The Lungs of Gaia

By Philip Mulholland and Stephen Wilde

A fundamental concept at the heart of climate science is the contention that the solar energy that the disk of the Earth intercepts from the Sun’s irradiance must be diluted by a factor of 4.  This is because the surface area of a globe is 4 times the interception area of the disk silhouette (Wilde and Mulholland, 2020a).

This geometric relationship of divide by 4 for the insolation energy creates the absurd paradox that the Sun shines directly onto the surface of the Earth at night. The correct assertion is that the solar energy power intensity is collected over the full surface area of a lit hemisphere (divide by 2) and that it is the thermal radiant exhaust flux that leaves from the full surface area of the globe (divide by 4).

In between these two geometric relationships of energy collection and departure back to space lies the Atmospheric Reservoir, the Earth’s gaseous coating within which all climate processes occur. The following table and figure adapted from the canonical model of Kiehl and Trenberth (1997) are used to illustrate a model in which the fundamental realities of a lit (day) and unlit (night) hemisphere are retained as the irreducible logical minimum geometric relationship for the energy budget of the Earth’s climate.

Table 1: The Atmospheric Reservoir Energy Recycling Process for a single Lit Hemisphere Model.

In the following figure the parameters have been adjusted by using hemisphere dependent thermal exhaust flux values of 200 W/m2 (day) and 270 W/m2 (night) based on a Dynamic Atmosphere Energy Transport model of the Earth’s Climate (Wilde and Mulholland, 2020b).

Figure 1: The Atmospheric Reservoir Energy Recycling Process.

Key Features of the Diagram

  1. It demonstrates that the concept of the Atmospheric Reservoir can be made to work for a Lit Hemisphere (Divide by 2) Solar Irradiance.
  2. It shows how the Atmospheric Reservoir behaves as both a store and a transporter of energy.
  3. All captured fluxes are doubled by the process of infinite geometric recycling (the half lost; half retained process by which an infinite series of halves of halves sums to one).
  4. In the daytime the Troposphere expands as it stores potential energy with work done against gravity.
  5. Potential energy cannot be radiated away so the daytime loss at the Top of the Atmosphere (TOA) is reduced as the atmosphere expands.
  6. During the night the Troposphere contracts as it cools, this converts potential energy back into kinetic energy which accounts for the enhanced night-time loss of energy to space.
  7. The atmospheric reservoir gross value of 780 W/m2 is halved to the 390 W/m2 canonical value because the surface area of the emitting globe is twice that of the solar collection hemisphere.
  8. The daytime processes of thermals and evapo-transpiration are driven primarily by direct solar energy and so do not occur at night (lots of caveats here: if the surface is moist then the evaporation process can also occur at night e.g. land versus sea, moist tropical forest versus dry desert, weather systems advection etc).
  9. The Earth’s surface is a huge slow release storage radiator that emits its captured solar energy at night and in the winter.
  10. The bypass radiation occurs both during the day and at night at the same rate (40 W/m2) as in the canonical model because of the same surface area issue of collection versus emission as listed in point 7.

The Lungs of Gaia

One could liken the process of the daytime capture of solar energy that causes the atmosphere to expand, followed by the night-time contraction of the atmosphere as it cools – to the Earth ‘breathing’. The atmosphere being the lungs of our planet which expand and contract over the course of a 24-hour cycle, and in doing so varies the supply of potential energy back to the surface. This rhythmic process acts to maintain hydrostatic equilibrium for the atmosphere as a whole by matching thermal radiant energy out to space with high frequency radiant energy coming in from the sun.

References

Kiehl, J.T and K.E. Trenberth, 1997. Earth’s Annual Global Mean Energy BudgetBulletin of the American Meteorological Society, Vol. 78 (2), 197-208

Wilde, S.P.R. and Mulholland, P., 2020a. An Analysis of the Earth’s Energy Budget. International Journal of Atmospheric and Oceanic Sciences. Vol. 4, No. 2, 2020, pp. 54-64. doi: 10.11648/j.ijaos.20200402.12

https://www.researchgate.net/publication/344539740_An_Analysis_of_the_Earth’s_Energy_Budget

Wilde, S.P.R. and Mulholland, P., 2020b. Return to Earth: A New Mathematical Model of the Earth’s Climate. International Journal of Atmospheric and Oceanic Sciences. Vol. 4, No. 2, 2020, pp. 36-53. doi: 10.11648/j.ijaos.20200402.11

https://www.researchgate.net/publication/342109625_Return_to_Earth_A_New_Mathematical_Model_of_the_Earth’s_Climate

129 thoughts on “The Lungs of Gaia

  1. Finally someone who looks at radiation balance from a frequency standpoint. I always wondered if the day/night frequency brought any specific effects (it sure should do!) that would not be there compared to a “flat” modeled balance.
    Everyone coming from electronics should know that resistance of a given system is a function of frequency but I never saw this topic in climate sciences before (well I’m not knowing in every paper there is, so I might be very wrong).
    If anyone has more on this topic I would be grateful! 🙂

    • What matters is the period of the stimulus relative to the time constant. In electronic circuits, the time constant is R*C which has units of time while for the climate, the time constant is a more complicated function of the heat capacity, the current temperature and the energy flux, where owing to the T^4 relationship between W/m^2 and temperature, the time constant is reduced as the temperature increases, while in electronic circuits, the time constant is independent of the state or stimulus.

      Time constants of land are generally very short, otherwise, we would notice no difference between day and night temperatures. Large time constants are generally assumed so that ‘future’ warming that has not manifested can be claimed, but if the time constant were as long as they require, we would not even notice changes in the seasons, much less differences between night and day.

      Relative to the climate, the period of the stimulus has no influence on the net radiant balance, which is driven by solar energy alone. For a body tidally locked to the Sun, or when the period is far larger than the time constant, you need to divide solar energy by only 2 in order to establish the average steady state surface emissions and its corresponding temperature while the peak ‘noon’ temperatures at the equator are based on achieving equilibrium to all of the solar energy, for example on the Moon.

      The ‘consensus’ seems to think that the Moon is hot because it has no atmosphere. It’s hot because the Sun is up for 14 Earth days at a time which is enough time for the surface to be in equilibrium with the peak incident solar energy. This never happens on Earth.

      If Earth had a day/night cycle as long as the Moon, daytime temperature would be far higher
      and nighttime temperatures would be far lower, but the average emissions of the planet will be the same as they are now, just distributed across the surface differently. Average temperatures calculated as a linear average will not be the same owing to the T^4 relationship between emissions and temperature, but then again, a linear average of temperature is not physically significant to the radiant balance and is only significant relative to the amount of energy stored by the system.

      One problem with climate science is the widespread assumption baked into the analysis that emissions are linear to T. While temperature is linear to stored Joules, in the steady state, the temperature has already changed and all that matters is the work required to maintain that temperature which is proportional to T^4.

      • Thank you for your explanation. About the incoming Radiation. Based on the T^4 of planck curves CO2 must absorb way more energy coming from the sun (in terms of raw joules) and reemit it into space, than catch outgoing radiation (and reemit it on the earth). That’s where I guess the notion from CO2 beeing a cooling gas actually comes from.
        But why wouldn’t that be the case. Is it that it can give it’s energy to the other molecules around before it reemits it’s energy?

          • Thanks Ferdinand!
            Yes I realized this mistake myself when I went to sleep that day, as energy distribution and actual Intensity are obviously sort of depending on distance from source… That overview is very helpful thank you alot. So Methane and NO seem only really relevant in an absolute dry (and therefore hypothetical) Atmosphere, where the concentration of H20 is in the magnitude of those other two, is that right?

          • Mr. Engelbeen,

            your statement is somewhat wrong, because the high energy photons are found at the wavelengths the sun emits, since its coming from a much higher temperature.
            The emissions from CO2 or water vapour are at much lower energy.

            If you try to explain it, please explain it properly.

        • Knalldi,

          Most of the energy emitted into space in absorption bands originates from the emissions of energized GHG molecules. Nearly all of this emitted energy, either into space or back to the surface, originated as surface emissions. Just as geometry dictates dividing by 4 to get an energy average for solar across a planet (or 2 for a node locked planet), surface emissions absorbed by the atmosphere are split roughly in half between being emitted into space or returned to the surface.

