This is the first formal, peer-reviewed response paper to Gerhard Gerlich and Ralf Tscheuschner and their alleged greenhouse falsification. It is here toward the bottom. It does not appear too many people have easy access, so I can only suggesting contacting one of the authors (such as Prof. Halpern) for a PDF. If you leave your email address in a comment on this blog I can do it as well and it will not be published online. I also encourage discussion on this at this forum


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  1. Let me add also, that for readers who want the technical background to how the greenhouse really works, one of the best descriptions is provided by Chris at this blog: go read Greenhouse effect revisited…. BTW, I am also the admin at the form Chris mentions, Climate Physics Forums, where we’ll be trying to maintain high standards of mutual courtesy and substance; and I am also a co-author of the comment, along with Chris and Josh Halpern, and Joel, Arthur, and Jörg.

  2. Hi;

    I’d like a copy of the paper.

    To me, the idea of trying to argue that the atmosphere
    must be in equilibrium is by nature missing the point.


  3. Thank you for the opportunity to comment on the 2010 article of Halpern et al (hereafter collectively referenced as “H”).

    In the abstract to their article, H state that Gerlich and Tscheushchner (hereafter collectively referenced by “GT”) “…claim to have falsified the existence of an atmospheric greenhouse effect.” This statement is prone to being misunderstood for, as GT demonstrate in their 2009 article, the literature describes many such effects. In their article, GT claim to have falsified all such effects that had been described at the time of publication of this article.

    One of these effects is described by the University Corporation for Atmospheric Research (UCAR) at ( ). UCAR references this effect as “the greenhouse effect.” While GT claim to have falsified “the greenhouse effect,” H argue GT have done no such thing. In the following remarks I argue that H’s argument fails from its violation of a principle of logic.

    The conflict between GT and H over “the greenhouse effect” of UCAR centers on the “back radiation” that is featured by the type of diagram which I’ll call a “Kiehl-Trenberth” (K-T) diagram after its inventors. In a K-T diagram, the back radiation is represented by an arrow with its tail in “greenhouse gases” and its head pointed at Earth’s surface. A caption states that the back radiation is “absorbed by surface.”

    The back radiation has a magnitude. In UCAR’s K-T diagram, this magnitude is 324 watts per meter squared. In H’s K-T diagram, the magnitude has the different value of 333 watts per meter squared reflecting a recent update.

    The K-T diagram asserts that the magnitude of the back radiation participates in a heat balance at Earth’s surface. In particular, the sum of the magnitudes of the incoming flows
    equals the sum of the magnitudes of the outgoing flows. “The greenhouse effect” of UCAR results from the requirement for the outgoing flows to increase in the amount of any increase in the magnitude of the back radiation for the balance to be preserved. The magnitude of the back radiation increases with the concentrations of the greenhouse gases hence a monotonic increase in surface temperatures with time.

    H argue that heat can flow as back radiation from colder matter in the atmosphere to hotter matter in Earth’s surface without violation of the second law of thermodynamics because the second law does not govern this flow. H assert it is only the
    “net heat flow” that must be from the hotter to the colder matter under this law. The magnitude of the “net heat flow” is the difference between the respective magnitudes of the upward flow of radiation and the back radiation.

    H’s argument employs an unusual and troublesome use of terms in the languages of thermodynamics and radiative physics in reference to concepts of the two fields. In the language of thermodynamics, the energy that flows across the boundary of a material body is referenced by the term “heat.” Under the second law, the “heat” flows only from relatively hot to relatively cold matter, for if it were to flow in the opposite direction, the entropy of the universe would spontaneously decrease. However, H’s “heat” flows also from relatively cold to relatively hot matter. To decode what it is that H are claiming by their argument, the reader must discover a mapping between H’s use of terms and the associated concepts.

    In discovering this mapping, it is essential to have a symbol for the concept that is referenced by the word “heat” in the language of thermodynamics. Going forward, I’ll use the symbol “heat-t” for this purpose. As it is subject to the second law, H’s “net heat” must be an example of heat-t. As it is not subject to the second law, H’s “heat” must not be an example of “heat-t.”

    From the fact that it flows from colder to hotter matter, it follows that the back radiation is not a flow of heat-t. If it is not such a flow, what concept is referenced by the term “back radiation” when H employ this term in their argument?

    By the descriptor “radiation” and the context of the associated heat transfer problem, the back radiation must be an example of electromagnetic radiation. H assert that this radiation “flows.” The K-T diagram implies that the magnitude of this radiation participates in a heat balance at Earth’s surface. That it “flows” and participates in a heat balance implies the back radiation can be represented by a Poynting vector. Thus, one concludes that when the term “back radiation” is used by H, this term references a Poynting vector.

    Radiation that can be represented by a Poynting vector matches the description of a flow of heat-t. Thus, the “back radiation” of H’s argument must be a flow of heat-t.

    It has been proved that, in the terminology of H’s argument, the “back radiation” is a flow of heat-t and is not a flow of heat-t. On the basis of this contradition H’s argument logically fails, from its violation of the law of non-contradiction.

    • See

      When dealing with heat transfer via radiation, one must take the vector sum of Poynting vectors as the heat flow; the different components of this total heat flow may go in opposite directions. (Further, radiation can pass through some other material on it’s way from emission to absorption, so it is possible to have a radiant heat flow that is locally in the direction of cold to hot if it is between objects at greater distances.)

      The term ‘heat’ is often used imprecisely, but a rose by any other name is still described by the same physics and mathematics.

    • In case it wasn’t clear, the heat flow between the surface and atmosphere is the portion of upward emitted flux from the surface that is absorbed by the atmosphere minus the backradiation emitted from the atmosphere that is absorbed at the surface. That heat transfer is from a higher temperature to lower temperatures.

    • Terry Oldberg,

      We know back-radiation from the atmosphere exists because we can measure it. Google “pyrgeometer.”

  4. Terry Oklberg’s post above was very well done.
    The basic cause and effect of the Sun-Earth-Atmosphere system is:

    The Sun heats the Earth and the Earth heats the atmosphere.

    The Sun is the only energy source and the Earth and atmosphere are merely passive receivers of the Sun energy.

    Now, some points about “Kiehl-Trenberth” (K-T) diagram:

    Let’s look at Trenberth’s balance of energy at the Earth’s surface.

    Incoming energy at the Earth’s surface:

    1) Solar Energy = 168 w/m^2 (the ONLY energy source)
    2) Back-radiation = 324 w/m^2 (comes from the atmosphere that is NOT an Energy source and gets ALL it’s energy ultimately from the SUN!)

    Total = 492/w^2

    The only energy source, the Sun, only provides 168 w/m^2 and the Back-radiation 324 w/m^2 exceeds this value, so energy was created violating the Law of Conservation of Energy.

    Totaling these to give 492/w^2 is like having a Battery powering an electronic circuit and adding the watts received by a resistor to the watts the Battery supplies.

    Outgoing energy at the Earth’s surface:

    1) Thermals = 24 w/m^2
    2) Evapo-transpiration = 78 w/m^2
    3) Surface Radiation = 390 w/m^2

    Total = 492 w/m^2

    ALL the above MUST get ALL their energy from the only energy source, the SUN.
    The Sun only provides 168 w/m^2 so energy was created again.
    The important points are:

    - The Back-Radiation of 324 w/m^2 is constantly required to heat the Earth’s surface to maintain a +15 deg C average temperature.
    - This Back-Radiation is avaliable Day and Night.
    - The Back-Radiation exceeds the Solar Energy of 168 w/m^2.
    Parabolic Dishes are used to concentrate energy at a focal point.

    These are used in applications ranging from Parabolic Microphones, UHF antennas, Microwave Antennas and Parabolic Mirror Solar Ovens.

    The Parabolic Mirror Solar Ovens will concentrate visble light from the Sun as well IR Back-Radiation at it’s focal point to produce heating.

    Remember the “Kiehl-Trenberth” (K-T) diagram has Solar Energy only at 168 w/m^2 and Back-Radiation at 324 w/m^2 (available Day and Night).

