Where Is the Top Of The Atmosphere (TOA)?

Guest opinion: Dr. Tim Ball

On WUWT, Bob Tisdale recently examined the disparity of results between IPCC models in No Consensus: Earth’s Top of Atmosphere Energy Imbalance in CMIP5-Archived (IPCC AR5) Climate Models” and wrote that

“There are astonishing differences in the modeled estimates of the past, present and future imbalances and the three components that make up the top of the atmosphere (TOA) energy budget.”

There were several earlier studies, but the supposed accuracy improved after satellite data became available. Rossow and Zhang did a study similar to Tisdale in a 1995 article titled, “Calculation of surface and top of atmosphere radiative fluxes from physical quantities based on ISCCP Data sets 2. Validation and first results.”

Our validation studies suggest that the specification of cloud effects is no longer the dominant uncertainty in reconstructing the radiative fluxes at the top of atmosphere and at the surface. Rather cloud property uncertainties are now roughly equal contributors to the flux uncertainty, along with surface and atmospheric properties.

Erhard Raschke did a similar study in 2005 titled, “How well do we compute the insolation at TOA in radiation climatologies and in GCMs.” He found that,

In the spatial and temporal variations of the insolation at TOA as computed by 20 models participating in the AMIP-2 project and for the ISCCP data-set we discover that none of the models reproduced accurately the prescribed TSI value of 1365 Wm−2.

Some of the factors listed as problematic were

Some models ignore leap years. Moreover, leap years are included in different ways either leading to a small increase (0.34 Wm−2) or decrease (0.92 Wm−2) of the annual mean of insolation at TOA.

Most models produce seasonal insolation fields at TOA that deviate from their zonal means. More importantly, the corresponding latitudinal profiles (of zonal averages) differ, as illustrated by deviations to a “reference profile” (here: ISCCP data set). These different latitudinal gradients of insolation are expected to affect the atmospheric circulation in integrations over multiple years. The largest deviations exceed ±5 Wm−2 (in conjunction with extended low sun-elevation times) at high latitudes and polar regions.

Figure 1 is a graph of the latitudinal discrepancies.

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Figure 1

These discrepancies compare unfavorably to an absolute accuracy requirement for all radiation quantities at the TOA of 1.5 Wm−2 [Ohring et al., 2004].

Tisdale’s material shows that nobody, including the IPCC, dealt with Raschke’s recommendations.

We recommend that in all climate models and in all “radiation climatologies” the incoming solar radiation at TOA must be identical for any given time period and area on the globe. Modelers should use the real length of the tropical year. Since a similar analysis of IPCC AR4 simulations shows qualitatively the same deficiencies as described here for the AMIP simulations, we think, that there is a need for sensitivity tests that investigate impacts of detected differences in the TOA insolation on circulation structures developing in the model’s climate system.

The Real Problem

Maybe the problem is the same one associated with climate models in general. They are built on inadequate data and inadequate understanding of the structure and mechanisms of the real world. These problems are then exacerbated and aggravated by creating mechanisms to hide, ignore or even falsify the situation. As Raschke notes in a paper titled, How accurate did GCMs compute the insolation at TOA for AMIP2?”

All models should reproduce the known major state and related fluxes of energy, mass and momentum with high accuracy. But quite large disagreement was found in various quantities, in particular at higher latitudes over both hemispheres [Gates et al., 1999].

Recently other articles (here, here, here and here) discussed the TOA, but they don’t tell you what or where it is. Here is one description that provides an explanation, but as with most climate science measures, it only adds to the confusion.

Technically, there is no absolute dividing line between the Earth’s atmosphere and space, but for scientists studying the balance of incoming and outgoing energy on the Earth, it is conceptually useful to think of the altitude at about 100 kilometers above the Earth as the “top of the atmosphere.” The top of the atmosphere is the bottom line of Earth’s energy budget, the Grand Central Station of radiation. It is the place where solar energy (mostly visible light) enters the Earth system and where both reflected light and invisible, thermal radiation from the Sun-warmed Earth exit. The balance between incoming and outgoing energy at the top of the atmosphere determines the Earth’s average temperature. The ability of greenhouses (sic) gases to change the balance by reducing how much thermal energy exits is what global warming is all about.

Consider the implication that TOA is a line 100km above the surface and equidistant around the Earth. Now look at the known structures of the atmosphere and factors that affect weather and climate.

Most weather occurs in the Troposphere, and that is far from uniform or spherical. There is inadequate horizontal surface data to construct the General Climate Models (GCM) and even less in the vertical. More layers make no difference if you have no data. William Ferrell proposed a three-cell model of circulation within the Troposphere in the 1850s (Figure 2). It is still in many textbooks, with the middle cell named after Ferrell, Figure 2 is from 2012.

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Figure 2:

Figure 3 is a more recent approximation of what is going on within the Troposphere. Notice the Ferrell cell is now an “Indirect Cell”. There is a debate about whether it exists because the diagram shows an average condition. The Polar Front shifts seasonally, from approximately 38°N in the winter to 65°N in the summer. The Southern Hemisphere range is from 40°S to 65°S because of the land/water ratio difference

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Figure 3

The top of the Tropopause also changes seasonally. The height at the Equator ranges between 17 and 18 km while it is 7 to 10 km at the Poles because of the greater seasonal temperature range. As the diagram shows, the Tropopause is a distinctive but not continuous boundary with breaks associated with the Jet Streams. All these factors affect the energy flows between the surface and the TOA. It is like trying to cross a very turbulent, fast flowing, constantly changing river. I suggest it is impossible to model such a complex dynamic system with virtually no data. There are serious limitations with accurate measures at high latitudes from the surface up.

Then there is the problem of the different direction of incoming solar radiation and outgoing irradiation. The Earth is a rotating sphere and that complicates everything. Figure 4 shows that solar energy strikes only half the Earth and varies considerably in the angle of incidence. The outgoing long wave passes through considerably different depths of the atmosphere with constantly varying constituencies including clouds, aerosols and gas levels.

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Figure 4.

The Ozone layer also lies within the 100 km TOA. Usually, it is dealt with as a homogenous zone but in reality the interaction between ultraviolet radiation and oxygen varies considerably at different levels. It is not unusual for ozone levels to increase at one level while decreasing at another. It also varies considerably spatially as the so-called ozone hole attests.

Another important factor essentially ignored is magnetism and its influence on numerous components of the energy balance. I wrote about one possible relationship in a previous WUWT article. A Danish study by Mads Faurschou Knudsen and Peter Riisager showed a relationship between precipitation patterns and geomagnetism. They attribute the relationship to the same mechanism identified by Svensmark.

Their work, which only looks at Earth’s magnetism, does not include the distortion of the entire atmospheric system from the magnetosphere on down by the pressure of the solar wind. Figure 5 shows the impact on the upwind side and the elongation on the downwind side, but again this is a static image. In reality, the area of maximum pressure is constantly moving as the earth rotates.

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Figure 5

In their introduction Mads et al., underline the general problems

It remains difficult to capture the complexity of Earth’s climate system in numerical models. A meaningful discussion of past and future climate variability cannot, therefore, rely solely on mechanistic computer models, but must, at least to some extent, be based on actual climate observations. Because the instrumental records are too short to elucidate several aspects of the climate system, new insights often have to rely on crude comparisons between climate-proxy records and potential climate-forcing factors recorded in geological archives. The controversial role of the Sun as a driver of climate change represents a good example, as geological proxy records are important for our endeavor to understand climate variability.

Tisdale focuses on the modeled oceans as one source of discrepancy in the TOA numbers. As he notes,

We can simply add ocean heat accumulation and TOA energy imbalance to the list of things that climate models do not simulate properly.

A very good indication of the complexity of the problem of creating accurate models for the energy balance at the TOA is the fact Raschke noted a variation in results of plus (0.34 Wm−2) or minus (0.92 Wm−2) or a range of 1.26 Wm−2. Also, he found that

The largest deviations exceed ±5 Wm−2 (in conjunction with extended low sun-elevation times) at high latitudes and polar regions.

To put this in perspective, Lenaert Bengtsson, previously the Director of Research at ECMWF and Director of the Max Planck Institute for Meteorology noted,

…the radiative forcing by greenhouse gases (including methane, nitrogen oxides and fluorocarbons) has increased by 2.5 watts per square meter since the mid-19th century.

As with most climate measures, the supposed impact of all greenhouse gases is less than the error factor in a multitude of the inadequate data sources.

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222 thoughts on “Where Is the Top Of The Atmosphere (TOA)?

  1. “[climate models] are built on inadequate data and inadequate understanding of the structure and mechanisms of the real world.”

    Climate Science 101
    The less adequate the data and understanding, the more flamboyant the claims.

    • And here I thought that climate models started with basic physics, and the fact that the earth rotates one every 24 hours (or thereabouts).
      They sure fooled me.
      g

      • And here I thought that climate models started with basic physics, and the fact that the earth rotates one every 24 hours (or thereabouts).

        They do. In fact, they do a lot better than suggested in the top article with trying to manage all of this stuff. CAM (for example) being sort-of-open-source lets you look at what they do with the orbital stuff, and the answer is “Take pretty much all of the physics into account” — eccentricity of the Earth’s orbit, synodical vs sidereal time, the inclination of the axis, and so on. There may be models that do not, but it is not correct to state (as John Marshall claims right above this reply) that they are “flat earth” models. That is simply false. I’m no fan of models and think they end up getting a lot of physics wrong, but the real point (IMO) of Dr. Ball’s top article is that even if they do this stuff right, when one compares what the models actually produce at the TOA to what actually happens at the TOA, they are off by as much as the entire supposed additional forcing due to CO2 over a much longer timeframe.
        This also appears in the internal dynamics. The models are not really conservative in that when one computes all of the energy flow in each timestep, it doesn’t add up to detailed balance. That is, energy appears or disappears that doesn’t come from a known source or flow into a known sink. This error is typically managed or renormalized in some way, but the problem with numerical errors of this sort in a timestep is that one cannot ever guarantee thereafter that a change (such as a temperature increase) that represents cumulated energy in a set of specific reservoirs is real or is the result of the cumulation of this error (however you try to resolve it). Even very small errors, if they have a systematic bias, can cumulate into big differences.
        It doesn’t even have to be a direct error in quantity. It can just be a tiny error in rates. As I just remarked on a different thread, another way models are not being properly compared to reality is via the Fluctuation-Dissipation Theorem (FDT). If a model produces (per run, not averaged over many runs!) the wrong temporal power spectrum for the global average temperature and the wrong autocorrelation spectrum, they get the dissipative dynamics wrong, period, on the timescales involved. Because of the cumulation of errors, that basically means that the model is producing nonsense, at least as far as any sort of comparison to the Earth’s actual climate is concerned. There is an enormous amount of information encoded in the statistical decomposition of the various timeseries that represent the major components of the Earth’s climate, and to the extent that models fail to match the climate in a similar satistical decomposition, we can be quite certain that they have the key physics wrong.
        This is a lot more subtle — and important — than asserting that models are “flat earthed” in some way, which does the skeptical argument absolutely no good when it is so easily refuted.
        rgb

    • It could not be said clearer than this:-
      “In climate research and modelling, we should recognize that we are dealing with a coupled-nonlinear chaotic system, and therefore that long-term prediction of future climate states is not possible.”
      IPCC Third Assessment Report (2001), Section 14.2.2.2, page 774 – I wonder why the IPCC still uses models??

      • The IPCC goal is to prove people cause dangerous global warming IN THE FUTURE, not to analyze the actual climate without bias.
        The underlying and rarely discussed UN goal was a redistribution of wealth from rich to poor nations as “climate reparations”, and more power for the UN.
        Computer games can “prove” anything.
        You quote page 774 of a report !
        Ha Ha Ha
        You may be the only person on Earth who read that far !
        In fact, a few hundred pages later, some drunk “climate” scientists inserted jokes in the back up documents, knowing no one would ever read that far. I’ve heard there is a dirty joke on page 997 — no one has noticed it yet.
        Reporters read the IPCC press release, and decide what sentences to quote.
        Top reporters read some of the Summary for PolicyMakers written/edited by politicians, that fails to honestly summarize the back up reports, and sometimes creates brand new conclusions !
        The back up data are not even released until months AFTER the Summary for Policymakers.
        It that’s not smarmy politics, I don’t know what is !

  2. “I suggest it is impossible to model such a complex dynamic system with virtually no data. There are serious limitations with accurate measures at high latitudes from the surface up.” ~Tim Ball
    Like this:
    http://recipes.familyeducation.com/images/food/230×230/allfre196daiegg_012.jpg
    Except…It moves.
    And we all need to remind ourselves that diagrams are extremely wonderful art forms by scientists (in fact it is my favorite art), and can show instead of tell. But they are only conventions and averages used to discuss matters.

    • A chart is an inaccurate representation of a partially understood truth.

  3. As with most climate measures, the supposed impact of all greenhouse gases exceeds the error factor in a multitude of the inadequate data sources.

    That can’t be proven to be true.

    • What can’t be proven? That the error is in the range of 5W m-2 or that the greenhouse gases effect is 2.5? Or both? I would agree that the 2.5 number is controversial, but does anyone think that the error is less than 5 Wm-2? I am assuming in this that he is saying the error exceeds the impact, no the other way around.

      • If he is saying the error exceeds the impact, not the other way around, then it seems arguable.
        But he is saying the opposite.

        the supposed impact of all greenhouse gases exceeds the error factor

        That can’t be known at least because there are unknown errors..

  4. “As with most climate measures, the supposed impact of all greenhouse gases exceeds the error factor in a multitude of the inadequate data sources.”
    Should this read “As with most climate measures, the supposed impact of all greenhouse gases is less than the error factor in a multitude of the inadequate data sources.”? Please clarify if I’m misunderstanding your intent.

    • Because the last sentence as written makes no sense, I’ve taken the liberty to change it on my own authority. If Dr. Ball objects, of course I’m happy to change it back.
      w.

      • The original makes more sense to me than the correction.
        Doesn’t “the supposed impact of all greenhouse gases exceeds the error factor in a multitude of the inadequate data sources mean that the modeled effect of greenhouse gases is greater than the error factor in the data the models are based on?
        If the supposed impact is LESS than the error factor, what’s the big deal?

  5. Here is an interesting 2015 paper regarding the use of Lidar for measuring CO2. There seems to be a large (~20 ppm) discontinuity in CO2 at a hight of 2 km…. They say it is due to the growing season, but this is a very new technique (one that I like as it is a qualitative measure). It would be interesting to see this data set extended in the spectral as well as in area…
    http://ssed.gsfc.nasa.gov/co2sounder/pdf/Co2CloudSlicingRamanathanGRL3-27-15.pdf

  6. Technically, there is no absolute dividing line between the Earth’s atmosphere and space, but for scientists studying the balance of incoming and outgoing energy on the Earth, it is conceptually useful to think of the altitude at about 100 kilometers above the Earth as the “top of the atmosphere
    Which I think is logical and should be used as a standard.

    • Salvatore – “..for scientists studying the balance of incoming and outgoing energy on the Earth..”
      I would write those scientists simply consider TOA as the orbit of CERES et. al. If the satellite orbit was any amount higher, the balance data would be immaterially different. The 100km is just a convenience. Voyager data is trying to nail down the extent of the Sun’s atmosphere (Fig. 5 above).

  7. The fact that the Earth is neither frozen nor scorched means that in the long run the incoming energy perfectly balances the outgoing energy AT ANY HEIGHT. If we postulate that there is no convection above the troposphere, then there is a radiative balance in average over time and globe at any stratospheric elevation. The notion of the top-of-atmosphere is totally arbitrary and meaningless.

  8. You know, when GRACE was falling, the deteriorated orbit brought it into regions which caused all kinds of variable drags.

    • Yet they claimed GRACE could measure aquifer levels, and even soil moisture in various horizons under the surface of the soil.

      • Zeke, you would enjoy essay Pseudoprecision on sea level rise. Folks tried to use GRACE to show that a supposed three year SLR slowdown was due to rainfall, especially on Australia. That went hilariously wrong. Even got a Six month GRACE Australia water table estimate image.
        How such stuff gets past peer review is beyond my comprehension.

    • GRACE satellites were not spherical, and a tumbling irregularly-shaped object experiences varying atmospheric drags. What does this re-entry have to do with a GRACE mission? The interpretation of GRACE data is a separate issue.

  9. As with most climate measures, the supposed impact of all greenhouse gases exceeds the error factor in a multitude of the inadequate data sources….
    I assume this means that researchers continue to claim a dominant role for climate forcing from CO2 despite inadequate proof of such.
    I think the idea of a control volume bound by a surface at a height of 100km is a useful concept as long as one realizes we cannot perform an energy balance yet to the resolution of 2 W/m^2 on a continuous basis. I’ll bet the actual imbalances are 10 times this large.

  10. Some models ignore leap years. Moreover, leap years are included in different ways either leading to a small increase (0.34 Wm−2) or decrease (0.92 Wm−2) of the annual mean of insolation at TOA.

    OMG. Concepts like “leap year” and “tropical year” were well understood even before 1582, when Pope Gregory XIII introduced his calendar reform. Therefore some bright climate scientists slept for more than 4 centuries, then as soon as they were awoken, started programming crap. That’s how computational climate models are “based on first principles of physics”. It is certainly worse than we thought.

    • “That’s how computational climate models are “based on first principles of physics”.”
      Based on the first principle, perhaps, but not many of those that followed. 1582? Hilarious!

  11. An additional false assumption in the models is that solar insolation is TSI/4, but this fails to consider Earth’s precession angle of 23.44 degrees, which reduces the divisor down to TSI/3.5. TSI/4 is only true for a planet with a precession angle of zero degrees.
    This is because each pole receives no solar insolation for half of each year, thus, the area of the Earth receiving any insolation must be accordingly reduced.
    http://hockeyschtick.blogspot.com/2015/07/new-paper-finds-increased-co2-or.html

    • That’s not true. Incoming solar radiation integrated for the entire surface is indeed TSI/4, unconditionally. That’s simple geometry. On the other hand, albedo of Earth varies between 28% (June) and 31% (December), while TSI is highest in January (1403 W/m2) and lowest in July (1315 W/m2) due to orbital ellipticity. Still, global average absorbed solar radiation flux is 22 W/m2 higher in January than it is in July. On the other hand, annual average of absorbed radiation (for a full tropical year) is almost exactly the same for the two hemispheres (within 0.1 W/m2).

      • It absolutely is true. TSI/4 is only valid for a planet with a precession angle of zero. A planet with a precession angle of 90 degrees would only receive solar insolation of TSI/2 because one-half of the sphere would never receive any solar insolation at all, ever. With Earth’s precession angle of 23.44 the divisor obviously has to be between 2-4, and the exact mathematical determination by Chilingar, Sorokhtin, et al shows the correct divisor to be 3.5. Please read the whole paper I linked to above for further explanation.

      • Hockeyschtick, I’d never stopped to consider that before.
        The example of the precession angle of 90 degrees makes it obvious.
        Thanks.

      • hockeyschtick
        August 29, 2015 at 2:44 pm
        “A planet with a precession angle of 90 degrees would only receive solar insolation of TSI/2 because one-half of the sphere would never receive any solar insolation at all, ever.”
        Consider Uranus, with axial tilt of c98°… (stress on first syllable please)
        “The Uranian axis of rotation is approximately parallel with the plane of the Solar System, with an axial tilt of 97.77°… more like a ball rolling on the plane of the ecliptic than a spinning top like the other planets. Near the solstice, one pole faces the Sun continuously and the other faces away. […] At the other side of Uranus’s orbit the orientation of the poles towards the Sun is reversed. Each pole gets around 42 years of continuous sunlight, followed by 42 years of darkness. Near the time of the equinoxes, the Sun faces the equator of Uranus giving a period of day–night cycles similar to those seen on most of the other planets.”
        https://en.wikipedia.org/wiki/Uranus
        (my bold)
        https://en.wikipedia.org/wiki/File:Uranusandrings.jpg
        Your hypothetical planet would have the same pole always facing the Sun, but the real-world example of Uranus contradicts that scenario.

      • markx August 29, 2015 at 5:04 pm

        Hockeyschtick, I’d never stopped to consider that before.
        The example of the precession angle of 90 degrees makes it obvious.
        Thanks.

        A spinning planet with the axis pointed directly at the sun will not rotate in the plane of the ecliptic at all. It’s like a gyroscope, the spin stabilizes it.
        This means that six months after one pole points at the sun, the other pole will point at the sun.
        So yes, it’s TSI/4 regardless of precession.
        w.

      • “This means that six months after one pole points at the sun, the other pole will point at the sun.
        So yes, it’s TSI/4 regardless of precession.”
        Hi Willis,
        Respectfully disagree, wrt Earth, each pole receives zero solar insolation for 6 months of the year due to the precession angle, thus the surface area not receiving any solar radiation at any given time must be subtracted from the assumption that the entire sphere/globe is receiving some solar radiation over each 24 hour period.
        Details and calculation here:
        https://books.google.com/books?id=QHbeAq8YeXoC&pg=PA476&lpg=PA476&dq=Sorokhtin+precession+angle&source=bl&ots=72GZViHUt9&sig=0kjuZPdwjaGKGlhJqATv2Dl82bY&hl=en&sa=X&ved=0CB4Q6AEwAGoVChMIw4fpz93PxwIVDTOICh3vKwJZ#v=onepage&q=Sorokhtin%20precession%20angle&f=false

      • HS – Berényi Péter, Willis and Steve P are correct, this is why the CERES data is annualized. The Chilingar formula (2) is unit emissivity and only for a point in time.

      • Interesting. I think you’re both right. Its trivially true that the solar radiation is TSI/4 as expected for the earth as a whole but its also true that some area of the earth can be considered to have not a diurnal cycle, but instead an annual cycle of incoming solar radiation.
        That may not impact on the total average energy the earth receives but it certainly impacts on the rate different regions receive it. And arguably increases it above its portion of the TSI/4 locally for periods measured in months. Obviously the reverse must also be true that other regions receive less than their portion of the TSI/4 locally for periods measured in months.
        I dont think there’s anything new there except perhaps for how one perceives how the sun warms the planet.

