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.
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.
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.
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”.
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.
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.
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.
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.
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).
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]
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.