          The evidence of this is significant energy at TOA over clear skies in bands where the probability of a photon emitted by the surface and being absorbed by the atmosphere is 100%. In fact, the amount of energy at TOA is typically about half of what it would be without any absorption at all. The only place this energy at TOA could come from is the emissions of GHG molecules very high up in the atmosphere since no other atmospheric gases will emit photons in those bands.

          The only real ‘thermalization’ occurs as energized H2O (or CO2) molecules become encorporated in droplets of liquid water in clouds. This can be observed in the emitted spectrum as slightly more than 3 db attenuation around some of the stronger H2O absorptuon lines.

          • Thank you for your reply.
            There are still alot of things I have to learn here and right now I’m browsing through the CO2 slides part of the link provided to your website.
            It’s a very interesting read and will keep me busy for a while, while reminding me of the good old 90’s websites ;).

          • Here’s something more recent that shows some straight forward math quantifying the Earth’s effective emissivity of about 0.62 and why, given that the atmosphere is chaotically self organized, it’s average value is not likely to take on any other value.

            http://www.palisad.com/chaos2gold.pdf

            The effective emissivity, e, is such that, Po = eoT^4. where Po is the average outgoing emissions flux at TOA, o is the SB Constant and T is the average surface temperature from which TOA emissions ultimately arise.

    • The factor of 1/2 , solar irridiance 1368 / 2, is also discussed in “ Critical analysis of the global climate theory, Disproof of basic study of IPCC greenhouse effect, Kiehl and Trenberth 1997, with measure values of ERBS satellite on an new model. “, 2019, Avalable as eBook at amazon in USA and Europa. With these, the observed global warming of approx 1.2 Kelvin between 1850 and 2018 can be explained without the influence of CO2 by long-term cloud change (albedo change). By using 1/2 in this new model, it can be proven, that a greenhouse effect for our Earth with measure values of the satellites ERBS, TERRA and AQUA CERES) does not exist.

  2. Can anyone explain how it is possible for the power of the solar irradiance that is collected by a planetary orb to be diluted by a factor of 4 BEFORE it has entered the atmosphere?

    • No one says that is the case.

      The calculation is the 24h average and due to the fact that as you get away from the equator 1m2 of ground does not present 1m2 of area in the direction of the sun ( cosine of latitude ). Near the poles it’s nearly side on.

      It’s really rough as guts approximation since there is more reflection at the poles and then you need to start making arbitrary ( conveniently tweaked ) guesses about “average albedo” of the Earth.

      and that it is the thermal radiant exhaust flux that leaves from the full surface area of the globe (divide by 4).

      No, that’s divide by 1 😉

      I really don’t see what the point of this article is and since the “adjustments” made to table are not documented, it all becomes a waste of time.

        • How can some people not comprehend that the S/4 value of solar flux does NOT represent the *instantaneous* TOA illumination of the whole Earth, but instead the time-averaged (1-day or longer) solar energy available to the whole Earth. There is no flat-Earth assumption involved (in fact, dividing by 4 is because the Earth is approximately spherical). It is used in only simplistic treatments of Earth’s average energy budget. Detailed calculations (as well as 4D climate models as well as global weather forecast models) use the full day-night (and seasonal) cycle in solar illumination everywhere on Earth. The point isn’t even worth arguing about.

          • “The point isn’t even worth arguing about”.
            Roy
            Thank you for engaging.
            Please confirm that the TOA solar irradiance value in a climate model cell follows the full 24 hour rotational cycle of daytime illumination and night time darkness.

          • Philip Mulholland, you said: “Please confirm that the TOA solar irradiance value in a climate model cell follows the full 24 hour rotational cycle of daytime illumination and night time darkness.”

            Oh, my, Philip… you cannot be serious.

            Every one of the 24+ climate models run around the world have a full diurnal cycle at every gridpoint. This is without question. For example, for models even 20+ years ago start reading about the diurnal cycles in the models on page 796 of the following, which was co-authored by representatives from all of the modeling groups: https://www.ipcc.ch/site/assets/uploads/2018/02/WG1AR5_Chapter09_FINAL.pdf

          • Philip:

            For each cell in a climate model (say, 5 degree by 5 degree, or 1 degree by 1 degree) and for each time interval (say, 15 minutes), the first calculation done is the angle of the sun relative to the surface. Then the “S” value (say, 1366 W/m2) is multiplied by the sine of the elevation of the sun.

            So, for example, if the sun is 30 degrees above the surface for a given cell in a given time interval, the sine is 0.5, so the local TOA S value (let’s call it S’) can be calculated as:

            S’ = S * sin(30) = 1366 * 0.5 = 683 W/m2

            Of course, for negative elevation angles (aka “night time”) the effective sine value is zero.

            It is this S’ value that is used for starting calculations for that cell in that time interval.

            If you average all of the S’ values of the entire earth, you will find that

            S’avg = S / 4

            which should have been obvious from basic geometry.

            Climate models have many, many problematic intervals, but this is NOT one of them.

          • “If you average all of the S’ values of the entire earth, you will find that
            S’avg = S / 4
            which should have been obvious from basic geometry.”

            Ed Bo
            That is the emission area.
            I am talking about the power intensity for the collection area that is illuminated by sunlight.
            The sun never shines onto the surface of the Earth at night.

          • Philip, Ed Bo has hit the nail on the head. Your response to him suggests you do not understand even the basics of climate modeling, and I am a little dismayed that your post appeared on WUWT. What Ed Bo said WAS referring to solar radiation. And, yes, I know you have a “peer reviewed” publication on this, but you have managed to get your paper past peers who know little to nothing of the subject (I have looked at the online journal and the list of reviewers… geologists are good in their field, but I wouldn’t expect an atmospheric radiation expert to review a paper on geology, and we can’t expect geologists to know atmospheric radiative transfer).

          • Dear Philip Mulholland and Stephen Wilde,

            Thank you for sending me this very interesting piece of work. I have no immediate reaction.
            It will take time and hard work to understand the details. I will let you know if I reach any
            clear conclusions about it. In the meantime, I welcome your fresh view of an old problem.
            Yours sincerely, Freeman Dyson.
            .

          • So the sum of the total sun impact is (2S) * integral of (sin a) from a=0 to a=pi/2) for any specific cell? How does latitude figure in?

          • Thank you, Dr. Spencer.

            The whole thing about representing the Earth’s energy budget on a simplistic basis is what causes the confusion. The Solar flux at the top of the atmosphere is an average of 1,362 W/m^2, which is what the disc of the Earth, plus the annulus of its atmosphere, intercepts at any given instant. Even these intercepts become more complex with latitude, day of the year, and time of day, as the Earth’s rotation moves water and land into position. All of the Earth’s surface reflects more of the incident energy with decreasing angle of incidence, especially water – so the illuminated pole will reflect far more than its equatorial counterpart.

            All of the general circulation models for climate research model these factors. None that I know of use a 1,362/4 = 340.2 W/m^2 Solar flux normal to the surface of the Earth. That’s just a fiction used to simplify calculations of the Earth’s radiative energy budget, not one that is employed in large-scale, “high fidelity” models. (The Earth’s disc presents an area of pi*Re^2 to the Sun, so the total average insolation at any instant is 1,362*pi*Re^2. But to simplify energy budget illustrations, it is often that authors use that intercepted power, and distribute it over the whole planet, whose area is approximately 4*pi*Re^2 – hence the division by 4. I personally find it bad practice.)

            The problems with “high fidelity” GCMs are actually far more obvious than this, though one must have a command of numerical modelling to speak authoritatively about them. At the forefront is the fact that, with modern computers, one cannot achieve more less than 100 km spatial resolution in the grid used for numerical analysis of the equations of fluid motion. And, of course, the computational analysis of turbulent fluid motion requires abandoning the purely physics based Navier-Stokes equations for the Reynolds-averaged Navier-Stokes equations. Reynolds averaging adds more variables to the set of equations, making them indeterminate. There are no more physics-based equations available to close the set, so empirical relations (e.g. the k-epsilon turbulence model) are added. These contain adjustable parameters, which can then be tweaked to make the solution conform to measured data (within a few percent). That, in turn, requires experimental measurement. In aircraft development, is done in a wind-tunnel. There’s no similar way to experiment on the Earth’s atmosphere.

            The Earth’s atmosphere is quite turbulent, and many of its properties are determined by that fact. The turbulence scale ranges from centimeters to kilometers, yet we can model only on the 100 kilometer scale. That’s not much of a model.