    Here is an experiment done by the Physics Dept. at Brigham Young Unversity that PROVES that Back-Radiation CANNOT heat the Earth.

    Solar Cookers and Other Cooking Alternatives

    “The second area of solar cookers I looked at was their potential use for cooling. I tested to see how effective they are at cooling both at night and during the day. During both times, the solar cooker needs to be aimed away from buildings, and trees.

    These objects have thermal radiation and will reduce the cooling effects. At night the solar cooker needs to also be aimed straight up towards the cold sky. During the day the solar cooker needs to be turned so that it does not face the Sun and also points towards the sky.

    For both time periods cooling should be possible because all bodies emit thermal radiation by virtue of their temperature. So the heat should be radiated outward.

    Cooling should occur because of the second law of thermodynamics which states that heat will flow naturally from a hot object to a cold object.

    The sky and upper atmosphere will be at a lower temperature then the cooking vessel. The average high-atmosphere temperature is approximately -20 °C.

    So the heat should be radiated from the cooking vessel to the atmosphere.”
    This link shows that heating of the Earth’s surface cannot occur from the Back-Radiation of the colder atmosphere.

    In fact, the article shows how to COOL items placed in the Solar Oven at NIGHT AND DAY!

    All you have to do is point the Oven away from the Sun during the Day and the Oven will transfer heat from the WARM object in the Oven to the COOLER atmosphere!

    It can even be used to produce ICE when the ambient air temp is +6 deg C!

    “If at night the temperature was within 6 °C or 10°F of freezing, nighttime cooling could be used to create ice. Previous tests at BYU (in the autumn and with less water) achieved ice formation by 8 a.m. when the minimum ambient night-time temperature was about 48 °F.”

    And, this also confirms the validity of 2nd Law of Thermodynamics….heat energy CANNOT flow from Cold to Warm objects.
    AGW theory and the Greenhouse Effect has been proven to violate the 2nd Law of Thermodynamics and the Law of Conservation of Energy.

    Actual measurements confirm this.

    If Back Radiation actually reached and heated the Earth as Trenberth shows, then Parabolic Mirror Solar Ovens would produce heating Day and Night!

    Why do the AGW so called “scientists” not promote the use of Back-Radiation as a clean energy source available DAY and NIGHT and solve all our energy problems?


    AGW/Greenhouse Effect has been presented to the public as some sort of ‘scientific fact’ when it is actually based on false science.

    • You can’t do heart surgery by studying Valentine’s Day cards. Listen very closely: 1+1 = 2. Got it?

      • Patrick 027

        … not to imply that K&T or K,T&F, or hyperphysics, or any of Gord’s sources in general, are mere cartoons. The problem of course is that cartoons are what Gord insists on seeing.

  5. In my previous post above, I have shown how Trenberth’s balance of energy at the Earth’s surface violates the 2nd Law of Thermodynamic, The Law of Conservation of Energy and actual measurements that prove that Back Radiation, from a colder atmosphere, cannot heat-up a warmer Earth.

    The Law of Conservation of Energy violation, in Trenberth’s balance of energy diagram, comes about due to atmospheric and Earth radiation exceeding the Sun energy recieved by the Earth’s surface.

    There has been wide-spread false information regarding the fantasy “Greenhouse Effect” heating the Earth from a blackbody no-atmosphere temperature of 5.3 deg C to the +15 deg C average Earth temperature (with an atmosphere) that we have today.


    Now onto the SUN.

    The Sun is the ONLY energy source used in Trenberth’s Earth Energy Budget, so it HAS to account for ALL the heating of the Earth.

    The fact is, Trenberth and others have used a much reduced Sun Temperature of 5778 K !!

    Temperature on the Surface of the Sun
    There are five sources for the surface temp of the Sun (6000,5500,5700,6000 and 5600 deg C).
    The average is 5800 deg C or 6073 K and a max of 6000 deg C or 6273 K.

    I have seen a number of AGW’er papers and other sources that correctly state that the actual Sun temperature is much higher than 5778 K.

    Here is one example:


    “3. If the Sun were a blackbody, this emissivity would correspond to a surface
    temperature of 5798°K. However, the wavelength of maximum intensity is at
    0.475 microns (green light). By Wien’s Law, this is the maximum that would be
    produced by a blackbody at a temperature of 6101°K.”

    Here is another… Sun’s emissivity curve as a function of wavelength:

    File:EffectiveTemperature 300dpi e.png

    See how the Solar spectral irradiance exceeds the black body approximation in the visible light range (400 to 700 nm).
    The visble light spectrum from 400 nm to 700 nm (that will absolutely heat the Earth) has been under valued with a Sun Temp = 5777 K!!

    If you look closely at the Effective Temperature graph above you will see that the Green Light real peak is at about 462 nm and using Wein’s Displacement Law will produce a Sun temperature of 6273 K (thats 6000 deg C) and agrees with the link I quoted above!
    This equation relates Sun Temperature to Earth Temperature

    TE = TS (((1-a)^0.5 * Rs)/(2*D)))^0.5)
    Where TE is blackbody temp of the Earth in K
    TS is the surface temp of the SUN in K
    Rs is radius of the Sun (6.96 X 10^8 meters)
    D is distance between the Sun and Earth in meters (1.5 X 10^11)
    a is albedo of the Earth

    Results: (Albedo = 0, Black Body Earth WITHOUT AN ATMOSPHERE)

    TS = 5778 K (Trenberth’s “lowered” Sun Temperature)
    TE = 278.68 Kelvin
    TE = 5.53 Celsius

    Note: This is very close to the value I mentioned earlier:
    “If an ideal thermally conductive blackbody was the same distance from the Sun as the Earth, it would have an expected blackbody temperature of 5.3 °C. )

    TS = 6073 K (average Sun temperature)
    TE = 292.91 Kelvin
    TE = 19.76 Celsius

    TS = 6101 K (as per the AGW’er Heating The Earth link above)
    TE = 294.26 Kelvin
    TE = 21.11 Celsius

    TS = 6273 K (max Sun temperature)
    TE = 302.55 Kelvin
    TE = 29.40 Celsius

    All the Sun temperatures (except Trenberth’s) produce Earth temperatures that exceed the Earth’s average temp of +15 deg C.


    - Trenberth and most of the AGW papers have used a Sun temperature of 5778 K that is far below the average Sun temperature or other estimates.

    - Using the Average Sun temperature or other estimates shows that the Sun easily accounts for an Earth temperature (with an atmosphere) of +15 deg C.

    - All measurements done, like water will FREEZE in a Solar Oven when the Solar Oven is pointed at the Colder Atmosphere, confirm the atmosphere will COOL the Earth.

    - This complies with the 2nd Law of Thermodynamics, The Law of Conservation of Energy and all Principles of Science.

    The “Greenhouse Effect” is very clearly a fantasy.

    Response: Well, then. Go publish your results and claim your nobel prize for revolutionizing climate and space sciences. By the way, we can measure the incoming sunlight, and know its value is about 240 W/m2 after albedo and geometry is accounted for. The steady-state temperature can thus not exceed the fourth root of 240/sigma, which is 255 K. Please, no more pseudo-science that you read off the equivalent of a cracker jack box.– chris

  6. Chris

    In case you don’t know it, the 240 w/m^2 incoming Sunlight is a calculation based on the average Solar radiation Earth being absorbed by a disk instead of a Sphere.

    No variations between the Poles and Equator, no tilt of the Earth, no orbital difference, no seasons and no night and day.

    Kinda hard to measure that!!!
    The only Sun temperature measurements are done using the direct w/m^2 and using spectral analysis, which is what I quoted in my links.

    Funny how Sun temperature measurements in text books, confirmed by many, many other sources (including AGW sources) show the Sun temperature that Trenberth uses to be far too low.

    And, I used the EXACT same AGW equations to PROVE that the Sun (the ONLY ENERGY SOURCE) easily accounts for the +15 deg C Earth temperature.