      • TimTheToolMan – Yes, right. If you look at HS 7:18pm ref. the Chilingar formula is shown as 13.11′ which is for “other earth areas” denominator could be 3.502. For the full earth as observed annually by CERES, the ref. shows 13.12, denominator 4, which taking into account other eqn.s is the classic potential temperature formula 13.12′. The Ts=288.2K at Po= 1atm. is from CERES annually observing precessing plus and minus the 23.44.

      • No the Chilingar formulas calculate solar insolation on an annualized basis. Please read the second paragraph again. The fact remains that not the entire surface area of the sphere/globe receives some solar insolation over either 24 hours or on an annualized basis. TSI/4 assumes that the entire surface area of the sphere/globe is receiving at least some solar insolation throughout the year. Clearly, the surface area of the alternating poles receiving no insolation has to be removed from the total surface area of the sphere/globe, thus the divisor reduced.

      • HS – Chilingar formula (2) at unit emissivity is only “for the other earth’s areas regularly illuminated by the sun” at current precession angle 23.44, denominator 3.502 eqn. 13.11′. The full earth annually over all seasons +/-23.44 is denominator 4 in eqn. 13.12 simplifying to the classic potential temperature eqn. 13.12′.

      • The fact remains that not the entire surface area of the sphere/globe receives some solar insolation over either 24 hours or on an annualized basis.
        I would suggest that’s not a fact at all.

      • Trick, what is your point? You seem to agree with Chilingar et al yet don’t agree somehow? Please read their latest paper which also uses the exact same method of calculating the annualized solar insolation (TSI/3.5) and the (gravito-thermal) greenhouse effect.
        http://hockeyschtick.blogspot.com/2015/07/new-paper-finds-increased-co2-or.html
        and please let me know specifically what you agree or don’t agree with on this issue.
        We all agree, I believe, that there is never a 24 hour period in which the entire surface area of the globe/sphere receives solar insolation. Therefore, the annual average of 24 hour periods of solar insolation is over a surface area less than that of a sphere. The fact that the non-illuminated part switches from one pole to the other doesn’t change the fact that there is always all-year-long a significant portion of the total Earth surface area not receiving any insolation.

      • Therefore, the annual average of 24 hour periods of solar insolation is over a surface area less than that of a sphere.

        Er no. That doesn’t follow. It means that the poles (the bits that dont get diurnal warming) get their insolation all in one go for (up to) 6 months of the year each. Annualised they get the right amount.

      • HS – “Trick, what is your point?”
        Point 1) That Berényi Péter, Willis and Steve P, TimTheToolMan are all correct, point 2) Chilingar formula (2) at unit emissivity is “for the other earth’s areas regularly illuminated by the sun”.
        Thus it is incorrect to write either: 1) “The fact remains that not the entire surface area of the sphere/globe receives some solar insolation over ….an annualized basis.”, or 2) “TSI/4 is only valid for a planet with a precession angle of zero.”
        Since page 475 is not part of the book review, formulas 13.9 and 13.9′ and b^alpha, Tt definition can’t be seen, your 7:18 ref. lacks some details. I would guesstimate what they are doing is coming up with 13.12 as modified from normal for some reason discussed more fully on the missing page. Alpha at 0.1905 and the scale factor b^alpha=1.093 are useful with the given denominator in some app. they have possibly for Uranus pole ward facing sun discussions.
        “The fact that the non-illuminated part switches from one pole to the other doesn’t change the fact that there is always all-year-long a significant portion of the total Earth surface area not receiving any insolation.”
        Sure for the 24 hour period there is darkness at one pole but the other pole gets that much more S in the 24 hours. The annual net is zero observed by CERES annually to get its mean annual ~255K brightness T and thermometer ~288K. Even with precession angle 23.44. I’m not familiar with Chilingar paper in your post perhaps the missing page 475 can be deduced on its close reading.

      • So Tim, lets say Chilingar et al is correct and only 3.5/4 = 85% of the total global surface area receives any insolation at all during any given 24 hour period every single day of the year, agreed?
        Therefore, if we take the average of 85%*365/365 we get an annual average of 85% of the total global surface area receiving insolation on an annualized basis.
        Tim, same question to you as Trick, please let me know specifically where you disagree with Chilingar in their latest paper I linked to above and which also explains the TSI/3.5 divisor.

      • So Tim, lets say Chilingar et al is correct and only 3.5/4 = 85% of the total global surface area receives any insolation at all during any given 24 hour period every single day of the year, agreed?

        No not agreed. Some of that 85% is receiving more that half in a diurnal cycle. Over a year, total solar insolation across the earth averages 100%. Its a no brainer…think about it from the “sun’s perspective”. It can see half the earth at any one time.
        There is no magic here. The energy doesn’t just disappear…

      • “There is no magic here. The energy doesn’t just disappear…”
        Of course the energy “doesn’t just disappear.” The energy is still the exact same TSI. That exact same TSI energy is being distributed over 85% of the total surface area of a sphere during any given day of the year, therefore that exact same TSI energy is being distributed over 85% of the total surface area of a sphere on an annualized basis as well. Of course for 6 months of the year only one pole receives insolation and of course that pole is receiving more than it would if it had a 12 hour day and night, but that does not change the fact that the TSI is never distributed over more than 85% of the total surface area during any 24 hour period or annualized period.
        Trick & Tim: Please see the Chilingar et al paper I linked to – the entire paper is in that post and explains this in detail.
        Trick, the same energy from TSI is being absorbed by a planet no matter whether the precession angle is 0 to 90 degrees, it is just distributed over surface areas which vary from 50-100% of the total surface area of a sphere. Earth’s “average” blackbody temperature of 255K wouldn’t change whether the precession angle was zero or 23.44 degrees.

      • HS – “Tim, same question to you as Trick, please let me know specifically where you disagree with Chilingar in their latest paper I linked to above and which also explains the TSI/3.5 divisor.”
        I don’t see any disagreement with the book or the paper. If you want to use their eqn. (2) and (13.12) with denominator 3.502, then you also need to use the scaling factor 1.093 on the front end and alpha as .1905 on the back end for earth. The reasons being more fully discussed on the hidden page 475. These scale factors seem to come from scaling up to the observed Tmean 288K. This may just be an actual emissivity (L&O& wet atm.) really is non-unity adjustment, dunno can’t read what Tt is.
        Chilingar calls (2) the temperature Tt distribution as if that is how the actual temperature (with the scaled emissivity) distributes over the various psi (-23 to +23) the earth moves through annually (“the other areas”), that may be better explained on the hidden page. Note when earth moves thru 0 in its orbit (+23.44 N pole toward sun to -23.44 N pole away from sun) the denominator goes thru 4.

      • HS – ”That exact same TSI energy is being distributed over 85% of the total surface area of a sphere during any given day of the year”
        Huh? No. 50% of total surface area every day of the year illuminated (1/2 a sphere), there is no shade in space the sun is always on. The Eqn. 13.11 says again the denominator is 3.502 “for the other earth’s areas regularly illuminated by the sun”. This is not fully explained. Seems to mean one pole could be down the other up by using that 3.502 and the scale factors. Psi = 0 means 4.0 denominator when both poles are each equally illuminated. Dunno, can’t see page 475.

      • That exact same TSI energy is being distributed over 85% of the total surface area of a sphere during any given day of the year

        No, its being distributed over 100% of half the planet in any diurnal cycle.
        I assume you can picture what the sun sees. There’s no question in my mind about that. Its straight forward geometry.
        Your 85% only applies to the portion of the planet that misses it “at this time of year”. In 6 months time it’ll be receiving solar radiation and at some times of the year those regions will be receiving solar radiation for the entire diurnal cycle, not just half of it. It makes up for lost time if you like. And then it all averages out over the year.

      • hockeyschtick August 29, 2015 at 7:18 pm

        “This means that six months after one pole points at the sun, the other pole will point at the sun.
        So yes, it’s TSI/4 regardless of precession.”

        Hi Willis,
        Respectfully disagree, wrt Earth, each pole receives zero solar insolation for 6 months of the year due to the precession angle, thus the surface area not receiving any solar radiation at any given time must be subtracted from the assumption that the entire sphere/globe is receiving some solar radiation over each 24 hour period.

        Thanks, HS. Consider the following:
        At the north and south poles, you get six months of sunlight, and six months of darkness. As a result, it is clear that the sun shines there half the time.
        At the equator, the day length varies slightly above and below 12 hours, with a 12-hour average. As a result, it is clear that the sun shines there half the time.
        And in fact, everywhere on the planet, the sun shines there half the time. All that happens is that the swings in day length above and below 12 hours gets larger and larger as you move poleward. But the average is still half the time.
        Since the sun shines everywhere half of the time, the use of the TSI/4 analysis is both totally justified, and totally independent of the size of the precession angle.
        If you doubt this, consider what would happen at the poles if the precession angle were 45° instead of 23.45°.
        Well, with the new precession angle, the poles would still get the same amount of sunshine—half the time the sun would still shine on the poles, and half the time it would still be dark.
        So it is clear that the hours of sunshine are unaffected by the precession angle—the sun shines half the time, everywhere on the earth, regardless of the angle of the earth’s axis from the perpendicular.
        Best regards,
        w.

      • Oh sheesh, of course at any given moment the Sun is illuminating 50% of a sphere! Never said otherwise, so please stop claiming that I am saying that. The point is that the Sun never illuminates >85% of the total surface area of the Earth during any given 24 hour period, and even though the poles that are illuminated change over the year, it simply does not change the fact that on a 24 hour and annual basis only 85% of Earth’s total surface area is illuminated. Of course, the location of the un-illuminated 15% changes during the year, but that makes no difference to the 24 hour and annual average of 85%.
        Chilingar et al clearly state this several times in their latest paper that I linked to, so Trick I don’t see how you can possibly say that you find no conflict with the book or paper or yourself.
        “Your 85% only applies to the portion of the planet that misses it “at this time of year”.”
        The point is that insolation is ALWAYS missing 15% of the planet at any time of year, even though the locations of the 15% missed portions change during the year, it does not change the annual average of 15% of the total surface area missed during a 24 hour or annual basis.

      • The point is that insolation is ALWAYS missing 15% of the planet at any time of year

        And always double counting a different 15% of the planet too.
        Net effect globally in terms of solar energy seen by the planet…zero. Locally, however, there is definitely an impact.

      • It is a little bit more than TSI/4 because of refraction in the atmosphere. That is why the sunset is red after the sun sets.
        For a planet tilted 90 degrees, yes it is zero on the dark side (0*TSI plus a bit) but the light side is TSI/2 so the total remains TSI/4 plus a bit

      • HS – “Oh sheesh, of course at any given moment the Sun is illuminating 50% of a sphere! Never said otherwise”
        Oh sheesh, you wrote otherwise right in the next sentence:
        “The point is that the Sun never illuminates >85% of the total surface area of the Earth during any given 24 hour period..”
        Incorrect wording. 50% of the total surface area of Earth is always illuminated, the sun never goes off, HS, as Willis again writes for you, pay attention, “the sun never illuminates >85% of total surface during 24 hours” is wildly incorrect. Correctly the book ref. writes Chilingar denominator in formula (2) at unit emissivity is “for the other earth’s areas regularly illuminated by the sun”.

      • I see Willis’, Tim’s, Trick’s points about everywhere the Sun is shining half the time, but Chilingar et al in the 3rd paragraph here state that “and taking sphericity of the sun-illuminated polar area into account, the divisor should be 2Ss/So, where Ss is the Earth’s near-polar area beyond the polar circle and So is the areal extent of the near polar area projection onto the planets near-equatorial plane” and then show the correction factor for this in eqn 13.10, which is what reduces the overall divisor from 4 to 3.5:
        http://1.bp.blogspot.com/-zd-JmYveAik/VeMe28_yfaI/AAAAAAAAHV0/yNwALp3moRQ/s1600/chilingar%2Bsorokhtin.png
        Are you Willis, Tim, Trick, etc. saying that Chilingar et al is wrong about this?

      • HS – “Are you…saying that Chilingar et al is wrong about this?”
        Not at all. I am writing 13.11 denominator shown as 13.11′ is 3.502 and that is in the authors exact wording “for the other earth’s areas regularly illuminated by the sun” other eqn.s are valid (but 13.9 is hidden on p. 475), thanks for that clip, makes it easier to ref. What “other” means is more fully explained on p. 475 which would be nice if you can clip also.
        Also, I’m writing if you choose to use Eqn. 13.11’ 3.502 in the denominator for Tt then you have to use the scale factor b and alpha as shown in 13.12. Chilingar for Tt Eqn. (2) adds the phrase “temperature distribution” like over all planet seasons for psi varying the pole illumination. I would think the “distribution” is also explained more on p.475 if you can find it.

      • Trick, I don’t have p 487, but here is another one of Chilingar’s books explaining the exact same formulas. They make it clear that the canonical TSI/4 formula (3.10) “is valid only if the axis of rotation of a planet is strictly perpendicular to the ecliptic plane, i.e. the angle of precession is equal to zero” as I stated above.
        http://3.bp.blogspot.com/-9gBs9QYyMuE/VeM1J2bWOeI/AAAAAAAAHWE/gDLyJGxF5_g/s1600/chiling%2B2.png
        http://2.bp.blogspot.com/-PEwiQ9ROwpE/VeM1Ni1Jr5I/AAAAAAAAHWM/FTRdokwK0_w/s1600/chiling%2B3.png
        Asking again, do you Trick, Willis, Tim argue that Chilingar is wrong about this and if so, specifically why?

      • HS: ”…argue that Chilingar is wrong about this and if so, specifically why?”
        P. 475 not p 487. Thanks for the new clip. I see nothing wrong HS, this is classic stuff except for their unusual ignoring of emissivity and their use of psi & polar regions being out of the ordinary. Willis is expert on CERES data so input from him would be interesting for what he sees as Earth moves N pole to sun and away intrayear. I would think just summer changing to winter.
        Note for BB Earth in ecliptic plane, they discuss Tmean 278.6K which is correct for 0 albedo and unit emissivity (Eqn. 3.10), not fn(psi). Then “The difference in temperature for psi=23.44 and psi=0 reaches 9.6-10C” They don’t explain this or show a calculation. So I can’t tell where/how they calculated it. Maybe you can.
        Possibly this might be somehow from the “distribution of avg. temperature in the troposphere” column 3.11 as fn(psi) intrayear N pole toward sun then away (summer in N, winter in S). Not sure. Again, if using 3.502 denominator for earth, must use their scale factor b and their fitted alpha.

      • Trick, I meant to say I don’t have page 475.
        It’s still unclear to me whether you are agreeing with Chilingar that the canonical TSI/4 formula (3.10) “is valid only if the axis of rotation of a planet is strictly perpendicular to the ecliptic plane, i.e. the angle of precession is equal to zero” as I stated above.
        I’d really like to know whether or not you, Willis, Tim, Bart, etc agrees with Chilingar or not, and if not, specifically where in the excerpts posted above. The HS greenhouse equation uses the canonical TSI/4, but I was planning to modify it to the Chilingar TSI/3.5 unless someone can show me an error by Chilingar et al.
        Thanks to all for your input.

      • HS – “It’s still unclear to me whether you are agreeing with Chilingar..”
        “I see nothing wrong HS..”
        “Not at all.”
        “I don’t see any disagreement with the book or the paper.”
        “If you want to use their eqn. (2) and (13.12) with denominator 3.502, then you also need to use the scaling factor 1.093 on the front end and alpha as .1905 on the back end for earth.”
        So if you modify denominator from 4.0 to 3.502 then must use (i.e. add-in) their scaling factors for Earth global Tmean=288.2K. Pretty simple.
        Do not see why my words are unclear HS. I am agreeing with Chilingar, it is mostly classic stuff (except the psi and unit emissivity). I don’t know exactly what their “temperature distribution” Tt is vs. “radiation temperature” eqn. 13.6 or even eqn. 13.9 are yet as you can’t get p. 475. I will go over to my college library Mon. see if they can get it. The ref. folks are always glad for a challenge to ply their trade.

      • Jeeze, guys. No matter what the axial inclination or lack of it, 1/2 of the surface area of the globe faces the sun at every instant of time. 4 \pi R^2/\pi R^2 = 4, period, since the cross-sectional area of the part facing the sun is \pi R^2. So it would be TSI/4, except that TSI is a silly concept as Berenyi pointed out due to the mix of ellipticity and albedo variation. “TSI” varies by roughly 91 W/m^2 over the course of a year (at least when I do the computation) and the “average” is not likely to be at all accurate as averages go.
        But real climate models don’t care, as they don’t use this.
        rgb

      • Dr. Brown, everyone agrees “1/2 of the surface area of the globe faces the sun at every instant of time,” including of course the Chilingar text excerpts above.
        However, where you apparently disagree with the Chilingar et al excerpts I posted above, which states that the canonical TSI/4 formula (3.10) “is valid only if the axis of rotation of a planet is strictly perpendicular to the ecliptic plane, i.e. the angle of precession is equal to zero” due to “taking sphericity of the sun-illuminated polar area into account, the divisor should be 2Ss/So, where Ss is the Earth’s near-polar area beyond the polar circle and So is the areal extent of the near polar area projection onto the planets near-equatorial plane”
        Would you tell me specifically why you (apparently) disagree with the Chilingar et al text above?

      • “So if you modify denominator from 4.0 to 3.502 then must use (i.e. add-in) their scaling factors for Earth global Tmean=288.2K”
        I don’t agree because the scaling factors are indeed based on the mean surface temperature, however, this makes no difference to their calculation of the affect of the precession angle (and which was from a paper by Sorokhtin et al many years ago before they even came up with their gravito-thermal equation).
        In other words, no matter what surface temperature is plugged into that equation to determine both scaling factors, it doesn’t change their TSI/3.5 precession angle correction.

      • HS – “I don’t agree..”
        So now HS doesn’t agree with Chilingar. Do you agree with the other paper you linked Volokin 2015, p.12: “The factor 1/4 inside the parentheses serves to distribute the stellar flux from a flat surface to a sphere and arises from the fact that the surface area of a sphere is 4 times larger than the surface area of a disk with the same radius.”? If not, why not?

      • “So now HS doesn’t agree with Chilingar”
        No Trick that’s a misquote. I’m disagreeing with your claim ““So if you modify denominator from 4.0 to 3.502 then must use (i.e. add-in) their scaling factors for Earth global Tmean=288.2K”
        because as I said “the scaling factors are indeed based on the mean surface temperature, however, this makes no difference to their calculation of the effect of the precession angle (and which was from a paper by Sorokhtin et al many years ago before they even came up with their gravito-thermal equation).
        In other words, no matter what surface temperature is plugged into that equation to determine both scaling factors, it doesn’t change their TSI/3.5 precession angle correction.”
        As to Volokin, you should keep reading pg 12-14 in which they specifically state that TSI/4 is an incorrect assumption and they instead use a spherical integration of the SB law.
        Thus, the jury is still apparently out and I am trying to gather opinions here for or against the canonical TSI/4 (which I did use in the HS greenhouse equation BTW), vs. Chilinigar, vs Volokin, Bart, you, Willis, Dr. Brown, and any other opinions. Clearly it is not as simple as TSI/4 given both the Volokin and Chilingar papers.

      • HS – “I’m disagreeing with your claim ““So if you modify denominator from 4.0 to 3.502 then must use (i.e. add-in) their scaling factors for Earth global Tmean=288.2K”
        That’s not my claim, HS, that’s Chilingar verbatim eqn. 13.12. You then disagree with Chilingar eqn.s if not going to use their full 13.12. And what’s more you haven’t even seen their p. 475 to fully understand them. Faux pas HS. Why not agree with 13.12? Your first try was insufficient hand waving.
        “they instead use a spherical integration of the SB law.”
        Yep but Volokin still uses the 1/4 method in Eqn. 3 & in their tables. Simplified the S-B method to (4c) with applicable moon parameters. But’s that not what Chilingar et. al. is doing & with which you know disagree. Volokin doesn’t criticize but actually uses the 1/4 method as they state. Why not agree?

      • Hockeyschtick, thanks for your question and comments. You ask:

        Are you Willis, Tim, Trick, etc. saying that Chilingar et al is wrong about this?

        I simply don’t understand what Chilingar is saying. But if he is saying what it seems he is saying then yes, he’s absolutely wrong.
        He is certainly wrong when he imagines a planet with its pole pointed towards the sun and he claims that it will receive TSI/2 on the side facing the sun. He’s wrong because what he doesn’t consider is that it is not physically possible for a rotating planet to rotate around a sun with its axis pointed constantly at the sun. No surprise that he hadn’t thought of this, he’s a petroleum geologist.
        In any case, here is the situation that he is mistaken about:
        https://wattsupwiththat.files.wordpress.com/2015/08/90c2b0-axial-tilt.jpg
        Figure S1. A planet with a 90° axial tilt revolving around a sun. Purple shows the illuminated side, line through planet shows planetary axis.
        As you can see, his idea that a rotating planet could revolve around a sun with the axis always pointed towards the sun is simply not correct. The planet is a gyroscope. If the axial tilt were 90°, then over the year, at some point one pole, and then six months later the other pole, will point directly at the sun.
        The same thing is happening with our polar axis. At some point in the year one end points towards the sun, and six months later, the other end points towards the sun. Imagine that the axial tilt were 70° … it would still be the same. At one point in the year one pole will point more towards the sun, and six months later the other pole will do the same thing.
        As a result, his claim that the planet will receive TSI/2 at the instant the pole points at the sun is meaningless … because in six months it will get zero, and the average will be TSI/4.
        And since that mistaken idea is the starting point for his claim that the insolation is between TSI/2 and TSI/4, that claims falls apart as well.
        Here is the short version.
        At any given instant, half of the earth is illuminated. Over any given year, any point on earth receives sunlight exactly half the time.
        The average of day and night at the equator? Half and half, it hardly varies above and below a twelve hour day/night cycle and it averages out to half day, half night.
        The average of day and night at the poles? Half and half, six months of sun, six months of night.
        The average of day and night anywhere on the planet?
        That’s right, half day and half night … and as the figure above demonstrates, this is true regardless of axial tilt.
        You do the math …
        w.
        PS—After this claim, I wouldn’t believe a word that Chilengar said on the subject … just sayin’ …

      • Further research supports my statement that I wouldn’t trust anything Chilengar says … see here for a thorough fisking of Chilengar by ScienceOfDoom.
        w.