            Getting back to the radiative issue… I’ve been doing a deep dive into a German GCM, and found a startling set of issues with its treatment of the annual variation of Solar insolation as a function of the Earth’s distance from the Sun versus time. That the phenomenon was addressed at all was gratifying. But the writeup asserted that its method of calculating that distance, involving the solution of a transcendental equation, had convergence problems, which the programmers had “addressed,” citing a reference on algorithms for celestial mechanics. I know a great deal about that solution (for Kepler’s equation), and what they wrote was flatly not true. I bought the book they referenced, and it did not contain the difficulty they had cited – in fact, it stated the exact opposite.

            Given that they had such difficulty with so trivial a programming problem makes me wonder how they thought that the stupendously difficult solution of the 3-D time-dependent Reynolds-averaged Navier-Stokes equations was done flawlessly.

          • Roy Spencer: I am a little dismayed that your post appeared on WUWT.

            Dismayed but completely unsurprised, welcome to my world. To add insult to injury, how would like a little trolling rubbed into your dismay?

          • Tim Gorman:

            You ask: “How does latitude figure in?”

            Of course, latitude also affects the sun’s elevation angle. For example, at the equinox, when the sun is directly over the equator, at noon at 40 degrees latitude, the sun’s elevation angle will be 50 degrees. Before and after noon, it will be even less than this. (You have to use some compound trig calculations.)

          • The modellers may well think that they have mathematically accounted for the diurnal range but they actually haven’t because they have failed to distinguish between the differing thermal properties of the emission area (the entire sphere), the collection area ( the daytime hemisphere), and the non-collecting area (the night time hemisphere).
            Those three areas interact in a highly complex fashion due to convection upwards, downwards and around the sphere.
            Once one models that convection driven interaction, as we have done, one can account for the surface temperature enhancement without involving radiative gases at all.
            By ignoring that aspect the models are effectively dealing only with two dimensions rather than three hence our assertion that they might as well be dealing with a flat Earth. They do not consider atmospheric movement as a factor in moving energy around within the system so as to delay emission of some incoming radiation back to space.
            So, Roy, and many others, you have it wrong on this occasion.
            There is no point criticising the numbers we allocate to the various energy flows either because they have to be rough estimates in the current absence of accurate numbers for any planet.
            Nonetheless we show that by apportioning the energy flows over time in a particular way (consistent with basic meteorology) one can achieve a warmer surface than predicted by S-B without invoking radiative gases or back radiation from atmosphere to surface.
            It works for multiple planets and moons with atmospheres and explains clearly why the temperature within the atmosphere of Venus at the same pressure as on Earth is much the same as on Earth subject only to accounting for a different distance from the sun.
            The inability of the radiative theory to account for that simple observation is a powerful indication that the radiative theory is wrong.
            We have run the numbers for Earth, Venus and Titan and they are sound in each case.

          • Roy,

            You said, “… and we can’t expect geologists to know atmospheric radiative transfer).” Even some of us mere geologists have academic backgrounds comparable to the well-known geophysicist Michael Mann. And, our formal degrees don’t really do justice to what we might have learned in the decades since graduating.

            I for one, spent the last 4 years of my career before retiring, reading and performing experiments, and providing the Chief Scientist with annual reports of ~100 pages summarizing what I had done in the field of imaging polarimetry. I didn’t receive even an honorary sheepskin, but I would say that I did a level of work comparable to a PhD. So, I don’t think that you should be so quick to denigrate someone who doesn’t have what you consider to be the appropriate formal education to dabble in a specialty. After all, even Mann doesn’t really meet your criteria.

          • Mr. Spencer,

            Energy is expressed in Joule. If you want to pick Joule over the surface, why not do so.
            If expressed as W/m2 the average over time has to consider the true area that the sun shines on.
            The point is worth arguing, because it leads to the conclusion that the S/4 energy budget is a flat earth argument.

            S/4 only exists for the assumptionn of the energy leaving Earth, it is false for Earth receiving Energy from the sun.

        • The sun ain’t shining where it is night, but yet the sun shines for 24 hours all day long in the weeks, month and years by the millions.
          A conundrum for climate energy artists who pretend to acknowledge this, but wrongly assume as to where the sun shines. It ain’t shine where it is night!

      • Ahh, albedo. It is sort of defined for daytime hours, but what is it at night? I think most models use the same value for day and night, probably incorrectly.

        • George:

          Albedo is fraction of incident radiation that is reflected. When we talk about Bond, or solar albedo, it is in particular the fraction of incident solar radiation that is reflected. The fraction absorbed is (1 – albedo).

          So the equation is:

          S[absorbed] = S[incident] * (1 – albedo)

          At night, S[incident] = 0 and the equation becomes:

          S[absorbed] = 0 * (1 – albedo) = 0

          I’m pretty sure the models get this right. (Not so sure about many other things…)

          • Ed
            You are close, but not quite right. Albedo is the fraction of incident radiation that is retro-reflected. Forward or side-scattering cannot be observed directly, and needs to be modeled to determine total reflectance, or use at least two other sensors simultaneously to characterize the total reflectance. However, even three satellites cannot provide a good characterization of total reflectance. One has to make many measurements to build a model of the hemispherical Bi-directional Reflectance Distribution Function (BRDF) for a large range of elevation and azimuth values for the incident radiation. The reflected/scattered components of a diffuse reflector have different intensities for every direction as defined by the elevation and azimuth with respect to the incident radiation. One can attempt a simplification by assuming a Lambertian scattering model, but it won’t be exactly right for most things, even clouds. For objects that have sub-aligned planar surfaces, such as snowflakes and waxy leaves, they can differ substantially from a Lambertian scatterer. Anyone who has gone skiing or snowshoeing on a sunny day is familiar with snow being brighter when walking into the sun compared to other directions. Put more formally, snow, while a diffuse scatterer, has a strong forward scattering lobe in the BRDF model.

            None of this addresses the behavior of pure specular reflection, which is dominated by forward reflection away from the source (sun) and has minimal retro-reflection for a small range of angles. In any event, all specular reflection has a very narrow range of angles, creating a sheaf of light rays that is equal to the angle of incidence, spread out by the curving surface of the Earth.

            Note that the term albedo has its origin in astronomical observations, where only retro-reflections are capable of being observed. To be consistent, and comparable, reference to albedo of Earth or Earth surface features, should be similar to the geometry of celestial objects. It should be clear that any estimates of Earth albedo based on observations of Earthshine reflected from the new moon, ONLY records retro-reflections of both Earth and the Moon. Therefore, the Earth ‘albedo’ estimate misses all light exiting Earth that isn’t retro-reflected, and is therefore a lower-bound on the total reflectance of Earth.

    • Philip Mulholland

      I recall that, especially on this blog, many people had problems with accepting a simple fact.

      When a far distant EM source hits a spherical celestial body, the energy flux computed in W/m² reaching the body has to be halved anyway because both the surface and and the hitting flux decrease with the cosine of the incident angle (0 at Equator, pi/2 at the poles).

      When integrating cos²(angle) over 0 <= angle <= pi/2, you obtain 0.5.

      This is the reason why you see pi * R² instead of 2 * pi * R² in the balance equations.

      J.-P. D.

      • “This is the reason why you see pi * R² instead of 2 * pi * R² in the balance equations.”
        Binididon
        A. The surface area of a sphere of radius r is 4πr^2
        B. The surface area of a hemisphere of radius r is 2πr^2
        C. The surface area of a disk of radius r is πr^2

        A. Is the Emission area.
        B. Is the Collection area.
        C. is the Interception area.

        Are we on the same page or maybe you need to take this up with Euclid of Alexandria?

        • Philip Mulholland

          It seems you too didn’t understand what I tried to explain.

          Like Roy Spencer, I seriously begin to ask me why you publish things you don’t understands the very basics of.

          Sorry, that’s a bit too boring for me.

          Rgds
          J.-P. D.

          • “It seems you too didn’t understand what I tried to explain.”
            Bindidon

            My father was a math teacher. He had a very simple teaching rule:
            If he did not understand something himself, then he could not explain it to his class.

        • Mr. Mulholland,

          correctly said.

          Not sure what Mr. Bindion us up to, but if he speaks for Mr. Spencer it is not far off him offering us a consent.
          We know where this leads too!