    Trenberth and the IPCC are the ones using pseudo-science that violate The 2nd Law of Thermodynamics, The Law of Conservation of Energy and ALL measurements.

    Any High School student knows that it is impossible to violate The 2nd Law of Thermodynamics and The Law of Conservation of Energy.

    Trenberth’s Earth Energy Budget is glaring example of this and is absolutely PROVEN to be a fabrication confirmed by ALL MEASUREMENTS.
    If you disagree, I give you a challenge.

    There has Billions of Dollars spent on the fantasy AGW myth and Thousands of “scientific” papers on the so called “Greenhouse Effect”, so there should be no problem for you to:

    - Post EVEN ONE Law of Science that supports the fantasy “Greenhouse Effect”.

    - Post EVEN ONE measurement, EVER done, that shows that a colder atmosphere can heat-up a warmer Earth.

    Good Luck!

    Response: You are rather arrogrant to assume that the entire physics, climate, astrophysics, and other communities has somehow forgotten about basic laws of science, since the greenhouse effect is invoked in virtually any study of planetary climate (past, present, on other worlds, etc). It is as central to the study of atmospheres as “atoms” and “molecules” are in chemistry. I have no quibbles with the second law or conservation of energy. However, you have no idea what they mean, or how they relate to the greenhouse effect. You are also clearly ignorant into calculation of incoming sunlight. You have already lost all right to be taken seriously, so please, read a basic textbook on climatology before you look even sillier. You might want to review our (Halpern et al) paper along the way. Come back in a year when you have taken a class or two, read a few books, and you will realize your post have the same level of lunacy as flat earth supporters. — chris

  7. - Post EVEN ONE Law of Science that supports the fantasy “Greenhouse Effect”.

    Schwarzchild’s equation (Beer’s law is a special case), which obey’s both the conservation of energy and the second law of thermodynamics.

    Although I’ve been over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over this with you before, a few points (not so much for your benifit as it is just for the record):

    1. You can’t say that the conservation of energy is being violated if you are refusing to account for some energy fluxes, which you repeatedly do. You can’t assume that the sum of all fluxes among components within the system must be less than the fluxes entering or leaving the system – the conservation of energy is not violated by flows of energy within a system. The components of the climate system (surface, various layers of atmosphere) are not at 0 K, they have enthalpy and they would all tend to lose heat if all heat inputs were cut off. When one component loses heat only to another component, no heat has entered or left the system. (I find it mind boggling that you haven’t understood this yet – it makes me question whether you believe what you say)

    2. Heat always goes from a warmer to a colder object – yes. But heat fluxes are generally net fluxes of energy. As allowed by limitations of kinetic barriers, energy and matter always tend to spread out from where they are and what they are to other places and forms. In complete thermodynamic equilibrium, it isn’t that all flows stop, but that the concentrations are such that all fluxes form pairs that are equal in magnitude with opposite directions (molecular motions, energy exchanged in molecular collisions, chemical reactions, emissions and absorptions of photons, etc). A positive concentration perturbation from such equilibrium increases the fluxes out of such a location or form, so that the net flux out is positive; the net flux into a negative perturbation will likewise be positive. HENCE, heat flows from higher to lower temperature.

    (The concept you seem to support is that conditions at some distance and at a future time determine whether or not photon is not emitted by some object at some time – apparently by some sort of magic (while there is some quantum weirdness in the world, I don’t think it applies to this case). Besides, your logic would have us believe that mirrors are physically impossible. I have seen mirrors!)

    3. A new point – your points about the sun’s temperature – the sun doesn’t radiate as an isothermal blackbody over all wavelengths. The optical properties of it’s matter have some wavelength variation – at wavelengths where the photosphere is less opaque, the brightness temperature will generally be higher because the radiation that leaves the photosphere is coming from deeper within it, where the temperature is higher. (The opacity of the photosphere actually produces a greenhouse effect.) The brightness temperature will also tend to be lower for radiant intensity measured from near the limb of the solar disk because such a direction passes through more material to get to the same depth within the sun; furthermore, the temperature is not constant horizontally, either. But to summarize – on a wavelength by wavelength basis, the brightness temperature of the sun will vary over some range. This variation doesn’t imply as much uncertainty in the total flux from the sun, over the whole spectrum.

    4. It can even be used to produce ICE when the ambient air temp is +6 deg C! If there were no backradiation, then why aren’t those solar ovens turned coolers able to bring objects down to near absolute zero K (or assuming the reflecting material has an emissivity of, for example, 0.1, about 300 K * 0.1^(1/4) ~= 169 K), regardless of what the air temperature is?

    And why can’t we use that backradiation as a useful energy supply? Well, we do in an indirect way (via the reduced radiant heat loss). But we can’t generally use it directly because devices that absorb that radiation will emit radiation, and they will tend to emit even more radiation than they recieve because of their temperatures relative to the air temperature (some exceptions will occur – nocturnal and polar inversions, etc.). Relative to typical near-surface temperatures that can be maintained without energy-consuming refrigeration, it’s a rather high entropy form of energy; most if not all is not available for conversion to work. Actually, the ability to use a solar oven to cool objects (because the backradiation intensicy is less than that emitted by the objects, due to their higher temperature) could be used to run a heat engine from ambient enthalpy via the supply of a low-temperature heat sink, but the problem remains that it’s difficult to cool a heat sink to much lower temperatures, limiting the efficiency of such a heat engine. That, and the low flux densities involved, may make it impractical (solar energy can be practical for use in a heat engine or analogous energy conversion device, not because the flux per unit area is much larger, but because the conversion efficiency can be much higher because of the much higher brightness temperature of the solar radiation).

    T H E E N D.

    • Clarification:
      (some exceptions will occur – nocturnal and polar inversions, etc.)

      As the surface cools in the absence of solar heating, it can (via net LW emission) get colder than some of the air above; in particular the temperature near the surface can increase with height; this inversion can grow because the surface doesn’t just exchange radiation with the air immediately above or with air in general but also emits some radiation directly to space as well (in the absence of sufficient water vapor and/or clouds, etc.).

      But to continue to cool, the LW emission has to be greater than the absorbed LW backradiation. However, at some wavelengths the backradiation flux per unit area can become larger than the emitted flux per unit area. Once an inversion is formed, if clouds form within the inversion, then the backradiation could increase and become larger. Another way to get backradiation larger than surface emission would be to have warm air advection with sufficient water vapor or clouds.

    • PS for other interested parties – the reason a solar oven (in the form of a reflective oncentrator, such as a parabolic dish) could have any use in cooling an object is that an object placed at the focus of such a concentrator would recieve radiant intensities at angles within the aperture as they would be otherwise, but radiant intensities seen from other directions would be near that of what is seen coming from the direction of the concentrator’s aim. The lowest radiant intensities tend to be away from the horizon, nearer the zenith – this is because there is less air between the surface and space along paths closer to vertical, and also, there is less of the warmer air near the surface along such a path between the surface and cooler layers aloft. There will be some exceptions – for example, if there is an inversion and if the opacity (of the absorbing/emitting type) is sufficiently high within the inversion or near the top of the inversion, then the highest radiant intensities would be from nearly vertical directions. But in general, a solar oven of a reflector-dish type, can both surround an object with atmospheric backradiation from all directions and reduce the backradiation flux per unit area from what it would be for a flat surface left out in the open, thus allowing an object to cool more than it would if just left outside on the ground, if the dish is not aimed at the sun (or if not recieving too much scattered solar radiation).

      • Patrick 027

        “thus allowing an object to cool more”
        - in terms of rate of heat loss, the surrounding of an object on all sides by smaller backradiation flux per unit area is helpful – the effect is from increasing the useful area.

        However, in terms of equilibrium temperature, it is only the reduced flux per unit area of backradiation that matters.

