Well, for those interested, the answers and my questions start here.

For many other readers who are sure the temperature inside a sphere can’t be higher than its outer surface – don’t you wonder why none of the people in agreement with you are able to write down just 2 simple equations (Ta and Tb)?

And why do people lag pipes if the inner temperature won’t increase?

]]>You agree that in case B, Tb = (P/Aσ)^{0.25} ….[eqn mk1] ?

Or not?

You say:

Scienceofdoom, you asked me if I agree whether Ta = 20.25.Tb = 1.2 Tb. My answer was no, because, as you demonstrated yourself, it is the wrong answer.

I have not demonstrated it is the wrong answer. It is the right answer.

If you do the algebra properly, you end up with nonsense like Ta = Ta.

Do you know how to solve 1 equation with 2 unknowns where you would like to find the actual numerical values?

It is not possible.

You need 2 equations. 2 unknowns requires 2 equations.

If you have one equation you can’t find the values.

To get Ta = 1.2Tb, or Tb = (P/Ao)^.25, Ta must be set to zero. As a result your answer is 0 = 1.2Tb, so Tb must be zero also. You have 0 = 0. More nonsense.

To get Ta = 1.2 Tb, Ta must be set to zero?

No. It is the solution to the two equations. If you plug Ta = 1.2 Tb, and Tb = (P/Aσ)^{0.25} you get an answer for Ta and Tb which are not zero.

*For any readers who don’t like maths but do have a calculator and are wondering if mikejacksonauthor is onto something, just try:*

P = 1000

A = 12

σ = 5.67×10^{-8}

Tb = [ 1000/(12 x 5.67×10^{-8}) ]^{0.25} = 196 K

Ta = 1.2 Tb = 235K

*mikejacksonauthor says Ta has to be zero but we can see that Ta is not zero and the equations are easily satisfied. This hopefully demonstrates to all readers that mikejacksonauthor is incorrect in very simple algebra.*

I asked:

“*I look forward to you explaining why your earlier equation for a shell with an internal power source no longer applies.*”

You respond:

Why should it no longer apply. I’m assuming the shell has a temperature and the surface has a temperature. The goal is to find the temperature of the surface. So Ta = (P/Ao + Tb^4)^.25. Put in values for Tb and P and A, calculate Ta and all will be well.

You say “why should it no longer apply?” yet your other statements I cited here claim the equation is wrong. At this point I realize you have no idea how to do simple maths or even confirm or deny a statement. Go back to my question at the start of this comment.

The only way you will learn anything is actually write out the 2 equations for yourself.

If at some stage you want to post up your **2 equations** for Ta and Tb under case B along with the working **then I will respond**. If not, I will ignore following comments.

If ERA40 has a bias which is an offset, e.g. too cold in the arctic, then it wouldn’t affect the calculation of slope.

The later CERES data used NCEP/NCAR reanalysis.

I’m interested in trying to do some CERES analysis myself. I did make a start quite a while ago but there is a bit of a mountain to climb before you can get started. Of course I got diverted on other climate interests.

I have dug out my old notes and will see if I can get any time to extract relevant data.

]]>“I look forward to you explaining why your earlier equation for a shell with an internal power source no longer applies.”

Why should it no longer apply. I’m assuming the shell has a temperature and the surface has a temperature. The goal is to find the temperature of the surface. So Ta = (P/Ao + Tb^4)^.25. Put in values for Tb and P and A, calculate Ta and all will be well.

]]>El Niño/Southern Oscillation (ENSO) is the most important coupled ocean-atmosphere phenomenon to cause global climate variability on interannual time scales. Here we attempt to monitor ENSO by basing the Multivariate ENSO Index (MEI) on the six main observed variables over the tropical Pacific. These six variables are: sea-level pressure (P), zonal (U) and meridional (V) components of the surface wind, sea surface temperature (S), surface air temperature (A), and total cloudiness fraction of the sky (C).

http://www.esrl.noaa.gov/psd/enso/mei/

ENSO originates in the upwelling zone of the eastern equatorial Pacific. It involves more or less upwelling of cold subsurface water – something that varies not just in 2 to 5 year ENSO cycles but over decades to millennia. The feedbacks include changes in surface temperature – which by the physical fact of warmer air holding more moisture influences specific humidity. Not surprising therefore that warmer air in EL Nino holds more moisture. There is of course other feedbacks – cloud, currents, wind, tropical upwelling – that collectively result in the increased planetary cooling from the tropics in El Nino.