    • “As Earth cruises through the black sea of space at about 67,000 mph (108,000 km/h), the planet’s magnetic field pushes aside solar wind — the constant stream of plasma particles ejected by the sun — the same way the bow of a speeding motorboat pushes aside water. Scientists call this phenomenon “bow shock” because of its similarity to a ship surging through stubborn waves.
      Researchers have long suspected that we can thank this bow shock for reducing the scorching solar wind into the mild breezes we feel on Earth, but they didn’t know exactly how this happened. Now, a new paper published May 31 in the journal Physical Review Letters adds a few billion electron-size pieces to the puzzle.”
      https://www.livescience.com/62734-bow-shock-thwarts-solar-wind.html

      • Today’s Solar wind protons arrive with about 830 eV energy each, at about 400 km/s, and at a density of 4.6E6 per cm^3. That amounts to an energy flux of 0.244 mW/m^2, or 18 millionths of a percent of the Solar flux. I really don’t think they’re a big issue.

  3. Rather confusing.
    What do you “divide by 4 or 2”?
    The Earth gathers the sun energy over the disc pi*R^2.
    This is trivial.
    It radiates the energy over the full sphere 4*pi*R^2, but depending on the local temperature T in 4th power, like T^4. This is a very strong dependence!
    The local temperature varies not only due to “night and day”, but depends on many things, mainly on the latitude, season, etc.
    Europe radiates much more than, e.g., Alaska, thanks the Gulf Stream.
    The energy is stored mainly in the water, much less in the soil.

    • The earth may gather energy over the disc pi*R^2 but the issue is how much energy does the disc collect at any specific point.

      The energy collected at the edges of the disc will be at a minumum because of the angle of incidence. The energy collected at the center of the disc will be at maximum.

    • Alex
      If one wants numbers to use for calculations, such as instantaneous flux rates (or short time intervals such as less than an hour), then one divides by 2 for the hemispherical area. If one is interested in long term averages, where the entire sphere experiences illumination, then one should divide by 4 to correct for the surface area of a sphere. It would seem to me that if calculations in a model are done on an hourly basis, then insolation should be corrected by dividing by 2 and taking into account the percentage of the hemisphere being illuminated.

  4. Somehow, I lose my interest to read this kind of story blogs, if the reference is to the “canonical” energy budget of Kiehl and Trenberth,1997. The year 1997 shows that it is badly out of date. The calculation basis of this energy budget has been US Standard 76. The researchers should know that it is not the average global atmosphere. Kiehl & Trenberth even reduced the water content and finally the water content was only 50 % of the real average global atmosphere. The term canonical is from the dark ages of history.

  5. The Earth has a high precision thermostat that controls the sea surface minimum at 271.3K and 304K maximum.

    Sea ice form at the lower limit to insulate the surface to reduce heat loss. High level monsoonal clouds and cyclones form near the upper limit, transferring ocean energy to land via and precipitation and limiting solar input by reflection. 50+ cycles annually, each covering a very large area and persisting from days to weeks with a reflecting average power of 300+W/sq.m rejects a lot of heat. So effective at rejecting heat that they can cool the ocean surface beneath while the sun is directly overhead; that is some sun shade.

    The only part of the sea surface that is warmer than 32C is the Persian Gulf. The reason is that cloud burst and cyclones cannot exist within the Gulf. The convective potential required to form cloudburst cannot be sustained in the high level dry air coming off the Zagros Mountains in Iran and ending up in the monsoonal trough in the Arabian Sea.

    I have serious doubts that there has been any global warming in the last century. Certainly none evident in the last 30 years according to the moored buoy data.
    https://www.pmel.noaa.gov/tao/drupal/disdel/

    If anyone is claiming there is global warming then look at the basis of their measurement system. I have grave doubts about the veracity of Roy Spencer’s satellite temperature. I would like to see it correlated against the tropical moored buoy record for that region of the globe, which cannot get warmer than it already is. The moored buoy data is the only data that is not manipulated by necessity or by divine intent, as in homogenisation.
    vie

  6. “The term canonical is from the dark ages of history.”
    Antero
    Where exactly in the code of the climate model is the raw undiluted power of solar irradiance applied to the TOA grid cell?

  7. One of the things wrong Trenberth’s 1997 diagram is that – energy in and energy out – it balances, and as we all know, the world has warmed up perhaps a degree since the 19th century. And so it was updated a few years ago, it may have gone like this:

    Once upon a time on a bright sunny morning a few years back, Dr. James Hansen was looking at Kevin Trenberth’s iconic “World Energy Budget”

    http://www.grida.no/climate/ipcc_tar/wg1/images/fig1-2.gif

    when he choked on his morning coffee because he realized that the darn thing balanced. That’s right, energy in equaled energy out. You see, he’s been saying for some time now that heat energy is slowly building up in Earth’s climate system and that’s not going to happen if the energy budget is balanced.

    So he did some fast calculations, snatched up his cell phone and punched in Trenberth’s number.

    “Hi Kev, Hansen here, how’s it goin’ with you? Got a minute?”

    “Sure Doc, what’s up?”

    “Glad you asked. I’ve been looking at your energy budget and it balances, can you fix that?”

    “What do you mean fix it, it’s supposed to balance?”

    “Kev, listen carefully now, if it balances, heat will never build up in the system do you see where I’m going?”

    “Uh I’m not sure, can you tell me a little more?”

    “Come on Kev don’t you get it? I need heat to build up in the system. My papers say that heat is in the pipeline, there’s a slow feedback, there’s an imbalance between radiation in and radiation out. Your Energy Budget diagram says it balances. Do you understand now?”

    “Gotcha Doc, I’ll get right on it” [starts to hang up the phone]

    “WAIT! I need an imbalance of point nine Watts per square meter [0.9 Wm²] for everything to work out right.”

    “Uh Doc, what if it doesn’t come out to that?”

    “Jeez Kev! Just stick it in there. Run up some of the numbers for back-radiation so it looks like an update, glitz up the graphics a little and come up with some gobbledygook of why you re-did the chart you know how to do that sort of thing don’t you?”

    “Sure do Doc, consider it done” [click]

    What it means is, all of the components

    Reflected by clouds
    Reflected by aerosols
    Reflected by atmospheric gases
    Reflected by surface
    Absorbed by the surface
    Absorbed by the atmosphere
    Thermals
    Evaporation
    Transpiration
    Latent heat
    Emitted by clouds
    Emitted by atmosphere
    Atmospheric Window
    AND
    Back radiation

    need to have an accuracy to those five places or better for the 0.9 Wm² to be true.

    Perhaps Hansen didn’t ring up Trenberth and bully him into changing his chart but, Trenberth did change it to show an imbalance and I bet he did so because he finally realized that if it balanced like his 1997 version, heat wouldn’t build up.

    And we are all supposed to sit still for this sort of thing.

      • Phil, You wrote in a comment above:

        Where exactly in the code of the climate model is the raw undiluted power of solar irradiance applied to the TOA grid cell?

        Did you expect an answer to that? Well no, you didn’t, no one on this blog has access to the code. Are you claiming that climate modelers don’t apply the sun’s radiation at the top of a grid cell appropriately from zero to 1366 W/m² in their models? I would expect that they at least get that right. Well, there must be something wrong, because the Global Cooling, Nuclear Winter, Global Warming, Climate Change, Climate Crisis scare as been going on for fifty years and not much has changed.

          • Your response reminds me of my post a few days ago (here) on these pages where I wrote:

            When I asked my favorite liberal, smart guy, way more brain cells than me and talented in many fields, “Do you really think that wind power and solar panels can power the world’s economy?” I got a simple “Yes” for an answer. For reasons of the cancel culture & political correctness, that ended the conversation.

            There isn’t just one model, the CMIP program started in 1995 and my very short search says CMIP6 is up to 40 models, so I’m guessing there are a few hundred models and so far most of them are wrong. The one or two that are right can probably be compared to stopped squirrels and blind clocks. Smart remarks aside, the people creating the models aren’t stupid. It’s a good bet that most them get the solar incident angle and its effect at the top of the grids correct. Their models run hot and probably do so for the same reason I didn’t continue the conversation with my favorite liberal.

            Well good luck on getting an answer.

    • I remember seeing that Trenberthian diagram with fluxes with +- values of several to mid teen variability.. (in W/m2)

      And down the bottom this comment saying the “trapped” energy was 0.6W/m2 or something like that.

      All I could do was laugh. 🙂

      It was probably the one diagram that made me realise it was all just JUNK SCIENCE. !