      • Patrick 027

        … of course, thermal insulation from immediate surroundings is also important…

      • Patrick 027

        … actually, solar energy may also more practical on the basis of the available flux per unit area. The net radiative cooling for emission of 396 W/m2 and absorption of 333 W/m2 is only 63 W/m2 (although the flux out of a heat sink won’t be as large as the flux into the heat source of a heat engine); reducing the effective backradiation by using a dish mirror requires increasing the aperature to an area greater than the effective emitting area of the heat sink. The efficiency limitations come in to play via the even smaller net cooling that can be achieved if the heat sink is to have lower temperature than the ambient surface temperature (for solar power, increasing the temperature of the heat source for a heat engine, or in a PV cell, increasing the energy of excited populations of electron and holes, increases the radiation emitted by the device and thus reduces the net absorption of energy, but the limitation is not as stringent because of the much larger brightness temperatures of the solar radiation intensity (on a spectral basis as well as in total amount, the first is important to the use of diffuse solar radiation where the intensity over the whole spectrum is not large)). Of course, there is conductive and convective cooling, but aside from evaporative cooling, there is a greater restriction on the temperature drop that can be achieved.

    • Correction: Heat always goes from a warmer to a colder object – yes.

      That is true for heat transfer by radiation and, relative to non-photon matter, sensible heat transfer by convection (aside from any net rearrangement of substances) and conduction.

      However, a flow of material with some enthalpy can also constitute a flux of heat, and in that case, the flow is shaped by the distribution of material.

      That is particularly important to the flux of latent heat. Sufficiently dry air can be used to cool a wet surface to a temperature lower than the air temperature via evaporative cooling. I’ve heard that ancient Persians produced ice in this way. The reduction in entropy from the flow of heat from lower to higher temperature is made up for by the increase in entropy associated with the flux of water molecules. (An example of why it is convenient to describe the second law of thermodynamics in terms of entropy.)

  8. Patrick 027…

    Beers Law demonstrates that some portion of incident light can be absorbed by a body that the light is passing through.

    This has the consequence, in the Earth-atmosphere system, that the atmosphere can absorb some of the IR Earth Radiation and increase in temperature all the way to the average -20 deg C temperature that it is.

    How do you get from Beers Law to having the -20 deg C atmosphere heating up a warmer Earth?

    - Fact: There are absolutely ZERO Laws of Science that support the fantasy “Greenhouse Effect”.

    Notice that in Patrick 027′s series of posts, he failed to Post EVEN ONE measurement, EVER done, that shows that a colder atmosphere can heat-up a warmer Earth.

    - Fact: There are absolutely ZERO Measurements, ever done, that shows that a colder atmosphere can heat-up a warmer Earth.
    The rest of Patrick 027′s post rambles on about:

    “1. You can’t say that the conservation of energy is being violated if you are refusing to account for some energy fluxes, which you repeatedly do.”

    The TRUTH is that I have used the fluxes PROVIDED BY TRENBERTH in his Earth Energy Budget Diagram.

    I neither added nor deleted ANY fluxes.

    Patrick 027′s statement above is completely FALSE.

    It looks like Patrick 027′s item No.2 tries to bypass the FACT that Trenberth’s Energy Budget has 324 w/m^2 flowing from the colder atmosphere to a warmer Earth thus causing HEATING of the warmer Earth’s surface.

    Of course, the FACTS are that Trenberth uses the constant 324 w/m^2 flowing from the colder atmosphere to account for a +15 deg C Earth surface temperature.

    Regarding the Sun’s temperature, Patrick 027′s No.3 again avoids the FACT that I have used actual measurements of the Sun’s temperature published in Text Books and other sources.

    He also avoids the FACT that I have used EXACTLY the same equations as Trenberth and others to prove that Trenberth has used a far lower Sun temperature than is KNOWN, to produce a fictionally lower Black Body Earth temperature.

    Regarding Parabolic Mirror Solar Oven measurements that prove that the Back Radiation CANNOT HEAT THE EARTH, Patrick 027′s item No.3 does not address the facts of the measurements

    and instead talks about “inversion layers” and how the flux densities of IR produce less conversion efficiency to produce heat as compared to Solar Energy…etc..etc.

    Of course, Trenberth’s Energy Budget Diagram disagrees with Patrick’s “theory”.

    Here is what Trenberth’s Energy Budget Diagram shows:

    Incoming energy at the Earth’s surface:

    1) Solar Energy = 168 w/m^2 (the ONLY energy source)
    2) Back-radiation = 324 w/m^2 (comes from the atmosphere that is NOT an Energy source and gets ALL it’s energy ultimately from the SUN!)

    Total = 492/w^2

    The 324 w/m^2 is clearly used as a HEATING SOURCE that EXCEEDS the heating of Solar Energy!

    The Fact is that the 324 w/m^2 Back-radiation, even when CONCENTRATED at the focal point of a Solar Oven, cannot prevent a tiny bit of water from FREEZING!

    Meanwhile, if the Solar Oven is pointed at the wimpy Sun, the water will BOIL!

    The results produced totally comply with the 2nd Law of Thermodynamics and proves that the “Greenhouse Effect” is a pure fantasy.
    Like I said…

    There has Billions of Dollars spent on the fantasy AGW myth and Thousands of “scientific” papers on the so called “Greenhouse Effect”, so there should be no problem for you to:

    - Post EVEN ONE Law of Science that supports the fantasy “Greenhouse Effect”.

    - Post EVEN ONE measurement, EVER done, that shows that a colder atmosphere can heat-up a warmer Earth.

    Good Luck!

  9. Chris…

    I see your last post was very heavy on “verbage” but contains ZIP as far as any Science goes.

    You have not addressed ANY points in my posts except to offer your “opinion”.

    As far as Halpern’s paper is concerned, it is FULL of errors!

    Here is an example: see his Fig.4 Heat and entropy exchange between two parallel, infinite plates at temperatures TA =
    300 K and Ta = 260 K.
    First some Physics FACTS:

    All Electromagnetic Fields are Vector fields that have a Magnitude and Direction and this includes Heat Flux.

    Heat flux
    “Heat flux or thermal flux, sometimes also referred to as heat flux density or heat flow rate intensity is a flow of energy per unit of area per unit of time. In SI units, it is measured in [W·m-2]. It has both a direction and a magnitude so it is a vectorial quantity.”

    Vector addition of fields

    This link shows how resultant field vectors are calculated.
    Using superposition, many, many sources can analysed at any point in space to produce a SINGLE RESULTANT VECTOR.
    There can only be ONE RESULTANT VECTOR.

    Heat Radiation
    “Radiation is heat transfer by the emission of electromagnetic waves which CARRY energy away from the emitting object. For ordinary temperatures (less than red hot”), the radiation is in the infrared region of the electromagnetic spectrum. The relationship governing radiation from hot objects is called the Stefan-Boltzmann law:

    Heat Transfer by Radiation using the Stefan-Boltzmann Law

    P = e*BC*A(T^4 – Tc^4)

    Where P = net radiated power (Watts), e = emissivity, BC = Stefan’s constant, A = area, T = temperature of radiator and Tc =
    temperature of the surroundings.

    ..when rearranged gives

    P/A = e*BC*T^4 – e*BC*Tc^4 (Watts/m^2)

    This is an obvious subtraction of two Electromagnetic Fields and is found in all Physics and Engineering Text books.

    It also fully complies with the Vector subtraction of Electromagnetic Fields, which are VECTORS.

    The resultant Electromagnetic Field will have a magnitude of P/A and have a direction of propagation in the direction of the larger field produced by the hotter body.

    There is absolutely no energy flow from cold to hot, complying with the 2nd Law of Thermodynamics.
    Now let’s look at Fig. 4. Heat and entropy exchange between two parallel, infinite plates at temperatures TA =
    300 K and Ta = 260 K in Halpern’s paper.

    He has multiplied w/m^2 by 1 sec to get J/m^2.
    Here are his results Between the Earth surface (Ta) 459 J/m^2 and atmosphere (Tb) 259 J/m^2:

    Qa = Qab + Qba = −459 + 259 = -200 J/m^2
    Qb = Qba + Qab = -259 + 459 = +200 J/m^
    Q = Qa + Qb = 0

    What a laugh.
    He has NOT properly treated these heat fluxes as Vectors.
    You CANNOT have TWO resultant VECTORS.

