000 to 2010,” D. R. Feldman et al, Nature 519, 339–343 (19 March 2015)
      http://www.nature.com/nature/journal/v519/n7543/full/nature14240.html

      Press release: “First Direct Observation of Carbon Dioxide’s Increasing Greenhouse Effect at the Earth’s Surface,” Berkeley Lab, 2/25/15
      http://newscenter.lbl.gov/2015/02/25/co2-greenhouse-effect-increase/

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    Peter C

    New Science 8: Applying the Stefan-Boltzmann Law to Eart

    One more quick post of mostly uncontroversial foundation for the math-and-physics-heads among us.

    Mostly Uncontroversial!
    Sorry Jo, I do not think so.

    Even Roger Brown at Duke University thinks it is a can of worms. A Darn hard problem.
    http://wattsupwiththat.com/2012/01/12/earths-baseline-black-body-model-a-damn-hard-problem/

    The effective black body temperature of the Sun is not definitely established.
    The effective black body temperature of the Earth is even more controversial

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      It seems like both Joanne and David have accepted that there is such a thing as a Stefan-Boltzmann Law, rather than a useful S-B equation, and that such can in any way apply to a compressible radiatively dispersive fluid atmospherewith variable temperature,pressure and density. Perhaps they are going along with such nonsence from the CAGW Clown Model (CCM) for some yet to be disclosed reason!
      So far this 8 part, Most Controversial Essay is unacceptable to all, who for good reason, consider any CCM to be deliberate hoax!

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        bobl

        To show fault with the model one must first understand it.

        I too agree that David will invent a new climate mousetrap that is likely still incapable of catching mice by proceeding based on a pretty badly and possibly fatally flawed baseline, but I think he is proceeding the right way. He may well break up the log jam that is the basic physics model so that progress can be made, he may show that the basic model is so flawed as to be worthy of discarding. Either way he does the world a service, a step along the path to the truth. He did say from the outset that he wanted to be challenged, a baptism of fire to make his work robust.

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          bobl October 3, 2015 at 8:59 am

          “To show fault with the model one must first understand it.”

          Not at all when some model is but the most trivial fantasy!
          Even to try to discuss, it is only whether the purple Unicorn’s horn has straight or spiral flukes! A diversion! You are being scammed!!! Ask your daughter, ask your pet dog, ask anyones kitty-kat! They all just lick ass at such scamming!
          The current Climate Clowns are the most highly paid professional, bankers, politicians, lobbyists, or temple money-changers ever encountered!! Truly Climate Change is the most destructive challenge to all earthlings. This destructive challenge is not from earthlings and certainly not from climate, but only from professional Climate Clowns. Such must first be strictly contained, as with any pathogen, and allowed to destroy itself!

          “He did say from the outset that he wanted to be challenged, a baptism of fire to make his work robust.”

          This will happen AFTER!

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    Manfred

    David, what distance into space from the notional average reflecting ‘surface’ of Earth is required before a uniform assumption of terrestrial emissivity may be made?

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    KinkyKeith

    The Earth or the representation of it through its’ “radiating levels or layers” is NOT a Black Body as per Stephan Boltzmann and probably not even a grey body or even a light grey body if I bothered to look up the old definition.

    Both Christopher Monckton and David are accomplished mathematicians and have each performed incredible good works in moving the debate on CAGW towards some resolution. They are to be applauded for that.

    The United Nations and attached Warmers are not to be applauded however, since whether through fervent belief or absolute deceit they continue to block every obstacle which stands between them and the keys to the treasury of every western nation on Earth.

    We must still keep in mind that this series is about DECONSTRUCTION of the accepted “Models” for CAGW so that the errors can be identified and widely publicised.

    I am amazed at the number of people on this blog who have read in full or in part the details of the Models at the core of the debate.

    I could not be bothered because it was evident that far too many factors had been omitted from the “Models” for them to be anything but

    models of a Trojan Horse designed to carry the beliefs and cash and votes of ardent non scientific minds towards creating a better world for

    the new elite.

    KK

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      Roy Hogue

      The United Nations and attached Warmers are not to be applauded however, since whether through fervent belief or absolute deceit they continue to block every obstacle which stands between them and the keys to the treasury of every western nation on Earth.

      Thank you Keith. That is something we dare not lose sight of. No matter what we debate here on Jo Nova their agenda is all political, money and power.

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    Assuming that a change in radiating bandwidth of gases equates to a change in emissivity,this link below becomes interesting. In it they say:

    Atmospheric pressure strongly affects the absorption spectra of gases (through
    pressure broadening). This poses a major problem in computing the transfer of IR
    radiation through the atmosphere with varying pressure, temperature, and amount
    of gases.

    Does this mean that broader bandwidths at lower altitudes will mean that radiation from the extreme wavelengths of each band can fly up without being absorbed but cannot fly down without being absorbed. Like a diode in your resistor diagram.
    More if global warming means an increase in atmospheric pressure then does this effect become a strong negative feedback?
    http://irina.eas.gatech.edu/EAS8803_Fall2009/Lec6.pdf

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      Thinking about this overnight I see yet another outward going diode involved in the CO2 pipe pass bands. The bandwith pressure broadening would be acompanied by a reduction in resonant Q at lower altitudes.
      Thus the amplitute of the ringing oscillation would be greater at altitude with less pressure. So as well as the outer edge wavelengths going up unabsorbed by the same gas, the radiating power would be stronger in the centre of the passband and weaker at the extremes for the same temperature at height. This would result in more outward than inward field strength at the passband center frequency. At the same time the pass bands of other gases narrows with height. So less of this stronger narrower signal is absorbed by them.

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      bobl

      I think you have to think about what creates the broadening (remembering that PV=nRT) creates the broadening, if you believe as I do the the width of the stopband for a gas is related to the doppler shift effect which is dependent on particle velocity then it’s faster hotter gasses tbat have broader spectrum and that is related to pressure through the gas law this paper is simply wrong because it assumes a causal effect that does not necessarily
      exist, mars has a CO2 partial pressure 10 x earth but emits narrower CO2 lines, because the CO2 is much colder.

      Using the doppler theory, pressure is only correlated to bandwith at constant temperature and volume.

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        Good comment bobl.
        However partial pressure is a bit of an artificial construct itself. Google says “the pressure that would be exerted by one of the gases in a mixture if it occupied the same volume on its own”
        The actual surface pressure on Mars is about 0.6 that of Earth.

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        bobl
        A bit more checking and BOTH your Dopler broadening and the Pressure broadening are real!
        A formula and explanation of them and another third type are given here.
        http://www.phy.ohiou.edu/~mboett/astro401_fall12/broadening.pdf
        The formula for pressure (collisional) broadening contains T and 4π in two different places so it is related to temperature but is not linear.
        The leaky diodes are real!

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        gai

        I agree with you there bobl

        FROM WIKI
        The Pound–Rebka experiment (VERY IMPORTANT because gases are moving randomly and in random directions)

        …The test is based on the following principle: When an atom transits from an excited state to a base state, it emits a photon with a specific frequency and energy. When an atom of the same species in its base state encounters a photon with that same frequency and energy, it will absorb that photon and transit to the excited state. If the photon’s frequency and energy is different by even a little, the atom cannot absorb it (this is the basis of quantum theory). When the photon travels through a gravitational field, its frequency and therefore its energy will change due to the gravitational redshift. As a result, the receiving atom cannot absorb it. But if the emitting atom moves with just the right speed relative to the receiving atom the resulting doppler shift cancels out the gravitational shift and the receiving atom can absorb the photon….

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    Have we counted the amount of man made EMR that leaves the planet seperately(except from North Korea at night)? Every street light, warm roof and 1MW TV transmitter etc. What percentage of that come from hydro?

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    • #
      bobl

      Nooooo, of course not, it’s assumed negligible, and it to some extent is. You can estimate it by looking at average world energy output in watts (2.7E12 ) watts and dividing by surface area (510 E 12 square metres). World electricity is therefore about 5.3 mW per square metre.

      However that:
      Doesn’t take acount of thermal efficiency, which takes it to 3 times that
      Doesn’t take account of other fuels especially oil.
      Doesn’t take account of biological heating 300 watts per human, = 4.1mW and probably at least the same for companion, human pest species (eg rats, mice, pigeons) and human food animals.

      IEE estimates world energy supply at 14000 million tonnes of oil equivalent. A toe being 41.8 GJ, so do the numbers and total energy released by man is average 36mW per square metre plus bioheat of man and mans animals of say another 10 or about 45mW per square metre.
      Not much eh? You’ll need to run the stereo a bit louder hey.