      I also remember pointing this out to my rather cute hippy-style girlfriend…

      oops… end of relationship ! 🙁

  8. So, Earth emits 4pi r^2*σ255^4 while it sunlight hits TOA at TSI=σ394^4.

    Radiative heat transfer, S-B equation:

    σ(394^4 – 4pi r^2*255^4)=σ290^4

    Surface temperature ~290K.

    Or, to get effective emission, turn it around:

    σ(394^4 – 290^4)=4pi r^2*σ255^4

    What is transferred to the surface is what´s emitted.

  9. This whole mess also assumes that the half globe disk is heated equally.. which it isn’t !

    Angle of incidence, the amount of atmosphere the energy has to pass through.

    Its basically just nonsense.

  10. The purpose of this short, light hearted, piece is to illustrate how our far more detailed Dynamic Atmosphere Energy Transport model fits the concept of the Earth (or any planet with an atmosphere) as a self regulating organism as proposed by the Gaia hypothesis.
    It struck me as amusing that so called climate deniers could come up with a proposition that is consistent with a basic tenet of the most woolly minded environmentalists.
    Where the sun heats the surface the atmosphere breathes energy in (via expansion) and when the surface is not being heated the atmosphere breathes energy out (via contraction).

        • “Maybe a bit Off Planet, but would the model apply to Venus, who breathes a very different atmosphere?”

          bonbon
          Not off topic at all. Our model is designed to be applied to all terrestrial planets and moons with an atmosphere. The model was originally designed for Venus with its slow rotation and hemisphere wide pair of Hadley cells. We also applied it to Titan also a slow rotator, and then with modification to fast rotating Earth with its 3 atmospheric cells per hemisphere (Hadley, Ferrel and Polar).

  11. Figure 1 above shows Daytime terrestrial radiation as 200 W/m^2 and Night-time terrestrial radiation as 270 W/m^2. That, of course, is counter-intuitive. One would expect daytime radiation to be greater because daytime temperatures are higher than night-time temperatures.

    There are satellite measurements of upwelling LW flux. A quick web search finds this paper. There is a graph, Mean LW Flux vs Viewing Zenith Angle (Jan-Mar 1998), which gives daytime and nighttime flux and has daytime flux exceeding nighttime flux.

    • commieBob

      Some of the daytime flux is diverted by conduction into upward convection / expansion of the atmosphere and so less escapes from surface to space than would otherwise be the case.
      On the night side, downward convection / conduction from contraction of the atmosphere causes more to escape from surface to space than would otherwise be the case.
      The Mean LW flux figures that you refer to would measure from the surface temperature before expansion has drawn energy from the upward flux on the day side and before contraction has added energy back to the upward flux on the night side.
      When adjustments are made for the energy requirements of expansion and contraction it actually does turn out that more gets past the atmosphere and out to space from the night side.
      That must be the case since, under steady irradiation, there is a net energy gain on the day side and a net energy loss on the night side.
      It is indeed counter intuitive until one realises the effects of atmospheric expansion and contraction on the upward flux.

    • “That, of course, is counter-intuitive. One would expect daytime radiation to be greater because daytime temperatures are higher than night-time temperatures.”
      CommieBob
      At the surface yes, but we are dealing with the Top Of a thermally radiant semi-opaque Atmosphere (TOA).
      Global warming relies on the idea that as the atmosphere expands the TOA cools and so the radiant emission to space reduces.
      This grain of truth hides the fact that at night the atmosphere contacts, and so as the TOA falls in the Earth’s gravity field it warms and emits more thermal radiant energy to space.
      Climate models have no night-time so they fail to model this fundamental daily 24-hour cyclical meteorological process.

      • We are to believe that the atmosphere expands as it warms during daytime, except for the part of the atmosphere that radiates to space (the TOA). These special molecules (like the magic CO2 molecules) expand as they cool, and then contract as they get warmer. Riiight!

        • A possible explanation would be that the energy taken up by the expansion on the day side is not sufficient in our atmosphere to reduce the daytime emissions to space to a level lower than night time emissions to space. A more dense atmosphere could, however, achieve that.
          That would require an adjustment to and reallocation of energy flows within our Fig 1 but does not affect the underlying hypothesis.
          In the end it is still the energy recycling within convective overturning that provides a resistance to radiative emission to space and thus leads to a higher surface temperature than the S-B equation predicts.

        • “As far as I can tell, the satellite data graph I cited is for the Top Of Atmosphere flux.”

          CommieBob,
          Have a look at the CERES image in our previous WUWT post Calibrating the CERES Image of the Earth’s Radiant Emission to Space
          The first point is that this CERES image is a full disk compilation at the Equinox so it must include night and day and the Sun must be over the equator.
          The second point is that the image is likely to be timed at 00 hours GMT because the centre of the image is the middle of the Pacific Ocean.
          Now this is a Mollweide projection so the latitude lines diverge, however I believe that this image supports our model.
          The maximum land values of the Sahara and also India are 350 W/m^2 and these are night-time values, India at longitude 78 degrees East is just before dawn at 00 GMT on the Equinox

          Notice that the values for Western Australia (Long 120 E) and Arizona (Long 112 W) are also high for these lit daytime locations, but this may be a dry air effect. (For pre-monsoon night-time India the air is moist).
          The really neat thing however is the way the daytime values that peak at 300 W/m^2 over the Pacific appear on the CERES image to be waisted in shape for the tropical Hadley cell. The north south latitudinal reach of the high values during the day is less than the latitudinal reach over the night-time areas (even after accounting for the Mollweide display distortion).
          Lots of caveats about land versus sea, and one swallow does not make a summer etc. but this single image may be a pointer that we are going in the right direction with our simple model that shows daytime loss to space due to atmospheric expansion being less than the night time loss.

  12. The application of the Stefan-Boltzmann-Law to the earth in Climate Sciences is wrong, because not illuminated areas (the night side oft the earth) are included in a global „factor-4“-inversion: https://www.eike-klima-energie.eu/2019/12/15/kelvin-allein-zu-haus-der-unterschied-zwischen-zwei-watt-ist-deren-umgebungstemperatur/ (the Google translator may help)

    You’l find about 25 posts about my hemispherical (factor-2) S-B-Model at EIKE, if you search for „Uli Weber“: https://www.eike-klima-energie.eu/

    And some scientific articles are included in this book: https://www.bod.de/buchshop/all-what-matters-uli-weber-9783752887037

  13. commieBob

    Some of the daytime flux is diverted by conduction into upward convection / expansion of the atmosphere and so less escapes from surface to space than would otherwise be the case.
    On the night side, downward convection / conduction from contraction of the atmosphere causes more to escape from surface to space than would otherwise be the case.
    The Mean LW flux figures that you refer to would measure from the surface temperature before expansion has drawn energy from the upward flux on the day side and before contraction has added energy back to the upward flux on the night side.
    When adjustments are made for the energy requirements of expansion and contraction it actually does turn out that more gets past the atmosphere and out to space from the night side.
    That must be the case since, under steady irradiation, there is a net energy gain on the day side and a net energy loss on the night side.
    It is indeed counter intuitive until one realises the effects of atmospheric expansion and contraction on the upward flux.

  14. Something strange about the chart. It shows that the night half of the globe radiates more energy to space than does the daytime half. Because radiation depends so strongly on effective temperature (4th power) this must mean that the effective temperature at night is higher than the effective temperature during daytime, contrary to what we experience in the real world. I understand that the atmosphere can expand and contract a bit, but only if it is warmer during the day than at night. If the atmosphere is warmer during the day, and certainly the surface is warmer during the day, why would the “exhaust flux” be greater at night than during the day?

    • “Something strange about the chart”
      hiskorr
      Thank you for engaging positively.
      The chart is based on our whole Earth PVT version of the Dynamic Atmosphere Energy Transport model in which the individual 3 atmospheric cells (Hadley Ferrel and Polar) are all lumped together.
      So in a sense we are looking at a model “night” that is also “winter” and I need to make this clear in my labeling.
      Please note that the standard climate model takes no account of meteorological processes, they are all “averaged out”
      I am happy to adopt constructive criticism, that is what I hope that we are all here for.

    • hiskorr
      See my reply to commieBob above.