    Here is the correct calculation from my Physics link above:
    P/A = e*BC*T^4 – e*BC*Tc^4 (Watts/m^2)

    Qab = Qa – Qb = 459 – 259 = 200 J/m^2

    This is the ONLY resultant Vector and has a Magnitude of 200 J/m^2 and a Direction of propagation towards colder atmosphere Tb.

    There is ZERO J/m^2 flowing from the colder atmosphere to a warmer Earth, complying with the 2nd Law!

    Further, Halpern has ignored the fact that the atmosphere will also radiate 259 J/m^2 upwards to Cold Space!!!

    All the Earth’s radiation HAS to reach cold space or there is a violation of The Law of Conservation of Energy.

    This is easily calculated using proper Vector addition of the EM fields.

    The resultant Vector between the Earth and Atmosphere has already been calculated to be 200 J/m^2 in a Direction towards the colder atmosphere.

    Past the atmosphere this resultant vector will ADD with the atmosphere vector of 259 J/m^2 upwards to Cold Space giving a resultant EM field vector of magnitude 200 + 259 = 459 J/m^2 with a Direction of propagation towards cold space.

    This complies with the 2nd Law and The Law of Conservation of Energy.

    Notice that there is NO POSSIBLE WAY for Halpern’s calculation to comply with The Law of Conservation of Energy!!!
    Chris, you should read and study the Physics Links that I have posted for a year or two.

    Maybe then you will be able to respond with some Physics instead of your un-educated and ignorant “opinions”.

    Response: Sorry, but energy can radiate from a colder body to a warmer one. If you place two objects on a table next to each other at two different temps, the colder one is still radiating energy because it’s above absolute zero. And the photons don’t really care that a hotter object is next to it. There’s nothing else here to rebut, you simply don’t understand the physical laws which you are arguing for or against– chris

  10. Gord,

    in discussing resultant vectors, you have implicitly (and explicitly in prior discussion) admitted that their can be ‘opposing fields’. So why not just add the vectors in the KT&F or K&T diagrams? If you did, you’d find heat fluxes going from warmer to colder bodies. But you have refused to acknowledge this. It makes me think you are not being sincere.

    The formula P/A = e*BC*T^4 – e*BC*Tc^4 applies to two surfaces, each isothermal within itself, facing each other, with either one surface a perfect blackbody and the other with emissivity e, or with the produce of emissivities being e with both being ‘greybodies’. More general situations can be described by Schwarzchild’s equation and it’s implications. Beer’s law describes absorbtion and transmission of radiation without any emission along the path; Schwarzchild’s equation includes that emission.

    You say I ramble and dismiss Chris’s statements as opinion. I suspect you’d do the same for anyone providing good information. As for rambling, I’m sorry, but the real world has complexities that deserve description. Don’t bother telling us to look at your links; I don’t think either of us has a problem with your links. I think hyperphysics is a good site. But it doesn’t get deep into the complexities of radiative fluxes in various situations. A good textbook provides more in depth information.

    In fact, Gord, you continue to add fluxes willy-nilly without regard for what they are. You can’t take 10 apples and 5 bananas and get 15 mangos. You certainly can’t add 10 apples and subtract 5 apples and get 15 apples. Again, it’s getting hard to believe that you believe what you say.

    In case you don’t know it, the 240 w/m^2 incoming Sunlight is a calculation based on the average Solar radiation Earth being absorbed by a disk instead of a Sphere.

    No variations between the Poles and Equator, no tilt of the Earth, no orbital difference, no seasons and no night and day.

    Kinda hard to measure that!!!

    Approx. 240 W/m2 is the value calculated for a sphere (it can be calculated based on measurements. You don’t always need to measure everything directly). It is the global annual average absorbed solar flux per unit area of the Earth’s climate system. Solar heating is not constant over the globe over time, nor is the temperature. But the fact remains that all parts of the Earth emit radiation according to their temperature and optical properties. Radiation escapes to space from all over the globe, day and night, all latitudes, all year. So you can’t just take the maximum solar heating and calculate an equilibrium temperature for that and expect the global average temperature to be able to get to that in equilibrium – unless you cover the rest of the globe with a perfect mirror (which would be a greenhouse effect, though not of the same sort provided by gases and water clouds). If you avoid the problem by having each part of the Earth radiate to space according to the local and time-dependent solar heating, then your global average temperature has to include the zero K over the whole night side. But if the temperature variations are not too large (via heat capacity and horizontal heat fluxes), then, absent a greenhouse effect and with an approximately blackbody (in the LW portion of the spectrum) surface, a global average equilibrium temperature can be calculated based on global average fluxes and the result will not be so far off from the actual equilibrium average temperature. But do NOT think that actual scientists have been content to just accept such approximations in all work (at least GCM climate models go farther).

    - Post EVEN ONE measurement, EVER done, that shows that a colder atmosphere can heat-up a warmer Earth.

    For the record:

    The observed global climate and observations/inferences of past global climates and observed and past solar forcings and albedos.

    Observed surface optical properties.

    Observed optical properties of atmospheric components.

    Satellite measurements of outgoing LW radiation, showing the variation with wavelength and over area that would be expected based on the properties of clouds and gases, showing that generally more radiation escapes to space when the atmosphere is less opaque, with a few exceptions that are, far from puzzling, actually quite well understood and actually required from known physics.

    Other planets.

    Also, though a bit outside the usual usage of the term ‘greenhouse effect’, the sun (the temperature within the sun gets much hotter than the effective surface temperature) and other stars – or for that matter, the Earth’s interior (if some portion of the upper mantle were transparent to LW radiation, then the lower boundary of such a layer would experience a large radiative heat loss, cooling that region).

    But to be clear, you are actually using a bit of a bait and switch here.

    Often people use terms informally, including heat; it is understandable that scientists might use terms in an imprecise or colloquial manner when sharing information with the public, simply for the sake of brevity and accessibility. But a rose by any other name is still a rose – if you see terms used incorrectly, ask yourself if it has any effect on the mathematic formulations of the physical laws. If Q = f(T(x,y,z)), then it is true regardless of the word used to identify Q.

    If heat is to be defined as only the resultant vector, then it is not the case that the atmosphere is heating the surface in the direct sense. But as vectors have components, then it is convenient to describe components as being of the same quantity as their sum. Thus the radiation from the atmosphere that is absorbed by the surface is a component of surface heating and atmospheric cooling, even though it is not ‘heat’. A total heating rate can be described as a sum of contributing heating rates, some possibly of opposite signs to the total.

    But refering to heat as the total flux, it is not that the greenhouse effect heats the surface, but that it reduces the cooling rate of the surface for the same temperature distribution. The temperature distribution has to be different in order to sustain the same cooling rate (radiative + other), such as that which would balance solar heating.

    Though the relative importances of radiation, convection, conduction, and diffusion (ie of a substance carrying latent heat, such as water vapor) are not the same, a general analogy can be made to an actual greenhouse, or for that matter, to a winter coat. The coat will be (averaged over it’s thickness)colder than your sking – so how does it keep your skin warmer? By reducing radiative loss, by reducing convective loss (including water vapor), and, relative to some other materials, a good coat will limit the conduction of heat through itself. In other words, it forces your skin to get to a higher temperature before it can lose heat at the same rate as it would without the coat. The heat source is your metabolism – of food – from the solar radiation – from nuclear fusion – from nuclear potential energy – from the big bang/etc.

    The bait and switch – you insist that backradiation itself is not heat – maybe a fair point (?) but it doesn’t change the math at all – and then ask how the atmosphere can heat the surface – when by the strict definition of heat, that is not how the greenhouse effect works, and with your own knowledge, YOU SHOULD HAVE BEEN ABLE TO FIGURE THIS OUT, especially with my REPEATEDLY TELLING YOU how in the most pedantic manner.

    Pardon my ‘rambling’. For shorter version: greenhouse effect = reduced heat loss for same temperatures.

