Unified Theory of Climate

(Image: NASA)

Guest Post by Peter Morcombe

In October 2011, Nikolov & Zeller published a poster called the “Unified Theory of Climate” (Direct link to Poster) claiming that planetary surface temperatures can be calculated accurately if pressure and TSI (Total Solar Irradiance) are known.   If their claim is correct, so-called “Greenhouse Gasses” such as carbon dioxide are not responsible for the observed “Global Warming” since 1850.  This has major implications with respect to energy policies worldwide.

These ideas are hardly new as PaAnnoyed, Steven Goddard, Harry Dale Huffman, Leonard Weinstein, gallopingcamel and others have made similar assertions.  N&Z boiled it all down to a few equations.  Their claims are being hotly debated with critics dismissing it as sophisticated curve fitting.  While that makes me wonder whether those critics bothered to read the N&Z poster, I have some criticisms of my own.

Albedo

The idea that one can calculate planetary temperatures without allowing for the proportion of incident energy that is reflected seems nonsensical.  Surely a planet like Venus with a high Bond albedo (0.75-0.90) will be cooler than it would be if its albedo was more like Earth’s (0.306).  Albedo is quite complex given that it is wavelength dependent and varies with time for planets that have clouds, vegetation or ice fields.   However, one might be able to ignore the albedo if it was similar  for incoming solar radiation (peaking at 500 nm) as for the long wave radiation that planets radiate into space.

Vapors

Planets that have substantial atmospheres tend to have vapors that can form clouds, seas or ice fields.  Venus has sulphuric acid clouds, Earth has water vapor, Jupiter has ammonia clouds and so on.  These clouds affect many things such as albedos, adiabatic lapse rates and the transport of heat from low to high latitudes.  It is hard to take a theory that ignores these effects seriously.  Imagine the planet Earth with all of its water magically removed; are N&Z implying that this would not have a major effect on temperatures?  Is that credible given that adiabatic lapse rates are significantly greater for dry air than for damp air?

They may be right given that when moisture is introduced into the atmosphere there are two opposing effects.   When humidity is high the adiabatic lapse rate falls but at the same time the altitude of the tropopause rises.   Thus to a first approximation the effect of adding water vapor may be small.  It does not worry me that I can’t properly explain this process as I doubt that anyone can convincingly explain the effect of water in its various forms on surface temperature.

Suspend disbelief

In spite of my misgivings I propose to suspend disbelief and probe N&Z’s theory using data that is easily available on the Internet.   The starting point should be N&Z’s equation (8):

Ts = 25.3966 (So + 0.0001325)0.25 NTE(Ps)

The first part of this equation is not controversial, based as it is on the Stephan-Boltzmann radiation equations and the ~2.7 oK black body temperature of the universe.

The second part of the equation that includes the NTE(Ps) is controversial in the sense that this can be criticized as an exercise in “curve fitting”.  However there is a simple way to test N&Z’s core claim that the NTE is a function of pressure while avoiding the charge of “curve fitting”.

Earth

To avoid having to discuss the detailed nature of NTE(Ps) I will work at a constant pressure of 1 bar (100,000 Pa) so that the function becomes a constant.   I will start by determining the “Atmospheric Constant” = 25.3966 NTE(1).  The best data we have for evaluating this constant is from the planet we occupy,  Ts = 288.2 K  and  So = 1,366 W/m2 from which NTE (1) =  47.41.

Already, my computations have tip toed around a serious error.   The temperature Ts above is the average global temperature that has wide acceptance in the scientific community but what pressure is it measured at?  Here are the three possibilities:

N&Z             One Bar         One Atm.

Pressure (Pascal)           98,888.2        100,000.0        101,325.0

Temperature (Kelvin)        287.6               288.2               288.9

The first numbers are from the N&Z poster which I have corrected for 1 Bar of pressure rather than 1 Atm.  The above pressures cover a range of only 2.5%  but the corresponding effect on  temperature is 1.3 degrees Kelvin.   Some might think this too small an error to worry about were it not for the fact that the observed “Global Warming” since 1850 is ~0.8 degrees Kelvin.

Venus

Now let’s apply the atmospheric constant to Venus where So = 2,614 W/m2 .   The corresponding temperature should be 339 Kelvin or 66 oC.   Direct observations are available thanks to the Magellan mission and Jenkins et al.   The measured temperature at an altitude of 49.5 km was 339 Kelvin and the pressure was …………. 1,000 mBar = 1 Bar.

