This is my first post? or comment ever. I have followed the discussions about the Virial Theorem on this blog for some time and I think there is a misconception about this theorem. In it’s simplest form it relates potential and kinetic energy in a volume of gas, for instance, where the kinetic energy is that of the gas molecules mv2/2 (only linear motion, no vibrations or rotations). This directly describes the gas temperature. The potential energy is the one between the gas molecules, not including a constant gravitational force. This is the way the gas laws would be formulated and applied on the surface of the earth, or up in the atmosphere. Also, a uniform velocity of the gas volume (due to the rotation of the earth), or the constant earth’s gravity do not enter the basic definition of the Virial Theorem. See for instance “Classical Mechanics” by Herbert Goldstein ,pp 82 to 85. In this basic case the VT is the one Miskolsczi has used:
2KE=PE.

As soon as you mention resonance everyone goes on crank-alert!

When you factor a store of long term natural variation in the oceans ACO2, variations in solar forcing must have a much larger impact than the same amount of CO2 forcing. Its a bit like a swing. A small push in-sync with the swing will over many cycles lead to a large amplitude oscillation. But a constant push, like in increase in ACO2 will only displace the mid-point slightly. This is why we haven't been able to explain the large 20 year signal in the data, from the observed variation.Because clouds and temperature vary together, and a host of different effects conspire to make hot days hotter, and cool days cooler, and the excesses are absorbed by the ocean, it sets up a type of momentum allowing the heat balance to exceed (or stay below) its equilibrium value for long periods, only held in check ultimately by the restoring force of thermal equilibrium.You don't need CO2 to explain the last 30 years warming when you have a natural ocean variations that can stay under or over budget for that period of time.

Of course M's is an equilibrium theory and so can't be expected to represent dynamics. For my theory to work, there needs to be an ocean turnover in the order of 60 years, to maintain the warm vs cold phases. This would require an ocean curren of around 2cm/sec by my calculations, based on a round trip of 40,000km and 60 years, which AFAIK is in the right ballpark for deep ocean currents.While current GCMs don't seem to represent oscillations on the 60year time frame, it would not be expected unless they had oceanographic components that represented deep ocean currents. A 'swamp' can't represent such a slow oscillation. If any models do have potential for such long time frame ocean components, it would be worthwhile to look for it.

Further to this, I wonder whether you have considered the influence of the entire global photoautotrophic biomass as a possible store of long term variation? It is evident that, in the absence of other limitations, the magnitude of the global biomass increases when surface insolation increases.If we take just the (simpler) case of the land for example, it is now known that annual evapotranspiration (ET) is a relatively simple function of annual precipitation and the % distributions of forest (>70% canopy), heathland and shrubbery, and grassland – the latter in that order. About 89% of the variance in ET is explained by this simple function (Zhang et al, 1999, 2001, 2004 – some of the highest citation index papers in modern geography). What this means is that if the overall climatic heat pump is working at a constant rate giving a constant annual precipitation, % forest naturally increases at the expense of % heathland, swamps etc and % heathland, swamps etc increase at the expense of % grassland (as biomass increases) Thus for constant annual precipitation, annual ET goes slowly upwards as the biomass increases due to the slow trend towards more trees. As annual ET goes up then cloud cover slowly increases (aided by higher CCN production), then insolation goes down, surface temperatures decrease and so on and so forth. To paraphrase you, your 20 year signal may also simply reflect, in just one example, the typical mean lifetime of trees. You don't need CO2 to explain the last 30 years warming when you have natural continental plant biomass variations that can stay under or over budget for that period of time, varying Bond albedo 'on the fly', via low cloud cover variation. Thinking about it from an MEP viewpoint, I note that biotic entropy increases with increasing biomass too (entropy decreases when every cell dies, increases when every cell is born). Biological evolution is just another clever way nature found to accelerate its thermodynamic evolution i.e. accelerate its production of entropy.I won't bore you with another long spiel as to how this also works with oceanic photoautotrophic biomass. Trust me (;-).So, please also consider the vast global photosynthetic biomass as another 'ocean' easily and equally capable of long slow oscillations affecting global climate.

It just seems to fit doesn’t it. Stability to me means the solution to conservation relations, so the notion of stable cycles (and non-stable equilibria) is easy to take.