      Yet another issue here: manmade CO2 by altering the climate is supposed to be doing more heating than is actually chemically present in the fuel to begin with by almost 100 times. Man’s best machines to do this manage a COP of 4 and maybe 5 at a stretch! If CO2 is this good why aren’t we heating our homes with it.

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        How wonderful! Please keep thinking! Best is just after getting laid. Not so good but still effective is dronk, lying on back, truly wondering about the bottom of the table!
        All the best! -will-

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      • #

        Bobl tried the numbers a different method and got even lower numbers than you. Cranking the stereo up and lying drunk under the table did not help.

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      • #

        Actually CO2 traps of order a million times more heat than is generated from burning the fuel which creates it:

        http://davidappell.blogspot.com/2012/04/impressive-fact-about-carbon-dioxide.html

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        • #
          Bob Fernley-Jones

          @ David Appell,

          If as a mere engineer I can follow that, it sounds like you have an opportunity to develop and patent quite a useful energy saving device.
          It sounds rather good to be true, and I hope it wasn’t a wording error.

          Best of luck in this David!

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          • #

            Except the “lifetime” of the atmospheric CO2 is ~1000 years. Atmospheric CO2 will still be higher in 100,000 years because of the CO2 we emit today.

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          • #

            Bob, you might find this interesting:

            “Harvesting renewable energy from Earth’s mid-infrared emissions,”
            Byrnes et al. PNAS | March 18, 2014 | vol. 111 | no. 11 | 3931.

            Abstract: It is possible to harvest energy from Earth’s thermal infrared emission
            into outer space. We calculate the thermodynamic limit for
            the amount of power available, and as a case study, we plot how
            this limit varies daily and seasonally in a location in Oklahoma. We
            discuss two possible ways to make such an emissive energy harvester
            (EEH): A thermal EEH (analogous to solar thermal power
            generation) and an optoelectronic EEH (analogous to photovoltaic
            power generation). For the latter, we propose using an infraredfrequency
            rectifying antenna, and we discuss its operating principles,
            efficiency limits, system design considerations, and possible
            technological implementations.

            You can’t run a heat engine from the atmosphere to the surface, though, because the former is cooler than the latter.

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          Bob Fernley-Jones

          @ David Appell,

          “Actually CO2 traps of order a million times more heat than is generated from burning the fuel which creates it:” [AND]

          “Except the “lifetime” of the atmospheric CO2 is ~1000 years. Atmospheric CO2 will still be higher in 100,000 years because of the CO2 we emit today.”

          Thanks for the humour David. It sounded rather different to what you claim. Of course the quantity of energy is unchanging since the CO2 molecule is rapidly emitting as well as absorbing photons. Notice how on a cloudless night the surface air temperature can drop dramatically especially in deserts yet the CO2 is a great deal older than the hours of night.

          DO YOU UNDERSTAND?

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          • #

            Bob: I didn’t write anything meant to be humorous.

            Yes, CO2 emits IR photons and well as absorbing them. But the net photon flux is upward, from the surface. CO2 intercepts this upward flux, and then re-radiates in a random direction, so some of the photons will go downward, heating the lower layers.

            When making this rigorous, and assuming the case of a blackbody emitter (which emits isotropically), one can eliminate the angular dependence and ends up with two differential equations, the two-stream equations (sometimes called the Schwarzschild equations), which specify the vertically upward and vertically downward energy fluxes in the atmosphere.

            I suspect the desert cold on cloudless nights is due to no clouds and low humidity.

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            • #
              Bob Fernley-Jones

              @ David Appell,

              “ Yes, CO2 emits IR photons and well as absorbing them. But the net photon flux is upward, from the surface. CO2 intercepts this upward flux, and then re-radiates in a random direction, so some of the photons will go downward, heating the lower layers.”

              So are you avoiding what you said before (?) or have moved the goalposts or something:

              “Actually CO2 traps of order a million times more heat than is generated from burning the fuel which creates it:”

              There is that thingy about conservation of energy and those photons don’t hang around for long. (Certainly not 100,000 years {typo ?} as you also seem to have jested and they get out really fast at night in hot dry deserts)…….. (erh even faster during the day)

              “I suspect the desert cold on cloudless nights is due to no clouds and low humidity.”

              As far as I’m aware, say in the Sandy Arabian Desert, the humidity could be lower in the day but CO2 is much the same (negligible plant life), although there will be a great deal of shorter wavelength IR whizzing out conversing with the sun after a brief dally with some GHG’s.

              Am I missing something?

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              • #

                Bob: I haven’t avoided anything.

                The greenhouse effect does not violate conservation of energy — it takes place because of it. Nor does the fact that atmospheric CO2 concentration is still of order +10% after 100,000 years violate it. Conservation of energy is built in to all the principles and equations of radiative physics.

                I certainly did not say photons hang around for 100,000 years.

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  • #
    KinkyKeith

    There are two points which might help eliminate Human Origin CO2 as a player:

    1. There is definitely a mechanism by which CO2 absorbs ground origin IR ENERGY which

    is INSTANTANEOUSLY TRANSFERRED TO NEIGHBOURING GAS MOLECULES BY STANDARD MECHANISMS OF GAS PHYSICS.

    2. The problem is that Human Origin CO2, despite the reality of the IR absorption mechanism, is effectively a non-starter when it comes to a

    quantitative input. It just doesn’t rate against natural origin CO2 and water.

    So if we really want the truth we need a model which ONLY models Man Made CO2 input effect.

    KK.

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    • #
      Roy Hogue

      So if we really want the truth we need a model which ONLY models Man Made CO2 input effect.

      I expect that’s true. But how does one distinguish between human origin and natural origin CO2 or determine how much of it is of human origin?

      Sorry that’s a rhetorical question just to make a point. There is no reasonable way that I know of. Perhaps no unreasonable way either.

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      • #
        KinkyKeith

        It’s interesting Roy that “The Models” discuss the effects of Total CO2 (and do it incorrectly) whereas they then complain about the CO2 emitted by Humans.

        IF the issue really was about CO2 then logic would say: “go to the largest factor” ie natural origin CO2, which is 96% or so of all atmospheric CO2.

        CO2 is also “trapped” in the oceans and can readily top up any loss in atmospheric CO2.

        The models are deceitful in not clearly showing the effects of doubling human CO2 output; it would be 4% of the total claimed CO2 effect and if the real GHG was incorporated correctly then water is maybe 48 times more plentiful that ALL CO2.

        No need to deconstruct false models because they are deliberately false.

        KK

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        • #

          No. We’ve increased atmospheric CO2 by about 120 ppm, from a starting value of 280 ppm. That’s about 40%.

          Manmade CO2 has a different radioactive signature than natural CO2, but as isotopes they have the same atomic properties and absord IR in the same way.

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          • #

            Position of absorption line centers differs for isotopes of the same molecule.

            http://irina.eas.gatech.edu/EAS8803_Fall2009/Lec6.pdf

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            Roy Hogue

            David Appell,

            This is probably a dumb question from your perspective. But nothing ventured, nothing gained, so here goes…

            I understand that there are a number of isotopes of carbon, some of which are radioactive, So far, so good.

            What I don’t get, don’t understand at all, is why “man made” CO2 would have a different ratio of one isotope relative to another than the natural.

            Radioactive and non radioactive carbon have both been around for the same length of time and the radioactive atoms have been breaking down spontaneously for the same length of time, each according to its half life no matter where they’re located. So I guess my real problem is that I don’t get the theory behind radiocarbon dating. And that’s what you’re talking about.

            Only radioactive decay can change the ratio of one isotope to another in some object or sample of CO2. And no matter where it’s found I would expect the ratio of radioactive to non radioactive carbon to be the same, or much too close to the same, to be useful for anything. You would get the same level of radiation from the carbon in everything. And non radioactive isotopes would not change their ratio at all. So as far as I can see, so much for using radioactivity or atomic weight for anything useful.

            I have never found a good enough explanation of this to satisfy me. The only way this can make sense to me at the moment is if radioactive carbon was not uniformly distributed from the beginning. And if that were true, the starting condition would be unknown and invalidate any theory about using it for dating things or identifying one source from another. Yet obviously this is used for dating many things and I don’t understand why it works. What am I missing? HELP!

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              Roy Hogue

              …to be the same, or much too close to the same, to be useful for anything.

              Poorly worded.

              Try: …to be the same, or much too close to the same and not be useful for anything.

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            • #

              Roy: Good question. The answer is that plants prefer to utilize (“take up”) lighter carbon isotopes, i.e. 12C compared to 13C. (Both are radioactively stable.)

              So fossil fuels, which come from ancient plants, have a higher 12C/13C ratio (i.e a lower 13C/12C ratio) than does the atmosphere.