Vindication for N&Z?  Yes, but before one gets too excited it should be noted that there are plenty of sources of error.   Note for example that the measurements refer to a latitude of 67N; low latitude temperatures could be significantly different.  A measurement at one latitude can hardly be mistaken for a global average.

This result suggests that James Hansen’s theory of a “Runaway Greenhouse Effect” is as real as the Easter Bunny and the Tooth Fairy.  Venus has an atmosphere which is ~96% carbon dioxide in sharp contrast to Earth’s ~0.004% but it appears to have no effect on the planet’s temperature.  The ratio is 240,000:1 or more than 17 “doublings” of CO2 concentration. Taking the IPCC’s “best estimate of 3 oC/doubling (AR4), the corresponding effect on Venusian temperatures should be ~51 oC; given that the temperature enhancement at the surface of Venus is >500 oC, Hansen’s theory fails miserably.

Other bodies

Besides Earth and Venus, N&K discuss Mercury, Earth’s moon, Mars, Europa, Titan and Triton.  Only one of these has a significant atmosphere, namely Titan, so let’s check it out.   So = 15.1 W/m2 which would correspond to a temperature of 93 Kelvin.  According to the European Space Agency’s HASI experiment, the observed temperature at 1 Bar is 85.8 Kelvin.  Here is the relevant data:

Altitude (m)       Pressure (Pa)            Temperature (K)          Density kg/m3

7,536.0            99,914.00000                   85.8031                      3.9349000

7,512.0          100,053.00000                   85.8261                     3.9399000

7,487.0          100,183.00000                  85.8563                      3.9454000

The difference between predicted and observed temperatures is large enough to make me look for  sources of error.  Unlike the Magellan measurements that used radio occultation from an orbiting platform, the Titan measurements relied on a probe that landed at a latitude of 10S.  If you dropped a probe through Earth’s atmosphere repeatedly to the same point, the readings could vary dozens of degrees either way from day-to-day or season to season.   With that in mind, a difference of 7 K is impressive.

Gas Giants

While N&Z’s equations include the emissivity and albedo for a planet’s surface they should apply to any arbitrary layer within a planet’s troposphere so why not review the gas giants?

As with Titan, observations for Jupiter have been made by a probe descending on parachutes.    Considering that giant planets generally have “Weather” on a gigantic scale one should not expect more than a “Ball Park” estimate of planetary conditions from one probe.  The other gas giants have yet to be visited by atmospheric probes so the observed temperatures in the table below depend on indirect methods that include complex thermochemical models.  Models of Earth’s atmosphere are controversial so one should not expect from models based on sparse data sets.

Figure 1

The correspondence between the calculated and observed temperatures was less impressive than in the case of Venus or Titan.  However, some of these planets radiate more energy than they receive from solar radiation which implies they have internal heat sources.  Where the dominant heat transfer process is convection (as in a planet’s troposphere) it is immaterial whether the heat comes from above or below.  I therefore adjusted the TSI in proportion to the fourth root of the energy balance (Figure 1).


Jupiter        Saturn          Uranus        Neptune

TSI                                      50.5           14.9             3.71           1.51       Watts/m2

Energy balance                      1.67           1.78           1.06           2.61

Calculated temperature*     144            108               67              67          K

Observed temperature       170            134              76              72            K


[*Updated from original post  where the figures (in error) read 126, 93, 66, 53]

Conclusions

N&Z’s bold hypothesis that pressure and TSI are the primary determinants of planetary temperatures fits observations in striking fashion.  Now we need to ask ourselves why pressure should be so  dominant compared to albedo, emissivity, “g”, vapors, chemical composition, ocean currents and so on.  It may be time for physicists who are used to making testable hypotheses to take over from so-called scientists who claim that whatever the climate does, CO2 is the cause.

The modern era is an interglacial period in an Ice Age that N&Z say followed the loss of 53% of our planet’s atmosphere around 50 million years ago (see Figure 9 in the N&Z poster).   That sounds much more scary than adding traces of CO2 to the atmosphere and it is another testable hypothesis.

Addressing the wrong problem is like rearranging the deck chairs on the Titanic.