      The thing is that the same unit of surface heat cannot be both radiated to space and conducted to the atmosphere simultaneously. It has to be one or the other and of course beneath a convecting atmosphere where the air in contact with the surface is constantly replenished it is a variable mix of the two processes depending on the speed of air flow.
      A single unit of energy cannot be in two places at once. Either it gets radiated away or it gets conducted away.
      So, a surface at a given temperature beneath a moving atmosphere cannot radiate to space in accordance with the S-B equation.
      Beneath the expanding half of an atmosphere it will radiate to space at a lower rate than S-B predicts and beneath a contracting atmosphere it will radiate to space at a higher rate than S-B predicts. The two rates will then net out to what the S-B equation predicts for the system as a whole so viewing from space the system complies with S-B since, from space, one takes the temperature at a point within the vertical column of the atmosphere and not at the surface.
      The S-B equation is applicable to a vacuum but has been mistakenly applied to a situation where air is constantly circulating up and down and around a rotating sphere with a conducting and convecting atmosphere interfering with the radiative flux.

      • ‘The thing is that the same unit of surface heat cannot be both radiated to space and conducted to the atmosphere simultaneously.’

        To add further complication, in addition to ‘conduction’ (i.e. convection) from the surface to the atmosphere and direct radiation from the surface you must add a third pathway, which is mass transfer, i.e. the evaporation of water, from water-bodies, vegetation and damp soil, which is then transported to the upper atmosphere by mass transfer, from whence it condenses, with the energy of condensation being radiated, much of it into space and bypassing the GHGs in the atmosphere which is below the altitude where the condensation occurs. This mechanism is likely to be the most important of the three.

  15. “The atmosphere being the lungs of our planet which expand and contract over the course of a 24-hour cycle, and in doing so varies the supply of potential energy back to the surface.”

    It takes Earth 23 hours and 56 minutes and 4.09 seconds to spin 360 degrees on its axis, so if they are using an average 24 hours in a day, they are already out nearly 2 minutes of solar insolation a day (on average) in their calculations as well as 2 minutes less time in the dark radiating heat away from the planet at night. Just pointing out the obvious that there isn’t quite 24 hours in a day which is almost 4 minutes less rotational time than just averaging 24 hours. It is still half lit and half dark per average day over a full yearly orbit of the Sun of approximately 365.2422 days in a full year. Maybe a moot point, but just saying there is 24 hours in a day isn’t quite accurate.

    • Earthling2:

      When dealing with the effect of solar radiation on the earth, it is entirely correct to use the 24-hour solar day. The fact that the earth has to rotate a little more than 360 degrees relative to the distance fixed stars to have the same line of longitude facing the sun again is irrelevant.

      • Ed Bo,

        you are wrong about this one entirely. The averaging does not work over 24 hours, because it very much depends on the location of Earth orbiting around the sun, how much area is even lit up.

        The arctic winter means that the solar energy is distributed over a smaller area. There is only two days you can claim the 24 hours are correct.
        Pretty bad odds out of 365 days in a year!

  16. Am I right in calculating that the radiation from the sun heats an area of pi *r2, where r is the radius of the earth and area of heat loss by radiation and convection is 4*pi*r2?

    I have acquired an infra red thermometer for use in fridge and freezer, and have been playing about with it taking readings from different ground covers, and the sky in various states by day and night, with and without clouds.
    Will the figures I obtained mean anything?
    There is a remarkable difference both day and night between clear skies and when cloud cover comes over.
    Recently the clear sky at night gave a reading of -24.5 C, and when cloud cover came over the reading was -2.5 C.
    At present the ground temperature is 15.5 C, cloudy sky 7.1 C, and clear sky -8.5 C.
    Does this mean the ground will be losing heat by radiation to the bottom of the clouds as well as the sky?

    Just asking, as I know there are many very clever commentators to this website, compared to whom I feel like Winnie the Pooh, a bear of very little brain.

    • StephenP
      That is an issue that I’ve considered previously.
      It appears that IR thermometers are designed to measure the temperature at a point where the density of the material being measured is high enough compared to its immediate surroundings to trigger the sensor.
      Obviously no problem if aiming it horizontally at a solid surface through the air.
      If one then aims it upwards then the sensor will trigger at a height where the mass of the atmosphere between user and sensor provides enough density to trigger that sensor.
      It will then take the temperature at that height.
      So, if you aim it upwards through clear air it will register the temperature at a cold, high level.
      If you aim it upwards towards a cloud base it will register the temperature at the lower, warmer level of the cloud base.
      If there were no atmosphere at all it would measure the temperature of space.
      Thus have IR thermometers been incorrectly used in climate discussions.

      • No Stephen, an IR thermometer does not measure temperature, it measures incoming IR radiation. The thermometer has no “knowledge” of distance, nor density. You seem to misunderstand what the device actually does.

        • If the IR thermometer doesn’t measure temperature, why do they use one to supposedly measure temperature at the GP surgery?
          Also what are they measuring when used in shops to check the temperature of chill cabinets?

          • They are measuring incoming infrared radiation. There is a “model” inside of the device that converts this to a number displayed on the display.

          • Similarly, a mercury thermometers does not measure temperature, it measures the height of a column of mercury. There is a “model” on the device that converts this to a number displayed on the display.

      • Thanks for the explanation.
        Does that mean that with the ground temperature at 15°C and the cloud base at 7°C the surface must be losing heat to the cloud base via radiation and convection?
        What is the proportion of heat lost to each route?

        • The decline in density with height determines the fall in temperature with height represented by the lapse rate slope. Therefore it is neither radiation nor convection / conduction alone but both acting in parallel within that decline in density.
          I describe the lapse rate slope as determining the points where the combined total of radiation and conduction is sufficient to keep the decline in atmospheric density with height matching the decline in temperature with height.
          As one gains height conduction becomes steadily less powerful relative to radiation.
          The greatest proportion of heat transfer by conduction is density dependent so one has a maximum relative to radiative transfers at the surface.
          I would expect the relationship set at the surface to remain steady as one moves up along the lapse rate slope to the boundary with space.
          Changes in the proportions do occur along the way however because atmospheric chemistry can distort the lapse rate slope.

      • Curious.
        How about an IR thermometer with variable emissivity setting :
        https://ennologic.com/emissivity-infrared-thermometer-readings/
        What setting would be good for a column of air, humid or not?
        I’ll bet all these instruments are for simple surfaces.
        I would send a tunable modulated IR signal, and compare the received signal. Not known if someone is doing that. (Idea from Dr. Happer’s Guide Star). One could adapt a DWDM IR laser used daily in optical network switching.

  17. Hidden in the metaphoric ‘breath’ is an indication of the insignificance of CO2. With high humidity, day to night temperatures range 10-20°F, in dry climes, 40-50° diurnally.

  18. I read a good bit of logic on the subject of averages one time. Let’s say there are 6 billion humans on the planet and 6 billion testicles. It works out mathematically to one testicle per human. Does that average actually describe anything? No. Half the population has two and the other half has none. So the average of one is meaningless.

  19. Over at
    https://www.newclimatemodel.com/why-the-radiative-capabilities-of-gases-do-not-contribute-to-the-greenhouse-effect/
    “As a separate issue CO2 molecules would have an imperceptible effect on surface temperature anyway because mass and gravity provide almost all of the greenhouse effect and CO2 comprises a miniscule proportion of the atmospheric mass.”

    Would it not be better to call the GHE actually the ATE Atmospheric Thermal Effect of Nikolov and Zeller?

    • Nikolov and Zeller are on the right track but propose no mechanism.
      We have covered that missing aspect.
      The ATE/GHE is a consequence only of atmospheric mass being convected up and down and around a rotating sphere, thereby providing a resistance to the free flow of solar energy through the system
      Nothing to do with radiative gases at all.

      • At least the continuum ATE keeps green houses out of the field.
        A convergence of mechanism and continuum, sounds like two flanks bearing down on the entire scam.
        It is surprising how many “skeptics” are radiators.

  20. There are 34 numbers in that top chart, all quoted to one part in a hundred accuracy(!) in which we detect (how?) an extra 3.5 W/m2 driving global warming and thence predict catastrophe and dire consequences accurate to better than a few percent accuracy?

  21. Philip Mulholland and Stephen Wilde,

    Thank you for the essay.

    Personally, I don’t think the Gaia metaphor contributes much, but it was amusing to read of “lungs” referring to energy not air.

    It’s good of you to respond to comments.

    “How great is the approximation error introduced by treating the Earth as a uniform disk” has always been a worthy topic. Without simplifications/approximations no calculations are possible at all, but the error of approximation has to be well known for the calculations to be informative.