              So by burning fossil fuels, we’re lowering the 13C/12C ratio in the atmosphere, and that agrees with what is observed.

              More details here:

              http://www.realclimate.org/index.php/archives/2004/12/how-do-we-know-that-recent-cosub2sub-increases-are-due-to-human-activities-updated/

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                Roy Hogue

                Thanks David.

                I have learned a lot from asking questions as I just did. And one of the things I try to do is reconcile any new information I get with what I already know, a cross check to see if I have a good coherent picture of things. So forgive just one more sticking point. From the linked article…

                Isotopes are simply different atoms with the same chemical behavior… [emphasis mine]

                and…

                …because plants have a preference for the lighter isotopes (12C vs. 13C); thus they have lower 13C/12C ratios.

                If the chemical behavior of various isotopes is the same (which I have believed all along since college) and since there is no way a plant knows what isotope it has available to use unless it has a different chemical behavior, I still cannot see the logic behind this theory. It implies that plants would have to be sensitive to something I don’t see any way for them to be sensitive to, atomic weight or radioactivity.

                So again, HELP!

                I can see the method working, however precise or imprecise it may be in any given situation if I can see how the plants can differentiate between chemically indistinguishable carbon atoms. This is what has bothered me for years.

                And thanks again! I really do appreciate your time to answer me.

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                Roy Hogue

                Oops, neither 12C nor 13C is radioactive. So that’s not a factor.

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              • #

                Roy: Sorry, I’m not an expert in plants. I don’t know, off the top of my head, why some plants preferentially take up 12C compared to 13C.

                This may help:

                http://www.madsci.org/posts/archives/2003-06/1055532737.Bc.r.html

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              • #
                Roy Hogue

                Thanks again. That boils it down to a game of atomic tag in which the slower player loses out more of the time than the faster.

                I would never have guessed it — the chemical properties of different isotopes are not really equal after all, are they? But it does make sense if speed of an atom’s motion is a factor in the chemical reaction.

                Or maybe all isotopes are equal chemically but like the pig said, some are more equal than others. Reality can be very strange. ;-)

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            KinkyKeith

            Statement:

            “No. We’ve increased atmospheric CO2 by about 120 ppm, from a starting value of 280 ppm. That’s about 40%”

            What do you mean by WE?

            We did not change the world’s CO2 levels.

            Did CO2 levels really change?

            Lot of records dispute that.

            Selective reading is very harmful to the brain.

            KK

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              By “we” I meant, of course, humans.

              There is no question whatsoever that atmospheric CO2 concentration has changed since the beginning of the industrial era.

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      bobl

      I don’t think you can say that, the IR energy manifests in an elevated electron, the thermal energy manifests as greater average translational (motion) energy of the whole molecule through space. The elevated bond energy can’t be converted to molecular velocity absent some sort of conversion event. This conversion event (intersection with the force field of another atom ie collision has to happen before the excited bond collapses and reradiates the photon). Maybe that happens, maybe it doesn’t, maybe it happens in some places and not in others, for example in the thin upper atmosphere collisions are far less probable

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      KinkyKeith October 2, 2015 at 9:44 pm

      There are two points which might help eliminate Human Origin CO2 as a player:

      “1. There is definitely a mechanism by which CO2 absorbs ground origin IR ENERGY which is INSTANTANEOUSLY TRANSFERRED TO NEIGHBOURING GAS MOLECULES BY STANDARD MECHANISMS OF GAS PHYSICS.”

      Kind of! A CO2 aggregate gas molecules with effective cross sectional linear dimensions greater than 3.75 microns (1/4 wave) have finite probability of absorbing/emitting some wee 15 micron power in the form of EMR. If such happens individual molecular temperature must change by 1/10^20 kelvins. Can such be transfered elsewhere? For you my special friend, datala,datala,datala, until you buy such!!!

      “2. The problem is that Human Origin CO2, despite the reality of the IR absorption mechanism, is effectively a non-starter when it comes to a quantitative input. It just doesn’t rate against natural origin CO2 and water.”

      Who cares if you are paying? ;-)

      [Minor Editorial discretion applied] Fly

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        KinkyKeith

        Yes Will

        I know that its VERY rough scientifically and only very roughly on target with the mechanisms

        but the message that Man Made CO2 is not relevant is ABSOLUTELY INDISPUTABLE.

        Some of your comments will are a bit cryptic. What is the datala thing?

        :)

        kk

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    peterg

    I suppose the approximate back-of-the-envelope model I use is to assume that the upper troposphere is the layer of the atmosphere roughly at black-body equilibrium with the sun and outer space, with the earth’s surface being correspondingly warmer due to minimum lapse rate required to transfer heat by convection. Adding GHG will presumably raise the height of this equilibrium layer, so increasing surface temperatures due to lapse rate considerations. However adding GHG will also increase the radiation to outer space of energy absorbed in this layer from convection and also UV radiation absorbed by ozone. So adding GHG should increase temperatures, but there should also be large negative feedbacks.

    I am obviously an eccentric because nobody I know sees it this way.

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    • #

      peterg, that’s roughly how I see it here, except I am going a bit further (out of necessity) and saying four main emission layers instead of just one (CO2, water vapor, cloud tops, and surface) and watching the interplay between them.

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    • #

      Actually climate models assume that ALL layers of the atmosphere emit according to the Planck Law, as a function of wavelength, temperature, and optical depth (or pressure) The resulting differential equations are called the Schwarzschild equations, or the two-stream equations. Calculationally, these are integrated (numerically) across a finite number of atmospheric layers — typical numbers are about 20 layers or so.

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  • #
    A C Osborn

    One thing that becomes apparent when the “Stefan-Boltzmann Law” is applied to earth and analysed as it is here is that it is definitely NOT Science.
    There are too many assumptions, estimations and fudges for it to be proper science.
    One question that I have for Jo/David, how can the emissivity of the gases surrounding the Surface be higher than the emissivity of the Earth’s surface when the it is the Earth’s surface Temperature that is being used?
    Surely it must be the Surface temperature of each “emitter” and it’s respective emissivity that should be used?

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    • #

      A C Osborn, it is not the Earth’s surface temperature (288 K) that is being used in the SB equation, but the radiating temperature (255 K). Note however that the “radiating temperature” here is merely the temperature that satisfies the SB equation applied to Earth — that is, with the OLR and emissivity of Earth as seen from space.

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      • #
        Mike Flynn

        David,

        Sorry to keep at it, but tell me what the relevance of the SB equation is to a hot body such as the Earth, which in the absence of external energy sources such as the Sun, has a surface temperature of around 33K or so.

        It is often overlooked that the Earth is a large ball of molten and semi molten matter, with a very thin congealed crust – about the thickness of an apple skin, if the the Earth was apple sized. Just for fun, consider when the Earth’s surface temperature was 1000K. Would you be so sure that the 745K difference between the SB result and the actual temperature was due to a mythical greenhouse effect?

        Or if the surface temperature was measured at 288K, would you blithely assert that the 33K difference was due to CO2 warming?

        I guess you would for one, but probably not for the other. Am I right? How about when the surface temperature was 300K? (And it must have been at one time, as the Earth cooled from a molten surface state!) 112K due to CO2 warming?

        Examining models based on false assumptions is pointless. Attempting to reliably predict the future from the past, whether it be flood, drought, the price of gold, interest rates or whatever, is doomed to failure. “Predictions”, such as “The sun will rise tomorrow” are assumptions that any 12 year can make. Climatologists have to do better than a naive persistence projection to have any credence, and they can’t.

        A pointless waste of billions of dollars, with precisely no discernible benefit to mankind to date. Do you not agree?

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      • #

        This temperature is called the “brightness temperature.”

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          David Appell: No, it’s not quite the same:

          “The brightness temperature is a measurement of the radiance of the microwave radiation traveling upward from the top of the atmosphere to the satellite, expressed in units of the temperature of an equivalent black body.”

          Brightness temperature is the temperature a black body in thermal equilibrium with its surroundings would have to be to duplicate the observed intensity of a grey body object at a frequency”

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            I think it’s the same, because of spherical symmetry.

            “The Earth is a cool object in space: this is the prime
            reason why the FIR is so important to an understanding of
            the climate system. If we measure the brightness temperature
            of the Earth (that is, the temperature of an equivalent
            blackbody) with an instrument in space, we would measure
            something like 255 K.”

            – Harries et al, The Far Infrared Earth, Reviews of Geophysics, 46, RG4004 / 2008.

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            • #

              From the distance of the Moon the specular intensity of the Earth and its atmosphere are nowhere near that of a blackbody! Why do you claim your fantasy 255 K? Which, BTW, has never been measured! :-(

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  • #
    Den Volokin

    To All:

    Here is a new paper that provides a great deal of insight about how shortwave radiation and atmospheric properties determine the average surface temperature of planets with diverse atmospheres across the entire Solar System… Note that Earth is a part of a continuum that has not been understood before!