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15 Responses to Unified Theory of Climate

  1. Peter

    Nice post; You say

    ‘Now we need to ask ourselves why pressure should be so dominant compared to albedo, emissivity, “g”, vapors, chemical composition, ocean currents and so on. ‘

    In what practical way can we measure the effect of pressure and thereby know it is significant when we seem to have trouble enough coming to grips with the effects of solar radiation and clouds.

    In our part of the world (south Coast of Britain) it was very grey today with a maxcimum of 8C. A couple of miles away the sun poked through the murk and in the same air/weather system/latitude etc it was 14C.. A difference of 6C and a very graphic illustration of the effects of the sun AND clouds and that both are not factored enoiugh into the IPCC climate change scenario.

    So in what similar practical measurable way will pressure have an effect?
    tonyb

  2. Genghis says:

    I am impressed.

    And to look at the pressure question very simply, adjusting the valve on a boiling pressure cooker directly controls the temperature of the contents (everything else remaining the same).

  3. Doug Cotton says:

    The calculation of that 255K figure for the Earth is discussed in the Appendix to my paper http://tallbloke.wordpress.com/2012/03/13/doug-cotton-radiated-energy-and-the-second-law-of-thermodynamics/#more-5303

    I don’t believe you can calculate an approximately correct figure without (1) integrating over a 24 hour perod (2) taking into account conduction rates into and out of the land surfaces and convection rates in the oceans and atmosphere. The rotation rate is also needed. An Earth without an atmosphere, but still spinning at the same rate, would probably not have such wide fluctuations as the Moon which has much longer days and nights in which to warm up and cool down. But you obviously can’t assume the temperature is close to 0 K at night, even on the Moon, because of the retention of thermal energy under the surface. It becomes more complicated with Earth, also, because of the core temperatures and the thermal energy generated there and in the mantle and crust.

  4. Genghis says:

    Doug Cotton, first off we are on the same side, but you have been tricked by the AGW propaganda into fighting against its half truths, it is a very insidious trap. Let me try and explain the misdirection.

    The core AGW proposition is that the Earths energy is NOT in equilibrium (ever heard the phrase Climate change?). ‘IF and only IF’ that proposition is true then GHG’s warm the surface, albedo cools the surface, etc., but only because they affect the RATE of temperature change.

    BUT if the Earth’s energy is in Equilibrium then GHG’s, Albedo, emissivity, etc. are effectively ‘netted out’. That is very broadly what N&Z, PaAnnoyed, Steven Goddard, Harry Dale Huffman, Leonard Weinstein, gallopingcamel, Peter Morcombe, the guys over on Tallblokes site, etc. are saying. I agree with them.

    You seem to be agreeing with the AGW proposition that the earths energy balance is in constant change and you are battling against the idea that increased insulation will warm a planet that isn’t in equilibrium. It will.

    However if the planet is in energy equilibrium increased insulation will not warm the surface. In other words if the temperature on either side of an insulator is the same there is no flux regardless of the amount of insulation.

    The AGW disguises their half truth by focusing on temperature anomalies, not on absolute temperature and energy content. As soon as anyone looks at absolute temperatures and energy content, the AGW proposition falls apart.

  5. As Ghengis points out we are on the same side although I find myself disagreeing with Doug Cotton on some details over on “Tallbloke”:
    http://tallbloke.wordpress.com/2012/03/13/doug-cotton-radiated-energy-and-the-second-law-of-thermodynamics/

    No matter how wrong we are on the details, we are trying to explain what is going on in terms of equations and observations. That is why we are in much better shape than the CAGW folks like James Hansen with their fairy tales and hand waving.

    “Nullius in Verba” provided a couple of interesting links over on Roy Spencer’s blog that I had not seen before including one by Carl Sagan that explains the high temperatures on Venus:
    http://judithcurry.com/2010/11/30/physics-of-the-atmospheric-greenhouse-effect/#comment-16901
    http://adsabs.harvard.edu/full/1967ApJ…149..731S

    tonyb,
    We are talking about global average temperatures that we can measure to a fraction of a degree on Earth but with less accuracy on Venus. On Earth we know that temperatures vary over a huge range from night to day and season to season. Yet we can still measure the average temperature with reasonable accuracy by making many measurements.
    When it comes to the outer planets and moons data is so sparse that the average temperature is not known with much precision, so N&K may be even closer than they appear to be……or not!