      • Thanks again Willis and I agree with your points. I used TSI/4 in the HS ‘greenhouse equation’, but the recent Chilingar paper gave me doubts, and I agree they don’t make it clear what they are claiming with regard to
        “taking sphericity of the sun-illuminated polar area into account, the divisor should be 2Ss/So, where Ss is the Earth’s near-polar area beyond the polar circle and So is the areal extent of the near polar area projection onto the planets near-equatorial plane”
        so will withhold further judgement until this particular point is clarified one way or the other.
        To further complicate matters, as discussed with Trick above, the new Volokin et al paper also claims the TSI/4 assumption is incorrect and that one must do a spherical integration of the SB law to properly calculate solar insolation. See pages 12-14 in this paper (full paper in post):
        http://hockeyschtick.blogspot.com/2015/08/new-paper-confirms-gravito-thermal.html
        What do you think about Volokin’s SB spherical integration?
        As to SoD’s critique of Chilingar, to me almost the whole post is “duh, we already knew that” and fails to even address the thrust of the paper, the gravito-thermal GHE.
        And SoD repeats what I firmly believe to be a misconception at the heart of the radiative GH theory: “The higher the concentration of “greenhouse” gases, the more optically thick the atmosphere, and therefore radiative cooling to space takes place from higher up in the atmosphere” for the nine reasons in this post:
        http://hockeyschtick.blogspot.com/2014/11/why-global-warming-is-not-explained-by.html

      • HS – “..the new Volokin et al paper also claims the TSI/4 assumption is incorrect..”
        Can you find a statement in the Volokin paper to support this? They do use the 1/4 factor in Eqn. 3 and use Eqn. 3 in the tables.

        Willis – Thanks for the SOD link. As HS notes, the complaint isn’t about psi angle on a quick read.
        Chilingar only discusses the TSI/2 for the polar regions which I notice are dark for half the orbit in your diagram.
        Somehow Chilingar uses unit emissivity and adjusts the denominator based on a psi argument more fully explained on missing p. 475 which should be obtained before moving on. I think the argument that a revolving planet bulges at the equator to an oblate spheroid has merit so that when a pole is pointed at the sun more sunlight is intercepted (thus increasing Tt by reducing the denominator) than when a pole is at psi = 0 (which partly includes the bulging equator effect also).
        I will try to find p. 475 before moving on. Maybe p. 475 can be crowd sourced.

      • Willis Eschenbach @ August 30, 2015 at 8:36 pm
        Yes, that is physically impossible, but you can do physically impossible things in a gedanken. But, if you don’t like having the axis rotating, try assuming the planet is tidally locked with the Sun, like they used to think Mercury was, to get the one face pointing toward the Sun all of the time.
        I’m not advocating Chilingar, mind you. Just trying to facilitate the conversation.

      • Trick et al: The prior paper by Volokin et al is very interesting and available open access here:
        http://www.springerplus.com/content/3/1/723
        Excerpt: “If such an ASCO orbited the Sun at Earth’s distance, had a regolith of zero thermal conductivity, and were only heated by solar radiation, then the equilibrium temperature of the illuminated point would be
        T1 = [So (1 – αo)cosθ/εσ]^0.25 = 349.6 K
        assuming αo = 0.12 (a typical value for rocky surfaces), a solar incident angle θ = 45°, and ε = 1.0. The temperature of the shaded point would be T2 = 0, because it receives no radiation since cos θ < 0 and there is no heat release from the regolith at night due to zero heat storage.
        Thus, their spherically integrated SB law does appear to depend upon the precession angle or obliquity and perhaps is a simplified version to the Chilingar equation.
        In addition, one of the authors (I believe) commented on my blog:
        “I brought up the 33 K issue only because you stated in your blog article that the new paper explains the 33 K GE through gravity. There is no 33 K GE nether there is a 66 K GE. There estimates are based on mathematically incorrect calculations using 1-D models, which are prone to aggregation errors. The thermal effect of Earth’s atmosphere is ~ 90 K. The correctness of this estimate is explained in this paper: http://www.springerplus.com/content/3/1/723.
        By the same token, temperatures calculated from the averaged absorbed radiation by a planet (i.e. from TSI/4 or TSI/3.5) are non-physical quantities that have no meaningful relation to actual physical (measurable) temperatures at the planet’s surface. This is also explained in the same SpringerPlus paper: http://www.springerplus.com/content/3/1/723
        http://hockeyschtick.blogspot.com/2015/08/new-paper-confirms-gravito-thermal.html?showComment=1440348705102#c3489651528738272369

      • HS – “the equilibrium temperature of the illuminated point would be” fn(cos(theta)).
        I don’t buy their argument as written HS. Rays coming in from the sun incident on “airless” ASCO would be very nearly collimated, so there is no cos(theta) effect in that manner. A ray (photon) is either completely absorbed or completely reflected (quantum electrodynamics).
        What I would buy is an increase in the percentage of rays reflected at the 45 degree point and consequent decrease in rays absorbed. To that physics apply cos(theta) based fn(latitude), cos(Theta) = 1 at equator, =0 just barely past the terminator.
        “There is no 33 K GE..”
        Depends on basis scenario. If basis is for “airless” earth then w/no oceans & moon optics regolith, yes, agree the Volokin paper typical et. al. Earth GTE ~ 90K is the result.
        If basis scenario is Earth with very optically thin surface 1bar atmosphere and oceans in place (i.e. not “airless”), then GTE ~33K as Tmean measured by annual global thermometer ~288K optically thick atm. vs. interannual CERES at its TOA orbit measured brightness T ~255K.

      • HS – “..temperatures calculated from the averaged absorbed radiation by a planet (i.e. from TSI/4 or TSI/3.5) are non-physical quantities that have no meaningful relation to actual physical (measurable) temperatures at the planet’s surface.”
        Don’t buy that either as my IR thermometer brightness temperature comes out close to thermometer temperature when observed object emissivity is close enough to 1.0 in every test I’ve done. Backed by substantial analysis, tested physics developed since around CY 1900, you know, the Feynman compliant science method.
        I think the learning from Chilingar is that 4.0 may only be idealized denominator given a non-ideal oblate spheroid will not map directly to the flat disk intercepting the rays. The emissivity number is adjusted to add in the psi angle issues so I think the Chilingar approach has merit for say Uranus at around 98 psi angle. For that I would say set emissivity to 1.0, rounded, as they do and let the effect of psi on oblate spheroid be the denominator as in their eqn. 13.12 with scaling to nature.
        Still looking for p. 475…

      • “What I would buy is an increase in the percentage of rays reflected at the 45 degree point and consequent decrease in rays absorbed. To that physics apply cos(theta) based fn(latitude), cos(Theta) = 1 at equator, =0 just barely past the terminator.”
        How would you re-write the Volokin SB equation above?
        “There is no 33 K GE..”
        “Depends on basis scenario. If basis is for “airless” earth then w/no oceans & moon optics regolith, yes, agree the Volokin paper typical et. al. Earth GTE ~ 90K is the result.
        If basis scenario is Earth with very optically thin surface 1bar atmosphere and oceans in place (i.e. not “airless”), then GTE ~33K as Tmean measured by annual global thermometer ~288K optically thick atm. vs. interannual CERES at its TOA orbit measured brightness T ~255K.”
        Well, what the rest of the Volokin paper shows is that the only thing that matters to the surface temperature is surface pressure and solar insolation, nothing to do with GHGs or optical thickness, pressure only.
        Trick August 31, 2015 at 12:07 pm
        HS – “..temperatures calculated from the averaged absorbed radiation by a planet (i.e. from TSI/4 or TSI/3.5) are non-physical quantities that have no meaningful relation to actual physical (measurable) temperatures at the planet’s surface.”
        “Don’t buy that either as my IR thermometer brightness temperature comes out close to thermometer temperature when observed object emissivity is close enough to 1.0 in every test I’ve done. Backed by substantial analysis, tested physics developed since around CY 1900, you know, the Feynman compliant science method.”
        Yes I’ve done that too and get a clear sky temp at night ~ -10C, close to the -18C/255K atmospheric blackbody temp, but alas this is just from a single point on the globe, so not that meaningful to me.
        “I think the learning from Chilingar is that 4.0 may only be idealized denominator given a non-ideal oblate spheroid will not map directly to the flat disk intercepting the rays.”
        Agree.
        “Still looking for p. 475…”
        I’m thinking the better reference to find is the original Sorokhtin et al paper listed in Chilingar’s references, but it is in a Russian journal so best of luck.

      • HS – “How would you re-write the Volokin SB equation above? “
        Instead of inserting cos(theta) as they do I would find plots of tested emissivity and reflectivity vs. view angle for regolith & earth L&O surface and insert that function.
        “Well, what the rest of the Volokin paper shows is that the only thing that matters to the surface temperature is surface pressure and solar insolation, nothing to do with GHGs or optical thickness, pressure only.”
        Not the Volokin 2015 paper dealing with the 6 planets/moons, eqn. (4c) uses moon albedo, and emissivity as applicable all “airless” objects and see in the conclusion where they explicitly write their results include GHG (you know, IR active gas).
        “..but alas this is just from a single point on the globe..”
        See, it works at point A! Now go to point B, it will work the same, so forth; when you get back from tropics (0.95) and polar points (0.7), report in. What you will find is global Earth atm. emissivity ~0.8 looking up. (Hint: experimenters have done this already…save time, look up their work.)
        “I’m thinking the better reference…is in a Russian journal..”
        Ack. THAT doesn’t make it better, my local ref.librarian is good enough for local language ref.s, your original ref. published in GB. We’ll see if their ref.computer is up to it. Might even be in the stacks.

    • hockeyschtick August 29, 2015 at 2:44 pm
      You say:

      A planet with a precession angle of 90 degrees would only receive solar insolation of TSI/2 because one-half of the sphere would never receive any solar insolation at all, ever.

      Never … ever? I don’t think that your statement is correct.
      For a start I think you mean axial tilt and not precession angle.
      A rotating planet with an axial tilt of 90 degrees will experience daylight in both hemispheres during the course of a planetary year. Start at midsummer with the sun directly overhead at the north pole. Half a year later the sun will be directly overhead at the south pole.
      Remember that for the Earth the north pole always points at the fixed star Polaris throughout the course of the year. A planet with an axial tilt of 90 degrees can also have a pole star because a planet’s axis of rotation does not turn to follow the sun during the course of its annual orbit.
      So you are wrong, the only way for a planet in your words to never … ever receive sunlight over half its surface is for the planet to be turning so that the length of its day equals the length of its year. For this to be true the planet’s axial tilt must be zero degrees and not 90 degrees.
      HS
      Please remember that the divide by 4 calculation is a lazy mathematical trick to determine the surface area distribution of the annualised outgoing planetary IR radiation and not the annualised distribution of the incoming solar radiation. Because during the course of the year there is nowhere on Earth that does not receive a total sum of six months daylight, then for any given year the sun’s illumination is distributed over the whole of the Earth’s surface. For the general case of a spherical rotating planet (but not the very special case of one that has a zero degree tilt angle and is annual rotation phase locked) incoming solar energy is intercepted by a disk area at any one time, outgoing planetary energy emanates from the surface area of a sphere at any one time, therefore divide by 4 for the annualised climatic effect.

      • Philip Mulholland

        For the general case of a spherical rotating planet (but not the very special case of one that has a zero degree tilt angle and is annual rotation phase locked) incoming solar energy is intercepted by a disk area at any one time, outgoing planetary energy emanates from the surface area of a sphere at any one time, therefore divide by 4 for the annualised climatic effect.

        But the incoming and reflected solar radiation is reflected (or absorbed) immediately each minute of each 24 hour day. It is NOT “absorbed” (and passed into a perfect idealized battery) and its effect “averaged” out over the total year.
        Though you can measure the capacitor (delayed effect) of the sun’s energy every day -> The hottest hours of the day are 13:00 – 15:00 – 1 to 3 hours after the highest solar elevation at noon each day. But the reflected energy (from water’s surface or from an ice pack or snow field) are reflected instanteously back into space – where they are lost forever. Further, an “averaged” solar year cannot demonstrate the difference between a January 5’s insolation maximum of 1410 watts/m^2 at TOA and July 5’s minimum of 1315 watts/m^2.
        Think latitude and day-of-year over the full year don’t matter? By September 22, at the annual minimum of the Arctic ice cap near 80 north latitude, the edge of the Antarctic sea ice at 59 south is receiving 10 TIMES the energy that the Arctic sea ice does.
        Even averaged over the entire year, each square million kilometer of Antarctic sea ice is receiving (or reflecting) 1.68 times the energy that a million square kilometers of Arctic sea ice receives.

      • RACookPE1978 August 30, 2015 at 5:45 am

        But the incoming and reflected solar radiation is reflected (or absorbed) immediately each minute of each 24 hour day. It is NOT “absorbed” (and passed into a perfect idealized battery) and its effect “averaged” out over the total year.

        I fully agree with you, which is why I described this analysis as a Mathematical Trick.
        Climate models are effectively frictionless systems and therefore totally bogus. The energy stored by the climate system is not accounted for. Never mind the biology what about the potential energy that the hydrological system stores when a continental icecap grows? Where is that recorded in these oh so perfectly balanced models?

      • Well, almost. How about we divide by something around 4.0012. The earth is actually an oblate spheroid, measuring 7901 miles pole to pole, but 7926 miles through the equator. This means that the solar “disk” of radiation is not a disc at all, but changes shape throughout the year, from a minimum apparent size at the equinoxes, to a maximum apparent size at the solstices. Is that included anywhere in the calculations?

      • RACookPE1978 August 30, 2015 at 5:45 am

        Philip Mulholland

        For the general case of a spherical rotating planet (but not the very special case of one that has a zero degree tilt angle and is annual rotation phase locked) incoming solar energy is intercepted by a disk area at any one time, outgoing planetary energy emanates from the surface area of a sphere at any one time, therefore divide by 4 for the annualised climatic effect.

        But the incoming and reflected solar radiation is reflected (or absorbed) immediately each minute of each 24 hour day. It is NOT “absorbed” (and passed into a perfect idealized battery) and its effect “averaged” out over the total year.

        Thanks, RA, but I fear I don’t understand this whole comment of yours. What does this have to do with the dispute? The question at hand is:
        Does the earth receive an energy flux of TSI/4 W/m2 when averaged over the earth’s surface for an entire year?
        Philip Mulholland and I and others say yes, solar input averages TSI/4 W/m2. HS and others say no.
        But none of this is discussing what happens to the energy after it passes the TOA. As you point out, some gets absorbed, some gets reflected, some melts ice, some warms my garden … but so what?
        None of that has anything to do with the question Philip is answering. So I don’t understand how you got from the question Philip and I and HS are discussing, (is TOA sunlight averaged over the earth’s surface equal to TSI/4 or not), to your post about what happens to that energy AFTER it passes TOA and enters the system.
        w.

      • the only way for a planet…to never … ever receive sunlight over half its surface is for the planet to be turning so that the length of its day equals the length of its year.

        Since my previous question remains unanswered, I’ll try rephrasing it.
        Given an axial tilt of 90° with an axis pointing to the sun and a precession of 1 year, wouldn’t one pole of a planet always point to the sun?

    • Just a minor nit HS – your nomenclature is not “wrong”, but is is unconventional. In astronomy, we usually refer to the 23.44 degree offset as the “obliquity”. Precession generally refers to the wandering of the axis of rotation over time which produces a small variation in obliquity.

      • I think TSI/4 is definitely wrong. While that is instantaneously the fraction illuminated, the question is by how much the input heat is retained at specific locations between the times they are illuminated. That would determine the average balance of heat retained.
        If all areas were illuminated daily, it would be a reasonable approximation, due to the high specific heat of the oceans. But, as you say, since some areas are illuminated only on a yearly basis, I expect it is not a very good one.
        I am sorry I do not have time right now to review Chilingar, but will do so when able.

      • A quick reality check:
        The area inside the Arctic Circle (or the Antarctic Circle) is 2 x 10^7 km^2. This is about 4% of the Earth’s surface area of 5.1 x 10^8 km^2.
        So on any given day, at least 96% of the earth’s surface sees some sunlight.
        There is only one day a year when the entire area inside the Arctic circle does not see any sunlight — the December solstice. Also only one day a year when the entire area inside the Antarctic circle does not see any sunlight — the June solstice.
        At the two equinoxes, every place on the planet’s surface sees 12 hours of sunlight.
        On an “average” day, ~98% of the earth’s surface sees sunlight.

    • It is quite simple. A disc with the diameter of the earth intercepts the sun’s incoming energy. The average of this over a sphere is one fourth of this based on the two areas involved. No one claims all parts of the earth receive the same amount. It is the weather (atmosphere and ocean) that moves the heat around to partially offset the differences in energy received from the sun. The remainng offset would depend on the precision angle.

  12. Wouldn’t it be great if we could accurately represent the physical laws in the atmosphere/oceans with thousands of mathematical equations and all we needed to do was plug in all the measured values(like CO2) so that we could project climate to the year 2100 and even regional variations in weather/climate between now and 2100.
    OK…………we’ve been doing that for over 2 decades now.
    The biggest problem in judging the skill of these model projections, is that the distant time frame allows them to be wrong for decades without having to be held fully accountable for the increasing disparity between projection and reality.

  13. Most climate models don’t extend past the stratosphere and conveniently leave out the mesosphere and thermosphere. The only 1D verified model of the atmospheric temperature profile from the surface to the top of the atmosphere/edge of space at ~100-120km is the 1976 US Standard Atmosphere mathematical model, and which remains the only atmospheric model verified with millions of observations.
    These early atmospheric scientists began this effort to model the atmosphere with the basic physics of gases and air known since the 1800’s from the ideal gas law, 1st Law of Thermodynamics, Newton’s second law of motion (F=ma=mg), the physical chemistry of molecular weights, partial pressures of each gas, heat capacities of individual gases and air at both constant pressure and constant volume, the gravitational acceleration constant, barometric formulae, Boltzmann’s constant, Avogadro’s number, mean atmospheric molecular weights, number density of individual species, total number density, atmospheric mass density, mole volume, scale height, geopotential height of gravitational potential energy (PE), mean air-particle speed, mean free-path of air molecules, mean collision frequency, calculated speed of sound, dynamic viscosity, kinematic viscosity, coefficient of thermal conductivity, and on and on…
    And never once used any “radiative forcing” from any IR-active greenhouse gases or any radiative calculations from any greenhouse gases whatsoever to produce an accurate 1-D model that could calculate Earth’s entire pressure, mass density, temperature, and molecular-scale temperature as a function of geopotential altitude (geopotential height ~ geopotential altitude ~ gravitational potential energy (PE)) profile from the surface to the edge of space.

    The entire 1976 US Standard Atmosphere document is available in this post:
    http://hockeyschtick.blogspot.com/2014/12/why-us-standard-atmosphere-model.html

      • Yes, and this new paper proves on 6 planets including Earth and Venus (and also true for Europa and Mercury as well -shown by Nikolov & Zeller), the surface temperature can be very accurately determined by only the 1) solar insolation and 2) surface pressure, and that greenhouse gas concentrations ranging from zero to over 96% have nothing to do with surface temperatures on any of these 8 rocky planets:
        http://hockeyschtick.blogspot.com/2015/08/new-paper-confirms-gravito-thermal.html

      • Dahlquist: “And if you look at THE VENUSIAN PRESSURE/TEMPERATURE GRADIENT http://www.datasync.com/~rsf1/vel/1918vpt.htm you will find that at the height where the pressure is roughly 1 atmosphere, ” The subsequent statements clearly refer to the capitalized sentence fragment, the level at which venusian atmosphere is at 1 Earth. I admit I also had to re-read.

      • Actually you will find at 1 atmosphere the temperature on Venus was measured at 66C or 339K which is 1.176 times the absolute mean temperature of Earth at sea level (according to Earth’s Standard Atmosphere) of 15C or 288K. This corresponds precisely to the calculations of temperature difference based solely on distance to the sun (square root of 93/67.25). Either this is an incredible coincidence of biblical proportions or proximity to the sun is the only variable of consequence in determining temperature in atmospheres denser than 200millibars (this is where the correlation begins).

      • “This corresponds precisely to the calculations of temperature difference based solely on distance to the sun (square root of 93/67.25). Either this is an incredible coincidence of biblical proportions or proximity to the sun is the only variable of consequence in determining temperature in atmospheres denser than 200millibars (this is where the correlation begins).”
        Yep, Robinson & Catling, Nature 2013, showed that despite very different atmospheric compositions and greenhouse gas concentrations, the lapse rates on all planets in our solar system with thick atmospheres are almost the same at pressures > ~.2 bars. The tropospheric lapse rates are in turn dependent only upon gravity and heat capacity at constant pressure, not GHG “radiative forcing.”
        http://3.bp.blogspot.com/-ALRV9LTa9ek/VHKuvTZ5oAI/AAAAAAAAGvY/Iv7RqcYLq3Y/s1600/robinson%2B%26%2Bcatling%2B2.jpg
        http://hockeyschtick.blogspot.com/2014/11/derivation-of-entire-33c-greenhouse.html

      • HS: “..this new paper proves on 6 planets including Earth and Venus (and also true for Europa and Mercury as well -shown by Nikolov & Zeller), the surface temperature can be very accurately determined by only the 1) solar insolation and 2) surface pressure..”
        This paper comes up with a mean global surface temperature estimate on Mars that is lower than all other published papers (as they write within) thus it can plot on their curve & work in the curve fit process so well.
        For 1) & 2) where Po=0, any “airless” planet or moon must have the same albedo and surface emissivity as Earth’s moon to work in the curve fitting process. That is how they eliminated some radiative balance variables. For Mercury to plot on their curve, it will have to be found with the same regolith properties as Earth’s moon. MESSENGER mean brightness T data will soon be available to find out if so. And eventually New Horizon’s in the other direction.
        ——
        wickedwenchfan and Robert – Nice proof of gas laws working on Venus too, P=density*R*T. If you get Venus density from those NASA observed measurements, and ratio brightness T based on orbital parameters, then sure P=1atm. is easily calculated. Different z heights though. Other Venus z heights will come out close also. This should not be news.