    Emergent model for predicting the average surface temperature of rocky planets with diverse atmospheres

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    • #

      And when you get to some average surface temperature based on insolation and lapse rate, do you have anything meaningful?
      Molecular noise temperature, thermometric (expansion) temperature, thermodynamic (energy/entropy) temperature, thermal radiometric temperature. What do you mean by temperature? Why would some average have meaning? How can reduction via dimensional analysis do anything except confuse the meaning of anything physical? See:discussion

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        Den Volokin

        Will,

        You need to learn some history of thermodynamics and fluid mechanics to understand the critical role of dimensional analysis in deriving new physical relationships and advancing theoretical understanding.

        Average temperature is meaningful simply because temperature is a LINEAR expression of the total kinetic energy in a system. Hence, the average temperature is a surrogate measure of the system’s energy content! This is basic thermodynamics …

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        • #

          Den Volokin.

          …temperature is a LINEAR expression of the total kinetic energy in a system.

          Which has the greater kinetic energy, an empty dam with a temerature of 20 degrees C or a full one at the same temperature?

          20

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            Bob Fernley-Jones

            @ Silligy

            I think Den Volokin does not explain that he is referring to molecular internal energy. (AKA quantum mechanics,theory)

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            • #

              Bob he seems to name these molecules Venus, Earth , Moon, Mars, Titon and Triton.
              The temperature of Venus has been shown to be cooling each time it has been measured. Just like in climate science the measurements were homogenised to agree with the theory that it is not cooling. Triton and Titon meanwhile store huge amounts of energy as abiotic hydrocarbons. While the CO2 on Mars fails to warm it much, the kinetic energy of the atmospheres on Mars and our Moon come and go with the solar wind.

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              • #
                Bob Fernley-Jones

                Immanuel Velikovsky predicted contrary to paradigm in the 1950’s that Venus was extremely hot because it was of recent violent birth. However, he used unlikely literature references from the Biblical Old Testament as part of his thesis, (some bits since proven false such as in V’s concatenations from within the Lamentations of Ipuwer).
                Never mind, Carl Sagan to the rescue of science…… it was all that CO2 on Venus that was the bovver.
                (A Book by Charles Ginenthal ‘Carl Sagan & Immanuel Velikovsky’ makes a very interesting read with much head shaking)
                Rog, might have something to say on Venus if he is still around!

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              Den is referring to gases. Basic thermodynamics: the temperature of a gas is proportional to the average kinetic energy of its molecules.

              30

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            Den Volokin

            Correction – I meant to say:

            “… temperature is a LINEAR expression of the total kinetic energy per unit volume in a system.”

            20

            • #
              Bob Fernley-Jones

              @Den
              Yes or no unless you elaborate what you mean by ‘system’, even if you might include engineers in the conversation. There are several kinds of kinetic energy (and heat) outside of the fairly recent elite definitions by physicists. For instance when a vehicle crashes into an unforgiving object it converts quite a lot of kinetic energy into heat (performs work in the process).

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        • #

          Den Volokin, your comment “Will,You need to learn some history of thermodynamics and fluid mechanics to understand the critical role of dimensional analysis in deriving new physical relationships and advancing theoretical understanding.” is harsh.
          Please note that thermodynamics, fluid dynamics, heat&mass transfer, reaction kinetics and dimensional analysis are engineering subjects. You can find them in the Perry’s Chemical Engineering Handbook. Thermodynamics started with the French engineer Lazare Carnot and was developed further by his son French engineer Nicolas Sadi Carnot. Most if not all dimensionless numbers are name after prominent engineers eg Reynolds Re, Prandtl Pr, Nusselt Nu, Grashhof Gr, Schmidt SC etc
          I believe Will is an engineer but I note you are not.
          Re your Aug 15 paper -it is interesting. I have it on file from a previous post (possibly Hockeyshtick) where I think I made some comment. The problem with most scientists (including physicists) is they have no actual experience with thermodynamics, heat&mass transfer or fluid dynamics.

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          • #

            I should have added some dates. Lazare Carnot wrote and published the essay “Essai sur les machines en general” in 1783 and developed that further as “Principes fundamentaux de l’equilibres et du movement” in 1803. Sadi Carnot published in 1824 “Reflections on the Motive Force of Fire” in 1824. In the latter are the principles leading to the second law of Thermodynamics which Rudolf Clausius re-interpreted in his publication “On the Moving Force of Heat” in 1850. See the book “Great Engineers and Pioneers in Technology” by Ed Roland Turner et al

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      Den, that’s an interesting approach and well written paper. Seems very reasonable.

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        Den Volokin

        Thank you, David. The findings reported in this paper hold the key to understanding planetary climates in a whole new light … :)

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    • #

      Den: About your paper — standard and simple radiative physics completely and accurately accounts for the Moon’s average surface temperature, and its variation on the day-side, as I showed here:

      http://davidappell.blogspot.com/2012/04/norfolk-constabulary-made-wrong-charges.html

      It’s really quite simple with nothing controversial about it at all.

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      • #
        Bob Fernley-Jones

        @David Appell,
        If it’s that simple, is that story that NASA screwed-up on their calcs not all that long ago false? Do you treat the thermal inertia effects of the regolith and and and …. as simple?

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        • #

          Yes, it’s that simple.

          I don’t know of any story about NASA screwing up the calculation.

          I discussed how I treat the regolith in my post — I took the regolith to be a constant 95 K on the dark side of the moon, as measured by Diviner.

          http://davidappell.blogspot.com/2012/04/norfolk-constabulary-made-wrong-charges.html

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            Bob Fernley-Jones

            @ David Appell,

            Do you understand what I mean in ‘thermal inertia’ which cannot be measured from a spacecraft as far as I’m aware?

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          • #

            Yes, I understand what thermal inertia means.

            The Diviner measurements show the temperature of the nightside of the moon varies little — it’s about 9-125 K:

            http://davidappell.blogspot.com/2012/04/norfolk-constabulary-made-wrong-charges.html

            So modeling it as a constant is a good approximate; I took it to be 95 K.

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              Bob Fernley-Jones

              @ David Appell,

              It sounds to me that you bypassed the complexities of having no thermal inertia data for the lunar regolith (at night?) by somehow assessing the average surface T to 95K from a range of 9K to 125K. Presumably that range varies from dusk till dawn, spatially and on a variety of surfaces…. Tricky.

              When you say above:

              “…standard and simple radiative physics completely and accurately accounts for the Moon’s average surface temperature, and its variation on the day-side, as I showed here:
              http://davidappell.blogspot.com/2012/04/norfolk-constabulary-made-wrong-charges.html
              It’s really quite simple with nothing controversial about it at all.”

              Sorry David but your modelling sounds far too simple and approximated to me.

              BTW, have you seen Den Volikin’s comment on the Moon and S & B below

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                Bob: The observations show the dark side of the moon varies little. So for a simple model there’s no need to consider thermal interia or conductivity through the regolith.

                My “simple model” completely explains the dayside temperature of the Mon — its values, and the shape of its curve.

                That’s because a complex model isn’t needed — the Moon’s dayside temperature is a straightforward application of simple radiative physics.

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    David,
    1. When and why was the so called “S-B Law” invented?
    2. Could you please supply the name of the individual or group that intentionally destroyed the very precise and useful S-B ‘equation’ that determined a theoretical maximum possible thermal radiative flux and the direction of such flux between two flat parallel surfaces in a direction normal to those surfaces?
    3. Was this done so as to claim necessary spontaneous thermal electromagnetic radiative emission (T^4) from any mass with temperature in every direction with no regard to an opposing thermal environment?
    4. Was this done to require belief in some radiative two stream approximation, to limit the need to asymptotic absolute zero temperature?
    5. Who profited from such endeavor?
    All the best! -will-

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      Oh come on Will, it’s not uncommon to refer to it as a “law”, and besides “law” has only three letters to type while “equation” scares many.

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        Yes David,
        But why refer to ‘LAW’ rather than ‘fantasy’ in this SCAM? The ‘equation’ while only declaring an asymptote of a ‘maximum’ of directional thermal flux. In each and every measurement this has always been supportive of correct. OTHO your single T^4 flux has never been detected observed, nor measured. Why do you support deceptive fantasy?

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          The S-B Law is a well-established law of radiative physics; it was discovered empirically in 1879. It’s since been shown to be a consequence of Planck’s law of radiation, one of the most fundamental discoveries of quantum mechanics.