    (PS Chris, I promise not to engage in any farther discussion with this ____, but also, I’d suggest you might want to block Gord from posting farther comments. I think he’ll just keep on posting the same nonsense over and over.)

    • Correction:
      But as vectors have components, then it is convenient to describe components as being of the same quantity as their sum.
      … as being of the same TYPE/CATEGORY as their sum … – is what I meant.

      (and of course, one can have many different resultant vectors for various subsets of the contributing vectors, and it may be of interest to consider one or more such subsets and their subtotals for various purposes)

  11. edit– You have already been corrected by Patrick and myself. You were advised to read material on global climatology and you have obviously not done so. More ignorant posts which are mere repetition of misunderstanding will be removed. Adding citations to articles describing what a “photon” or “electromagnetic field” is (or using caps locks) will not make your argument any more correct– chris

  12. Chris…

    Galileo Galilei

    “Galileo’s championing of Copernicanism was controversial within his lifetime, when a large majority of philosophers and astronomers still subscribed (at least outwardly) to the geocentric view that the Earth is at the centre of the universe. After 1610, when he began publicly supporting the heliocentric view, which placed the Sun at the centre of the universe, he met with bitter opposition from some philosophers and clerics, and two of the latter eventually denounced him to the Roman Inquisition early in 1615. In February 1616, although he had been cleared of any offence, the Catholic Church nevertheless condemned heliocentrism as “false and contrary to Scripture”,[10] and Galileo was warned to abandon his support for it—which he promised to do. When he later defended his views in his most famous work, Dialogue Concerning the Two Chief World Systems, published in 1632, he was tried by the Inquisition, found “vehemently suspect of heresy,” forced to recant, and spent the rest of his life under house arrest.”

    Sounds familiar.

    Response: Except no one has issued a scientifically coherent challenge to the current paradigm, nor offered an alternative explanation that beats (or even comes close to matching) the predictive and explanatory power of how the greenhouse effect influences planetary climates. You have only assumed the entire scientific community is ignorant to basic physical laws and that these have been overlooked, and apparently you are the Galileo that is the voice of reason. I think it was this link you meant to have cited, — chris

  13. edit– ranting about how the greenhouse effect is a fairly tale will not make it right. Please find another forum to confuse its members. People are not so gullible here– chris

  14. I am more persuaded by Gord’s arguments because he seeks to fairly apply the laws of vectoring which climatologists appear to misunderstand (please, no appeal to authority because the recent Oxburgh Inquiry into climategate affirmed that climate scientists are poor mathematicians!).

    Vector calculus (or vector analysis) compels you to address natural forces acting in three dimensions and describe the movement of gases from one point to another.

    Gavin Schmidt on Real Climate stated (April 2007) that backradiation is ascribed a factor of two in NASA’s Earth energy budget because it moves ‘up and down’ and thus this justifies the multiplication by the factor of two (?).

    However, vector calculus requires that any three-dimensional forces that run parallel but in opposition (i.e. the ‘up and down’ effect of back radiation), must be equated to zero because they cancel each other out. Thus when correctly rated to zero greenhouse gases add no value to Earth’s energy budget.

    This law is well understood and not controverted by mechanical engineers who, in the REAL WORLD, apply vectoring rules accordingly. I fear academics with no such real world sense of what works misunderstand that this essential point cannot be subverted.

    Even granting you that such fluxes impact here, as Gary Novak, a long-time climate researcher with a science masters degree, explains in his study ‘Back Radiation does not Create a Greenhouse Effect:’

    “Approximately one sixth of re-radiated energy would go into outer space, one sixth toward the surface of the earth and two thirds into the surrounding atmosphere. The logic is that there are six equal sides involved, not that there are three areas to emit into. Then the atmosphere absorbs half of the radiation going toward the earth reducing it to one twelfth.”

    So even if the ‘up and down’ back radiation effect were plausible under vector rules, NASA should never have doubled the numbers but divided them by twelve.

    Response: Unfortunately the GHE cannot be reduced to adding arrows. It requires comprehending a planet in radiative equilibrium (which is where your “net” flux is indeed zero) with a convective troposphere. As such, the interaction of radiation with gases needs to be spectrally weighted and account for the temperature structure of the atmosphere. You will find that, in equilibrium, both the top and bottom of the atmosphere energy budgets are properly satisfied once you account for other heat transfer terms. This is a very well understood principle of planetary climate. It is also somewhat correct to say that GHE is not “driven” by back-radiation but instead involved a reduction in the rate of energy loss out of the planet.

    Finally, the arrogance is really starting to become annoying. Thousands of scientists who spend decades and decades doing research on this stuff (extending back to the 1800′s) are not all incompetent mathematicians who can’t make sense of an arrow cartoon. If you have a pet theory that inherently assumes the stupidity of many climatologists and physicists then properly submit it in the literature, and when it’s rejected you can find another blog with another moderator to annoy. That you believe “climate-gate” shows climatologists are bad mathematicians shows that you really haven’t the foggiest clue what is happening– chris

    • Chris, everyone who has read the Oxburgh inquiry most assuredly will NOT have read any claim that climate scientists were poor mathematicians. O’Sullivan distorts the facts. To quote directly from the Inquiry report:
      “Although inappropriate statistical tools with the potential for producing
      misleading results have been used by some other groups, presumably by
      accident rather than design, in the CRU papers that we examined we did not
      come across any inappropriate usage although the methods they used may not have been the best for the purpose. It is not clear, however, that better methods would have produced significantly different results.”
      “Although there are certainly different ways of handling the data, some of which might be superior, as far as we can judge the methods which CRU has employed are fair and satisfactory.”

      Response: I know. Eventually you get a feel for the types of things official reports do and do not say. They tend to be rather specific, cautious, and detailed. Over-generalizations to a whole community (which compromises thousands of people with different intellectual and regional heritage), and their skill set with mathematics is not one of them.– chris

  15. Re John O’Sullivan -

    You can’t just add and subtract vectors without knowing what they are.

    An isothermal layer of atmosphere (with isotropic optical properties) emits radiation emits the same flux upwards and downwards. I can see how such a statement might be misread, so let me clarify – this does not mean that the same photons are emitted up and then down – what it means is that two fluxes are emitted by the layer, one up and one down, and they are of the same magnitude. What sense does it make to sum those vectors to zero? – because they are not going past each other at the same level (or in other words, what would the resultant vector be a measure of, exactly?) For two fluxes in opposite directions past the same location, a vector addition gives the net flux parallel to those directions at that location, which is a rather useful quantity to be able to identify. That would apply to a pair of fluxes between two layers.

    The flux per unit area in a given direction is the power per unit area normal to the direction from all photons that are propagating in a direction with a positive component of that direction being in the same direction. Typically, the fraction of photons that are precisely at right angles to any one direction is actually zero because such a range of directions has zero ‘width’ (solid angle). For isotropic radiation, half of all photons will cross a surface from one side to another and half will do the opposite, even though a number of those will do so at a grazing angle. There is a very precise and well-understood mathematical formulation for all this: (upon rereading, I see that the paragraph that starts with “For LW (longwave) radiation”, the different thoughts are not arranged in an easy-to-follow manner, sorry.)

    The intensity is a flux of photons (in terms of their energy, per unit time) passing through a unit area in the direction normal to the unit area per unit solid angle of directions. The contribution to a flux per unit area in a different direction is proportional to the cosine of the angle between directions, because an area facing one direction projects onto a larger area in a different direction. This is consistent with the following relationship: For an intensity in some direction, it is true that the contribution to a flux per unit area facing that direction is equal to a vector sum of the contributions to fluxes per unit areas in three mutually-orthogonal directions. This is not necessarily a more helpful way to see it, though.