  14. There are two intertwined issues in this post. Tisdale’s referenced guest post exposed yet another BIG model/observation discrepancy. This post argues data inadequacy/uncertainty as the underlying reason. But there is another: incomputable resolution forcing parameterization requiring attribution assumptions. A previous guest post. Both are at work.
    Two independent ‘impossibilities’ do not make something possible. And trying harder with newer supercomputers is not an answer. Just a waste of time and money.

  15. The radiation balance at TOA coud tell something. I just wonder what f.inst. 1W/m2 would mean for the temperature development on Earth. How fast would it warm/cool.
    We have seen 1K over 100 year, what would that be in radiation imbalance?

  16. Where Is the Top Of The Atmosphere (TOA)?
    It is at the altitude where the atoms and molecules of the gas get knocked out into space by the solar wind, and therefore It is continuously variable, it is generally function of the magnetosphere’s strength at the time.

  17. On pages 90 and 91 of this book https://books.google.com.au/books?id=HmqOicm_YXUC&pg=PA90&lpg=PA90&dq=lidar,+radar+are+heating+up+the+atmosphere&source=bl&ots=ad3Q38rQYr&sig=Oflo0kc4XdMtKx3gQQCiY6WsRbY&hl=en&sa=X&ved=0CFQQ6AEwCGoVChMIhN6-qqHPxwIVixyUCh2kLQ3g#v=onepage&q=lidar%2C%20radar%20are%20heating%20up%20the%20atmosphere&f=false things become clearer to why the atmosphere is behaving the way it is.
    A hot sphere with a 6000 C core will always radiate outwards to freezing cold space, while cold space is trying to rush in and create equilibrium.
    The Earth and Sun are electromagnetically connected and it all starts at the bow shock (first line of resistance) http://sci.esa.int/cluster/49637-cluster-reveals-earth-s-bow-shock-is-remarkably-thin/
    Words with pictures paint a clearer picture https://www.youtube.com/watch?v=HOIlIMdJV5k
    Mainstream Science has lost it way because of propaganda .
    Propaganda. information, ideas, or rumors deliberately spread widely to help or harm a person, group, movement, institution, nation, etc. the deliberate spreading of such information, rumors, etc. the particular doctrines or principles propagated by an organization or movement.

  18. Isn’t the top of the atmosphere made of plastic like in the controlled greenhouse gas laboratory tests? That’s how they proved global warming, remember?

  19. The total incoming radiation is the only thing that can be calculated with any accuracy. This will equal the total outgoing radiation. Everything else is organised chaos interacting with itself inside the total system. Yes we can label different areas as generally behaving in a described manner, but they are not separate from other areas and they are not absolute in geography or form.
    The only property of this organised chaos that we can completely discount as having zero effect is the claimed influence of so called greenhouse gasses on temperature. It is completely unphysical to claim any molecule has the ability to increase temperature or to block heat flow. This would be completely true if the magic molecules were fixed in place much less constantly moving.

    • “It is completely unphysical to claim any molecule has the ability to increase temperature or to block heat flow. This would be completely true if the magic molecules were fixed in place much less constantly moving.”
      Yes, greenhouses, panes of glass, blankets, insulation in the attic, etc. and the other false analogies to CO2 all work by limiting convection, not “radiative forcing,” and GHGs do not limit convection. In fact, GHGs accelerate convection by preferentially transferring heat via collisions with N2/O2 rather than emitting a photon. Thus all of these false analogies to CO2 are the opposite of the acceleration of convection by CO2.

    • wwf and hs, your disbelief in the greenhouse effect is disquieting, as you seem to be quite intelligent. Let me encourage you to read and re-read a couple of my posts until you clearly understand what is actually happening in a “greenhouse” situation.
      The Steel Greenhouse 2009-11-17
      There is a lot of misinformation floating around the web about the greenhouse effect works. It is variously described as a “blanket” that keeps the Earth warm, or a “mirror” that reflects part of the heat back to Earth, or “a pane of glass” that somehow keeps energy …
      People Living in Glass Planets 2010-11-27
      Dr. Judith Curry notes in a posting at her excellent blog Climate Etc. that there are folks out there that claim the poorly named planetary “greenhouse effect” doesn’t exist. And she is right, some folks do think that. I took a shot at explaining that the “greenhouse effect” is a…
      There are many reasons to disbelieve the claims of the climate alarmists. But the claimed nonexistence of the greenhouse effect isn’t among them … for the simple reason that the greenhouse effect actually exists.
      w.

      • Willis, I do not “disbelieve in the greenhouse effect,” on the contrary, fully endorse that there is a 33C gravito-thermal “greenhouse effect” from the 255K ERL at ~5.5km/center of mass of the atmosphere, as well as an even larger negative -35C anti-greenhouse effect from the 255K ERL to the 220K tropopause. I do dispute the cause as radiative forcing from GHGs, and have shown in many posts that Maxwell, Clausius, Carnot, Boltzmann, Feynman, the US and International Standard Atmospheres, Chilingar, the HS greenhouse equation, etc etc all clearly demonstrate that the 68K tropospheric temperature gradient is solely a function of atmospheric mass/gravity/pressure. This has now been demonstrated on 8 planets including Earth and Venus (links above) that surface temperatures and lapse rates are independent of GHG concentrations and only depend on surface pressure and solar insolation. Gravity/pressure merely redistributes the heat energy from the only source the Sun, more towards the surface and less towards the top of the troposphere, creating the 68K tropospheric temperature gradient or so-called greenhouse effect.
        I did re-read the steel greenhouse post and don’t agree that it proves an Arrhenius radiative GHE or applies as an analogy to our atmosphere, reasons including:
        1. Gases do not limit convection like a solid steel containment vessel
        2. On the contrary, GHGs accelerate convection by preferentially transferring heat via collisions with N2/O2 rather than emitting a photon. The N2/O2 kinetic energy leads to adiabatic expansion, rising, and cooling of air parcels, followed by adiabatic compression, falling, and warming of the air parcel, creating the gravito-thermal GHE.
        3. For heat to be transferred from the cold shell to inner sphere requires an impossible reduction of entropy, forbidden by the principle of maximum entropy production/2nd law.
        4. The maximum that a say 255K BB could warm a second BB shell, whether by either radiation or conduction, is limited to a maximum of 255K.
        4. If one were to create a theoretical Carnot engine between the inner sphere and 3K space, Eout from the hot reservior sphere to the cold reservoir 3K space would be >> Ein, a perpetual motion heat engine, forbidden by both the 1st and 2nd laws.
        There are other reasons as well, but hitting the sack now.
        My best regards.

      • HS: ..68K tropospheric temperature gradient is solely a function of atmospheric mass/gravity/pressure.”
        The gradient, yes, however you will not be able calculate a surface temperature from those unless you are able to measure or calculate from radiative balance at least one temperature. That T is known as the intercept. The paper you discuss got that one temperature from Diviner observations of the moon mean brightness T and was all they needed once the paper assumed radiative properties of Earth’s moon regolith are the same on other “airless” bodies.

      • “HS: ..68K tropospheric temperature gradient is solely a function of atmospheric mass/gravity/pressure.”
        Trick says: “The gradient, yes, however you will not be able calculate a surface temperature from those unless you are able to measure or calculate from radiative balance at least one temperature.”
        That’s what the HS greenhouse equation does – calculates the equilibrium temperature 255K of the Earth with the Sun using the standard SB equation. From that temperature only, the surface temperature and entire tropospheric temperature profile may then be calculated.
        http://3.bp.blogspot.com/-xXJOurldG_E/VHjjbD6XinI/AAAAAAAAGx8/8yXlYh8Lcr4/s1600/The%2BGreenhouse%2BEquation%2B-%2BSymbolic%2Bsolution%2BP.png
        The “Greenhouse Equation” calculates temperature (T) at any location from the surface to the top of the troposphere as a function of atmospheric mass/gravity/pressure and radiative forcing from the Sun only, and without any radiative forcing from greenhouse gases. Note the pressure (P) divided by 2 in the greenhouse equation is the pressure at the center of mass of the atmosphere (after density correction), where the temperature and height are equal to the equilibrium temperature with the Sun and ERL respectively.
        http://hockeyschtick.blogspot.com/search?q=greenhouse+equation

      • HS – ”From that temperature only..”
        Yes, HS, as I wrote you needed that one temperature, the intercept, from Earth 255K brightness T data, confirmed by CERES multi-annual observations & also needed for “airless” Moon 197K measured by Diviner in addition to mass, insolation and gravity. You used radiative optical emissivity and albedo balance in the book ref. Eqn. 13.6, with measured data, and the more recent paper with 6 planets/moons Eqn. (3), (4c) and plotted Fig. 4.

      • The point I’m making is that to determine the entire so-called 33C “greenhouse effect” or gravito-thermal effect, one only has to know the radiative forcing from the Sun and the gravity/mass/pressure/density/Cp, none of which are dependent upon “radiative forcing” from GHGs.

      • HS – “one only has to know the radiative forcing from the S..
        And an object in radiative balance with S from surface emissivity & setting albedo 0.3 which you also used (but leave off the list) for your Tmean =255K which is for a ~transparent atmosphere, L&O surface doing ~much of the reflecting, so of course if you set the atm. optically transparent (same as Diviner for the moon brightness T = 197K with neglible atm.) then not dependant on your neglected IR active gas. This agrees with CERES et. al. interannual observations at TOA meaning its orbit.
        You reached same conclusion as your going in assumption. Try the exercise again with Tmean = 288K intercept, same mass, insolation, gravity. You will need an atm. at emissivity around 0.8 looking up and surface emissivity approx. 0.98 with albedo 0.3. No kidding since this agrees with what your book ref. shows in 13.7 for GTE (they call GHE). “Earth has a relatively dense atmosphere…convection..not only radiation..” This is the convective-radiative atmosphere balance you are using in that formula.

      • HS – “one only has to know the radiative forcing from the S..& setting albedo 0.3 which you also used (but leave off the list)”
        The radiative forcing from the Sun is after taking out the the reflected portion from the assumed constant albedo of 0.3 shown (twice) in the equation above.
        It makes no sense to assume the Tmean is 288K. Energy in = Energy out. The 255K equilibrium temperature with the Sun is exactly the BB of Earth seen from space, which must also be the temperature of the “ERL” of 255K, located exactly at the center of mass of the atmosphere.
        Why at the center of mass? Because Newton’s 2nd Law F=ma=mg for system of particles is applied to the center of mass:
        http://www.colorado.edu/physics/phys1110/phys1110_sp01/Notes/Chap10.htm
        “This is the convective-radiative atmosphere balance you are using in that formula.”
        The troposphere is in radiative-convective equilibrium in which convection dominates radiation by a factor of ~10 times, thus any change in “radiative forcing” is easily reversed by increased convection, and that’s just one reason why GHG “radiative forcing” isn’t necessary to determine the entire 33C gravito-thermal GHE.

      • HS – “thus any change in “radiative forcing” is easily reversed by increased convection..”
        The monthly anomaly observed data disagree with this, no smoothness. Convection has a stability mechanism all its own, once uneven surface radiative balance temperature destabilizes, as observed by mostly hydrostatic balance in troposphere except for, you know, storms.
        “It makes no sense to assume the Tmean is 288K.”
        No need since that is thermometer measured on Earth. Your challenge is to compute surface Tmean for an optically thick atm. from just mass, insolation, gravity. Can’t be done. You also will need one radiatively balanced T, an intercept, by calculation or measurement to get the surface Tmean in presence of the optically thick radiative convective atm. Sure, once you have 255K at a certain level, then you have an intercept T.
        If you can do surface Tmean in optically thick atm. with just mass, insolation, gravity – let’s see it, just do it. THEN you will prove Chilingar wrong.

      • HS – “thus any change in “radiative forcing” is easily reversed by increased convection..”
        The monthly anomaly observed data disagree with this, no smoothness from “easily reversed” RF. Convection has a stability mechanism all its own, once uneven surface radiative balance temperature destabilizes, as observed by mostly hydrostatic balance in troposphere except for, you know, storms.
        “It makes no sense to assume the Tmean is 288K.”
        No need since that is thermometer measured on Earth. Your challenge is to compute surface Tmean for an optically thick atm. from just mass, insolation, gravity. Can’t be done. You also will need one radiatively balanced T, an intercept, by calculation or measurement to get the surface Tmean in presence of the optically thick radiative convective atm. Sure, once you have 255K at a certain level, then you have an intercept T.
        If you can do surface Tmean in optically thick atm. with just mass, insolation, gravity – let’s see it, just do it. Then you WILL disprove Chilingar.

      • hockeyschtick August 31, 2015 at 12:54 pm Edit

        Willis, please re-read that whole Feynman chapter, your quote is at the beginning of the chapter of Feynman’s thought experiment and he first proposes a hypothetical isothermal atmosphere. If you just continue reading the chapter you will find that Feynman crushes that false thought experiment stating our atmosphere “is not isothermal” …

        HS, your reply is appreciated. Our atmosphere is not isothermal? Is this supposed to be news? Of course it is not isothermal, we didn’t need Feynman to tell us that … but that doesn’t “crush” the fact that a thermally isolated column of air is isothermal.
        Nor does Feynman anywhere make the claim you make, that his thought experiment is a “false” thought experiment. That is you claiming that Feynman’s thought experiment is wrong, he never said that.
        You go on to say:

        Instead, [Feynman] talks about how gravity causes the conversion back and forth between gravitational potential energy (PE) and kinetic energy (KE), which is what causes (my term) the “gravito-thermal GHE” or 68K tropospheric temperature gradient.

        You are correct in the first part of that. When something sits up high in a gravity field, it has potential energy. When it falls from on high, it converts that to kinetic energy. For example, this is happening constantly in Feynman’s thought experiment, as gas molecules move up and down the column.
        What I don’t understand is why you think that is a source of a thermal difference, when Feynman (and Dr. Brown, and I, and many others) agree that a thermally isolated column of gas in a gravity field will be isothermal. Why doesn’t your “gravito-thermal” effect operate in that situation to make the bottom of the column warmer than the top of the column?
        Because assuredly, as you say, “gravity causes the conversion back and forth between gravitational potential energy (PE) and kinetic energy (KE)” in each and every molecule of gas in Feynman’s thought experiment … but that’s exactly what you say causes the “gravito-thermal” effect. So why isn’t the purported G-T effect happening in Feynman’s thermally isolated column?
        Perhaps if you could explain to us why the “gravito-thermal” effect DOESN’T work in that situation, it would be clearer why you think it works in other situations.
        Regards and thanks,
        w.

      • Willis says “Our atmosphere is not isothermal? Is this supposed to be news? Of course it is not isothermal, we didn’t need Feynman to tell us that … but that doesn’t “crush” the fact that a thermally isolated column of air is isothermal.
        Nor does Feynman anywhere make the claim you make, that his thought experiment is a “false” thought experiment. That is you claiming that Feynman’s thought experiment is wrong, he never said that.”
        No it’s obviously not new, and Carnot in 1824 was the first to explain why the atmosphere is not isothermal and uses the atmosphere as his “model” or thought experiment for a giant heat engine/air conditioner throughout his classic book and was the first (as far as I know) to describe the basis of what I’m calling the gravito-thermal GHE.
        Maxwell in 1872 also clearly states that such a column of air in a gravitational field would not be isothermal, and describes the Poisson relation, which is the basis of the gravito-thermal GHE, and now proven on 8 rocky planets incl. Earth and Venus and explains how temperature varies with pressure, nothing to do with GHG concentrations or radiative forcing whatsoever.
        Getting back to Feynman, immediately after talking about the isothermal thought experiment, only true in the absence of gravity, he says,
        “If the temperature is the same at all heights, the problem is to discover by what law the atmosphere becomes tenuous as we go up. If N is the total number of molecules in a volume V of gas at pressure P, then we know PV=NkT, or P=nkT, where n=N/V is the number of molecules per unit volume. In other words, if we know the number of molecules per unit volume, we know the pressure, and vice versa: they are proportional to each other, since the temperature is constant in this [thought] problem. But the pressure is not constant, it must increase as the altitude is reduced, because it has to hold, so to speak, the weight of all the gas above it. That is the clue by which we may determine how the pressure changes with height. If we take a unit area at height h, then the vertical force from below, on this unit area, is the pressure P. The vertical force per unit area pushing down at a height h+dh would be the same, in the absence of gravity, but here it is not, because the force from below must exceed the force from above by the weight of gas in the section between h and h+dh. Now mg is the force of gravity on each molecule, where g is the acceleration due to gravity, and ndh is the total number of molecules in the unit section. So this gives us the differential equation Ph+dh−Ph= dP= −mgndh. Since P=nkT, and T is constant, we can eliminate either P or n, say P, and get
        dndh=−mgkTn
        for the differential equation, which tells us how the density goes down as we go up in energy.
        We thus have an equation for the particle density n, which varies with height, but which has a derivative which is proportional to itself. Now a function which has a derivative proportional to itself is an exponential, and the solution of this differential equation is
        n=n0e−mgh/kT.(40.1)
        Here the constant of integration, n0, is obviously the density at h=0 (which can be chosen anywhere), and the density goes down exponentially with height…”
        to be continued…

      • Willis says, “What I don’t understand is why you think that is a source of a thermal difference, when Feynman (and Dr. Brown, and I, and many others) agree that a thermally isolated column of gas in a gravity field will be isothermal. Why doesn’t your “gravito-thermal” effect operate in that situation to make the bottom of the column warmer than the top of the column?
        Because assuredly, as you say, “gravity causes the conversion back and forth between gravitational potential energy (PE) and kinetic energy (KE)” in each and every molecule of gas in Feynman’s thought experiment … but that’s exactly what you say causes the “gravito-thermal” effect. So why isn’t the purported G-T effect happening in Feynman’s thermally isolated column?”
        As highlighted above, Feynman’s first thought experiment was to first assume thermal equilibrium of the entire column and thus an isothermal column, but then immediately goes on to explain how gravity/mass/pressure disturbs the column such that there is only a local thermodynamic equilibrium at each isotherm or geopotential height in the atmosphere. That is what creates the 68K semi-linear tropospheric temperature gradient or gravito-thermal GHE.
        “Perhaps if you could explain to us why the “gravito-thermal” effect DOESN’T work in that situation, it would be clearer why you think it works in other situations.”
        The G-T GHE “works” for any long column of gases in a gravitational field that is being inflated by an energy source at the bottom, regardless of GHG composition, has nothing to do with GHG radiative forcing, proven now on 8 rocky planets with observations and theory.

      • hockeyschtick August 31, 2015 at 3:54 pm Edit

        Willis says,

        “What I don’t understand is why you think that is a source of a thermal difference, when Feynman (and Dr. Brown, and I, and many others) agree that a thermally isolated column of gas in a gravity field will be isothermal. Why doesn’t your “gravito-thermal” effect operate in that situation to make the bottom of the column warmer than the top of the column?
        Because assuredly, as you say, “gravity causes the conversion back and forth between gravitational potential energy (PE) and kinetic energy (KE)” in each and every molecule of gas in Feynman’s thought experiment … but that’s exactly what you say causes the “gravito-thermal” effect. So why isn’t the purported G-T effect happening in Feynman’s thermally isolated column?”

        As highlighted above, Feynman’s first thought experiment was to first assume thermal equilibrium of the entire column and thus an isothermal column, but then immediately goes on to explain how gravity/mass/pressure disturbs the column such that there is only a local thermodynamic equilibrium at each isotherm or geopotential height in the atmosphere. That is what creates the 68K semi-linear tropospheric temperature gradient or gravito-thermal GHE.

        Thanks for the reply, HS, but … say what? I find nothing from Feynman saying the either gravity, mass or pressure disturbs the thermally isolated column. I’d need a specific quotation for that claim.

        “Perhaps if you could explain to us why the “gravito-thermal” effect DOESN’T work in that situation, it would be clearer why you think it works in other situations.”

        The G-T GHE “works” for any long column of gases in a gravitational field that is being inflated by an energy source at the bottom, regardless of GHG composition, has nothing to do with GHG radiative forcing, proven now on 8 rocky planets with observations and theory.

        So what you are saying is that the GTE effect works to heat the bottom of a thermally isolated column … but only as long as the bottom of the column is being “inflated by an energy source”???
        Um … er …
        w.
        PS—Please don’t say a theory is “proven”, as nothing can be proven in science. It makes you appear to be an amateur, and I don’t think that’s true at all.
        But it’s worse than that. The “proof” you refer to is merely another one of Johnny von Neumann’s nightmares, a multi-parameter fit to a very, very small dataset, only eight points. Yes, the model fits … and yes, the elephant can wiggle his trunk … and no, that doesn’t mean anything other than “with five parameters I can make him wiggle his trunk”. The model you cite is only the latest in a string of models, all of which claim to do the same thing, and no two of which agree on either variables or the parameters.