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      Will, Jozeph Stefan developed his equation in 1879. Somewhere in my files I have a copy of his original treatise. He based his equation on actual experimental data at temperatures around 250-450C (as well as I can remember) of a flat surface radiating in a vacuum to a colder surface. His original finding was just that the heat flux was proportional to the 4th power of absolute temperature. Together with his student Ludwig Boltzmann they then determined the proportionality constant for a theoretical blackbody from thermodynamics. Engineers at the time objected that there were few or no blackbodies so an emissivity factor was introduced. Also it was found for actual heat transfer that the temperature of the receiving body must be taken into account. Planck actually used some of Boltzmann’s work to develop his theory. Planck assume that dry air at temperature in his range of working did not absorb radiation and acted like a vacuum. The Stefan-Boltzmann constant can be derived from from Planck’s spectral distribution of energy flux because it originated from Boltzmann.

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        jim2

        A hollow cavity with a hole small in proportion to the cavity size is used in the lab as a black body. It doesn’t matter that the outside surface of the cavity container is not a black body. All that matters is that the radiation exiting the hole has a distribution of radiation and power predicted by the hypothesis under test and it matches Plank’s formula.

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          Jim2 -not quite, a cavity has an internal surface and the nature of absorption and emission depends on the nature and configuration of the cavity. See “On the Equation which governs Cavity Radiation” by Pierre-Marie Robitaille Progress in Physics July 2014 P157-162

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            “On the Equation which governs Cavity Radiation” by Pierre-Marie Robitaille”

            Is but a juvenile attempt by Marie,to be considered important. Most cavities like most trimer+ molecules are designed to be resonant at one or more frequencies.
            A properly designed ($$$) black body cavity, cannot be perfect. But any discovered resonance would immediately put the builder out of business.

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    Bob Fernley-Jones

    I’ve not had time to follow this series well but I don’t think there is any discussion on the fact that radiation is uniformly distributed in all directions within the atmosphere (but mostly hemispherically from the surface and S & B relates to a single small flat surface in the lab with effectively no surrounding reabsorption).
    In a simple analogy, if you count the dimples on a golf ball; predominantly they mostly orientate towards the horizontal versus not much up and down. Interestingly, in any local horizontal stable packet of air, the bulk of the emissions have a net effect of zero, (hence constant T). Some complexities include greatly varying Gaussian (I think) distributions of photon path lengths (distance to absorbing molecules), molecular collisions (heating of non GHG’s), and curvature of the global surface.
    Unfortunately, I don’t think that the IPCC (= Kevin Trenberth) considered these matters in their wonderful “Earth’s Energy Budget” chart.
    I have a more elaborate study on this if anyone is interested.

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      bobl

      I’m not sure Trenberth understood much physics or chemistry at all.

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      ‘I’ve not had time to follow this series well but I don’t think there is any discussion on the fact that radiation is uniformly distributed in all directions within the atmosphere’

      Please there is no such FACT. Electromagnetic radiative flux at any frequency can only be dispatched, powered or spontaneously in a direction of lower opposing field strength (radiance) at each frequency.
      Any opposing POV must supply at least one measurable occurrence of such contradiction of Maxwell’s equations. This minimum occurrence is but the possibility of some conjecture, let alone hypothesis or theorem. Where has your claim ever occurred?

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      Yes, all climate models take into account the uniform distribution of radiation. Symmetry means you can easily integrate over all (the angular coordinates) but the coordinate that represents altitude.

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    wkg_in_bham (the one in the US)

    To all #1: I think everyone should take a deep breath and relax. Wait until you’ve read the whole thing before going “you’re wrong, you’re wrong.”

    To all #2: I think David is right that GW crowd and their experts need to be addressed using their models, assumptions, equations, etc; you know the “settled science”. Anything else gets blown off as. He’s already has the burden of being and EE and mathmatician and not a climate “scientist”.

    To all #3: I think any comments should be along the line of “I don’t quite understand this statement” and perhaps the nature of your befuddlement.

    To David: I know you don’t want to make a careear of this series. Will you consider followup sessions to address issues that are not considered by the standard model(s)or are considered but improperly (in addition to what you have/are going to discuss)? The first one could be: “OK, there’s my case”. What has been omitted that you think is important or is included but wrongly. The responses to this need to be short – a sentence or two. These should be tabulated, in the best case, we take them an issue at a time in following sessions where people can vent to the heart’s content.
    wkg

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    Bob Fernley-Jones

    @ Will Janoshka,
    Say; what time of day is it over there in Arkansaw?

    My comment related to, quote: “any local horizontal stable packet of air”

    There is apparently no problem with potential differences within the limiting photon free path lengths in the atmosphere in any direction. I say apparently because some have claimed those limits to be measured in metres at relevant atmospheric pressure levels, last I looked. For any given air temperature, regardless of the depth of the local parcel, there is a large variation in molecular energy levels, (proven in lab), and the average T in a stable local parcel of air varies little anyway.
    Do you have some new information Will?

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      “For any given air temperature, regardless of the depth of the local parcel, there is a large variation in molecular energy levels, (proven in lab)”

      Really where how? Nothing but innate nonsense!!

      “and the average T in a stable local parcel of air varies little anyway.”
      What the hell may be some average T? Each and every atmospheric molecule expresses its own noise power as kT/t at every instant of your time. If you wish to fantasize that as some average T, That is fine! My kitten will still eat your face off, independent of your temperature!

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        Bob Fernley-Jones

        @Will Janoschka

        1) I can’t be bothered finding a reference for a lab test but an elegant demonstration is that a basic reason that evaporation of a liquid results in cooling at the surface is because it is predominantly the higher energy molecules that fly off (leaving a greater proportion of lower energy molecules behind).

        2) You seem to agree that in a stable sample of a fluid (e.g. a small local parcel or local thermal thingy) there is in fact a distribution of molecules having a range of individual energy levels. If you insert a thermometer into that sample and obtain a reading there will be what I mean as average T in the context of T being an indicator of the net of the molecular energy levels. See also Den Volokin’s; T being a linear representation etcetera above.

        PS Sorry for misspelling you surname earlier

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    Bob Fernley-Jones October 3, 2015 at 5:19 pm

    “@ Will JanoshkaJanoschka,Say; what time of day is it over there in Arkansaw?“Arkansas? Idiot!
    Right now here TOD is, Kitten screams ‘wheres my food’!

    My comment related to, quote: “any local horizontal stable packet of air”

    What may you mean by ‘packet of air’, stable or not in any direction? Atmosphere cannot be both parceled and well mixed. Take your pick!

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    KinkyKeith

    Blast from the past:

    AndyG55
    February 13, 2013 at 6:53 am

    Hi Harry,

    I do keep trying to bring the fact that the temperature is controlled by the pressure gradient in the atmosphere, and that the actual atmospheric constituents have very little to do with it.

    The same heat gradient will eventually establish itself even with the multi-phase chaos of H2O.

    Maybe one day they will realise the truth of this.

    Not holding my breathe though.

    Report this

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    KinkyKeith
    February 13, 2013 at 7:49 am

    Andy

    You’re my hero.

    That was a great summary.

    For those of us who understand it, it is the end of CAGW, otherwise known as Incineration by Carbon Dioxide.

    The core mechanism that is at work is contained in the understanding about gas molecules of one type in the air; They have neighbours and are never alone.

    Even if CO2 is able to specifically absorb extra energy, it will instantaneously share and transfer that energy to nearby gas molecules making the entire atmosphere participate.

    CO2 can’t do much anyhow because there is not much of it ; water fills any role that might be seen for CO2 as being “dangerous to humans”.

    Effectively the entire atmosphere absorbs the energy under discussion by CAGW enthusiasts, not just CO2.

    If CO2 was missing entirely, the air would still get to the same temperature.

    KK :)

    Report this

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    Streetcred
    February 13, 2013 at 8:29 am

    The entire premise that CO2 is the ‘killer’ gas is dependant on the non-existent process of perpetual warming enhancement by water vapour. It is common knowledge that this is bollocks so the idea of CO2 being dangerous must fail at the most fundamental hurdle.

    Report this

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    KinkyKeith
    February 13, 2013 at 11:15 am

    Exactly Streetcred.

    After the initial try at getting CO2 demonised on its own failed they thought up the

    “process of perpetual warming enhancement by water vapour” junk you mention.

    If this CO2 – H2O interaction was open ended then we would have been incinerated long ago because of the unlimited supply of water vapour available.

    It is obvious that this process is a self limiting system.

    Extra water vapour in the air, rather than lead to warming actually reduces heat energy reaching

    Earths bio-zone and leaves us well regulated .

    As a matter of fact I’d say things at the moment are Just About Perfect.