If the THC is responsible for the PDO/AMO cycles, then these must be the longest cycles attributable to ocean currents (as they can’t be much longer than one circumference). A longer cycle must be due to some other endogeneous process (such as biotic, glacial nutrient related, who knows) or else be truely external to the system.

May be there are many others, but for me is being very interestign to read these links in order to begin to understand what the Virial Term may meanhttp://adsabs.harvard.edu/full/1954AJ…..59..137HAnd the ones titled “Virial Theorem made easy” http://math.ucr.edu/home/baez/virial.html which has another links inside that could be useful for people with no deep knowledge of physics like “Can gravity decrease entropy?=” http://math.ucr.edu/home/baez/entropy.htmlBecause in fact all those terms of potential and kinetic energy are variations of energy in time

That would blow that theory if there was no oscillating store of heat.

Doesn't the 60 year [PDO] cycle pretty much correlate with OHC;http://landshape.org/enm/wp-content/uploads/200…Eespecially after thew recent NODC adjustment;http://i48.tinypic.com/14e6wjn.gif

Doesn’t the 60 year [PDO] cycle pretty much correlate with OHC;

http://landshape.org/enm/wp-content/uploads/2009/10/fig3.png

Eespecially after thew recent NODC adjustment;

http://i48.tinypic.com/14e6wjn.gif

“identify the actual 60 year current cycle” I mean the physical location and velocity of ocean currents.

Any idea where this whopping +10% increase in OHC between 1970 and 2010 went? Shouldn't this have manifested itself somehow in an increased rate of surface pCO2 rise due to the reduced CO2 solubility. Or did all that warm water sink rapidly below say 50 m or so (;-)?Doesn't seem to be any warm water near the Great Southern Ocean below 40 S (SO) as the rate of increase in surface CO2 levels over the whole SO actually decreased relative to the rate of increase in the global mean surface CO2 over 1983 – 2008 at least.This means that the rate of increase in surface CO2 levels over the whole SO actuallu decreased even more rapidly relative to the rate of increase in the NH oceanic mean surface CO2. This points to less not more mixing between NH and SH at least near the surface.http://jump.fm/DOHSOWe seek it here, we seek it there, that mysterious submarine 'hot spot'.

Your file sharing service made my antivirus software nervous so I didn't download the spreadsheet. There's a big jump in OHC somewhere between 2000 and 2004 that seems too big to be true. I think they're still having trouble reconciling ARGO measurements with the older measurements. If the jump were really that large, it would have shown up in the sea level measurements. It doesn't.

F. Miskolczi has replied to a disparaging comment I made on a thread at The Air Vent. He claims to have corresponded with Toth and convinced him that he (Miskolczi) dealt with degrees of freedom properly elsewhere in his paper. I didn't much like the tone of his posts and don't want to play any more, although I admit that I basically poked him in the eye with a sharp stick. If anyone else wants to play, it's this thread: http://noconsensus.wordpress.com/2010/04/19/rad…

Give it to him Steve; but preserve your copyright.

Give it to him Steve; but preserve your copyright.

Inefficient, yes, but much easier to interpret what's going on than code. I wonder what M.'s reaction would have been if Steve had offered him an R script.I still don't understand how tau, which seems to be a mathematical construct like the global average surface temperature, can somehow be related to thermodynamics. A global average tau only means something for a single slab atmosphere, which is a toy model.

I don't know about the rest of you, but I'm an idiot. Miskolczi is correct about the Virial Theorem. However, that doesn't mean that the rest of his theory is correct. The conclusion I should have drawn from Toth is that the Virial Theorem statement is a trivial result and is already included in Physical Meteorology. It should have been obvious when Toth used the Virial Theorem to calculate the heat capacity of a molecular gas.Physical Meteorology already uses the heat capacity in, for example, the dry adiabatic lapse rate, g/Cp. The obvious conclusion then is that any stable atmospheric temperature profile, from dry adiabatic to isothermal for example, will comply with the Virial Theorem. Yes, an isothermal atmosphere has a higher kinetic energy than an atmosphere with a dry adiabatic lapse rate, but it also has an altitude vs pressure profile that drops less rapidly than an dry adiabatic atmosphere so the gravitational potential energy is higher too. But it's the atmospheric temperature profile and resulting density profile that determines the optical thickness for a well-mixed ghg. Forcing from CO2 is quite a bit higher in the Tropics than in the Arctic because the atmosphere in the arctic is colder and denser and the optical thickness for the same concentration of CO2 is less. So saying that the atmosphere is governed by the Virial Theorem tells us nothing we don't already know.