  22. The diagram appears to be simplified in several ways. First, aerosol and Rayleigh scattering scatter light in all directions, including the forward (toward the ground). Aerosol scattering is highly complex and varies spatially as well as with light wavelength. Second, cloud reflections also vary and do not always reflect backward into space. Lastly, thermal radiation by the atmosphere is in all directions, it also does not all go upward into space.

  23. AFAIK given a terrestrial grid cell the path of incoming radiation varies with the sun’s angles, and so the surface heating effect must vary by these angles and also the varying length of the atmosperic path.

    But, the outgoing radiation from the surface goes in all directions irrespective of the time of year and time of day and so the lengths of the radiated atmospheric paths will not change.

    Can anybody say whether the summing these effects is a feature of basic climate models?

  24. Dr Spencer

    The Stefan-Boltzmann-Law describes a „just in time“-relation (temperature=>specific radiation power) and does not allow any time-averages of both. Consequently, a S-B-Inversion (specific radiation power=>temperature) must not use a 24h-time-average of the specific radiation power to calculate a temperature-equivalent. A 24h-time-average destroys the S-B-T^4-relation because it calculates specific radiation power [W/m²] back from energy [(W/m²)*s=Joule/m²].

    Citation from your article „A Simple “No Greenhouse Effect” Model of Day/Night Temperatures at Different Latitudes“:
    “I hope this will help convince some who are still open-minded on this subject that even intense tropical sunshine cannot explain real-world tropical temperatures. The atmospheric greenhouse effect must also be included. The temperature (of anything) is not determined by the rate of energy input (say, the intensity of sunlight, or how fast your car engine burns gas); it is the result of a balance between energy gain and energy loss. The greenhouse effect reduces the rate of energy loss at the surface, thus causing higher temperatures then if it did not exist.”

    1. The S-B-temperature-equivalent of the solar constant (1367W/m²) is about 120°C. That’s much more than the real-world tropical temperatures count. And because of the heat capacity of water the temperature on the night side of the earth drops only in temperature models to 0 Kelvin.

    2. The greenhouse effect is said to account for 33°C. But how should any object get that 33°C warmer by less cooling? That object only cools slower down from its original temperature…

  25. From “Atmospheres” by R. M. Goody 1972.

    “Our theory (The Greenhouse Effect on Earth) is inadequate ( that the surface temperature should 45ºC warmer at 60ºC than the observed 15ºC ) because radiation is not the only process that carries heat upward from the ground and from the lower levels of the troposphere. Another process tending to hold down the temperature at the ground and to increase the temperature of the upper troposphere is known as convection.”

    • Convection doesn’t heat the upper troposphere because the expansion with height cools the rising without any loss of energy.
      The significance of convection and the gas laws is entirely missing from all the models.
      Convection upwards cools the surface and convection downwards warms the surface due to conversion of energy between potential and kinetic forms.
      That delays the emission of solar radiation to space which warms the surface beneath a convecting atmosphere.
      If radiative imbalances occur then the consequential distortion of the lapse rate slope alters the speed of convection in order to maintain stability for the system as a whole.
      Thus there is no overall thermal effect from varying amounts of ghgs.

      • “If radiative imbalances occur then the consequential distortion of the lapse rate slope alters the speed of convection in order to maintain stability for the system as a whole.”
        Agreed, except for:
        “Thus there is no overall thermal effect from varying amounts of ghgs.”

        Concentrating on water vapour as the main radiative gas and taking the effective temperature for Earth to be -18ºC. at 3km. altitude with a skin temperature of -60ºC at a tropopause at 12km. radiative transfer theory calculates that in the presence of water vapour the surface temperature should be 60ºC.
        But the reality is that as the sun warms the surface, convection kicks in as soon as that resistance to radiative surface cooling (radiative imbalance) occurs to enable extra sensible and latent heating and a cooling of the surface to the observed 15ºC.
        On a global scale the latent heat is moved polewards from the equatorial regions to be revealed in the downward dry air at the sub tropics.
        At night the more humid the air, the less likely there will be a ground frost.
        The ratio of sensible to latent heating is determined by the biosphere at the surface.
        Sensible heating tends to be confined to the boundary layer, whereas above that the troposphere is warmed more by latent heat when clouds form, only to be revealed as such when dry air closes the loop on its descent.

        https://www.britannica.com/science/climate-meteorology/Biosphere-controls-on-the-structure-of-the-atmosphere#ref967546

  26. [[A fundamental concept at the heart of climate science is the contention that the solar energy that the disk of the Earth intercepts from the Sun’s irradiance must be diluted by a factor of 4. This is because the surface area of a globe is 4 times the interception area of the disk silhouette (Wilde and Mulholland, 2020a).

    [[This geometric relationship of divide by 4 for the insolation energy creates the absurd paradox that the Sun shines directly onto the surface of the Earth at night. The correct assertion is that the solar energy power intensity is collected over the full surface area of a lit hemisphere (divide by 2) and that it is the thermal radiant exhaust flux that leaves from the full surface area of the globe (divide by 4).]]

    While it is true that the infamous leftist-run U.N. IPCC has tried to bolster their fake physics CO2 15 micron -80C global warming hoax by miscalculating the potential warming from the Sun, this entails more than just dividing the Earth’s surface area by 4 and turning it into a flat disk. They also divide the Sun’s power by 4, and no surprise, the Sun can’t keep the Earth from freezing.

    Like with the 15 micron problem, the IPCC just can’t face the fact that the Sun is a Planck (blackbody) radiator, like the Earth’s surface, and is subject to an ironclad law of Nature. The Planck power-wavelength curves are all parameterized on the temperature, and to cut the curve by a factor of four switches it to a new lower temperature. This of course makes the Sun weaker, solving their problem by carnival-level sleight of hand. In truth, the Sun is quite capable of keeping the Earth from freezing without assistance from fake CO2 radiation heating. The Sun shines on a hemisphere at a time, and bears down on a given spot for several hours, heating it up, while the atmosphere slows down the cooling process. Every time the temperature reaches 100F in Arizona, you know they’re pushing a sick hoax. The only proper calculation method is a computer program that slowly rotates the Earth while calculating the opposing processes of heating and cooling and keeping score. Where in all the billions spent on IPCC did they create such a program and release the source code for all to check their work? Never. Instead, they churn out boatloads of fake global temperature data from a Seinfeld restaurant in Manhattan 🙂

    https://www.quora.com/What-are-the-most-important-principles-you-can-apply-to-save-the-Earth-from-global-warming/answer/Tracy-Zeron

    The exact amount the Sun’s temperature is reduced when the power is reduced by a factor of f is
    (1/f) * (4th root of f). When f=4, the reduction is 35%, brrr!

    http://www.historyscoper.com/howmuchisthesuncontributingtoglobalwarming.html

    • “The only proper calculation method is a computer program that slowly rotates the Earth while calculating the opposing processes of heating and cooling and keeping score. ”

      TL Winslow
      I have been thinking about this on similar lines.
      The key point is to decouple the lit hemisphere collection process from the full globe emission processes and place the atmospheric reservoir in between as the “keeping score” vector process that it so clearly is.

      • To Phil Mulholland

        “The key point is to decouple the lit hemisphere collection process from the full globe emission processes and place the atmospheric reservoir in between as the “keeping score” vector process that it so clearly is.”

        I hope this includes the varying lengths of the sun’s-rays through the atmosphere, and also the changing albedo of the clouds as they are illuminated from the sides …. particularly the tropical daily cu-nim formations (per Willis)…. etc.

