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]]>– The paper by Toth, as well as the more general approach taken in the paper he references by Pacheco and Sañuco, show that a careful application of the Virial Theorem to the planetary-atmosphere situation results in:

(2/3) =

relating the kinetic energy to the potential energy in a homogeneous gravitational field.

(2/5) =

for a diatomic molecular gas, if you include rotational energy in the kinetic energy.

– The result attributed by Miskolczi to the Virial Theorem is:

2 =

This is inconsistent with the above results.

– In any case, the application Miskolczi makes of this equation is somewhat mysterious: relating the ratio of two energy fluxes to the ratio of the gravitational and kinetic energies, for no very clear reason.

]]>The 95% confidence interval of the slope of your equation 10 plot is rather large, 0.69-1.25. The square of the correlation coefficient R is 0.45. The residual plot is clear evidence of non-linearity. Thirteen out of the first 14 residuals are positive and so are 9 of the last 14. 27 of the middle 33 residuals are negative. That’s proof only that x and y are somewhat correlated. It is extremely weak evidence at best that the implied relationship is correct.

Considering that the range of OLR values is less than 2% of the median, it’s a rather large stretch to imply that this is a general relationship that can be applied over a larger range. In fact, it’s a large stretch to assume that actual OLR, as opposed to calculated OLR, varied over that large a range for the time period, given the known large uncertainty in the NCEP/NCAR reanalysis data.

If we go back to the incorrect equations of M2007, the relationship of equation 7 only holds for τ > 3. Ed/Eu is only constant if τ is constant. For a purely radiative gray atmosphere, Ed/Eu doesn’t reach a value of 5/3 until τ = 2.92.

]]>I have updated spreadsheet to see if the HARTCODE output of NOAA 61 years agrees with equation 7.

The Excel file is here:

http://members.shaw.ca/sch25/Ken/hartcode_61yearNOAA2.xls

See the graph at cell AO29.

The top straight line is equation 7:

Su – OLR +Ed -Eu = OLR. (I replace Fo with OLR)

The best fit of the HARTCODE NOAA data has a lot of scatter, but the slope of 0.9696 is very close to 1.

There has been a lot of criticism of equation 7. It is an empirical relationship. The equation is not a true conservation of energy equation.

Equation 7 is not used in M2010. The flux density ratio equation, Equ 11 of M2010 is derived using only the Ed/Eu = 5/3 equation 10 and the Aa = Ed (approximately) equation 5. The graph of equation 10 shows that Ed/Eu is constant with changing Su, but the value is closer to 1.645 rather than 1.6667.

]]>My personal point is that I’m glad I’m not a scientist and just a, run of the mill, ‘universal millwright type’ (pardon the pun), engineer.

My point of reasoning for the link to that paper is to show that the Virial Theorem ‘alone’ isn’t enough for an accurate demonstration of phenomenological energy transition. All the supporting formulae need to be integrated into it as well (see “3 General Covariance and the Weight of Light”) to provide the required ‘degrees of freedom’ that a representative ‘model’ is expected to mimic. Thus, I think you’ll need Ferenc’s ‘notes’.

Best regards, Ray Dart.

]]>suricat,

thanks for this article…

Ferenc

]]>I have no idea what your point is.

]]>“If your special form of the virial theorem has radiant flux = kinetic energy then:”

Hold on there SoD. My first reaction was ‘well what about E = m, c^2’. Then I thought of ‘The Principle of Equivalence’ and googled.

I now realise how I, as an engineer, rely heavily on ‘Equivalence’ and a pertinent version of ‘The Virial Theorem’!

I’m happy that the ‘health and safety commission’ (HSC) here in the UK only permit ‘good practice’ for practising engineers (and I’m not currently in practise) because without this input engineers would be faced with the ‘proof of provenance’ that current science demands. From your writings here, it seems that the ‘science’ isn’t decided. That worries me. While googling I turned this up:

Hope it helps. 🙂

Best regards, Ray Dart.

]]>Just a minor note that item 3 should have a proportional sign in the first part of the statement, not an equals sign:

*3. The basic equation relating kinetic energy ∝ temperature (mv2/2 = 3KT/2) is wrong, or*