    KK :)

    self limiting

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    ScotsmaninUtah

    “radiation from a non fixed point in space”

    finally got to read this post , and what a thoroughly brilliant piece of work by Dr Evans.
    Applying the concept of “radiative temperature” to SB law is a very workable abstraction
    In our work in 3D graphics we constantly have to deal with light rays and calculating the “normal” from either a static/dynamic surface or a static/dynamic point source in order to calculate the effective radiation (light) to model what the eye should see.
    In the 3D graphics world we use volumetric polygons to model those surfaces that do not have a tangible surface (clouds ), the similarities here are remarkable and this idea of Dr Evans is very intriguing !

    Enjoying the series immensely

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    Franktoo (Frank)

    David: This post is elegantly and accurately written, but IMO applying the S-B equation to gases invariably leads to problems. The initial assumption in the derivation of Planck’ Law is that radiation has come into equilibrium with the medium surrounding it. You may remember that this law was developed to explain the radiation emitted by black cavities designed to produce such equilibrium. Planck’s Law (and the S-B equation) are technically not valid when such equilibrium doesn’t exist (although the Schwarzschild equation is valid assuming LTE and can be modified to include scattering). Sooner or later the S-B equation creates dilemmas:

    1) Emission depends on the amount of GHG present, but emissivity does not? Actually, we wave our hands and say that the emissivity of an “optically thick layer” is independent of the amount of GHG present, but the emissivity of an “optically thin layer” is proportional to the thickness of the layer, its density and absorption coefficient. We pretend emissivity is both an intrinsic and extrinsic property of a gas.

    2) Above you wrote: “However, of the 239 W m−2 of OLR emitted by the Earth, all but 90 to 100 W m−2 comes from greenhouse gases — principally water vapor, CO2, methane, and ozone. These gases do not reflect infrared, so their emissivity is one.”

    You could apply the same argument to nitrogen, which doesn’t reflect infrared either. Is nitrogen’s emissivity one too?

    3) Emissivity is a fudge factor which allows us to wave our hands about why many solids and liquids emit less than blackbody intensity radiation. As best I can tell, that type of emissivity develops from scattering/reflection at the interface between two materials, explaining why emissivity = absorptivity for a given wavelength. That explanation isn’t relevant to gases. That explanation doesn’t work for semi-tranparent gases or thin films of solids or liquids

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      Frank: Technically this post does not apply the SB equation (although it “effectively” does so).

      The radiating temperature is defined as the temperature that would make the S-B equation true if the SB equation was applied to a solid surface emitting into space with the same OLR and (presumed) emissivity as the Earth.

      [And also the solid surface must be isothermal (same temperature all over) at all times. See Den Volokin's comment 21.1.2. Thanks Den.]

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        David Evans October 5, 2015 at 3:58 pm

        ‘Frank: Technically this post does not apply the SB equation (although it “effectively” does so).’

        “The radiating temperature is defined as the temperature that would make the S-B equation true if the SB equation was applied to a solid surface emitting into space with the same OLR and (presumed) emissivity as the Earth.”

        In 1984 we all agreed that the concept of ‘brightness’ was very confusing as to meaning. At that time, along with the concept of absolute zero temperature. ‘brightness’ was depreciated and replaced by precise luminance (radiant power) as feeling observed by earthlings non-linear frequency eyeball response to ‘brightness’,over the visible range. Weard I know! but DONE. Radiance now becomes the normalized, in three orthogonal directions, and normalized, (1/t) for EMR power, independent of mass, velocity, or anything else. Simply power in one direction. W/sr. So very sorry for how that clear simplification turned out in the vast realm of human snake oil salesmen.
        All the best! -will-

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        Den Volokin

        That’s correct, David!

        More precisely, the temperature calculated directly from the S-B law refers to a thermally homogeneous surface such as an isothermal disk. A fundamental assumption of the S-B equation is that the surface in question is isothermal (the same temperature throughout) and that the emitted LW flux is therefore spatially homogeneous. These conditions are NOT met in case of a spherical body such as a planet (or moon). As a result, the radiating temperature calculated from the average absorbed radiation by a sphere using the S-B law is always different from (larger than) the sphere’s true mean surface temperature. This difference is mathematically explained by the so-called Holder’s inequality between integrals. The inequality arises when a non-linear function (such as the flux-temperature relationship of the S-B laws) interacts with a non-uniform distribution of the physical driver (such as the absorption radiation flux by the surface of a sphere).

        This is all explained in our paper.

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          Bob Fernley-Jones

          @ Den Volikin,

          Makes good sense. Can you give us a quick idea of the amount of difference the Earth’s curvature gives versus a flat plate.

          BTW, at any instant in time is it not the surface T that matters? I was unaware that S & B demanded constancy or was aware of anything happening under the surface.

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            Den Volokin

            Bob,

            Here is an example of the difference we are talking about illustrated with the Moon as an example. The S-B equation using the average absorbed radiation by the Moon yields Te = 270 K for Moon’s mean global temperature. The actual mean global temperature of the lunar surface is 197.3 K. So, the error arising from using the simple S-B formula to estimate Moon’s average temperature is 270 – 197.3 = 72.7 K. Quite substantial!

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              Bob Fernley-Jones

              Thanks Den,

              I find that to be highly surprising. Presumably it is a good bit less pronounced for the Earth though.

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              Den: Again, a local application of the SB Law to the lunar daytime surface, assuming local thermal equilibrium, completely explains its temperature and its temperature variation:

              S(1-albedo) = sigma*T^4

              where S is the solar irradiance. S varies with latitude and longitude of the lunar surface; on the equator it is S0*cos(longitude), where longitude (the angle from the zenith) goes from -90 degrees to +90 degrees, and S0 is the solar constant at Earth’s distance, 1365 W/m2.

              More details here:

              http://davidappell.blogspot.com/2012/04/norfolk-constabulary-made-wrong-charges.html

              All this stuff about Holder’s inequality is unnecessary and irrelevant. Not surprisingly, it doens’t get the right answers. Standard radiative physics does get the right numbers.

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              Den Volokin wrote:
              “The S-B equation using the average absorbed radiation by the Moon yields Te = 270 K for Moon’s mean global temperature.”

              You get the wrong answer because you’re using an equation that doesn’t hold.

              The Earth has an atmosphere. So it’s a good approximation to assume that the entire atmosphere is in thermal equilibrium with the surface, hence that the surface is at a constant temperature, which can be calculated via

              S(1-albedo)/4 = sigma*T^4

              But the Moon does not have an atmosphere. Hence one cannot assume the surface is at a constant temperature. Hence you cannot use the above equation to calculate its average temperature. Not surprisingly, that equation gives the wrong result for the Moon.

              But you can assume local thermodynamic equilibrium at each point on the Moon’s surface. That *does* give the right value for the lunar surface temperature, and hence for its average, as I keep pointing out here:

              http://davidappell.blogspot.com/2012/04/norfolk-constabulary-made-wrong-charges.html

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    The Stefan-Boltzmann law applies to a body with a surface radiating into space, and is blah,blah blah. What total nonsense!
    You write only, not of any precise S-B equation of some maximum. You write only of the Planck formula for maximum “specific intensity”, (spectral radiance) that can only be a radiant potential, never radiant flux.

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    JonH

    All very fascinating, and absorbing, David (and others who have responded), but is it possible please to put all this in layman’s terms? Trying to understand it all with my limited knowledge of mathematics is doing my head in.

    Congratulations on your (I think) good works.

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      JonH, I do my best in the intro’s, but it is a bit of a paradigm shift, so we’ll be discussing this with more diagrams and even cartoons in future to help. It is difficult.

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      Den Volokin

      JonH, I’m afraid that grasping new concepts in planetary science is not possible without at least some mastery of math. One key aspect of the discussion about the difference between effective radiating temperatures and physical (measurable) surface temperatures is understanding the effect of non-linearity on system’s response.

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        Bob Fernley-Jones

        @ Den Volokin,

        Yes, but it would be better if you guys wrote in a less elitist style that ordinary people, (heaven forbid, even policy makers), might understand. For instance, here is one of your classics from above:

        “You need to learn some history of thermodynamics and fluid mechanics to understand the critical role of dimensional analysis in deriving new physical relationships and advancing theoretical understanding.
        Average temperature is meaningful simply because temperature is a LINEAR expression of the total kinetic energy in a system. Hence, the average temperature is a surrogate measure of the system’s energy content! This is basic thermodynamics …”

        Not only is your wordsmithing too complicated but in parts you display your elitism as an apparent physicist and seem to think that quantum theory contains the only form of thermodynamics, even if some parts of quanta-speak defy the long established (classical) thermodynamics.