      • warrenlb:
        “Work must lead to a warming of the atmosphere”
        Wrong! The Work done by gravity is pulling back the adiabatically expanding, rising, cooling air parcels which are accumulating gravitational PE along the way followed by compression & warming of the air parcels as they exchange their gravitational PE for kinetic energy KE.
        Did you even bother to read the atmospheric thermodynamics lecture slides I provided which PROVE this is the case? Obviously not:
        http://clas-pages.uncc.edu/matt-eastin/files/2014/01/METR3210-adiabatic-process.ppt
        “And then saying GHE does not warm the atmosphere!”
        It doesn’t add any heat, it re-distributes the heat from the only energy source the Sun, making the surface 33K warmer and the top of the troposphere 35K colder (220K) than the equilibrium temperature with the Sun. The thermodynamic Work done is this re-distribution of the heat from the Sun to create the 68K gravito-thermal temperature gradient.
        “And then saying (or implying) that GHE is the effect that warms the climate rather than the greenhouse effect, which you claim doesnt exist (even though its standard science!)”
        The Arrhenius 33C confuses the cause (33C gravito-thermal GHE) with the effect (IR absorption/emission from IR-active gases).
        http://hockeyschtick.blogspot.com/2014/12/why-man-made-global-warming-theory.html
        “And then claiming that both Maxwell and Feynman (!) support GHE when its clear in the works you cited that they don’t.”
        Total BS, you obviously have no comprehension of either work.
        “And then you claim the GHE is included in published in energy budgets AND in college textbooks!”
        I gave you the links to the published energy budgets without GHGs and you chose to ignore them. There are several others published in the peer-reviewed literature since I wrote that post in 2010, but I’m not wasting any more time looking them up for you since you’ve ignored what I’ve already provided.
        I explained all the barometric formulae I used to derive the HS greenhouse equation are in millions of textbooks and have been known since the 1800’s. The HS greenhouse eqn. perfectly reproduces the US Standard Atmosphere. Hundreds The physicists and atmospheric scientists produced the 1976 US Standard Atmosphere derived from these same basic physical principles. That’s another published reference as well which you also choose to ignore.
        “I’m glad you put your GHE ‘theory’ on a website –it’ll be a source of considerable fun throughout the Science community.”
        You’re just an ass with very poor reading comprehension. I’m glad your ignorant comments will be preserved here for all eternity as a “source of considerable fun throughout the science community.”
        This will now be the end of my further engagement with you.

      • Willis:
        “I find nothing from Feynman saying the either gravity, mass or pressure disturbs the thermally isolated column. I’d need a specific quotation for that claim.”
        It’s in your Feynman quote above: “Let us begin with an example [the 1st thought experiment of an isolated isothermal column]: the distribution of the molecules in an atmosphere like our own, but without the winds and other kinds of disturbance.
        The “other kinds of disturbance” is primarily adiabatic expansion/compression of air parcels driven by mass/gravity/pressure, which is what Feynman immediately discusses next and has already been quoted here a couple times. The adiabatic expansion/compression of air parcels driven by mass/gravity/pressure is what creates the 68K temperature gradient or “gravito-thermal GHE” or Boltzmann distribution.
        As Feynman demonstrates, a pure N2 or N2/O2 Boltzmann distribution atmosphere would have essentially the same non-isothermal temperature gradient as our current atmosphere.
        Pure N2 Boltzmann distribution Earth atmosphere also calculated here:
        http://hockeyschtick.blogspot.com/2014/11/why-greenhouse-gases-dont-affect.html
        Willis, why would Feynman write an entire lecture on our atmosphere, the only writing of his on the atmosphere I’m aware of, and not mention one single time radiation, radiative forcing, greenhouse effect, greenhouse gases, CO2, etc., and not do one single radiative transfer calculation if he really thought GHGs had anything to do with the (68K) temperature gradient/Boltzmann distribution? Seems quite implausible.
        “So what you are saying is that the GTE effect works to heat the bottom of a thermally isolated column … but only as long as the bottom of the column is being “inflated by an energy source”???
        Um … er …”
        Mass/gravity/pressure/density do not add any heat, they merely re-distribute the heat from the only source the Sun, more toward the surface which is enhanced 33K and less towards the 220K top of the troposphere (an even larger -35K anti-greenhouse effect) in comparison to the 255K equilibrium temperature with the Sun.
        Obviously the Sun is necessary to inflate the atmosphere, without which the atmosphere would collapse to the surface and thus no atmosphere.
        “PS—Please don’t say a theory is “proven”, as nothing can be proven in science. It makes you appear to be an amateur, and I don’t think that’s true at all.”
        Well, your standard of absolute “proof,” even apparently the physical laws that can be derived mathematically, seems unreasonably high and I don’t know why we’re wasting all this time then pursuing things that will never be “proven.”
        “But it’s worse than that. The “proof” you refer to is merely another one of Johnny von Neumann’s nightmares, a multi-parameter fit to a very, very small dataset, only eight points. Yes, the model fits … and yes, the elephant can wiggle his trunk … and no, that doesn’t mean anything other than “with five parameters I can make him wiggle his trunk”. The model you cite is only the latest in a string of models, all of which claim to do the same thing, and no two of which agree on either variables or the parameters.”
        The Volokin et al paper authors were apparently unaware of any of the 40+ works/papers I’ve cited in this post which derive the same Poisson relation gravito-thermal effect that Maxwell et al have described. Nonetheless, Volokin finds that all of the dimensionless models incorporating GHG concentrations performed far worse than the one model using only pressure & insolation. Further, Volokin et al state,
        “The fact that only one of the investigated twelve non-linear regressions yielded a tight relationship suggests that Model 12 might be describing a macro-level thermodynamic property of planetary atmospheres heretofore unbeknown to science [not true – it’s just the Poisson relation]. A function of such predictive skill spanning the breadth of the Solar System may not be just a result of chance.
        “May not be just a result of chance” with an R2 of 0.9999 I think is about as close as we’re going to get to absolute “proof” in this solar system.
        As an “anti-proof” of the Arrhenius GHE, Prof. David Archer shows it fails miserably in calculating temps of Earth, Venus, and Mars.
        http://hockeyschtick.blogspot.com/2011/08/professor-inadvertently-explains-why.html

      • hockeyschtick August 31, 2015 at 11:26 pm

        Willis:

        “I find nothing from Feynman saying that either gravity, mass or pressure disturbs the thermally isolated column. I’d need a specific quotation for that claim.”

        It’s in your Feynman quote above:

        “Let us begin with an example [the 1st thought experiment of an isolated isothermal column]: the distribution of the molecules in an atmosphere like our own, but without the winds and other kinds of disturbance.”

        The “other kinds of disturbance” is primarily adiabatic expansion/compression of air parcels driven by mass/gravity/pressure, which is what Feynman immediately discusses next and has already been quoted here a couple times. The adiabatic expansion/compression of air parcels driven by mass/gravity/pressure is what creates the 68K temperature gradient or “gravito-thermal GHE” or Boltzmann distribution.

        I’m sorry, my friend, but that is not responsive to my question. Perhaps I wasn’t sufficiently clear. I asked where Feynman said that “either gravity, mass or pressure disturbs the thermally isolated column.” In your quote from Feynman, he specifically says that gravity, mass, or pressure do NOT disturb the thermally isolated column.
        But certainly, the thermally isolated column has mass, has a pressure that varies bottom to top, and is affected by gravity. So let me try rephrasing my question:
        Feynman and Dr. Brown and I and others all agree that the air contained in a thermally isolated column of the atmosphere is isothermal. There is no lapse rate inside the column.
        Now, you claim that the creation of the lapse rate is “driven by mass/gravity/pressure”.
        SO … since the air inside the thermally isolated column has pressure, and has mass, and is affected by gravity, and these are what you claim drive the G-TE, why does your purported gravito-thermal effect NOT heat the air at the bottom of the thermally isolated column, or even create a lapse rate in the thermally isolated column of air?
        w.

      • A further comment:
        hockeyschtick August 31, 2015 at 11:26 pm

        Willis, why would Feynman write an entire lecture on our atmosphere, the only writing of his on the atmosphere I’m aware of, and not mention one single time radiation, radiative forcing, greenhouse effect, greenhouse gases, CO2, etc., and not do one single radiative transfer calculation if he really thought GHGs had anything to do with the (68K) temperature gradient/Boltzmann distribution? Seems quite implausible.

        While I’m reluctant to ascribe motives to Feynman, what he is doing is very specific. He is deriving the theoretical dry-air temperature lapse rate from first principles. As such, I would not expect him to discuss radiative transfer in the slightest. Why should he? Radiation is not necessary in the derivation of the lapse rate from first principles, and since it is not needed it has no place in those calculations anywhere.
        I note that he also doesn’t discuss the effect of water vapor on the lapse rate, again presumably for the same reason—because he is deriving the dry adiabatic lapse rate, not the wet adiabatic lapse rate, and water vapor has no place in those calculations.
        However, the fact that Feynman does not discuss water vapor DOESN’T mean that water has no effect on the lapse rate. We know that water vapor affects the lapse rate, because the measured wet lapse rate is different from the dry lapse rate. But despite that, Feynman doesn’t discuss water vapor. Why not?
        Because it is not needed for the derivation of the lapse rate from first principles.
        Similarly, the fact that Feynman does not discuss radiation DOESN’T mean that radiation has no effect on the lapse rate. You cannot make that assumption. Radiative effects were simply not necessary for his calculation of the lapse rate, because lapse rates exist whether or not there are greenhouse gases in the atmosphere … but that doesn’t mean radiative effects on the lapse rate don’t exist.
        Regards,
        w.

      • Willis: “Feynman and Dr. Brown and I and others all agree that the air contained in a thermally isolated column of the atmosphere is isothermal.”
        Y’all may agree Willis, doesn’t change that Maxwell’s constant T profile equilibrium work has been improved. As I wrote below, later work shows the potential temperature profile introduced as improvement to Maxwell’s constant T profile by Prof. H. Helmholtz in 1888 paper is the max. entropy equilibrium profile. Feynman left the scene before this was generally known (by at least 1998).
        The Helmholtz profile has been shown to have higher entropy at equilibrium than constant T profile and no higher equilibrium entropy T profile is possible for isolated column.
        —–
        HS – “..Volokin finds that all of the dimensionless models incorporating GHG concentrations performed far worse than the one model using only pressure & insolation.”
        Incorrect HS. Volokin 2015 uses the albedo, emissivity radiative balance of the moon at brightness T 197K “applicable” in their eqn. Tna (4c) and the tables. Calculate Tna, find Ts from the graph inclusive of radiative balance.
        In the conclusion they explicitly say their graph Ts/Tna v. surface pressure results depend on “greenhouse gases” for non-airless planets/moons they plotted. Poisson relations come from gravity, radiative balance comes from the thermal work hence gravito-thermal effect. Better is radiative convective atm. (just drop the convective for “airless” objects).

      • Trick,
        thanks for the Helmholtz reference and “The Helmholtz profile has been shown to have higher entropy at equilibrium than constant T profile and no higher equilibrium entropy T profile is possible for isolated column,” thus falsifying the isothermal column by the principle of maximum entropy production, which of course, is analogous to a Boltzmann distribution.
        Could you post a link or quotes on that for Helmholtz?
        “In the conclusion they explicitly say their graph Ts/Tna v. surface pressure results depend on “greenhouse gases” for non-airless planets/moons they plotted. Poisson relations come from gravity, radiative balance comes from the thermal work hence gravito-thermal effect. Better is radiative convective atm. (just drop the convective for “airless” objects).”
        I just re-read the Volokin conclusion and find nothing saying their graph Ts/Tna v. surface pressure results depend on “greenhouse gases” for non-airless planets/moons they plotted. Please quote the specific sentence(s) you are referring to.

      • HS – Simply google this string, use 3rd hit, p.78, eqn.s leading to 3(c), the theta has become known as potential temperature (term from Prof. Bezold actually a few years later in same hit): Helmholtz 1888
        Search Volokin 2015 paper for “greenhouse”. Find specific ref. in: 5. Conclusions, 1st paragraph, p. 43.

      • @Willis: “SO … since the air inside the thermally isolated column has pressure, and has mass, and is affected by gravity, and these are what you claim drive the G-TE, why does your purported gravito-thermal effect NOT heat the air at the bottom of the thermally isolated column, or even create a lapse rate in the thermally isolated column of air?”
        1. It doesn’t add any heat, it merely re-distributes the heat that is there from the only source the Sun. more toward the surface which is “enhanced” 33K and less towards the 220K top of the troposphere (an even larger -35K anti-greenhouse effect) in comparison to the 255K equilibrium temperature with the Sun. No 1st or 2nd law violations whatsoever (unlike the Arrhenius GHE).
        2. There would definitely be a lapse rate in the column. The lapse rate
        dT/dh = -g/Cp
        is dependent only upon gravity and heat capacity at constant pressure, neither of which have anything to do with radiation or radiative forcing. A pure N2 column obviously has a heat capacity Cp and gravity, thus, by definition, must have a lapse rate.
        I calculated the lapse rate for a pure N2 Boltzmann distribution here,
        “Thus, a 100% Nitrogen atmosphere without any greenhouse gases would have an atmosphere with essentially the same dry adiabatic lapse rate (~10C/km) as Earth’s, and the average adiabatic lapse rate in a N2 atmosphere would be higher than Earth’s average 6.5C/km lapse rate due to the lack of water vapor, which increases Cp to decrease the lapse rate and causes cooling.”
        http://hockeyschtick.blogspot.com/2014/11/why-greenhouse-gases-dont-affect.html
        Now of course, if water vapor is added, water vapor has a very high heat capacity, but since dT is inversely related to Cp, that drops the lapse rate by ~1/2 from dry to wet, cooling the surface as I’ve calculated up to a maximum of 25.5C. CO2 also has a somewhat higher Cp than N2 or O2, thus drops the lapse rate as well to cool the surface.
        “We know that water vapor affects the lapse rate, because the measured wet lapse rate is different from the dry lapse rate. But despite that, Feynman doesn’t discuss water vapor. Why not?
        Because it is not needed for the derivation of the lapse rate from first principles.”
        True as I stated above.
        “Similarly, the fact that Feynman does not discuss radiation DOESN’T mean that radiation has no effect on the lapse rate. You cannot make that assumption. Radiative effects were simply not necessary for his calculation of the lapse rate, because lapse rates exist whether or not there are greenhouse gases in the atmosphere … but that doesn’t mean radiative effects on the lapse rate don’t exist.”
        Although you have claimed that radiation somehow controls the lapse rate, I don’t see how that’s possible, so please provide me with both the mathematics and theory demonstrating this claim.
        If Feynman really thought GHGs “trap heat” to increase the temperature of the surface by a huge 33K, don’t you think he would have made one single mention of that in his one and only lecture on the atmosphere? Why did he only use N2 and O2 in derivations in the chapter and none of those all-so-important GHGs that are “trapping heat” in the atmosphere? Why does he quote Maxwell extensively, who also said such a column would not be isothermal? (link above)
        More on Feynman “falsifying” isothermal thought experiment:
        If the temperature is the same at all heights [isothermal thought experiment], the problem is to discover by what law the atmosphere becomes tenuous as we go up. If N is the total number of molecules in a volume V of gas at pressure P, then we know PV=NkT, or P=nkT, where n=N/V is the number of molecules per unit volume. In other words, if we know the number of molecules per unit volume, we know the pressure, and vice versa: they are proportional to each other, since the temperature is constant in this problem [the isothermal thought experiment]. But the pressure is not constant, it must increase as the altitude is reduced, because it has to hold, so to speak, the weight of all the gas above it. That is the clue by which we may determine how the pressure changes with height. If we take a unit area at height h, then the vertical force from below, on this unit area, is the pressure P. The vertical force per unit area pushing down at a height h+dh would be the same, in the absence of gravity, but here it is not, because the force from below must exceed the force from above by the weight of gas in the section between h and h+dh. Now mg is the force of gravity on each molecule, where g is the acceleration due to gravity, and ndh is the total number of molecules in the unit section. So this gives us the differential equation Ph+dh−Ph= dP= −mgndh. Since P=nkT, and T is constant, we can eliminate either P or n, say P, and get
        dndh=−mgkTn
        for the differential equation, which tells us how the density goes down as we go up in energy.”
        I don’t know how Feynman could be more clear that he is just starting with an isothermal assumption and then working through the “problem” that “the pressure is not constant” and the force from mass/gravity F=mg is not constant with height., therefore the column cannot be isothermal. QED

      • Trick,
        Thank you very much for the Helmholtz 1888 reference, it definitely does support the Maxwell/Feynman non-isothermal column and G-T effect, and the eqn. following 3e is very interesting relating P potential temperature to force of gravity, distance from center of gravity, + 1/2 (angular momentum^2*density^2).
        “Search Volokin 2015 paper for “greenhouse”. Find specific ref. in: 5. Conclusions, 1st paragraph, p. 43.”
        That paragraph only says that they looked at greenhouse gas partial pressures/density as one of the variables included in some of the (rejected) 12 models, however, the paper clearly shows model 12 which does not include greenhouse gas partial pressures/density at all was the only model that outperformed the rest by far. In other words, using GHG concentrations in their models made them perform much worse, not better. Thus, GHGs concentrations have nothing to do with the surface T on those 6 planets, solely surface P and insolation.

      • hockeyschtick September 1, 2015 at 8:04 am

        Trick,
        thanks for the Helmholtz reference and “The Helmholtz profile has been shown to have higher entropy at equilibrium than constant T profile and no higher equilibrium entropy T profile is possible for isolated column,” thus falsifying the isothermal column by the principle of maximum entropy production, which of course, is analogous to a Boltzmann distribution.
        Could you post a link or quotes on that for Helmholtz?

        Trick September 1, 2015 at 8:26 am

        HS – Simply google this string, use 3rd hit, p.78, eqn.s leading to 3(c), the theta has become known as potential temperature (term from Prof. Bezold actually a few years later in same hit): Helmholtz 1888

        Simply google WHAT string? Trick, that is easily the most confusing “link” I’ve ever seen. I tried to follow it, figuring that “Helmholtz 1888” was the string, and that gives me Wikipedia. I tried another string, “the Helmholtz profile” and I got nothing except chagrin at being fooled once again by some clever sod into yet another fruitless snipe hunt. Thanks a lot, pal, your reputation in my world just took a steep dive.
        So let me add to HS’s request for a LINK. Since it appears you don’t know what they are, a “link” is the little clicky thingy that you put your mouse cursor over and push the button, and it takes you to the paper in question.
        Why do people want to play cutesy with simple links and send people to do their googling for them? It is YOUR citation, Trick, and it’s not my job to google around looking for some unknown paper.
        w.

      • Willis – See in my note 3rd hit, go to that one NOT 1st wiki (ever). The reason I can’t link directly is the link that results is only a partial link and won’t work in this html environment. HS seems to have found it. Yes correct string is: Helmholtz 1888.
        That potential temperature (theta) profile proven to have higher entropy than constant T at equilibrium, by at least 1998. Post-Feynman lectures.
        ——
        HS: “..model 12 which does not include greenhouse gas partial pressures/density at all”
        Take off the blinders, HS, Model 12 is DERIVED from , plotted from, curve fitted from, their eqn. (4c) which includes greenhouse gas partial pressures, moon applicable albedo, and emissivity. Radiative convective Mars exists right on that plot only because of their much lower Ts est. than every other paper (they list).
        They don’t reject (4c) from GHG parial pressures or (3) at all, use them in their tables.

      • HS – Oh, and see Volokin 2015 eqn. (2) and compare to the first Helmholtz eqn. (above his 3(c)), notice it is the same form. Volokin 2015 goes to the trouble of plotting potential temperature and observes similar shape. If you apply potential temperature curve to Earth atm. find it is usually only 10% off or so from actual ELR, surface up to tropopause. The actual sounding T curve can be duplicated from convective radiative balance for near 0% difference these days.
        Still waiting for you to show Ts calculated from gravity, insolation and mass without resorting to an intercept temperature.

      • Willis the link is here:
        https://books.google.com/books?id=kGBDAAAAIAAJ&pg=PA3&lpg=PA3&dq=Helmholtz+1888&source=bl&ots=oLajNlWYf3&sig=umZmckt-fE17bDcKLBpNOdSU-hI&hl=en&sa=X&ved=0CCYQ6AEwAmoVChMIgf_Jlp7WxwIVh5qICh25xgYs#v=onepage&q=Helmholtz%201888&f=false
        @Trick: “Still waiting for you to show Ts calculated from gravity, insolation and mass without resorting to an intercept temperature.”
        Obviously you cannot do that without taking into account the heat energy provided by the solar insolation. That is the one and only temperature calculation in the HS greenhouse equation, i.e. the 255K equilibrium temperature from the Sun, which is entirely derived from constants. The gravito-thermal effect simply re-distributes heat by doing adiabatic compression/expansion thermodynamic Work on that atmospheric heat energy from the Sun to “enhance” the surface 33K by “removing” 35K from the upper troposphere in comparison to the 255K equilibrium temp.
        Disagree on Volokin and cutting to the chase, they state,
        “Our analysis revealed that GMATs [Global Mean Atmospheric Temperatures] of rocky planets can accurately be predicted over a broad range of atmospheric conditions [0% to over 96% greenhouse gases] and radiative regimes only using two forcing variables: top-of-the-atmosphere solar irradiance and total surface atmospheric pressure [a function of solely of atmospheric mass & gravity].”
        Obviously GHG concentrations have nothing to do with either of the only 2 forcing variables: total surface pressure or solar insolation, thus, GHGs concentrations have nothing to do with surface T.

      • hockeyschtick September 1, 2015 at 10:58 am

        Willis the link is here:
        https://books.google.com/books?id=kGBDAAAAIAAJ&pg=PA3&lpg=PA3&dq=Helmholtz+1888&source=bl&ots=oLajNlWYf3&sig=umZmckt-fE17bDcKLBpNOdSU-hI&hl=en&sa=X&ved=0CCYQ6AEwAmoVChMIgf_Jlp7WxwIVh5qICh25xgYs#v=onepage&q=Helmholtz%201888&f=false

        Thanks, HS. At least someone here knows how to post a link …
        However, I read the link and I see nothing in it about how a column of thermally isolated air will have other than an isothermal profile. Trick claims he see it. If so, surely he can point out the flaws in Feynman and Dr. Brown’s proofs that the profile is indeed isothermal.
        Best regards to you both,
        w.