  6. Verity Jones says:

    @GC,

    “Now we need to ask ourselves why pressure should be so dominant compared to albedo, emissivity, “g”, vapors, chemical composition, ocean currents and so on. “

    This theory only holds for planets with a significant atmosphere that can exert pressure.
    Gravity affects actual pressure and you have normalised to 1 Bar. We have huge storms etc. on Jupiter therefore I assume high convective mixing. Perhaps I’m just showing my lack of knowledge here, but surely the answer is that convection is a dominant process in setting and maintaining temperature? i.e. ‘trapping’ the heat and moving it around the planet, distributing it between the day (warming) side and the night (cooling) side, such that radiative gains and loses (albedo, emissivity) are much less important.

    Would factoring in speed of rotation (actual day length) as well as some sort of corrective factor for atmospheric density allow better fitting to actual data for the gas giants?

    • You probably noticed that there is a difference of 26 K between my N&K based calculation for Jupiter and the Galileo atmospheric probe. That sounds like a pretty bad error until you ask yourself how much would a single reading vary on planet Earth. Take a look at how much the temperature varied in Boston in April, 2008. You can find it in Richard Lindzen’s slide #15 here:
      http://diggingintheclay.wordpress.com/2012/02/27/lindzen-at-the-house-of-commons/#more-2975

      Voila! Thirty two Kelvin in a single month, which brings that Jupiter error into perspective. The European Space Agency was a little miffed because the Huygens probe descended into a “hot spot” in the Jovian atmosphere so they saw fewer clouds than expected. Consequently, their nephelometer had little work to do:
      “The Probe entered Jupiter near the edge of a so-called infrared “hot spot” believed to be a region of reduced clouds.”
      http://astro.sci.muni.cz/pub/galileo/first_science_summary.html

  7. Ned Nikolov says:

    I would like to make a few comments to Peter Morcombe’s article, which I like in general:

    (1) Eq. 7 in our original paper was derived using data from hard-surfaced planets ONLY. Hence, Eq. 8 (which uses Eq. 7) predicts only the mean SURFACE temperate of planets, and it should not be expected to produce accurate results for temperatures at various levels in the free atmosphere. The fact that Eq. 8 predicts so well the temperature on Venus at 1 bar pressure is due to the extremely thick (massive) Venusian atmosphere. However, if we compare predictions of Eq.8 for pressures less than 1 bar with actual observed temperatures at different heights in Earth’s free atmosphere, we’d find that, on average, Eq.8 produces higher temperatures than measured. That’s because the lapse rate in the free atmosphere is generally larger (i.e. more negative) than the lapse rate due to rising terrain elevation. This difference has been known in classical climatology for decades, but has been omitted in most modern text books. One can observed this effect of terrain in massive mountain ranges such as the Tibetan Plateau, where temperature drops with elevation typically much slower (2.5 – 4.0 deg / km) compared to temperature decline with altitude in the free atmosphere (5.5 – 10 deg / km). The reason for this is that air adjacent to a hard-surface (which absorbs most shortwave radiation) heats up much more than the air at the same pressure level in the free atmosphere located far away from an absorbing surface. While the relative enhancement factor (Nte) depends only on pressure, the absolute magnitude of the enhancement (measured as temperature difference) also depends on the absorbed solar radiation. Since heat absorption by air adjacent to a hard surface is generally higher than by air at the same pressure in the free atmosphere, the temperature declines slower with raising terrain than with increasing altitude in the atmosphere.

    Bottom line is that our Eq. 8 refers to surface temperatures ONLY, and not to free-atmosphere temperatures!

    (2) We have not claimed that the warming over the past 340 years had anything to do with pressure changes. Pressure affects global temperature over periods of hundreds of thousands to tens of millions of years, not on decadal or centennial time scales! In our view, recent warming has been entirely a result of declining cloud cover and related cloud albedo driven by solar magnetic activity. Earth’s albedo has likely declined about 1.2% since 1670 causing a 1.2K global temperature rise (according to our estimates, the sensitivity of Earth’s surface temperature to albedo changes is 1.03K per percent albedo)… The lack of warming over the past 13 years is (according to satellite observations) due to a sharp increase in low-level clouds, which took place over a 6-month period in late 2000 – early 2001. This was likely caused by a reversal in solar magnetic activity, which began declining in late 1990s. This decline is till continuing and will most likely move global temperature onto a cooling (negative) trend over the next 9 years.