        • “I hope this includes the varying lengths of the sun’s-rays through the atmosphere, and also the changing albedo of the clouds as they are illuminated from the sides”
          TonyN,
          Yes, that complexity must be located inside the black box of the atmospheric reservoir.
          In our model we apply the concept of the illumination divisor to account for the quantity of energy captured by the model globe at the Top of the Atmosphere (TOA). This concept is also used in the standard model which applies the concept of the Vacuum Planet equation from Astronomy, which is the ratio of the surface area of the intercepted disk silhouette to the surface area of the emitting globe, and has a ratio value of 4. So, the point at issue here is illumination intensity and its value due to geometric effects before the energy has even entered the atmosphere.
          In our model as applied here we use the ratio of the surface area of the intercepting disk silhouette to the surface area of the illuminated hemisphere, which is a value of 2. This power intensity dilution factor at the TOA is applied before any atmospheric processes are invoked (albedo, atmospheric absorption travel path etc.).
          If you wish to study the average annual illumination of the 3 main atmospheric cells (Hadley, Ferrel and Polar) then the illumination divisor for each is calculated as the ratio of their global surface area to the area of the disk silhouette that illuminates each cell.
          So, a pair of equatorial Hadley cells located between 30S and 30N that cover 50.00% of the Earth’s surface area cut a zone from the disk silhouette between 30S and 30N that is 60.90% of the disk silhouette illumination area. This relationship produces an average annual illumination intensity ratio of 0.60899 for the Hadley cell. (or its reciprocal of 1.6420 as a power intensity divisor).
          Similarly, a pair of mid-latitude Ferrel cells located between 30 degrees and the (Ant)Arctic polar circles cover 41.75% of the Earth’s surface area and cut a zone from the disk silhouette between latitude 30 degrees and each hemisphere’s polar circle that is 36.29% of the solar beam disk silhouette illumination area. This relationship produces an average annual illumination intensity ratio of 0.43462 for the Ferrel cell. (or its reciprocal of 2.3008 as a power intensity divisor).
          Finally, the pair of Polar cells located beyond the (Ant)Arctic polar circles cover 8.25% of the Earth’s surface area and cut a zone from the disk silhouette that is just 2.81% of the solar beam disk silhouette illumination area. This relationship produces an average annual illumination intensity ratio of 0.17025 for the Polar cell. (or its reciprocal of 5.8738 as a power intensity divisor). (using illustrative precision).

          The value of using this approach is that it proportions the illumination power intensity as an annual average for each atmospheric cell in toto. Please note that although we are often able to look directly at the setting Sun as it sinks below the horizon, the diminution in the intensity of the sunlight at the surface is due solely to atmospheric absorption. If you were standing on the surface of the Moon watching the sunset at the end of the fortnight long lunar day then you would be blinded because even though the horizon grazing angle of the setting sun is zero, there is no diminution in the solar beam intensity in the Moon’s vacuum. So too for the Earth at the TOA the power intensity of the solar irradiance normal to the beam is a constant value and is independent of the location of the intercepting grid cell, whether it be at the pole of rotation or on the equatorial terminator. (N.B. this is at the TOA!)

    • TL:

      You say: ” The only proper calculation method is a computer program that slowly rotates the Earth while calculating the opposing processes of heating and cooling and keeping score.”

      This is exactly what EVERY computer climate model has done for decades now, and if you had even a cursory knowledge of the subject, you would understand that. (I am certainly not claiming they do it perfectly, they all do what you want.)

      In the most basic description of any model, they will state the size of the elements they divide the earth’s surface into (e.g. 1 degree by 1 degree) and the size of the time interval (e.g. 15 minutes). In operation, for each time interval, for every single surface element (and multiple vertical slices for each surface element), they “calculat[e] the opposing processes of heating and cooling and keep[] score.”

      I have looked at the source code for one of the models and confirmed this fundamental point. Again, I am not claiming it is done perfectly, or even accurately enough to reach any conclusions, but it IS done.

      Do not make the mistake so many do of assuming that a highly simplified conceptual illustration for laymen is actually what is calculated in practice.

      • [[This is exactly what EVERY computer climate model has done for decades now, and if you had even a cursory knowledge of the subject, you would understand that.]]

        Duh, they all have subroutines adding in the fake physics CO2 back radiation, causing them to wildly overpredict temperatures out in the future based on ever-increasing CO2 levels.

        Yes, the models are one thing, their popular explanations are another. The weak Sun hoax is for the consumption of the public to make them think that without CO2 the Sun alone couldn’t keep the Earth from freezing, making CO2 global warming seem proved without further ado.

        [[I have looked at the source code for one of the models and confirmed this fundamental point. Again, I am not claiming it is done perfectly, or even accurately enough to reach any conclusions, but it IS done. ]]

        Do they really predict that without CO2 back radiation the Earth would always be freezing? It’s not about conclusions but about basic modeling. Of course real models can’t get accurate initial info. for all the cells, plus many physical processes happen inside cells so they can’t be modeled but only included in parametric form. Clouds are big problem. But I don’t want a weather prediction model just a basic climate model that disproves the CO2 warming hoax.

        We must take climate modeling away from all CO2 warming hoaxers and refound climate science sans CO2 back radiation.

        https://www.quora.com/Are-The-Global-warming-climate-change-theory-models-oversimplified-and-or-corrupted-by-data-that-is-not-accurately-representative-of-reality-the-main-reason-for-their-dismal-track-record-on-their-predictions-could/answer/TL-Winslow

  27. @ Philip Mulholland

    Your calculation in “Return to Earth: A New Mathematical Model of the Earth’s Climate” for the irradiation on the hemisphere is not correct.

    The static model is based on a central solar point. In the case of temperature distribution on a non-rotating spherical surface (hemisphere) with validity of Lambert’s law of cosines and Stefan-Boltzmann’s law, isothermal concentric circular bands form around the central solar point T0, where T0 = [(1-A)*S/(ε*σ)]^0.25. If the central solar point T0 is defined as the energy pole, then the temperature at the thermal latitude β after: T(β) = T0*cos(β)^0.25.

    The average temperature value of the circular area results in T(β,avg) = 306K, where this corresponds to an average energy flux density of j = ε*σ*T(β,avg)^4 = 0.96*5.67*10^-8*306^4 = 478 W/m^2. This value of 478 W/m^2 applies only to the circular area, but not to the hemisphere.

    Circle surface averaging is not the same as sphere surface averaging of a hemisphere. You can see this (example: edge darkening of the sun) by averaging the area of the regions of a circle and a hemisphere with |x| ≤ 1/2*r. For the area of the circle the result is π/3 + √(3)/2]*r^2, which makes up about 61% of the total circular area. For a hemispherical surface results in π*r^2, which is exactly 50% of the total surface of the hemisphere. In fact the pole regions are overweighted and the equatorial regions are underweighted in the circular averaging.

    One have to calculate with a weighting factor of π/[π/3 + √(3)/2], in order to calculate a circle area averaging on a hemisphere. This would result in an energy flux density for the hemisphere of 472.27 [W/m^2] * π/[π/3 + √(3)/2] = 775.5 W/m^2.

  28. Dr roy with his fisher price cold warms hot physics tried to hold the line for the luke-warmers, but soon fecked off when he knew he would be embarrassed by the grown-ups in the room…..

    I dont think any of the other luke-warmer phuckwitz the marks etc etc showed their faces.

  29. Lets face it Phil i mean no offense at all,, none at all……what took so long.

    How can it take 30yrs .. what happened to ”the science” the marxist march through the institutions that’s what happened, then the infiltration of the true skeptic’s the ones that were always right but became the equivalent of carnival barkers, they were banned from here if they stood their ground in the early years.
    I mean no disrespect to anthony or willis i like both now they have grown on me, and come along way down the rabbit hole, i sense they both doubt now the co2 rghe in ways, and both have been around long enough here to have read dozens of articles like this, but dr roy how can you respect that plum, he must know the RGHE is bullshit, but he still pushes it not wanting to rock the boat, and too many years invested in his bullshit its all true its just not as bad as we thought line, ……… but it is all ”real” honest…..

    The most fundamental part of AGW is the RGHE and its been protected all these years from within the skeptical side, alot of people have a decade or more defending it so they won’t eat humble pie on it, they are in it for life, and its just disgusting to me because a focused attack on that RGHE hypothesis would have destroyed ”the science” 25 yrs ago, and ive been doing the global warming rounds since the dial up days reading the debates, since before cookie and his crew of degenerates popped into existence.

    I always knew the defenders of it in debate were the bullshitters as they were always the ones that started running smart with the mouth, insult and sophistry, see the debates started for me reading them in educational fora, you know college sites/forums, and clever kids arguing the physics of it.
    That was until the sites got their warnings about being blacklisted unless they banned any GW stuff that didnt obey the progressive narrative, and the ”scene” changed and went more bloggish..

    • Gary,
      None taken.
      I started this work in earnest in Jan 2019 when I first wrote to Stephen and we began our collaboration.
      I am pleased to say that the Research Gate stats for our paper have gone up significantly thanks to this thread and once again I must thank Anthony for allowing us to publish here on WUWT.

  30. Balance is important.

    Upsetting the balance could tip us into warming or cooling.

    Setting up arbitrary warming by including the imbalance is very important to understand.

    The question is, where is the basis for that imbalance? Its not there!

    It was not there before!

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