      • Yes HS, as you show for 255K, need insolation, gravity, mass AND that one radiative balanced intercept T measured or observed (or estimated). Gravito-thermal effect. GHE. ATE. Radiative convective equilibrium is first principle best. Call it what you will.
        The GHG partial pressure concentrations are carried into the curve fit process from eqn. (4c). This works so well since CO2 effect logarithmically declines as ppm increases for fixed insolation. The redistribution happens naturally as the upper reaches are “shaded” by near surface thicker optical depth from its increasing opacity.

      • Trick September 1, 2015 at 10:16 am

        Willis – See in my note 3rd hit, go to that one NOT 1st wiki (ever). The reason I can’t link directly is the link that results is only a partial link and won’t work in this html environment. HS seems to have found it. Yes correct string is: Helmholtz 1888.

        I went to the damn third hit, just like you said, and IT WAS TO WIKI. This is why I hate it when people try to pull your kind of vague handwaving on me, saying “Just go to google blah blah blah”. It’s pretty pathetic when you have to depend on HS to find your own freakin’ citation …
        In any case, I read it and I find nothing that invalidates either Feynman’s or Dr. Brown’s separate proofs that the column is isothermal. Surely with your insight into Helmholtz you can explain exactly where two such gifted men got it 100% wrong, and point to the exact flaw in their proofs …
        w.

      • hockeyschtick September 1, 2015 at 8:51 am

        @Willis: “SO … since the air inside the thermally isolated column has pressure, and has mass, and is affected by gravity, and these are what you claim drive the G-TE, why does your purported gravito-thermal effect NOT heat the air at the bottom of the thermally isolated column, or even create a lapse rate in the thermally isolated column of air?”
        1. It doesn’t add any heat, it merely re-distributes the heat that is there from the only source the Sun. more toward the surface which is “enhanced” 33K and less towards the 220K top of the troposphere (an even larger -35K anti-greenhouse effect) in comparison to the 255K equilibrium temperature with the Sun. No 1st or 2nd law violations whatsoever (unlike the Arrhenius GHE).
        2. There would definitely be a lapse rate in the column. The lapse rate
        dT/dh = -g/Cp
        is dependent only upon gravity and heat capacity at constant pressure, neither of which have anything to do with radiation or radiative forcing. A pure N2 column obviously has a heat capacity Cp and gravity, thus, by definition, must have a lapse rate.

        Huh? Feynman and Dr. Brown have both proven, not asserted but shown through a thought experiment, that the thermally isolated column of air will be isothermal. This means it will have no thermal lapse rate, as the temperature doesn’t change with height, so dT/dh will be zero.
        If you think otherwise, you need to point out the flaw in either Dr. Brown or Feynman’s proof that the column is isothermal … good luck with that, I await your deconstruction of either man’s proof.
        My regards to you,
        w.

      • Willis – Eqn.s leading up to Helmholtz 3 (c) show T(z)/To = fn(P/Po). If isothermal, then the potential temperature eqn.s would show 1=fn(P/Po) i.e. T(z)=To at equilibrium. They do not. You should be able to see this on your own.
        There are no flaws in Dr. Brown’s or Dr. Feynman’s work, that I see anyway. The equilibrium constant T work was improved on and a higher entropy T profile was found to be Helmholtz’ potential temperature profile with no other higher entropy profile found to be possible, by 1998 at least.

      • Thanks for the reply, Trick. You say:
        Trick September 1, 2015 at 11:26 am

        Willis – Eqn.s leading up to Helmholtz 3 (c) show T(z)/To = fn(P/Po). If isothermal, then the potential temperature eqn.s would show 1=fn(P/Po) i.e. T(z)=To at equilibrium. They do not. You should be able to see this on your own.

        If I understand you, this means that you are claiming that a thermally isolated column is NOT isothermal.
        Then you say:

        There are no flaws in Dr. Brown’s or Dr. Feynman’s work, that I see anyway. The equilibrium constant T work was improved on and a higher entropy T profile was found to be Helmholtz’ potential temperature profile with no other higher entropy profile found to be possible, by 1998 at least.

        However, both Dr. Brown and Dr. Feynman prove by a thought experiment that the column IS isothermal, and you say there is no problem with their work.
        Could you please resolve this contradiction?
        Best to you,
        w.

      • “Huh? Feynman and Dr. Brown have both proven, not asserted but shown through a thought experiment, that the thermally isolated column of air will be isothermal. This means it will have no thermal lapse rate, as the temperature doesn’t change with height, so dT/dh will be zero.”
        “Proven” by a thought experiment? I thought you just said “nothing can ever be proven in science” and “to say so makes you sound like an amateur”???
        That’s what you claim Dr. Brown has proven, but by no means true for Feynman.
        @Willis says dT/dh = 0 = -g/Cp for a column of pure N2 in a gravitational field with a heat source at the bottom to inflate the pure N2 atmosphere.
        You’re effectively saying that g is 0, thus contradicting yourself that is column is in a gravitational field. Since the lapse rate dT/dh by definition for any composition of gases without or without GHGs is
        -g/Cp
        the lapse rate absolutely cannot be zero in a pure N2 column, since N2 is obviously affected by gravity and has a Cp. QED.
        As Feynman describes, ONLY using a pure N2 example without any GHGs whatsoever, there is a Boltzmann distribution of pressure isotherms, i.e. the “gravito-thermal GHE” non-isothermal temperature gradient.
        It is thus easy to calculate the lapse rate in a pure N2 Boltzmann distribution atmosphere the lapse rate:
        http://hockeyschtick.blogspot.com/2014/11/why-greenhouse-gases-dont-affect.html
        Thus, Willis, you are effectively claiming that a Boltzmann distribution in a gravitational field of a non-GHG cannot exist. Sorry, that’s just plain incorrect and also violates the principle of maximum entropy production, which is essentially what a Boltzmann distribution represents. This is also what Trick/Helmholtz is referring to, a column in a gravity field must stratify (Helmholtz’s word) by pressure/density in order to obtain maximal entropy. An isothermal column in a gravity field as you and Dr. Brown claim would require an impossible decrease of entropy, thus is falsified.
        Please provide as requested some math or theory why you claim GHG radiative forcing somehow affects the -g/Cp lapse rate.
        “If you think otherwise, you need to point out the flaw in either Dr. Brown or Feynman’s proof that the column is isothermal … good luck with that, I await your deconstruction of either man’s proof.”
        I guess you missed this comment, as I have already done here (and in other comments):
        http://wattsupwiththat.com/2015/08/29/where-is-the-top-of-the-atmosphere-toa/#comment-2018772

      • Willis – ..and you say there is no problem with their work.”
        You routinely say quote exact words. I used, as did you, the word “flaw”. Dr. Feynman’s and Dr. Brown’s reasoning (that I have read) are not flawed as I wrote, their reasoning is at least reasonably sound that I can see, comparable to following J.C. Maxwell (as HS repeatedly points out).
        Prof. Helmholtz came along 1888 and built on Maxwell’s 1870’s work introducing the concept of potential temperature profile T(z)/To=fn(P/Po) non-constant T at equilibrium. After Dr. Feynman checked out, this profile was found to produce higher entropy in an isolated column than constant temperature profile. Science progresses like a cluttered house kept by a sloven.
        It is easy concept but some robust work to resolve the “problem.”
        Take 1 sq. meter 1976 standard column of air say z=0 to 200mb (call it TOA for this exercise near midlatitude tropopause). Use Maxwellian equilibrium reasoning at T(z)=To, call To the standard T at z=0.0, it was voted long ago to be 15C.
        T=15C for all z up to 200mb. At this thought experiment Maxwellian equilibrium, compute the entropy in the column as E1. I have never seen Dr. Feynman or Dr. Brown do that, maybe I missed it.
        Then set Prof. Helmholtz’ T profile T(z)/To = fn(P(z)/Po) and do the same entropy calculation at equilibrium. Get entropy E2.
        Find E2 will be higher than E1 if properly done. Then by 1998 calculus was used to prove E2 is actually the highest possible equilibrium entropy therefore ruling out any other profile. Science progresses.

      • Willis – ” went to the damn third hit, just like you said, and IT WAS TO WIKI.”
        I feel your damn pain Willis.
        Off topic, you TOA interested thermodynamicists cover your ears. Like many others, I have been swept up into MS 10. From MS 7 as you know = recently. In MS 7, I had stopped using IE in that version as it had become too… shall we say quirky, slow, baffling, name your poison. I went to Chrome 100% and that fixed my need for early happy hours.
        Now to be fair, I am back in the game using MS 10 and giving newborn Edge a chance. I am here to tell Willis, Edge did not give the full link to copy and paste, it was abbeviated AND would not work in HTML Had I done that, Willis would have been equally tortured.
        Wiki was indeed the first link in Edge (the ref.s could have been used with some pain) and not the third, which was the book of historical papers. HS plowed on regardless, & was able to supply the long link, thx, pop a cold one. This exercise added torture to Willis’ day. Needing that early happy hour like me.
        I am putting this down as the first Edge catastophe. There have been many other new jalopy quirks added in, many nuances changed to just add frustration, still many removed during my test drive period. not willing to head to Chrome as yet. I might check if it gives the long link apparently abbreviated by MS Edge.
        Moral: Can’t win Willis, happy hour is the cause of, and cure for, many “problems.” It will not cure “flaws”.
        NB: I made a double post here the other day, figured that was due the WordPress looking for certain impolitic words & the mod.s finally fished them out. Maybe it was Edge having a burp with WordPress. Ok, happy hour is almost gone, out.

      • @Hockeyschtick
        1) GHE ignores the results of SF calculation and the 1st Law.
        SF calculations by standard science –by ALL scientists in the field – are consistent only with a significant elevation of planetary temperature –about 33C –and the planet’s corresponding IR radiation, yielding the back-radiation consistent with GE, not GHE.
        2) Your ‘GHE’ term appears nowhere in published energy budgets or in any college textbooks. You are claiming GHE, but the term ‘GHE’ appears NOWHERE on those charts — so you are apparently re-interpreting GE as YOUR GHE — so can deny GE!
        2) Since no other scientists make your claims, the only way you’re going to gain credibility is by publishing in a peer-reviewed journal. I won’t hold my breath.

      • hockeyschtick says, September 1, 2015 at 12:58 pm:
        “@Willis says dT/dh = 0 = -g/Cp for a column of pure N2 in a gravitational field with a heat source at the bottom to inflate the pure N2 atmosphere.
        You’re effectively saying that g is 0, thus contradicting yourself that is column is in a gravitational field. Since the lapse rate dT/dh by definition for any composition of gases without or without GHGs is
        -g/Cp
        the lapse rate absolutely cannot be zero in a pure N2 column, since N2 is obviously affected by gravity and has a Cp. QED.”

        HS, the derived “g/Cp” expression is specifically defined for the “dry adiabatic lapse rate (DALR)”, not ANY other lapse rate. Hence, it ONLY applies to a packet of air moving vertically in the atmospheric column, without condensation taking place inside the packet. Which means there has got to be (dry) convection going on, which requires active heating at the bottom and cooling at the top of the column through which the air packet travels. Such active heating/cooling does not occur – by definition – inside a thermally isolated column, and so there will be no convective currents, no DALR and no g/Cp.
        The real tropospheric lapse rate as observed is hardly ever a perfect DALR from surface to tropopause. The actual temperature gradient, the “environmental lapse rate (ELR)”, is determined by the balance between radiation and convection (including the release of latent heat of vaporisation).
        There is no escape, I’m afraid, radiation is an integral part of the ELR.

      • Kristian – “Such active heating/cooling does not occur – by definition – inside a thermally isolated column, and so there will be no convective currents”
        True at max. enrtropy only; prior to hitting that point (“heat death”) the initial conditions could have a colder layer being warmed from next layer below and that’s all you need for convection to ensue in a gravity field.
        A packet on the DALR does not move by definition since the assumption it is hydrostatic. The ones moving by being differentially warmed at the surface are not on the DALR until they achieve hydrostatic equilibrium by radiating and conducting to surroundings. Radiative convective equilibrium ensues.

    • A question: What is the approximate average temperature of the earth’s climate?
      And: If the earth had no atmosphere, what would be the average temperature of Earth?

      • If the earth had no atmosphere, what would be the average temperature of Earth?

        If the Earth had no atmosphere, it had no oceans either. There were no water, clouds or eucaryote life. So albedo needed to be estimated. Also there were no convective heat transfer, so polar regions were bit cold. The question is somewhat speculative.
        Anyway, I find HS a little bit disturbing. He presents an equation and claims he can calculate the surface temperature – and I’m embarrassed by the chutzpah he has.

    • @hockeyshtick and @Trick
      To paraphrase: ‘The gas laws are operative on Venus.’ Agreed, and obvious. But it says nothing as to WHY T, P, and density have the values as measured, since the three variables merely track each other according to the gas law.
      If one wants to establish WHY, the planet’s heat exchange relationship with space must be examined. And a calculation of the planet’s equilibrium temperature assuming no atmosphere, vs its measured equilibrium temperature (with atmosphere), should give the approximate value of planetary temperature elevation caused by the classic greenhouse effect.
      It seems you are familiar with the SB equation. Have either of you run such a calculation?

      • warrenlb,
        No I do not agree and tried to post comments there explaining why, but ATTP deleted most of my inconvenient comments. That site is just like SkS where they delete, snip, change comments that are inconvenient, so I will never waste time commenting at either of those sites. They have no interest in finding the truth.

      • hockeyschtick,
        Any blog that routinely deletes science-based comment is simply not a science site. Why bother with them?
        And warrenlb says:
        A question: What is the approximate average temperature of the earth’s climate?
        A fuzzy-headed question, since climate and temperature are two differnt things.

      • Warren,
        Had you read his comments, you’d see that HS is convinced that the so-called GHE is actually an effect of the mass of a gaseous atmosphere, not its chemical composition, ie not a result of the “reradiative” properties of GHGs, ie molecules compounded of different atoms, like water and carbon dioxide, but simply of the gravitational effect of all the gas molecules in the atmospheres of rocky planets and moons. whether of the same, eg O2 and N2, or different elements.
        Please correct me if wrong, HS.

      • Yes Gloria that’s right, and several of the greatest physicists in history have described what I’m calling the “gravito-thermal GHE” including Maxwell, Clausius, Carnot, Boltzmann, Feynman.
        Here’s Feynman explaining the gravito-thermal GHE in a pure N2/O2 Earth atmosphere with statistical mechanics, also quoting Maxwell on this extensively, and without any consideration of greenhouse gases or radiative forcing whatsoever:
        http://hockeyschtick.blogspot.com/2015/07/feynman-explains-how-gravitational.html

      • @Hockeyschtick
        Sorry, but your argument that gravity warms the atmosphere is bad Physics, and a fundamental misinterpretation of Clausius and Feynman:
        1) You seem to think Feynman says gravity warms the planet by doing work on the atmosphere. Feyman says no such thing–he merely derives a method for calculating atmospheric pressure as a function of altitude.
        2) Gravity cannot continuously warm the atmosphere because such warming requires work be continuously done on the atmosphere. But gravity is force, not work. Gravity doesn’t perform work on things for free without YOU first providing energy or work to battle gravity. The argument that gravity warms the atmosphere is a fundamental misinterpretation of Clausius and or Feynman.
        3) The molecular interchange of kinetic energy in the atmosphere — conduction and convection — is all internal to the atmosphere. NET heating of the atmosphere cannot occur by conduction or by convection since there’s no external mass in outer space in contact with the atmosphere.
        4) Only thermal radiation can transport heat to or from the Earth’s system –and those are Sun’s rays IN, and infrared radiation OUT from earth to outer space (plus some reflected radiation of the sun back to space).
        5) A discussion which leads to the greenhouse effect — the phenomenon of certain gases — mainly water vapor, CO2, methane, nitrous oxides, fluorocarbons and sf6– absorbing and re-radiating a portion of IR thermal radiation trying to leave earth — back to earth. A proven phenomenon known and studied by a long list of scientists and explained to you on this forum by several — and is the mechanism which sustains Earth’s temperature 33C warmer than its equilibrium temperature if its atmosphere had no greenhouse gases– since it is the only way the atmosphere can be warmed beyond its no-GHG equilibrium temperature.
        The effects you describe are only internal to the planetary system and therefore cannot add net heat to the planetary system.

      • @hockeyschtick
        ‘Nope’ is not a scientific response, nor is a link to your own blogs. Neither Feynman, Maxwell nor any other Scientist ever developed a theory in which gravity controls the temperature of e atmosphere. The ‘gravito thermo’ phenomenon exists in only one place…your mind. You’ll not find it in any college textbooks, nor in any science books…because it’s just baloney.

      • warrenlb – “Have either of you run such a calculation?”
        Many times, using the TOA as CERES et. al. interannual orbit.
        As far as terms, a radiative convective balance for an atmosphere that’s been around awhile seems superior to the poorly worded GHE. The terms gravito-thermal effect (GTE) or atmosphere thermal effect (ATE) are to me closer but not quite first principle as radiative convective atmosphere.

      • warrenlb.
        Nope. Absolutely False once again:
        Feynman Lectures: Statistical Mechanics: Vol 1 Chapter 40
        40–2The Boltzmann law
        Here we note the interesting fact that the numerator in the exponent of Eq. (40.1) is the [gravitational] potential energy of an atom. Therefore we can also state this particular law as: the density at any point is proportional to
        e−the potential energy of each atom/kT.
        That may be an accident, i.e., may be true only for this particular case of a uniform gravitational field. However, we can show that it is a more general proposition. Suppose that there were some kind of force other than gravity acting on the molecules in a gas. For example, the molecules may be charged electrically, and may be acted on by an electric field or another charge that attracts them. Or, because of the mutual attractions of the atoms for each other, or for the wall, or for a solid, or something, there is some force of attraction which varies with position and which acts on all the molecules. Now suppose, for simplicity, that the molecules are all the same, and that the force acts on each individual one, so that the total force on a piece of gas would be simply the number of molecules times the force on each one. To avoid unnecessary complication, let us choose a coordinate system with the x-axis in the direction of the force, F.
        In the same manner as before, if we take two parallel planes in the gas, separated by a distance dx, then the force on each atom, times the n atoms per cm³ (the generalization of the previous nmg), times dx, must be balanced by the pressure change: Fndx=dP=kTdn. Or, to put this law in a form which will be useful to us later,
        F=kTddx(lnn).(40.2)
        For the present, observe that −Fdx is the work we would do in taking a molecule from x to x+dx, and if F comes from a potential, i.e., if the work done can be represented by a [gravitational] potential energy at all, then this would also be the difference in the [gravitational] potential energy (P.E.). The negative differential of [gravitational] potential energy is the work done, Fdx, and we find that d(lnn)=−d(P.E.)/kT, or, after integrating,
        n=(constant)e−P.E./kT.(40.3)
        Therefore what we noticed in a special case turns out to be true in general. (What if F does not come from a potential? Then (40.2) has no solution at all. Energy can be generated, or lost by the atoms running around in cyclic paths for which the work done is not zero, and no equilibrium can be maintained at all. Thermal equilibrium cannot exist if the external forces on the atoms are not conservative.) Equation (40.3), known as Boltzmann’s law, is another of the principles of statistical mechanics: that the probability of finding molecules in a given spatial arrangement varies exponentially with the negative of the potential energy of that arrangement, divided by kT.
        More here: http://hockeyschtick.blogspot.com/2015/07/feynman-explains-how-gravitational.html
        And then read this lecture on atmospheric thermodynamics which clearly demonstrates how gravity does continuous thermodynamic Work on the atmosphere:
        http://clas-pages.uncc.edu/matt-eastin/files/2014/01/METR3210-adiabatic-process.ppt
        No warrenlb, it is ONLY YOU who thinks the ” ‘gravito thermo’ phenomenon exists in only one place…your mind. You’ll not find it in any college textbooks, nor in any science books…because it’s just baloney.”
        Pathetic. This phenomenon have been known since Maxwell described it in his 1872 book Theory of Heat. Look it Up.

      • warrenlb says:
        ‘Nope’ is not a scientific response, nor is a link to your own blogs.
        But Hockeyschtick’s link to Prof. Feynman does provide a scientific response, and one that you avoided addressing. If you disagree with Feynman, post your reasons here. But if you don’t produce a counter argument, then as they say: silence is concurrence. Feynman is right, thus your argument fails.
        And speaking of planets in general, besides Earth the other planets in our Solar System are also warming concurrently. What do you think is the common denominator causing that warming?
        Is it CO2? Or is it the Sun? Tell us, warrenlb.
        Or do you believe it is just a random, unexplained coincidence?

      • dbstealey August 31, 2015 at 12:02 pm

        But Hockeyschtick’s link to Prof. Feynman does provide a scientific response, and one that you avoided addressing. If you disagree with Feynman, post your reasons here. But if you don’t produce a counter argument, then as they say: silence is concurrence. Feynman is right, thus your argument fails.

        HS and db, I don’t see anywhere that anything Feynmann said supports the “gravito-thermal” hypothesis. To the contrary, what I find refutes the hypothesis.
        What Feynmann said in the reference HS cited, inter alia, was this (emphasis mine):

        Let us begin with an example: the distribution of the molecules in an atmosphere like our own, but without the winds and other kinds of disturbance. Suppose that we have a column of gas extending to a great height, and at thermal equilibrium—unlike our atmosphere, which as we know gets colder as we go up. We could remark that if the temperature differed at different heights, we could demonstrate lack of equilibrium by connecting a rod to some balls at the bottom (Fig. 40–1), where they would pick up 12kT from the molecules there and would shake, via the rod, the balls at the top and those would shake the molecules at the top. So, ultimately, of course, the temperature becomes the same at all heights in a gravitational field.

        Note that this is the same proof, in a slightly different form, as given by Dr. Robert Brown in his evisceration of another “gravito-thermal” hypothesis, that of Hans Jelbring.
        And given that the temperature is the same at all heights as Feynmann and Dr. Brown demonstrate … where is the work that you claim gravity is doing when you say “gravity does continuous thermodynamic Work on the atmosphere”. If gravity were actually doing continuous work we’d see a thermal difference top-to-bottom in a thermally isolated column of air in a gravity field … but both Feynmann and Dr. Brown have conclusively proven that that is not the case.
        w.

