From Toth:

> The virial theorem applies to the troposphere (given care with the DF.s);

> The tropospheric system’s energy is expressed in its height (or depth).

If there is a simple argument requiring that increased CO2 gives higher tropospheric energy = deeper troposphere (with riders that neither effective TOA temperature nor lapse-rate can decrease), surface AGW is proven. SoD’s detail then addresses the “how much?” following question.

Is this do-able?

If this works, it should apply whatever happens to cloud effects.

Pace, DeWitt Payne; if the virial theorem applies to the troposphere, it’s a fairly safe bet that other constraints in the system dictate its average lapse-rate.

]]>My understanding is that SoD (with many others) treats the atmosphere as a radiatively-driven assemblage, where Miskolczi treats it as a radiatively-coupled system.

I don’t understand your terminology.

Heat transfer between the atmosphere and the surface is by convection and radiation. Heat transfer between the surface/atmosphere and space is by radiation.

So in broad brush, the atmosphere is in radiative-convective equilibrium with the surface. (More specifically, it is never in equilibrium).

Miskolczi’s model treats the atmosphere as one where convection doesn’t exist. An atmosphere in radiative equilibrium.

While I find M2007 obscure in parts, falsifying M’s detail doesn’t eliminate his general model. It wouldn’t be the first time that a scientist got something (approx) right for the wrong reasons.

His model is based on detail. Your statement just means you haven’t understood his model.

To demonstrate this I challenge you to describe his model, its premise(s), and how it could be falsified.

His model is “empirical evidence” disguised as a theoretical paper.

The empirical evidence is not clear. It ignores the effect of clouds on optical thickness for example. This is important because clouds cover 62% of the sky and have a very high optical thickness. It ignores the effect of other GHGs.

]]>The Virial Theorem does not imply a lapse rate at all. It is true for any lapse rate or combination of lapse rates. What would change would be the pressure as a function of altitude. An isothermal atmosphere, for example, would have a higher altitude for a given pressure less than the surface pressure for the same surface temperature than for an atmosphere where the temperature declines with altitude.

Miskolczi is still wrong.

]]>Is anyone else taking this coupled-system approach? If not, I have a few ideas for comment.

Toth (2010) shows that the Virial Theorem can apply to an atmosphere, provided the potential energy (PE) is gravitational and associated only with the parallel (vertical) degree of freedom (DF). He restricts his finding to diatomic gases, but I suggest it extends to any mixture of diatomic and rigid linear molecules at a temperature too low to excite vibrational modes (so N2, O2, CO2, N2O). Note that KEz = PE/2, so each of horizontal-translation and rotation modes is associated with PE as each has 2 DF. He associates PE with troposphere depth.

For simplicity, assume a single GHG with a single saturated stop-band. On a radiance-wavenumber graph, pencil in three BB curves – middle, the bare Earth (controlled by the Solar constant and Earth’s albedo); upper, the “radiatively-forced” Earth; lower, the TOA. Mark the stop-band. For steady-state, the area between middle & upper outside the stop-band = area between middle & lower in the band. Aa & Ed differ considerably. The ratio of in-band OLR to Ed should be a fairly smooth function of their temperature ratio. The coupled system is “pumped” only by in-band Su-Ed. If this is large, the system PE rises, driving both of Ed & OLR up and reducing in-band Su-Ed; ie a negative feedback loop. The system thus has a credible mechanism to maintain itself.

Actual Su-Ed around this blog appears ~10-20 W/m2. The total non-LWR input (SW to atmosphere, latent + sensible heat) is 169 (K&T1997 Fig 7). This would reduce but not invalidate the feedback, and offset the original steady-state condition, allowing temp at TOA to be higher than bare-Earth. Ed approaches Su. Note that in a coupled system, point of input is immaterial.

Adding water (bent molecule, condensable) is beyond my expertise.

Can anyone falsify this so far? If not, has anyone examined actual TOA/BOA temperature ratios over their typical ranges, for comparison with OLR/Ed ratio (both in- & out-of-bands)? Does M2007 imply a prediction of the environmental lapse rate of -6½K/km?

btw, can I suggest that the basic model Earth is a water planet? This would place evaporation centrally in surface processes, where I think it should be.

JWR,

Why do you think the GHE or K&T’s diagram violates the 2nd Law? I’ve seen this claimed in many places, but I don’t get the objection because it’s not about heat going from the cold to warm through a conduction process.

Do you actually think that an emitted photon cannot travel from the colder atmosphere toward the warmer surface?

]]>I made a model of the atmosphere and I analysedMiskolczi’s variables

]]>DeWitt, this issue of the emissions from the tops of clouds was discussed by Steve in the thread I referred to; rather than continue to post slabs of the conversation the link is to David Stockwell’s site and the relevant comments begin 21 from the bottom:

]]>I disagree with Steve Short’s analysis of clear sky S_T. Only in the Tropics is clear sky S_T as low as 61 W/m². Everywhere else, it’s higher. In fact, K&T97 and TF&K09 use something close to US76 for clear sky emission and get S_T ≅ 100 W/m². I think that’s too high as US76 does have very low humidity. But the 30 W/m² for S_T from cloud tops is a more interesting number. Cloud tops are colder than the surface, but they’re also well above the surface. Most absorption of IR is from water vapor and well over half the water vapor resides in the first 2 km above the surface.

For example:

MODTRAN tropical atmosphere with low cumulus cloud cover, base 0.67 km and top 2.7 km. The surface temperature is 299.7 but the cloud top temperature is 280.5 K. Transmittance up from the cloud top is 0.3636 for the range 100-1500 cm-1, which makes S_T = 121.5 W/m². Higher clouds will be colder and emit less, but the transmittance will be greater too. The only way I can come up with something like 30 W/m2 directly to space from cloud tops is to subtract the difference in flux between the surface and the cloud top due to the temperature difference, (121.5 – (448.29-351.01)) = 24 W/m² for the Tropics. Maybe that’s it. That still makes global S_T = 70 W/m². Which makes global transmittance = 70/396 = 0.1768 for a value of τ = 1.73.

]]>“The total OLR curve from the TIGR data set is between the clear-sky and all-sky OLR curves from the ERBE, and the shape of the curves are very similar.”

That’s the problem in a nutshell. The total OLR curve from the TIGR data set is not representative of the planet as a whole. The albedo calculation proves it. Yet he goes on to write two more papers as if it were representative and proves his (fatally flawed) theory. It isn’t, and it doesn’t.

As William F. Buckley once said about Ayn Rand: Where Miskolczi is correct, he’s not original. Where he’s original, he’s wrong.

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