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    JonH

    I suppose my overarching question would be: if it is so difficult to explain, based on the levels of discussion among your peers, how on earth (no pun intended) does one convince the “masses” that all other models used by climate change advocates are incorrect and therefore all the zeal directed towards CAGW is totally misplaced…including all the penalties being applied for “emitting carbon” in things as simple as my energy bills? Thanx for your response, Joanne.

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    RogueElement451

    I still keep thinking about moments of inertia ,Omni directional radiation in the face of overwhelming force?
    I shall carry on reading and waiting for the nutters guide to climate models.
    All the best with the continuing unveiling of your Work Mr Evans , at least this time there is less vitriol than when your notch theory was revealed .
    Lets hope it stays that way.
    An awful lot of red thumbs appearing for no particular purpose unless of course Dave Apple is writing in which case …

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    William Palmer

    As water vapor streams up from the tropics do we know how much CO2 is converted into H2CO3 by aerosolic carbonic anhydrase? Maybe this is negatovely affecting the level of CO2? Carbonic acid prbably has a totally different infrared absorbtion spectrum.

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    Bart Bartholomew

    Too many approximations, whose average error seems unlikely to be zero.
    “About” does not seem to lend itself to “Scientific” testing.

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    arationofreason

    First let me acknowledge the (mostly) civilized comments on this web site. Thank you all (you know who you are).
    Much as I appreciate the entertainment and education that I have gleaned from these sincere discussions over the decades, I think that I have grown weary of the little progress toward resolution of the issue. Perhaps the declaration by those with too much alphabet soup following their names to be ignored should be acknowledged. Earth’s atmosphere/geology/biology dynamic energy balance is a random chaotic system and its future behavior cannot be accurately predicted. (Or as less delicately put; attempts at prediction is a ‘fools errand’) While I appreciate completely the heroic efforts of those with appropriate credentials to try to understand and resolve the issue from first principals and calculations, I cannot imagine an adequately (spatially and temporally) resolved model to serve as a foundation for resolution of the energy balance to the required accuracy.
    Unencumbered by formal credentials to participate in the discussion at the levels demonstrated by many here and the many scientific papers available (generated at no small expense to the taxpayer as well as personal sacrifice) let me pose a simple proposition for your consideration.
    To any increase in ‘forcing’ one must assume that respose of temperature and water vaporization increase to the atmosphere should be a given. Yes I understand the positive vapor feedback and warming in the microcosm of the atmosphere surface layer but this merely serves the enhance the efficiency of conversion of the surface energy to water vaporization and surface temperature increase. Convection of water vapor (carrying a large portion of the increased energy) to the upper troposphere is an observable fact. Since water vapor is the only significant source of IR radiation to space, water vapor by default, must result in a proportional increment to said radiation and thus represents a NET increase in energy loss to space resulting from any increase in surface heating.
    In all the random chaos of the atmosphere, water vapor is the only significant physical material transporting and radiating the balance of earth energy to space. (Direct IR radiation to space through the atmospheric “IR window” notwithstanding,) mother nature has no other significant tool to work with and must perforce, have solved these complex cross coupled condensation, convection, re-radiation equations to accomplish the feat. (Thank Thor and Allah since I’m unconvinced that our computing power will ever be up to the task).

    The water vapor cycle is therefore a NET NEGATIVE feedback.

    Since the conjecture of the CAGW house of cards rests fully on the assertion of positive water vapor feedback net planet warming, there is a disconnect in the logic in that assertion in the net effect of the hydrological system physics. I sincerely hope that in your invited comments that there is no effort to make the case that any additional water vapor introduced into the cycle is somehow a net planetary system warming when all of the other water vapor (there being no other significant option available) provides net cooling to the system.
    I’ve no illusion that with the enticement of $2.6 Billion/yr made available to and by the government research labs that my expensive entertainment and education will not continue.

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    Franktoo (Frank)

    David: As I read your later posts and look back through the links (which are very useful), I came back here to understand the difference between Planck and S-B feedback/response. (I’ll use the term “response” instead of feedback for clarity. Planck or S-B response are amplified by other feedbacks.) There appears to be a potentially fatal flaw with your equation 5), which I will rewrite for clarity. When you differentiate the S-B equation, you are assuming the change in emissivity with surface temperature is zero:

    W = eoT^4
    dW/dT = 4eoT^3 + oT^4*(de/dT) = 4eoT^3 (used in eq 5)

    Does this assumption make sense? I don’t think so. Feedbacks are all about how OLR is effected by temperature dependent changes in WV, LR, and clouds. The existence of these changes (which can be observed from space during seasonal warming) guarantees that de/dT is not zero. By adopting the S-B approach, your dW/dT (and dT/dW) will include some feedbacks. Values the IPCC reports using Planck response probably differ from the values appropriate for S-B response.

    If e = 1 at 255 K and e = 0.61 at 288 K, then a first approximation for de/dT is about -0.39/33. In that case, oT^4*(de/dT) = -3.9 W/K. 4eoT^3 = 3.3 W/K. This result is obviously nonsense – dW/dT (the sum of these terms) can’t be negative (without a runaway greenhouse effect). Therefore de/dT can’t be linear from 255 to 288 K. However, de/dT is negative and the value you use for dW/dT should be too big. Perhaps the right value for de/dT around 288 K is the value that makes S-B feedback equal to Planck feedback.

    When calculating Planck response (which assumes the earth behaves like a blackbody, emissivity is by definition a constant, 1. dW/dT is 4oT^3 or dW/W = 4*(dT/T). This approach cleanly separates the Planck response from other feedbacks.

    When first trying to teach myself climate science, I wondered whether the no-feedbacks climate sensitivity should be calculated using 255 K (and an emissivity of 1) or 288 degK (and an emissivity of 0.61). Choosing 288 K was attractive because it produced a lower no-feedbacks climate sensitivity. However, surface emissivity is not 0.61, so that choice can’t be correct. Is the emissivity of the atmosphere 1? For optically thin layers, emissivity is proportional to density, but we expect an optically thick layer to have an emissivity of 1. So 255 K makes the most sense to me. The problem with using 255 K is that the surface and atmosphere don’t warm the same amount in response to a forcing. However, that problem is addressed by lapse rate feedback

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      Frank: Only the “SB sensitivity” was defined here. The “response” as defined here includes feedbacks: response = sensitivity + feedbacks. I used “Planck sensitivity” as the parallel to SB sensitivity, which is the correct number for the model (feeding forward, from forcing to surface temperature) and avoids the naming fiasco of “Planck feedback” (it’s not a feedback because it does not feed back to affect what caused it).

      The SB equation can really only be applied to a solid, isothermal surface emitting into space (see Den Volokin’s comment 21.1.2). The Earth isn’t like that, obviously, so we applied it as is if the Earth was like that and defined the “radiating temperature” as what you would get if you could apply the SB equation to the Earth — using its OLR and emissivity.

      The emissivity is thus that of the Earth as seen from space, in infrared. The Earth looks from space on infrared like an opaque non-reflective gas (apart from the cloud tops and atmospheric window — and even in the latter you are probably mostly seeing water vapor continuum), which thus has an emissivity of one. See the section of the post entitled “The Earth’s Emissivity” — the emissivity overall is greater than 0.99. Most climate scientists for most purposes just use an emissivity of one.

      When the CO2 doubles, the emissivity does change by a tiny amount. But the overall emissivity is still just less than one. Which is why it is treated as a constant in Eq. (5).

      The idea of an emissivity of 0.61 is non-physical. It isn’t anywhere near that, and one might only consider such a value by misapplying the SB equation to the Earth’s surface — where it is not radiating to space, but convecting right through the SB “surface”! There is no proper way to apply the SB equation to Earth, and the least worst by a long way is as per the post, applying it to the whole earth — which gives a radiating temperature of 255 K, with an emissivity of just less than one.

      The “Planck feedback” is not actually a feedback, but the partial derivative that arises when deriving the conventional model (see post 2 and post 3). It is equal to the reciprocal of the SB sensitivity, tweaked a bit for the fact that the ozone and CO2 emission layers are mainly in the stratosphere, which is assumed to stay at the same temperature under the Planck conditions (which are the conditions deemed appropriate for holding everything constant — see post 2) as the surface warms, so not all of the radiating “surface” of the Earth rise in line with the surface temperature. The gory details of computing the Planck feedback/sensitivity are given in the spreadsheet for the project.

      The approach followed in these posts gets around all the familiar potholes you are describing in your comment, and is in line with establishment climate science (which is quite correct on these issues AFAIK).

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        Franktoo (Frank)

        David wrote: “Only the “SB sensitivity” was defined here. The “response” as defined here includes feedbacks: response = sensitivity + feedbacks. I used “Planck sensitivity” as the parallel to SB sensitivity”.