    To find vector components of fluxes it may be easier to forget unit areas and consider some given shape with fluxes (not per unit area, but in total). For isotropic properties and setting aside absorption, the flux of emitted photons (per solid angle of directions – ie the units of this quantity would be intensity * area) will be the same in all directions. The energy flux from photons going in one direction can be divided into vector components that contribute to the fluxes in those directions (this can be visualized by considering a population of photons with some energy density and considering that the energy moves with the photons (so far as I know – some ‘weird’ stuff can happen in materials with indices of refraction less than 1 or …, but in those cases, the energy flux is with the group velocity, which presumbably is the velocity of photons (wave packets travel at group velocity)) and then consider the vector components of photon velocity (group velocity when there is a distinction). So while the flux in any one direction has contributions from half of the photons (the other half contributing to the flux in the opposite direction), one can find 6 flux vectors of emitted photons from such a volume.

    However, the energy doesn’t move outward from such a volume in six directions; it moves out in all directions – the flux in some particular direction, absent absorption (or scattering or reflection or refraction) will be constant going outward in that direction, but it is spread over a larger and larger area facing that direction – actually it is infinite area to begin with since some contributions to that flux are from photons at a grazing angle, but the peak flux per unit area does diminish (though the intensity is conserved).

    Note that, absent emission and absorption (or etc.), flux is conserved if it is taken as the total flux through an inifinite plane. (That is how the total flux in any one direction is formulated two paragraphs above.) Take two parallel inifinite planes that surround some emitting volume, and note that as seen from that volume, they would appear to meet at a horizon. Essentially 100% of photons emitted from that volume that are not absorbed will cross one or the other planes at some point. This suggests that the total flux emitted by some volume is equal not to the sum of the magnitudes of all six flux vetors but to the sum of the magnitudes of any two opposing flux vectors. The other flux vectors describe how the concentration of the energy fluxes are spreading out perpendicularly to themselves.

    Note also that the total flux emitted, in the absence of absorption (etc.), is only found in the sum of the magnitudes of a pair of opposing fluxes through two infinite planes exterior to the emitting volume. The total flux is also equal to the flux per unit area summed over any closed surface enveloping the volume – of which, two infinite parallel planes is effectively an example (they ‘meet’ at the horizon having the effect of a closed surface) – notice in that case that each small bit of area has a flux through it that is perpendicular to the surface at that location. The flux passing through a plane where one or both intersect the emitting volume will not include all emitted flux in the same direction from the whole volume. If there is absorption of some of the same photons in the whole volume, then the flux through a closed surface or through two parallel planes that surround the source only include the net emission; their is no combination of surfaces forming a closed surface for which the fluxes through those surfaces sum to the total emission. The total emission is a flux in the sense that is a flux of energy from one form to another, but it doesn’t have a spatial location and direction; one could consider the total flux emitted in some range of directions from a volume, absorbed or not; it is a flux of energy from one form to another (the population of photons moving in some directions), but it can’t actually be measured across a closed surface, unless it is the net flux or if there is no absorption within the volume.

    Now consider the situation where there are horizontally expansive layers that are emitting fluxes of photons. The sideways fluxes include photons that are moving up or down but at an angle. However, the downward and upward fluxes include the downward and upward propagation of the same photons. As photons go up or down, they pass through different layers, while some may be absorbed along the way in some layers. The downward flux from a unit area of one layer will go downward through other layers, diminishing at the rate that it is absorbed along the way. (Etc. for the upward flux.) It spreads out at the same time, so that photons from one layer are absorbed in other layers over a larger horizontal area – some at a grazing angle may be absorbed very far away. But photons are also spreading out horizontally as they go up or down coming from horizontally different areas. For layers that are isothermal and optically homogeneous over infinite expanses, the downward or upward flux per unit area only changes by absorption and emission (setting aside scattering, reflection, and refraction), because the sideways movement of photons is balanced by opposite sideways movements of other photons. Even if the layers are not the same over horizontal expanses, if the horizontal layers are infinite or closed, the total flux over the entire horizontal expanse doesn’t spread horizontally because it can only spread into the areas it already occupies (it spreads into it’s own area), and thus, an average flux per unit area only changes by absorption and emission (setting aside scattering, reflection, refraction, and ‘apparent curvature’ of paths relative to layers) along a vertical distance through the layers, and in the approximation that the area of each layer is the same as that of the others. While closed horizontal layers around the globe vary in area and, due to their curvature, some downward emitted photons eventually end up going upward if they are not absorbed first, the relative vertical compactness of most of the mass of the atmosphere relative to the radius of the Earth allows the treatment of horizontal layers as being flat and of the same area to be a good approximation for at least some purposes.

    (The following specifically refers to monochromatic radiation; results must be integrated over the spectrum to find a total):

    The total flux emitted by a layer with no horizontal edges is the sum of upward and downward fluxes (see three paragraphs above). For a sufficiently thin layer, this is almost the entirety of all emissisions, but for layers of significicant optical thickness, some of the emitted energy is absorbed within the same layer; the flux of energy actually leaving the layer is the sum of fluxes upward and downward through the top and bottom of the layer. If an isothermal layer (in quasi-LTE) has large optical thickness (mainly from absorption), then the flux coming from that layer approaches the blackbody flux for the temperature of that layer; this is because the blackbody flux (and blackbody intensity that over a range of directions contributes to a blackbody flux) is the flux (and intensity) that would be in equilibrium with material at that temperature; for given optical properties, absorption is proportional to the intensity and emission depends on temperature, so if the intensity is larger or small than the blackbody value, absorption exceeds or is less than emission, so that, along the path taken, the intensity is always tending to adjust toward the blackbody value – it does this more effectively if the temperature varies more slowly or if the optical thickness per unit distance is greater. If the temperature variation is such that any nearly isothermal layer would have to be somewhat transparent, then the flux passing through a given level is a weighted average of blackbody values for the temperatures found over a volume from which the flux is coming; it consists of contributions from different parts of that volume; the parts farther away generally contribute less because a greater fraction of photons emitted from those parts are absorbed before they reach the location considered.

    (When refraction or scattering or reflection occur, the math and description gets more complicated but their is still a basic principle that applies; the intensity at a given location in a given direction is the weighted average blackbody value, with the weighting given by an emission weighting function, which itself has a volume integral of 1 and, if multiplied by the intensity in the opposite direction at the location considered, is equal to the distribution of absorption of that intensity, assuming quasi-LTE. Any location has a pair of oppositely directed intensities, each emitted by it’s emission weighting function and absorbed by the other’s emission weighting function; the net intensity depends on a difference between those values. The same relationship also requires that the flux emitted from an isothermal volume V1 that is absorbed in an isothermal volume V2 is larger than the reverse flux if the temperature of V1 is larger than the temperature of V2; of the flux emitted in one volume and absorbed in another, the net flux between a pair of volumes is from higher to lower temperature.)


    Gord’s big errors (if you’re wondering why I was so harsh with him from the outset here, see comments 235 to 510 starting here – I occasionally made some typos and one significant algebraic error that I recall, I believe all are corrected in subsequent comments) are

    1. not understanding what the physical basis of the second law of thermodynamics (see ), and even aside from that, ingoring the fact that two radiant fluxes in opposite directions have a net flux that agrees with what he understands (he spoke of resultant vectors but refused to apply vector addition to the K&T/KT&F diagram.)

    2. ignoring the fact that when a flux of energy leaves one thing and goes to something else, it LEFT that first thing. It was not created ex nihilo. A flux from the atmosphere to the surface removes energy from the atmosphere and brings it to the surface. A flux from the surface to the atmosphere does the opposite. Gord, for reasons I cannot comprehend, interpreted such fluxes to mean that energy was being created out of nothing, and then rejected such fluxes as being physically impossible for that reason. His logic is analogous to considering the situation where two people each have 10 dollars, and one gives 1 of those to the other person, and then the other person gives 1 back, and then concluding that they now both have 11 dollars; it makes NO sense.

  16. Oh, boy, I see the spin machine of climate crime apologism is at full speed here. Ok, let’s accept Chris’s assessment that Oxburgh was “cautious” in judging CRU.

    In this light we must then see the grave implications of the panel’s conclusion that, “We cannot help remarking that it is very surprising that research in an area that depends so heavily on statistical methods has not been carried out in close collaboration with professional statisticians.”