      • The temperature of the troposphere generally decreases as altitude increases. The tropopause is a temperature inversion, such that the stratosphere is stratified, with warmer layers higher up and cooler layers farther down. Then in the mesosphere, temperature once again decreases as the altitude increases.
        I suppose that these observations could be used to support HS’ hypothesis.

      • Willis, please re-read that whole Feynman chapter, your quote is at the beginning of the chapter of Feynman’s thought experiment and he first proposes a hypothetical isothermal atmosphere. If you just continue reading the chapter you will find that Feynman crushes that false thought experiment stating our atmosphere “is not isothermal” and he is taking about a PURE N2/O2 atmosphere only, and never ever mentions a single greenhouse gas, radiation, radiative forcing, “greenhouse effect,” etc.
        Instead, he talks about how gravity causes the conversion back and forth between gravitational potential energy (PE) and kinetic energy (KE), which is what causes (my term) the “gravito-thermal GHE” or 68K tropospheric temperature gradient. Nothing to do with greenhouse gases or radiative forcing.
        I have highlighted portions of the chapter which clearly show that this is the case:
        http://hockeyschtick.blogspot.com/2015/07/feynman-explains-how-gravitational.html

      • Willis please also read the quote above from Feynman:
        “observe that −Fdx is the work we would do in taking a molecule from x to x+dx, and if F comes from a potential, i.e., if the work done can be represented by a [gravitational] potential energy at all, then this would also be the difference in the [gravitational] potential energy (P.E.). The negative differential of [gravitational] potential energy is the work done, Fdx,…”
        Clearly, he is talking about the work done by gravity against the adiabatic expansion, rising, cooling of air parcels (collecting gravitational PE along the way), followed by the adiabatic compression, falling, warming of the air parcel (converting gravitational PE back to kinetic energy (KE)).
        That is the gravito-thermal GHE.
        Very simple, and known since at least Maxwell’s book Theory of Heat 1872. The only radiative forcing that enters the picture is that from the Sun, the only source of energy; there is no “radiative forcing” from GHGs creating a 33C increase in temperature, it is solely gravito-thermal.

      • Gloria says “I suppose that these observations could be used to support HS’ hypothesis.”
        Yes, but it was really the 1976 US Standard Atmosphere mathematical model, the only atmospheric model in existence that has been verified with millions of observations, that proved the atmospheric temperature profile from the surface to the edge of space is a linear function of kinematic viscosity, which has absolutely nothing to do with GHG concentrations or GHG radiative forcing whatsoever:
        http://2.bp.blogspot.com/-0t1dn_7gtb0/VIn1YHc-nmI/AAAAAAAAHBw/Lfi-SE7fukM/s1600/Fullscreen%2Bcapture%2B12112014%2B111709%2BAM.jpg
        http://hockeyschtick.blogspot.com/2014/12/why-atmospheric-temperature-is-linear.html

      • Willis – “And given that the temperature is the same at all heights as Feynmann and Dr. Brown demonstrate…”
        HS – “..the gravito-thermal GHE.Very simple, and known since at least Maxwell’s book Theory of Heat 1872.”
        Better to just write gravito-thermal effect (GTE). Radiative convective is best.
        Indeed Maxwell argued that constant T from say surface about 1bar to 200mb in isolated column in gravity field would be the equilibrium temperature.
        Even the grand-master’s work can be improved upon. Prof. Helmholtz in his 1888 paper advanced Maxwell’s theory by introducing the concept of potential temperature based on Poisson’s 1823 paper introducing the gas law relations.
        Turned out the max. entropy in the constant T column is less than the eventual higher entropy in the T profile given by the potential temperature equation at thermodynamic equilibrium. Both Chilingar and Volokin papers still show the concept of potential temperature. Proving this was achieved after Dr. Feynman left the scene so won’t find it in his lectures.

      • @Hockeyschtick
        Questions for you:
        1) As Eschenbach says, Feynman’s papers doesn’t support ‘Gravito-thermo theory — it refutes it. Then you retreat to cite Maxwell as putting forth the theory. I studied Maxwell in University, and he claims no such theory.
        So cite a reference that lays out Maxwell’s support for your theory.
        2) You disputed my claim that your theory appears in College Textbooks. Give us a college textbook citation, please.
        3) All published energy budget diagrams for Earth (or any planet) are notable for one thing –your gravito-thermo effect appears nowhere. Why not?
        4) Since Gravity is a force field, not an energy field, how do you explain how GHE adds heat to the atmosphere?
        5) And if GHE adds heat to the atmosphere, why hasn’t Earth warmed continuously since it first had an atmosphere?
        6) And if the elevation of Earths temperature is a constant 33C (or whatever value you claim), how can GHE be continuously adding heat energy to the atmosphere?
        Answer in concise sentences, if you would. These are not complicated questions.

      • warrenlb, unfortunately this thread has gotten split up. My replies to Willis are also above:
        http://wattsupwiththat.com/2015/08/29/where-is-the-top-of-the-atmosphere-toa/#comment-2018376
        “@Hockeyschtick
        Questions for you:
        1) As Eschenbach says, Feynman’s papers doesn’t support ‘Gravito-thermo theory — it refutes it. Then you retreat to cite Maxwell as putting forth the theory. I studied Maxwell in University, and he claims no such theory. So cite a reference that lays out Maxwell’s support for your theory.”
        False. See replies above. The “gravito-thermal GHE” is my term for describing the non-isothermal 68K temperature gradient of the troposphere. See what Maxwell wrote in 1872 Theory of Heat quoted here, which basically describes why the 19823 Poisson relation explains why our atmosphere, regardless of GHG concentrations, is not isothermal:
        http://hockeyschtick.blogspot.com/search?q=maxwell+poisson
        “2) You disputed my claim that your theory appears in College Textbooks. Give us a college textbook citation, please.”
        Please. Every single meteorology text on the planet since the 1800’s describes the Poisson relation, 1st law of thermo, ideal gas law, Newton’s second law, the atmospheric Carnot heat engine of adiabatic expansion/compression. THOSE are all the physical laws you need to completely derive the gravito thermal GHE. Add the Stefan-Boltzmann law to calculate the solar insolation [only, not for GHG RF] and you’re done.
        The very simple gravito-thermal GHE has been “hiding in plain view” since the 1800’s!
        “3) All published energy budget diagrams for Earth (or any planet) are notable for one thing –your gravito-thermo effect appears nowhere. Why not?”
        Not true. Here are Earth energy diagrams which have no GHG radiative forcing whatsoever! (One of my first posts way back in 2010):
        http://hockeyschtick.blogspot.com/2010/08/earth-energy-budgets-without-greenhouse.html
        The Trenberth cartoon is fiction, debunked hundreds of times on my blog. Type “Trenberth” in search box.
        “4) Since Gravity is a force field, not an energy field, how do you explain how GHE adds heat to the atmosphere?”
        Gravity is indeed a conservative force F=mg, which Feynman uses in his lecture excerpt above, however it does not add any heat anywhere. The gravito-thermal GHE merely redistributes the heat from the only source the Sun more towards the surface (increases 33K) and less towards the top of the troposphere (decreases 35C from the -18C equilibrium temp w the Sun). No violation of 1st or 2nd law whatsoever.
        In contrast, the Arrhenius GHE grossly violates both the 1st and 2nd laws!
        “5) And if GHE adds heat to the atmosphere, why hasn’t Earth warmed continuously since it first had an atmosphere?”
        It doesn’t “add heat” as I just explained.
        “6) And if the elevation of Earths temperature is a constant 33C (or whatever value you claim), how can GHE be continuously adding heat energy to the atmosphere?”
        It doesn’t “add any heat” as I just explained.

      • @hockyschtick
        You contradict yourself:
        First saying that gravity does Work on the atmosphere — when Work must lead to a warming of the atmosphere
        And then saying GHE does not warm the atmosphere!
        And then saying (or implying) that GHE is the effect that warms the climate rather than the greenhouse effect, which you claim doesnt exist (even though its standard science!)
        And then claiming that both Maxwell and Feynman (!) support GHE when its clear in the works you cited that they don’t.
        And then you claim the GHE is included in published in energy budgets AND in college textbooks!
        I’m glad you put your GHE ‘theory’ on a website –it’ll be a source of considerable fun throughout the Science community.

  20. There is a serious problem in using US Standard Atmosphere 76 (USST 76), because its absolute water content is only 1.43 prcm (precipitated water in centimetres). The real value of the average global atmosphere is 2.6 prcm. Kiehl & Trenberth used the USST 76 as a climate model in calculating the contribution of CO2 in the GH phenomenon and they got the result 26 % which is the mostly referred value but it is highly overestimated. The real value is in the range of 9-11 % depending on the spectral calculation formula for water. In the present day atmosphere the real strength of H2O in respect to CO2 is about 15:1.
    The irony of this case is that the IPCC model of the positive feedback of water would not work without this relationship. IPCC says that firstly GH gases have increased the temperature by 0.42 degrees from the year 1750 and because the relative humidity stays constant, the increased water content by 2.3 % increases the temperature again by 0.42 degrees – totally about 0.85 degrees in 2011. This means that the increase of water by 2.3 % has the same warming impact as the increase of CO2 by 35 %. By using complicated spectral analyses the same result can be achieved. More information: ClimatExam
    Because this would destroy the image of CO2 as a very strong GH gas, IPCC does not want to manifest it but to hide it. But there it is. Of course the assumption of the constant RH is wrong as anybody can see from the global RH measurements. Very probably the opposite is true that there is a negative water feedback and it works well, because water is a so strong GH gas.
    The spectral analyses show that the CO2 impact does not increase after the height of 2 kilometres but its relative portion in the GH phenomena decreases slightly thereafter because ozone in the stratosphere increases the total GH effect. In the radiation calculations the limit of stratosphere is good enough because thereafter the amount of material is so small that its impact is very small indeed.

    • The concentration of water vapor in the air falls off not only with latitude but of course with altitude as well.
      However this 2010 paper, which created fear in the alarmosphere, showed that stratospheric water vapor increased from c. 1980 to 2000, then fell in this century.
      http://www.sciencemag.org/content/327/5970/1219.abstract
      Contributions of Stratospheric Water Vapor to Decadal Changes in the Rate of Global Warming
      Susan Solomon1, Karen H. Rosenlof1, Robert W. Portmann1, John S. Daniel1, Sean M. Davis1,2, Todd J. Sanford1,2, Gian-Kasper Plattner3
      Stratospheric water vapor concentrations decreased by about 10% after the year 2000. Here we show that this acted to slow the rate of increase in global surface temperature over 2000–2009 by about 25% compared to that which would have occurred due only to carbon dioxide and other greenhouse gases. More limited data suggest that stratospheric water vapor probably increased between 1980 and 2000, which would have enhanced the decadal rate of surface warming during the 1990s by about 30% as compared to estimates neglecting this change. These findings show that stratospheric water vapor is an important driver of decadal global surface climate change.

  21. There is a serious problem in using US Standard Atmosphere 76 (USST 76), because its absolute water content is only 1.43 prcm (precipitated water in centimetres). The real value of the average global atmosphere is 2.6 prcm. Kiehl & Trenberth used the USST 76 as a climate model in calculating the contribution of CO2 in the GH phenomenon and they got the result 26 % which is the mostly referred value but it is highly overestimated. The real value is in the range of 9-11 % depending on the spectral calculation formula for water. In the present day atmosphere the real strength of H2O in respect to CO2 is about 15:1.
    The irony of this case is that the IPCC model of the positive feedback of water would not work without this relationship. IPCC says that firstly GH gases have increased the temperature by 0.42 degrees from the year 1750 and because the relative humidity stays constant, the increased water content by 2.3 % increases the temperature again by 0.42 degrees – totally about 0.85 degrees in 2011. This means that the increase of water by 2.3 % has the same warming impact as the increase of CO2 by 35 %. By using complicated spectral analyses the same result can be achieved.
    More information in the paper “The potency of Carbon Dioxide (CO2) as Greenhouse Gas”
    Because this would destroy the image of CO2 as a very strong GH gas, IPCC does not want to manifest it but to hide it. But there it is. Of course the assumption of the constant RH is wrong as anybody can see from the global RH measurements. Very probably the opposite is true that there is a negative water feedback and it works well, because water is a so strong GH gas.
    The spectral analyses show that the CO2 impact does not increase after the height of 2 kilometres but its relative portion in the GH phenomena decreases slightly thereafter because ozone in the stratosphere increases the total GH effect. In the radiation calculations the limit of stratosphere is good enough because thereafter the amount of material is so small that its impact is very small indeed.

  22. Spherical Surface area
    6,371 Radius, km
    15.8 Atmos Ht, km
    6,387 km
    A = 4 * PI() * r^2
    5.13E+14 sq m
    Relative to the radius of the earth ToA is paper thin .25%. Much blather about zip.
    Three Legged Stool of CAGW: 1) Anthropogenic 2) Radiative Forcing 3) GCMs
    Leg the 2nd
    Radiative forcing of CO2 warming the atmosphere, oceans, etc.
    If the solar constant is 1,366 +/- 0.5 W/m^2 why is ToA 340 (+10.7/- 11.2)1 W/m^2 as shown on the plethora of popular heat balances/budgets? Collect an assortment of these global energy budgets/balances graphics. The variations between some of these is unsettling. Some use W/m^2, some use calories/m^2, some show simple %s, some a combination. So much for consensus. What they all seem to have in common is some kind of perpetual motion heat loop with back radiation ranging from 333 to 340.3 W/m^2 without a defined source. BTW additional RF due to CO2 1750-2011, about 2 W/m^2 spherical, 0.6%.
    Consider the earth/atmosphere as a disc.
    Radius of earth is 6,371 km, effective height of atmosphere 15.8 km, total radius 6,387 km.
    Area of 6,387 km disc: PI()*r^2 = 1.28E14 m^2
    Solar Constant……………1,366 W/m^2
    Total power delivered: 1,366 W/m^2 * 1.28E14 m^2 = 1.74E17 W
    Consider the earth/atmosphere as a sphere.
    Surface area of 6,387 km sphere: 4*PI()*r^2 = 5.13E14 m^2
    Total power above spread over spherical surface: 1.74E17/5.13E14 = 339.8 W/m^2
    One fourth. How about that! What a coincidence! However, the total power remains the same.
    1,366 * 1.28E14 = 339.8 * 5.13E14 = 1.74E17 W
    Big power flow times small area = lesser power flow over bigger area. Same same.
    (Watt is a power unit, i.e. energy over time. I’m going English units now.)
    In 24 hours the entire globe rotates through the ToA W/m^2 flux. Disc, sphere, same total result. Total power flow over 24 hours at 3.41 Btu/h per W delivers heat load of:
    1.74E17 W * 3.41 Btu/h /W * 24 h = 1.43E19 Btu/day
    Suppose this heat load were absorbed entirely by the air.
    Mass of atmosphere: 1.13E+19 lb
    Sensible heat capacity of air: 0.24 Btu/lb-°F
    Daily temperature rise: 1.43E19 Btu/day/ (0.24*1.13E19) = 5.25 °F / day
    Additional temperature due to RF of CO2: 0.03 °F, 0.6%.
    Obviously the atmospheric temperature is not increasing 5.25 °F per day (1,916 °F per year). There are absorbtions, reflections, upwellers, downwellers, LWIR, SWIR, losses during the night, clouds, clear, yadda, yadda.
    Suppose this heat load were absorbed entirely by the oceans.
    Mass of ocean: 3.09E21 lb
    Sensible heat capacity: 1.0 Btu/lb °F
    Daily temperature rise: 1.43E19 Btu/day / (1.0 * 3.09E21 lb) = 0.00462 °F / day (1.69 °F per year)
    How would anybody notice?
    Suppose this heat load were absorbed entirely by evaporation from the surface of the ocean w/ no temperature change. How much of the ocean’s water would have to evaporate?
    Latent heat capacity: 970 Btu/lb
    Amount of water required: 1.43E19 Btu/day / 970 Btu/lb = 1.47E+16 lb/day
    Portion of ocean evaporated: 1.47E16 lb/day / 3.09E21 lb = 4.76 ppm/day (1,737 ppm, 0.174%, per year)
    More clouds, rain, snow, etc.
    The point of this exercise is to illustrate and compare the enormous difference in heat handling capabilities between the atmosphere and the water vapor cycle. Oceans, clouds and water vapor soak up heat several orders of magnitude greater than GHGs put it out. CO2’s RF of 2 W/m^2 is inconsequential in comparison, completely lost in the natural ebb and flow of atmospheric heat. More clouds, rain, snow, no temperature rise.
    Second leg disrupted.
    Footnote 1: Journal of Geophysical Research, Vol 83, No C4, 4/20/78, Ellis, Harr, Levitus, Oort

    • Please see Joe Postma’s model, rotating earth, correct TOA etc.. And realistic temperatures sans the GHE.
      Ref.- Copernicus meets the Greenhouse Effect. J. Postma.

  23. There are two nameable altitudes of the “top of atmosphere” as far as greenhouse gases are concerned.
    There is a higher altitude that has nearly enough all greenhouse gases and their radiative interactions below it. The lower altitude is a “representative altitude” that represents where greenhouse gas molecules are best at emitting thermal infrared photons towards outer space, with these infrared photons not being absorbed (and likely re-radiated, maybe downward) by another greenhouse gas molecule.
    The lower level, or a determination of which is used for radiation balance between “top of atmosphere” and the sun and outer space, seems to me as being in the upper troposphere, usually around the 400 to 350 millibar level.

  24. Let me propose that TOA should be defined at the level where air pressure decreases to 1/2 of that on the surface (average at about the height of 5 km). It is where average atmospheric temperature equals that calculated from Stefan-Boltzmann equation, with known output from the Sun and Earth assumed to be a grey body of albedo ~0,3.

    • But Mr. Alkalaj, that sounds more like the center, than the top.
      The 500 millibar level has as much air above it as below.
      Thunderstorms can rise to three times this high…and more that four times this high at the ITCZ.
      I think the idea is to choose a level which will simplify calculations, not make them impossible.

  25. Not only the TOA problem but where is the surface? Certainly not where the temperature is measured.

    • I justgot back from geologizing in a part of the world without electricity, let alone cell towers or Internet service.
      Thanks for asking.
      IMO the top of the atmosphere is where the gas molecules are too far apart to interact meaningfully. Above 100 miles, the molecules are so few and far between that sound waves can’t be transmitted But I’d place the effective top even lower than that, down around 60 miles.
      Best wishes.

  26. As a practical matter attempts to measure or estimate from model’s absolute energy unbalance at the TOA are doomed to fail because of the errors involved relative to the small changes of interest. Regarding the important question of global warming from increased CO2, it makes more sense to estimate the change in energy balance from it only because it might be unbalanced from natural changes. Furthermore the unbalance at any time from more CO2 depends on how fast the planet has already warmed to respond to the unbalance.
    The only thing that makes sense is to estimate global average temperature changes from the recent time when CO2 was nearly constant using simple energy balance models and estimated feedbacks, but not those from the complex computer models that have been shown to be grossly inadequate. The delay form ocean heat storage can then be estimated with a simple global model. High latitude areas and other places with less water vapor will warm more, and others less, but that correction can be added as a final step.

    • Actually, according to greenhouse warming from more CO2, the reduction in radiation to space because the CO2 final escape altltude moves up to to a higher, colder region (except around the 15 micron wavelength where it may get warmer) first warms the atmosphere around 10 km. The warming later trickles down layer by layer to the surface because of reduced convection and increased back radiation. Ocean heat storage delay of the surface temperarture will not delay the atmosphere warming. So this is more reason to not expect a noticeable unbalance at the top of the atmosphere from CO2. With CO2 increasing only about 0.55% year, the warming atmosphere can follow it and will only have a slight, undetectable delay. Any unbalance in measurements from CO2 is probably sampling error or sensor noise. And with the large computer model variations among themselves, it is obvious they mean nothing regarding the small difference in incoming and outgoing radiation.

  27. Why not just say the mesopause?
    This used to be considered to occur at around 85 km, but more recently there appears to be a second, stronger temperature minimum at around 100 km, however modeling is involved, so approach with caution.
    Xu, Jiyao; Liu, H.-L.; Yuan, W.; Smith, A. K.; Roble, R. G.; Mertens, C. J.; Russell, J. M.; Mlynczak, M. G. “Mesopause structure from Thermosphere, Ionosphere, Mesosphere, Energetics, and Dynamics (TIMED)/Sounding of the Atmosphere Using Broadband Emission Radiometry (SABER)”. Journal of Geophysical Research 112 (D9).
    Not to be confused with menopause, which features hot flashes rather than cold minima.