Multi-decadal variability in the Pacific is defined as the Interdecadal Pacific Oscillation (e.g. Folland et al,2002, Meinke et al, 2005, Parker et al, 2007, Power et al, 1999) – a proliferation of oscillations it seems. The latest Pacific Ocean climate shift in 1998/2001 is linked to increased flow in the north (Di Lorenzo et al, 2008) and the south (Roemmich et al, 2007, Qiu, Bo et al 2006)Pacific Ocean gyres. Roemmich et al (2007) suggest that mid-latitude gyres in all of the oceans are influenced by decadal variability in the Southern and Northern Annular Modes (SAM and NAM respectively) as wind driven currents in baroclinic oceans (Sverdrup, 1947). see more at – http://watertechbyrie.com/2014/06/23/the-unstable-math-of-michael-ghils-climate-sensitivity/

Greenhouse gases in the atmosphere have a fundamental different dynamic. It adds to warmth in the atmosphere – but whether or not the atmosphere actually warms depends on the collective behaviour of the climate system. Which shifts more or less radically every 20 or 30 years. If surface temperatures actually warm – which seems unlikely for at least a decade more – then we can happily accept that increased water vapour in the atmosphere is a trivial result in the midst of much complexity.

On another topic – you may be interested in – http://watertechbyrie.com/2015/05/05/the-devils-of-ecomodernism/ – while I can’t begin to draw conclusions on climate science the policy response to small anthropogenic pressures in a chaotic system need to be on a human scale and meet human needs.

]]>In your statement of May 6, 2015 at 5:00 pm you said:

No. If Ta = (P/Ao + Tb^4)^.25, then Tb = (Ta^4 – P/Ao)^.25, not (P/Ao)^.25.

Therefore Ta = (P/Ao – P/Ao + Ta^4)^.25

Ta = Ta when simplified.

You have taken one equation and by re-arranging it have proven what? You could re-arrange it and prove P=P or 0=0 or 1=1. You can do this with any equation.

E = mc^{2}, so m = E/c^{2}, therefore – amazing step, substitute m into the original equation and we get E = Ec^{2}/c^{2}, which when simplified gives E = E.

Hilarious! And, because E=mc^{2}, no other equation for E or m can ever be derived by knowledge of physics principles?

In a system with 2 unknowns we need 2 independent equations to solve for both values. The fact that an equation exists for a value doesn’t mean it is impossible to derive a **second** equation from physics principles.

In fact the second equation is necessary.

Luckily, we have a second boundary condition, which creates a second equation. I just showed that it comes from your earlier claim – at 9:59 pm.

I look forward to you explaining why your earlier equation for a shell with an internal power source no longer applies.

]]>This is why I asked you to write down the equations for 2a and 2b and not make a general assertion with “you can calculate using..”

You claimed in case A (May 5, 2015 at 8:56 pm) that the temperature of the shell, Ta = (P/Aσ)^{0.25}

*Your statement was:*

If To is 0 Kelvin and P is constant, then Ts = (P/eAo)^.25

Are you saying that in case B the temperature of the outer shell, Tb is not this value?

Tb = (P/Aσ)^{0.25}

If not, then why has the Stefan Boltzmann law changed? We have a constant internal power source of P. And a surface of area, A, emits power at the rate AσT^{4}.

In steady state, power in = power out. Power input = P. Power output = AσT^{4}.

What is the formula for Tb in case B? Please explain.

]]>I hate these “shell” models for the GHE. A shell, no matter how thin, can not conduct any heat outward when the temperature of the interior and exterior surfaces is exactly the same.

Well, then you must hate all numerical radiative transfer programs. They all, every single one, approximate the atmosphere as a series of isothermal layers. Once you get enough layers, about 30 seems to be a good number, increasing the number of layers does not significantly affect the results. It also matters little whether the layers are optically thin or thick. In fact, they are both at different wavelengths.

You’re over thinking the problem. Sure you could include a temperature gradient in the shell, but again, as the shell becomes thinner, it makes less and less difference, except in the calculation time and program complexity.

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