    Lord Oxburgh has even more reason to be “cautious” in any criticism being that he his also the same Lord Oxburgh who is Chairman of the Carbon Capture and Storage Association and the wind energy company Falck Renewables, UK Vice Chair of Globe International an “off-balance sheet,private company” funded predominantly by governments and NGOs that seeks to “bring legislators together – with a particular concern to the advancement of climate change legislation “(Climate Audit, Mar 24, 2010).

    Sadly, Oxburgh could only conclude, “It is not clear, however, that better methods would have produced significantly different results” because CRU defied freedom of information (FOIA) demands and lost/destroyed their algorithms!

    It is ‘not clear’ for a very pointed reason-evidence destruction. Any prosecution for that crime of evidence destruction was evaded solely due to the expiry of the FOIA statute of limitations-nothing short of a huge face-saving technicality.

    Despite his own personal reasons to tiptoe round the issues and be “cautious” Oxburgh was forced to conclude that CRU admitted that, “they would not do things that way today.” Clearly not!

    Based on only what evidence it had that was not already destroyed (criminally or otherwise) the panel found the mathematical skills of climate scientists should be better because it admitted there were “different ways of handling the data, some of which might be superior.”

    In further recognition of such failings the panel specifically suggests that in future there need be “closer collaboration and interaction between CRU and a much wider scientific group outside the relatively small international circle of temperature specialists.” Amen to that!

    Misrepresentation of the divergence between proxy and thermometer data was also addressed. Oxburgh lamented that not only was sub-standard statistical analysis a factor, but deliberate misrepresentation of such data undermined the IPCC’s case. The panel states, “presentations of this work by the IPCC and others have sometimes neglected to highlight this issue.”

    Poor mathematics is clear here because of the poor standards of ethics and competence of climate scientists. Further whitewashing of the facts merely makes your position ever less credible.

  17. Edit– More flat-earth theories are no longer welcome on my website. If you can’t have the self-courtesy to read an elementary book on climate, you no longer will be extended the courtesy to be respected on this site. The ability to misunderstand or misrepresent virtually every single possible angle of what you people talk about is outstanding, but do it elsewhere. I like Patrick’s posts but I also encourage him to cease talking people who clearly have no intention of learning from the very beginning.–chris

  18. but I also encourage him to cease talking people who clearly have no intention of learning from the very beginning
    Makes sense. I would highlight the rather obvious point that the statistics applied to temperature and paleclimatic data is rather independent of the mathematics in the physics of atmospheric radiation and other energy fluxes, and for that matter, momentum and mass fluxes (GCMs) – except wherein models are combined with paleodata to … (?) … anyway, enough of that for me. I might post a few equations that outline some points – yes, variants of what I’ve posted before but I might try to clean them up a bit – but not for just one person’s benifit.

  19. Allow me to make my point of view on the subject, even if late.
    Energy is a scalar physical quantity that acts in different forms, all equivalent between them. If not constricted (potential energy) it spreads in order to be shared with environment flowing according to the gradient of its density, measured in joules per cubic meter that correspond to newtons per square meter, that’s a pressure. In other words the energy flows in a gradient field and it’s well known that its field lines not intersect never, i.e. at any point of the space exists only one vector (the resultant of some presumable components) tangent to it and the effect caused at that point is only one: the vector, if not zero, solely operates in a direction or in the opposite direction.
    At the Earth’s surface the energy flows as sensible and/or latent heat and as EMR. There will occur only a single sensible heat flow, only a single latent heat flow, and for any frequency into the whole spectrum, only a single EMR flow that, in not zeros, are directed or upward or downward.
    Then, the feedback radiation isn’t possible because in this case the energy could flow in contrast to its gradient and hence to the second law of thermodynamics, that has a general value for any form of energy, not only for the heat. Otherwise we come back to the 19th century.
    The EMR energy density is given by Plank’s law that’s a decreasing function of the temperature, then the EMR energy can flow only according to decreasing temperatures, as does the heat flow. Naturally, this is solely valid for those frequencies for which there’s thermodynamic equilibrium between the thermal energy that becomes EMR energy and vice versa. That means that one can’t apply Plank’s law to CO2 15 microns IR into Earth’s atmosphere (or of another planetary atmosphere) since the planetary temperature is too low to thermally excite the CO2 molecule at the bending resonance frequency needed to emit a 15 microns photon. That can occur into a star, not into a planet. But that’s another matter.

    • Michele – please see above comments, but briefly:

      The radiant fluxes often described are often components of the net flux that corresponds to the resultant vector. The net flux between two volumes, each at LTE and each individually isothermal or else with temperature ranges that do not overlap, from point of emission to point of absorption, setting aside any Raman or Compton scattering, etc – in other words, with any scattering preserving photon energy – and also, assuming conditions stay constant in the travel time of photons (a reas0nable approximation within Earth’s atmosphere), is from the warmer to cooler volume – but this is because the flux emitted by the warm volume that is absorbed by the cooler volume is greater than the flux emitted by the cooler volume that is absorbed by the warmer volume.

      CO2, in the amount that is found along a path through the atmosphere or any layer thereof which is not too thin, has significant-to-large optical thickness (of the absorbing type, as opposed to scattering) at wavelengths at and near 15 microns. Given this condition occurs at LTE, and given Planck’s function, I must assume that, at some temperature typical of the atmosphere, whatever fraction (perhaps quite small? – that’s on the edge of things familiar to me) of CO2 molecules are excited properly to emit at some wavelngth, they are sufficient to emit photons at a rate according to optical thickness and the Planck function B(T) for some wavelength or frequency (specifically, the spectral intensity emitted per unit distance will be B(T) * optical thickness per unit distance = B(T)* emission cross section per unit volume; this sums to greater than B(T) over optically-large paths, but the absorption that also occurs limits the intensity that can be recieved from emissions along an isothermal path to be no greater than B(T); do note that the atmosphere is not generally isothermal).

      • Sorry, I can’t agree with what you said.
        As far as I know, into the space exists only one EM wave field due to interference (superposition) of innumerable EM wave fields. At any point of the space, given two or more EM waves that have the same or nearly the same frequency, you get the global EM energy flux (Poynting vector) by the vector (cross) product of Electric resultant field and Magnetic one. Hence, at any point of the space can exist only one EM vectorial effect, whatever it is, because the vectorial field lines never cross each other.
        I notice that the radiative transfer theory is the one physical theory that is characterized by a sort of omnipotence since both Planck’s and SB’s relationships take an absolute (rather than relative) significance assuming that a body radiates, always and however, regardless of environmental conditions. Not at all. That doesn’t make much sense. The radiative flux is physically analogous to any other flux induced within a transport phenomenon that’s always founded on the gradient of the driving physical property (pressure, temperature, altitude, electric potential, etc.), not on its absolute value.
        The Planck’s function implies that the probability of thermal radiation is the same for any wavelength or frequency and that’s true for liquids or solids but only partly for gases. Indeed, the CO2 heat capacity at room temperatures is about 5*(k/2) J/molecule telling us that for that gas are thermally significant only the three translational degrees of freedom and the two rotational ones (linear molecule), among which occurs the equipartition of the heat provided to gas, whereas the vibrational and higher level degrees of freedom stay thermally indifferent as if they were “frozen”. In fact, if all vibrational degrees of freedom were “unfrozen” the heat capacity would be equal to 13*(k/2) and this points out that the thermal vibrational excitation don’t occur at the same rate of its absorption. Really, the excitation can’t be completely excluded at room temperatures, but it can occur only by a very weak CHANCE.
        In other words, computing the radiative fluxes with Planck’s function needs to use a different probability coefficient between the translational/rotational frequencies and the remaining ones in the spectrum, because the Kirchhoff ‘s radiative symmetry is valid only for translational/rotational frequencies. You need to introduce an meaningful relevant weakening for the other ones when you use the spectral absorption of CO2 and other GHE at planetary temperatures.
        In practice, the atmosphere makes with IR what the ground makes with SW: it first thermalizes the absorbed IR radiation and then shifts its re-emission towards more lower frequencies.

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