  28. GHG idea is ridiculous
    COPY AND STUDY IN YOUR OWN TIME
    The CREATOR has not made gases for GHE to warm the earth. They are great coolant of one of many cooling systems of the nature. Gases are freely moving molecules. So, they can’t form ‘green house’. Only solid materials can be fixed to make four walls. Solid transparent materials like plastics and glasses are used to make green houses, so that the sunlight goes through to heat inside the green houses.
    So GHG idea is metaphorical, ridiculous, fake, imaginary, spurious and greatest fraud in the history of science. Gases are helping the earth to cool down by convection method of heat transmission all the time and man has no control over the process. Therefore, don’t blame gases for GHE.
    We can reduce the use of fossil fuel to almost zero percent for electricity by making correction in the hydropower engineering.
    (Details in the following post include- Part I about climate science with explanation of the cause of Climate Change and Part II – solution to Power Crisis ).
    CC or GW due to gases is ridiculous. gases are helping the earth to cool down by convection method of heat transmission.
    Part I CC due to gases is impossible and Part II solution to power crisis
    I. I. CLIMATE SCIENCE
    Key factor in climate system of Nature is Rain cycle, not gases. The best mitigation due to CC is to stop it or control it. We can control climate or present climate change is reversible (B3)
    CLIMATE CHANGE, ENERGY, WATER AND FOOD PROBLEMS CAN BE SOLVED SIMULTANEOUSLY and almost immediately. WE DON’T NEED FOSSIL FUEL OR BUCLEAR FOR ELECTRICITY. WE HAVE UNLIMITED HYDROPOWER AND WIND POWER.
    CC is manmade but not due to gases.
    Updated from time to time, the following list includes only the established known science and facts. No point is my opinion or assumption as GHG / GHE due to gases is imaginary. So if anybody could find any point wrong, I will be very much thankful. Hereby, I also request to state meaningful science instead of meaningless comments.
    (Dev – Retired science teacher educator; earned Ph.D. from Nottingham University (1986), NG7 2RD England, UK, for developing a training program for science teacher –”Radicalization of science education in Nepal.” – development of an innovation, a study in education technology.)
    A. GHG / GHE idea is ridiculous fake science. Worst, disgusting, embarrassing fraud in the history of science.
    1. Green house. It requires solid transparent materials to form a green house.
    2. GASES are freely moving molecules.
    3. Gases can’t form green house.
    4. They can’t be fixed to make walls / roof of a structure like ‘green house’.
    5. All matter / gases in Nature can hold Heat, so they can absorb heat like any gas e.g. CO2.
    6. Convection method of heat transmission. Heat is always transmitted from higher to lower temperature.
    7. O2 is 700 times more than CO2.
    8. N2 is 2700 times more than CO2.
    9. CO2 is not a pollutant. We carry the gas in our blood since birth and live throughout
    the life with the gas.
    10. Plants use the gas to prepare food. Then, HOW CAN THE GAS BE A POLLUTANT?
    11. If GW were due to ‘green house effect” (GHE), the upper layer of the Troposphere (our climatic atmosphere) should be warmer than the flat land areas because warm air goes up. So the top of the MT. Everest should be hot zone. The earth would have never been colder than the beginning 4 billion years ago.
    12. Our atmosphere is not closed like a green house but open to space.
    13. Our climatic atmosphere (Troposphere) should be always warm as the Sun always shines on the half of the Earth.
    14. It wouldn’t be cold during night (after the sun set and before the sun rise).
    15. Minimum temperature is recorded about half an hour earlier than the sun rise.
    16. We know it is always colder during night than during sunny days.
    17. REFLECTION: gases don’t reflect. They are transparent. Light pass through too small particles.
    18. Materials become opaque when they reflect light.
    19. Every molecule radiates absorbed heat when the surrounding is colder. It absorbs heat when the surrounding is hotter. All objects at a place try to equalize temperature.
    20. Foggy, smoggy, and cloudy days are colder than bright sunny days.
    21. Gases are not layered in the Troposphere; it is a homogenous mixture of gases. If it were layered the heaviest gas, CO2 would be at the bottom not on top. Then animals wouldn’t survive. We need O2 to be alive.
    22. Gases of atmosphere should be still (no breeze, no wind) to be layered. Breezes, winds, hurricane, tornadoes, convection current or any motion thoroughly mixes all the gases.
    23. Molecules of fluids move upwards when heated and downwards when cooled – the convection current.
    24. CO2 is transparent, colorless, odorless, and heaviest gas of the atmosphere. It does not make shadow as clouds do.
    25. If something does not allow going out means does not allow getting in as well. GHE applies only with the solid transparent materials like glasses and plastics not for the fluids (gases and liquids).
    26. Methane is negligible, only traces.
    27. Insulation traps heat partly. Gases alone can’t trap heat. Gases can’t work as an insulator in the open space. Our atmosphere is not insulating the earth. it should be air tight for effective insulation. The clothes we put on, the four walls and roofs etc. work as insulator, lesser the passage for air to pass through in and out the more effective is the insulation.
    # Physical properties of fluids (gases and liquids) and atmosphere don’t support them on GHG idea at all scientifically. GHG / GHE idea is metaphorical/ fake.
    B.1 Causes of CC
    (Just because you (NASA and IPCC) did not know or could not explain the cause of CC you are creating fake, imaginary, false, spurious and so on science to mislead the world.
    GW is not the problem but water.
    Here is the explanation for the cause of the CC. I challenge all the scientific institutions / organizations especially NASA and IPCC that support GHG / GHE idea to prove my scientific analysis is wrong. CC due to gases is impossible instead they are helping the earth to cool down by convection method of heat transmission.)
    So they don’t have proofs. My Scientific analysis is 100% proof
    So gases are not responsible for global warming but cooling the earth.
    Only purpose of the Quito protocol (only a propaganda or misinformation, jargon, cant, hoax and so on.) is for monopolizing the industry by the developed rich countries – saying indirectly to the poorer countries to stop industrialization; and, instead they would support the developing world by donations.
    B2. Mistaken Reason for CC –
    The main reason for global warming is due to the mistake done by human being for explaining the rain cycle wrong way that it occurs by the evaporation of the sea water. If it were so, now-a-days we should have rains more often than in the old days – global warming and expansion of the sea surface, both are favorable for evaporation needed for rain cycle. Sea surface temperature (average 15C) is not hot enough to lift water vapour to form cloud needed for the rain cycle. If that is possible we will have rains all the time, (even during winter we have that temperature in Nepal on the average). Water vapour evaporated from the sea surface must come over land to get lifted as the land surface gets heated by the sun and air moves upward as air current.
    We are making more and more land areas drier and drier by urbanization – covering land by concretes, black top roads, deforestation, and expanding deserts. So evaporation from the land areas is decreasing, as a result cooling of the land areas is decreasing significantly. Land areas are hotter than sea surface temperature.
    B3. We can control climate or present climate change is reversible
    – Just by determining how much land surface area of the earth to keep moist. More the land surface moist, the more is rain cycle and cooler earth surface.
    WE MAY NEED LOTS OF POWER TO PUMP WATER FROM RIVERS OR OTHER SOURCES. SECTION II SOLUTION TO POWER CRISIS SHOWS WAYS TO HARNESS LIMITLESS HYDROPOWER
    For the development of water supply net works so that we can keep every inch of earth’s surface moist, we need to pump water every where from rivers or other sources of water. For that we may need lot of power supply. Hereis the solution to power crisis (section II).
    I shall be grateful to you if you could go through my blog for details and share with your friends.
    C. Ozone depletion is not possible
    Ozone as such can’t exist as a layer. It is extremely unstable and heavier than O2. It breaks into oxygen atoms as soon as it forms (if not kept pressurized in a closed container).It is formed when oxygen molecules breaks into atoms with heat of high temperature (UV). Stratosphere is tremendously cold zone and extremely low pressure. Ozone formed breaks down into oxygen atoms as soon as it forms and releases heat. Even at sea level at NTP ozone is unstable. So ozone layer exists only in theory. Intermittently forming of ozone will continue until the oxygen is in the atmosphere and we receive UV from the sun. So ozone depletion is not possible. Ozone formation is a step to return heat back to space.
    It is not ozone that blocks heat but O2 and in the process O3 is formed to release the heat absorbed by O2
    D. Don’t blame CFC (too scarce and too heavy to reach the stratosphere) for thinning stratosphere. In reality, Millions of jet flights everyday are consuming too much of oxygen of the layer.
    Copy my list, go to NASA / IPCC and tell them about my challenge. Or, at least talk to your elementary sc. teacher to find out true sc. I will reward you for your efforts. Thus,
    Present CC is reversible and we can control climate
    WE MAY NEED LOTS OF POWER TO PUMP WATER FROM RIVERS OR OTHER SOURCES. SECTION II SOLUTION TO POWER CRISIS SHOWS WAYS TO HARNESS LIMITLESS HYDROPOWER
    II. SOLUTION TO POWER CRISIS: RUNNING TURBINES IN SERIES
    BLUNDER IN HYDROPOWER ENGINEERING: CORRECTION MEANS END OF
    POWER CRISIS.
    (concise water meters to apply to )
    If we make correction of the mistake there has been on hydropower engineering we wouldn’t need any other sources of power at all. The cleanliest power will be available by cheapest possible way we can think of. Please avoid the most dangerous power source.
    At present we are tapping only minimum hydropower by applying the principle of still water column that it exerts highest pressure at the bottom, so we run only one turbine at the bottom of the running water column. The property applies in standing still water column only . It is a blunder in hydropower engineering.
    In hydropower we have the running water condition. The pressure effect in a running water column is uniform through out, from intake to discharge points. Considering the properties of uniformly running water column, it is possible to run many turbines in series along a single uniform penstock pipe.
    We have to keep water running consistently to maintain constant revolution of the turbines. Uniformly running water column has uniform velocity and pressure throughout, from intake to the discharge points (Bernoulli Theory). So we can install turbines at any position of the running water column. And, by maintaining uniformity of the water column before, through and after the installed turbine, the velocity of the water column can be maintained constant.
    Turbines rotate with the same velocity as running water column. So there is no change in the velocity of water after running a turbine(s). Therefore the turbines don’t decrease the power of running water. So we can install as many turbines in series along a single uniform penstock pipe as space allows.
    Application of the properties of uniformly running water column can open the door for unlimited hydropower. Only limitation is the space required for placing turbines. This method not only can end the power crisis but will also help to reverse the present climate change as the power will be available to pump water from rivers as much as we need to keep the land surface always moist, recharge ground water, boost rain cycle and eventually reduce sea level rise.
    So we must consider the principle of running water column for installing turbines.
    Applying the property of standing still water column to a running water condition has been a blunder in hydropower engineering. Considering the fluid properties of water (pressure is exerted equally in all direction) and the nature of gravitational force (at a given point never reduced nor blocked nor shifted) multiple turbines can be installed in series along only one water running pipe. The turbines don’t decrease the power of running water, because the turbine rotates with the same velocity as the running water.
    DEMONSTRATION
    Water meter is a good example of miniature turbine. Many water meters can be connected along the same UNIFORM water supplying pipe in series and run all of them uniformly.
    (please scroll down for demo video clips in my blog)
    THUS IT IS POSSIBLE TO HARNESS many folds more hydropower than done by present practice.
    Engineering works has to be developed differently so that the running water column is uniform before the turbine, inside the turbine and after the turbine.
    Hydro power can be installed without reservoir / by runoff type, but making lakes as much as possible will hold water in and on land – will be eco friendly, cool climate, aquatic life, lower sea level rise, water sports, transports, greenery, enhance rain cycle, make water easily available in the nooks and corners etc. From the reservoirs we can install turbines as run off type water supply.
    NAMING ‘HYDROPOWER’ IS ITSELF WRONG. IT IS NOT POWERED BY HYDRO BUT ‘G’. WATER IS USED AS A TOOL TO CAPTURE ‘G’ FORCE. SO IT SHOULD BE ADDRESSED G-POWERED ELECTRICITY. ANOTHER FLUID IF THERE WERE AVAILABLE ABUNDANTLY COULD ALSO BE USED INSTEAD OF WATER.
    Retired science teacher educator; earned Ph.D. from Nottingham University (1986) England, UK, for developing a training program for science teacher –”Radicalization of science education in Nepal.” – development of an innovation, a study in education technology.

    • @indrdev200
      Your post discusses the wrong greenhouse effect. Apparently you don’t even know about the one that operates in the atmosphere. I suggest you read up on its physics..which doesn’t depend n ‘closed spaces’ in the atmosphere. Rather, it depends on the molecular response to IR frequency radiation, and has been well known by science since the 19th century.

      • Menicholas,
        warrenlb always ignores the fact that global warming stopped almost twenty years ago.
        That fact alone deconstructs everything he’s been preaching. The endless alarmist predictions were that a rise in CO2 would cause runaway global warming, resulting in climate disruption. There is no credible way around it: that prediction was flat wrong, which falsifies their conjecture.
        A stand-up guy would admit his prediction was wrong, and then work with scientific skeptics to figure out why it was wrong. Then maybe they could come up with an alternate hypoithesis that explains why global warming stopped, while CO2 continues to rise.
        That’s how honest science works. But since it would require warrenlb’s side to admit they were wrong, they will never work with other scientists on a new hypothesis. They simply cannot admit they were wrong, and that the hated skeptics were right.

    • Nitwit, the turbines slow the water down. If they were in series, the water would be moving so slowly the turbines would be LESS efficient.
      It is not ust the weight if the water, it is it’s velocity that lets the turbines create the power they do…it is given clear run to build up velocity…turbines are expensive, why have several that each only produce a fraction of what one produces.
      The energy contained in water is not limitless!
      What are ya, a puddinhade?
      The potential energy has to be converted to kinetic energy and then rotational energy and then electrical energy.
      The total potential energy is given by the mass of water times the height of the head times g, the gravitational constant.
      This is first year physics…for non-majors!
      If you ever took even one such class and still believe the crap you are spewing, you should demand a refund…you wuz robbed.

      • BTW, my credentials are: Just a guy, who knows a thing or two, and who is real glad that the people who taught the classes I took were not instructed by anyone you trained.
        Sorry to be this way…but nonsense has to be countered in the strongest terms, or some poor souls might happen across it and be misinformed.
        We do not need to propagate such nonsensical drivel.

  29. The popular IPCC GHE dismisses water vapor. It’s not man caused. The LWIR/SWIR perpetual heat loop violates thermo laws. The 2 W/m^2 of the CO2 added between 1750 and 2011 is trivial in comparison to the total heat balance. Without water vapor a greenhouse becomes an oven. It’s water vapor that runs the climate not CO2.
    IPCC AR5 TS.6 Key Uncertainties is where climate science “experts” admit what they don’t know about some really important stuff. IPCC is uncertain about the connection between climate change and extreme weather especially drought. IPCC is uncertain about how the ice caps and sheets behave. Instead of gone missing they are bigger than ever. IPCC is uncertain about heating in the ocean below 2,000 meters which is 50% of it, but they “wag” that’s where the missing heat of the AGW hiatus went, maybe. IPCC is uncertain about the magnitude of the CO2 feedback loop, which is not surprising since after 18 plus years of rising CO2 and no rising temperatures it’s pretty clear whatever the magnitude, CO2 makes no difference.
    http://www.writerbeat.com/articles/3713-CO2-Feedback-Loop
    Barring some serious flaw in science or method, Miatello’s paper should serve as the death certificate for AGW/CCC.
    http://principia-scientific.org/publications/PSI_Miatello_Refutation_GHE.pdf
    https://stevengoddard.wordpress.com/2015/07/04/dr-bill-gray-responds-to-pope-francis/

  30. Tim
    From when I studied Astrophysics at university I remember that TOA is often where the opacity changes in a star. In fact all the radiative transfer stuff comes from stellar physics, which is why you see things like blackbody approximations in “layers” of gas. Things that don’t apply to cold gases directly.
    So as far as I remember the TOA is dependent on the gas. For a star it is basically around the photosphere as you only need to consider H ions. For a multicomponent atmosphere each spectral component will have it’s own TOA and also should not on first glance have emissions that behave like blackbodies. It’s going to be more complicated as you say.

  31. Well, I can’t find the head of the long, long thread on the TSI/4, so I’m posting this here:
    Trick August 31, 2015 at 7:15 am

    I think the argument that a revolving planet bulges at the equator to an oblate spheroid has merit so that when a pole is pointed at the sun more sunlight is intercepted (thus increasing Tt by reducing the denominator) than when a pole is at psi = 0 (which partly includes the bulging equator effect also).

    That’s true, Trick, but it goes in the “Difference that doesn’t make a difference” file for me. The WGS-4 ellipsoid has the following radii:
    Equatorial radius (ER): 6,378.1370 kilometers (3,963.1906 mi).
    Polar radius (PR) : 6,356.7523 kilometers
    So looked at from the poles, the cross-sectional area intercepting sunlight is 2 π ER^2, or . And looked at from the plane of the equator, the area is approximately 2π ( ( ER + PR ) / 2 )^2. This works out to a difference of about three-tenths of a percent. However, that’s for the whole difference, polar vs equatorial view. But the axis tilt is only 23.45°, so the actual difference is even smaller than that. In either case it is certainly small enough to ignore in the type of analyses under discussion.
    Bart August 31, 2015 at 8:08 am
    Willis Eschenbach @ August 30, 2015 at 8:36 pm

    Yes, that is physically impossible, but you can do physically impossible things in a gedanken.

    Thanks, Bart, but you must use gedanken experiments much differently than I do. On my planet at least, gedanken experiments are used to determine the effects of real physical laws and real physical constraints on imagined situations. They are NOT used to explore “what if we totally ignore physics” fantasies like a planet rotating a star while ignoring the conservation of angular momentum and the gyroscopic effect …

    But, if you don’t like having the axis rotating, try assuming the planet is tidally locked with the Sun, like they used to think Mercury was, to get the one face pointing toward the Sun all of the time.

    True, that would make a difference … but why on earth would I assume that? Neither Chilingar nor any of us are discussing such a situation.
    w.

    • Because, Willis, that is how you get a sense of the range of possible solutions. Good grief, dude. This is Research 101.
      Einstein did gedanken experiments, e.g., supposing he were in a train traveling near the speed of light. Maxwell had demons in his. These impossible details were immaterial to the point being made. Why are you quibbling like this? Are you interested in thinking seriously about the issue, or just in stymieing discussion?

      • Bart August 31, 2015 at 2:05 pm

        Because, Willis, that is how you get a sense of the range of possible solutions. Good grief, dude. This is Research 101.

        I’m sorry, but imagining how things would be if we violate the laws of physics can only give us a sense of the range of impossible solutions …
        But heck, let’s play it your way. Let’s imagine a world with different physical laws, one free of the gyroscopic effect so that a planet can revolve around a sun with its axis always pointed towards the sun.
        Now, explain to me how that will help us decide if the proper calculation for the earth is TSI/4 or TSI/ 3.6215?

        Are you interested in thinking seriously about the issue, or just in stymieing discussion?

        On my planet at least, imagining that the laws of physics have been suspended is generally not known as “thinking seriously about a question”.
        But if that is “thinking seriously” on your planet, then just how does your impossible no-gyroscopic-effect planet rotation solve the TSI/4 question?
        Finally, you say:

        Einstein did gedanken experiments, e.g., supposing he were in a train traveling near the speed of light. Maxwell had demons in his. These impossible details were immaterial to the point being made.

        Let me try again to explain the difference. As I said before (emphasis mine):

        On my planet at least, gedanken experiments are used to determine the effects of real physical laws and real physical constraints on imagined situations.

        And that is exactly what Einstein did. He assumed he was in a train near the speed of light. That is an imagined situation. But Einstein did NOT then say “now imagine that momentum is no longer conserved” or “now imagine that the gyroscopic effect no longer exists”. He looked at the effects of real physical laws on his imagined situation inside the train.
        You, on the other hand, want to look at the effects of violating physical laws on an imagined situation, which is not the same thing in any sense. All that can give us is a range of impossible solutions.
        w.

    • Willis – Thanks for the workout you beat me to it. Think you mean WSG-84 though.
      Note the published monthly anomaly is like 0.2K out of 288K. Looking for scraps even church mice leave behind. And Chilingar has it closer to 12% when considering polar regions vs. equatorial on this oblate spheroid for some yet to be uncovered reason (may end up Holders inequality). Need to find p. 475 for Chilingar et. al. full reasoning.

      • Trick August 31, 2015 at 4:04 pm

        Willis – Thanks for the workout you beat me to it. Think you mean WSG-84 though.

        True ‘dat, thanks, typing fast.

        Note the published monthly anomaly is like 0.2K out of 288K. Looking for scraps even church mice leave behind. And Chilingar has it closer to 12% when considering polar regions vs. equatorial on this oblate spheroid for some yet to be uncovered reason (may end up Holders inequality). Need to find p. 475 for Chilingar et. al. full reasoning.

        I’ll pass on Chilingar’s full reasoning. The reasoning of anyone who thinks the answer is other than TSI/4 is of no interest to me.
        All the best,
        w.

  32. Hockeystick writes ,
    “Very simple, and known since at least Maxwell’s book Theory of Heat 1872. The only radiative forcing that enters the picture is that from the Sun, the only source of energy; there is no “radiative forcing” from GHGs creating a 33C increase in temperature, it is solely gravito-thermal.”
    There may not have been many man mad forcing’s back in 1872 . But 1872 isn’t 2015 were man has learnt to control radiation http://www.mpoweruk.com/radio.htm

  33. verdeviewer
    August 31, 2015 at 6:14 pm
    Given an axial tilt of 90° with an axis pointing to the sun and a precession of 1 year, wouldn’t one pole of a planet always point to the sun?
    I can’t imagine how that would work, although I’ve been trying since I saw your post. Earth’s axial precession takes c20,000 years, and describes a cone. “The gravitational force between the Sun and moon induces the precession in Earth’s orbit” –Wiki
    What you describe would require two or more massive bodies exerting their mutual gravitational forces on your hypothetical planet – I think – so that the result would be something like a gyroscope doing a midair sommersault, but a planet’s angular momentum would strongly resist that, and any bodies massive enough to exert the necessary force on said planet would probably tear it apart before the flips started.
    Others here will no doubt give a better answer, but meanwhile, please refer to the diagram Willis has posted upstream, while I pull my neck back in:
    http://wattsupwiththat.com/2015/08/29/where-is-the-top-of-the-atmosphere-toa/#comment-2017940
    (Once again, that doggone reply button has fragmented this interesting discussion into subthreads that are now very difficult to follow, and very time-consuming in the bargain, even if you manage the feat.)

    • Steve G, thanks for the reply to what’s obviously an esoteric question.
      My speculation was that, with a certain combination of planetary orbit, solar rotation, influence from other orbiting bodies, and internal dynamics, such a thing would be possible. But I lack the math skills to model it.
      Certainly Uranus and Saturn interact, and internal dynamics might influence Uranus’s stability. When Voyager 2 passed by, the magnetic axis was tilted 59° to the apparent axis of rotation, suggesting a different spin on the planet’s interior.
      And then there’s the question of what set Uranus on its side. There are now at least three theories on that, the latest being the loss of a large moon.

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