        Sorry we are getting confused (again) about terminology. I have been using the word response in the sense of how a blackbody or graybody responds to warming – the change in the radiation it emits is the “Planck response” or the “S-B response” to warming or cooling. We both agree that such “responses” don’t amplify themselves by a feedback loop. It appears as if my Planck response is similar to your Planck sensitivity and my S-B response is similar to your S-B sensitivity, although climate sensitivity is the reciprocal of these responses after they are modified by feedbacks. FWIW, I am never using Planck or S-B response to refer to the global response after feedbacks are included. The Planck response is modified by feedbacks to give a “global” change in OLR after surface warming, technically the climate feedback parameter. The climate feedback parameter isn’t part of a feedback loop (that requires summing an infinite series).

        Setting aside terminology, I tried to raise an important problem with applying the S-B equation to the planet. When you differentiate the S-B equation with respect to temperature, you can’t ignore the fact that emissivity is a function of temperature. de/dT is not zero or close to zero.

        W = eoT^4
        dW/dT = 4eoT^3 + oT^4*(de/dT)

        According to Soden&Held (2006), pdW/pdT is -3.2 W/m2/K in all climate models. If the earth were a blackbody at 255 K, pdW/pdT would be -3.76 W/m2/K if the de/dT = 0. 4eoT^3 = -3.2 W/m2/K, when T = 241 K and e =1. In other words, the earth emits like a blackbody at 255 K, but has the Planck feedback for a blackbody at 241 K (when de/dT is zero).

        If de/dT = 0, the earth would fit gray body model with a temperature of 300 K and an emissivity of 0.51 by emitting 239 W/m2 and having a “Planck feedback” of -3.2 W/m2/K. This is obviously absurd.

        The only way the earth can emit like a blackbody at 255 K and have a Planck feedback like a blackbody at 241 K is for de/dT not to be equal to zero. oT^4 is equal to 240 W/m2 at 255 K, so de/dT needs to be -.0022 (units of 1/K) if e = 1. So the earth behaves as if it has an emissivity modestly less than 1 and that emissivity is changing enough with temperature to produce pdW/pdT = -3.2 W/m2/K.

        I’m sure that you recognize the 0.55 W/m2/K difference (between a “Planck feedback” of -3.77 W/m2/K for a blackbody and the -3.2 W/m2/K that is observed with AOGCMs) has very significant consequences.

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          Frank, see Fig. 2 of post 3 and Fig. 1 of post 13 for terminology.

          As explained in the previous reply, the 17% difference between the Planck sensitivity (0.31 K per W/m2, see post 2), the reciprocal of the misnamed “Planck feedback” from AR5 (3.2 W/m2 per K), and the SB sensitivity (0.27 K per W/m2, see Eq. (5) above)) is due to the fact that under the Planck conditions the stratosphere is held at a constant temperature and involves the surface temperature, while the SB sensitivity holds under all conditions and involves the radiating temperature. That’s it. No change in emissivity is implied or required.

          Note how the Planck feedback arises as a partial derivative in post 2 or post 3, where all the feedbacks are held constant. The Planck conditions are the deemed holding-of-everything constant — tropospheric temperatures are allowed to vary in sync with the surface temperature, but stratospheric temperatures are held constant. Thus all emissions from the stratosphere stay constant when the surface warms, in constructing the Planck feedback value — which accounts for most of the 17% difference. However the SB sensitivity applies under all conditions– and it connects the OLR to the radiating temperature, not the surface temperature (note well). The radiating temperature is defined as the temperature an isothermal solid sphere emitting into space would have to produce the OLR.

          Calculations of the Planck and SB sensitivities, showing how their difference arises, is in the spreadsheet, on the sheet called “Sensitivities”. Note that there is a also a small factor due to the non-uniform distribution of temperature and the concavity of the t^4 function.

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    James

    David, you can not average a flux over an area of a sphere, this is so blatantly false. Just do it for both semi-spheres separately and your “climate sensitivity” is gone.

    Besides, you can not derive average temperature just from average radiation, this is even a greater blunder, because even an average high school student must know that if the dependency is not linear, averages can not be handled like that. Those two things disqualify you, like many other “climate scientists”, sorry.

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      James, note that the “radiating temperature” is defined here as the temperature that satisfies the Stefan Boltzmann equation applied to Earth as seen from space, that is, with the OLR and emissivity of Earth. This is the only way the SB equation can be “applied” to Earth.

      As for linearity, see Fig. (1) above.

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        “James, note that the “radiating temperature” is defined here as the temperature that satisfies the Stefan Boltzmann equation applied to Earth as seen from space, that is, with the OLR and emissivity of Earth. This is the only way the SB equation can be “applied” to Earth.”

        The S-B can never be applied to the Earth as the Earth plus its atmosphere (where the exitance is generated) cannot be an isotherm. It must have a gravitationally induced pressure density and thermal lapse! Only the temperature decrease is linear! The density lapse is what favors exit emission delta flux concentration to the mid troposphere for both WV and water condensate (cloud tops in the tropics). Your surface pipe in that 8-13 µ band is very limited by vast cloud coverage and a very limited solid angle, (use 1 steradian not PI steradians). To zenith water emissivity is 98% in that band. It decreases slightly to 50° from normal then drops to zero at 60° from normal this is where exitance should still be at 50% of that an zenith. Both poles are even worse! Ice to has 95% emissivity normal to the surface but the surface is 2.5D! From normal drops faster than water. If covered by ‘new’ snow, reflectivity is 90% in every direction.

        “As for linearity, see Fig. (1) above.”

        That graph would be helped by bands where in the range the four things tend an approximate percentage of total exitance.
        David,
        Not trying to bitch at your painful but excellent work. Just some items to be conversant with when the attacks come. If I have measured this ‘they’ know about it. Beware those that are paid to shatter your kneecaps if you stumble even once!
        All the best! -will-

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          Will, we applied the SB equation to Earth by pretending it is a solid isothermal surface radiating in all directions into space. If it was, and radiated the true OLR, its surface would be at the “radiating temperature” as defined.

          Of course you are right and the Earth is nothing of the sort, but it gives us a rough start and a benchmark behavior. Note also that it is in essence what the conventional basic climate model does (via the Planck sensitivity, which is just a slight variation on the SB sensitivity). Feedbacks then get applied to try and approximate how the OLR/radiating temperature really changes with changing surface temperature.

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            “Feedbacks then get applied to try and approximate how the OLR/radiating temperature really changes with changing surface temperature.”

            David, just who has ever demonstrated any connection, causation, or correlation between your OLR and surface temperature? Your “radiating temperature” is more of a fantasy1 than the CCC mess.
            When you had the “systems” approach the internal mechanism was not an issue. An increase in insolation results in a response of higher exit flux, with perhaps some delay.
            Your start here was also good. The basic approach to modeling the “system” is SO full of mathematical non physical nonsense, such must invalidate any possible conclusions of anything.
            Now you seem to be in the midst of the internal ‘how dey do dat’. Your new approach is with agreement of the CCC fantasy that surface temperature and atmospheric temperature gradients affect EMR exit flux in some knowable manner!! You agree to both CCC forcing and feed-backs as though they have some legitimacy in answering the ‘how dey do dat of this atmosphere!
            The huge variability of atmospheric WV,and airborne water condensate nicely regulate the characteristics of local climate at every location.. They certainly do this without regard at all for the earthling fantasy of temperature.
            All the best! -will-

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    “To make it clear, I am sure you are not stupid at all, you know very well that you are wrong, that’s why you hid my comment after it was posted and read by others. Are you not ashamed of yourself, trying to support the anti-human agenda? OK, it is naive of me, I know. Let me try again nevertheless:”

    Did you even bother to read the introductory articles? It appears you do not have even an basic understanding of the subject matter. Does your “the warmer than the the Sun can possibly do surface violates the Law of Conservation of Energy”, make any sense to you? It is not English, not a statement, nor a question. You seem to be using the word ‘warmer’ as a substitute for higher temperature. rather than the scientific ‘added sensible heat”!
    With thermally induced EMR, the only temperature limit of a remote receiving body “is” the temperature of the emitting body! This is well demonstrated by the surface emission control of all spacecraft. Do you make such claims from your personal experience in quantum electrodynamics, astrophysics, thermodynamics, aerodynamics, or fluid dynamics? Can you even state the “Law of Conservation of Energy”, and the conditions under which it applies? Your previous statement “Those two things disqualify you, like many other “climate scientists”, sorry.”; is now the biggest giggle for all that keep up with the Jonova site. close to ROFLMAO! What gives you the impression that Dr. David Evans could possibly want to be climate scientist, (whatever that may mean)?
    All the best! -will-

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