    (3) CO2 has nothing to do with any climate/temperature changes on Earth. That’s because the atmospheric ‘Greenhouse Effect’ (we call ATE) is a pure pressure phenomenon unrelated to atmospheric composition. Mechanisms such as water cycle, ocean currents, convection etc. only serve to re-distribute the kinetic energy provided to the system by solar heating and pressure. These processes do not and cannot affect the average surface temperature, because that temperature is a direct expression (manifestation) of the system’s total kinetic energy!

    (4) Cloud albedo is mostly a function of the pressure-induced thermal enhancement. Only a tiny portion of the cloud albedo (around 1.3%) is controlled by solar magnetic activity. That is why our Eq. 8 has been so successful in predicting surface temperatures over a wide range of planetary environments without explicitly accounting for albedo effects. The idea that cloud albedo is mostly a product of climate and not an independent driver of it is a new paradigm to climate science!

  8. Verity Jones says:

    Thanks for the detailed comment, I see this is getting much more discussion over at Tallbloke’s Talkshop http://tallbloke.wordpress.com/2012/03/18/peter-morcombe-comment-on-the-unified-theory-of-climate/ which is no surprise, given that this is a rather quiet backwater.

    Your theory is very elegant in its simplicity. Giving it some more thought overnight I found myself contrasting desert climates (with say NO water vapour) on Earth and maritime (moist) climates, where 24 hour average temperatures could be the same for the two systems – assuming the same solar input for each and little wind. Convection is important, but for the comfort and habitability of the planet not for ‘spreading the heat’ around as said in my ill-thought-out comment.

    The more I begin to understand influences on climate the more I am in awe of the perfect suite of climatic conditions on Earth and how well they are regulated by so many feedbacks.

  9. Ned Nikolov,
    Thanks again for taking the time to comment on my humble efforts.

    One of the interesting aspects of Jupiter’s troposphere was the fact that the measured lapse rate was within 0.1 Kelvin/km of the theoretical C(p)/g rate. The resulting temperature versus altitude graph was almost a perfect straight line until the probe stopped transmitting at -132 km below the 1 bar level.

  10. E.M.Smith says:

    Pondering the “convection” question…

    It occurred to me that convective movement is driven by density variations, and a more dense atmosphere can have more variations. Could it really be that simple? A very dense atmosphere can carry more heat (more mass / unit volume) and tends to convect faster due to greater density variations possible?

    I’d like to think that misses something, but can’t figure out what it would be…

    There’s not a conflict between density as causal and convection as causal due to one being proportional to the other. Similarly the mass flow of vapors. A more dense atmosphere can carry more total vapor (up to a limit when it becomes a liquid ;-) Again, proportional action.

  11. gallopingcamel says:

    Chiefio,
    The big issue is the dominant heat transfer process. In the upper atmosphere radiation dominates so the temperature gradient is strongly influenced by issues such as gas composition. That is why it is quite common to see temperature increasing with height where radiative energy transfer processes involving Ozone, CO2 and traces of water vapor dominate.

    N&K have clearly stated what many others implicitly assumed. They say that gas composition is unimportant in the troposphere. When convection, Coriolis eddies and latent heat are the dominant heat transfer processes you will find an adiabatic lapse rate according to simple physics L = g/Cp. A 100 ppm more or less of CO2 in the atmosphere has no noticeable effect on Cp and thus no effect on the adiabatic lapse rate in the troposphere.

    Quite commonly at high latitudes and to a much lesser extent in the lower latitudes the convective processes in the troposphere can be temporarily weak so that the adiabatic lapse rate changes sign. This phenomenon of “temperature inversion” associated with fog and freezing rain is caused by radiative cooling of the surface. Once convective processes resume mixing the air vertically the normal lapse rate is re-established.

  12. Verity Jones says:

    @GC,
    nicely written. When I was reading your post I knew there had to be interaction with convection etc. as well but was too tired/lazy to think it through. Your explanation conjured it up nicely in my mind just there without having to think too hard (which I don’t want to do on a Friday evening).

  13. Pingback: Unified Theory of Climate Revisited | Digging in the Clay

  14. David Appell says:

    Peter wrote:
    Now let’s apply the atmospheric constant to Venus where So = 2,614 W/m2 .

    However, that’s not what the planet receives, since it has a large albedo. Much of its sunlight gets scattered away, and you need to account for that. (Same for Earth, but it’s albedo is smaller (but still significant.))

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