I don't know so much about the Virial Theorem (which is somehow supposed to lead to the global (cloudy sky) average S_U to S_U = 3OLR/2. By my estimations (from scouring the published literature) the S_U/OLR for the typical range of average global cloud covers (NCAR data) is typically closer to 5/3 than 3/2. That ratio is certainly consistent with at least 85% of published global heat budgets over the last 15 years and anyone can verify that for themsleves.Just to stir the possum a little more, one other thing I have concluded is that Miskolczi's A_A = E_D i.e. his so-called Kirchoff's Law equality only applies (away from the clear sky extreme) if, and only if, his S_T flux from the surface somehow doesn't actually arrive at TOA in its entirety. Maybe this is why DeWitt agrees with A_A = E_D too (stated on the Air Vent)?So e.g. the cartoons Fig. 2 in M&M04 and Fig. 1 in M07 do not appear to be strictly true when they show S_T as departing BOA. In fact, by comparison with equivalent (cloudy sky) estimations by practically everyone else the (higher) Miskolczi S_T(s) must somehow be diminished along the way, perhaps by a partial downwards reflection of LW IR (to become part of E_D) off clouds. Hey, we know this actually occurs, and Miskolczi never mentions it, so why not?Perhaps this is why Miskolczi can have an S_T of ~60 W/m^2 at the global average cloud cover and everyone else has (or imply) a value of about 35 – 40 W/m^2. Take that extra 20 – 25 W/m^2 and add it to E_D and bingo – you get a balance with A_A (which =S_U – S_T by definition).As Thayer Watkins has pointed out , there is indeed a significant component of LW IR transmitted from BOA which is reflected off the bottoms of low clouds, especially evident at night.http://www.applet-magic.com/cloudblanket.htmMake me wonder if, in considering Ts and Te, FM forgot to ensure that the whole body of surface up/down radiative data he based his whole house of cards on was diurnally balanced. Now there's a scary thought!

IMO, A_A is only approximately equal to E_D. If there is a temperature inversion, as in sub-Arctic winter in MODTRAN, then E_D will be larger than A_A. In all other cases, E_D should be slightly less than A_A.

I don’t see why the S_U to OLR ratio should be constant. It should be a function of both ghg concentration and cloud cover. It looks to me as if one should treat the cloud top as the surface rather than the ground for cloud covered sky. That may be how M gets an S_T value of 60W/m2. In TFK09 it’s 70 W/m2, 40 from the surface and 30 from the cloud tops, if I read the cartoon correctly. Then you have to add the coupling between the cloud top and bottom and the coupling between the cloud bottom and the ground. Addition of a well-mixed ghg like CO2 should have an effect on cloud top temperature. That can be estimated for low clouds using MODTRAN, but mid-level clouds are going to be more difficult because you can’t ignore the atmospheric contribution to absorption/emission between the ground and the cloud bottom for mid-level clouds. I think MODTRAN only has low and high level (cirrus) clouds as options.

“IMO, A_A is only approximately equal to E_D. If there is a temperature inversion, as in sub-Arctic winter in MODTRAN, then E_D will be larger than A_A. In all other cases, E_D should be slightly less than A_A.”We agree on that.”I don't see why the S_U to OLR ratio should be constant. It should be a function of both ghg concentration and cloud cover.”We agree on that. But…..kinda jettisons Miskolczi's 'Virial Theorem hypothesis” though! I thought in your previous post you were claiming to be an idiot and that Miskolczi was right on that one? I'm confused. Or is that what you mean when you say; “However, that doesn't mean that the rest of his theory is correct.”? Sort of an enormous 'rest of his theory' though – like much of the whole edifice.”It looks to me as if one should treat the cloud top as the surface rather than the ground for cloud covered sky”In a sense you are right. And to give him fair credit Miskolcizi did thoroughly discuss that issue in a number of places.”That may be how M gets an S_T value of 60W/m2.” Yes, that is essentially exactly what I pointed out on Niche Modeling oh about 2 years ago now, and have just now restated in terms of well, does it include a downward-reflected portion of his S_T?”In TFK09 it's 70 W/m2, 40 from the surface and 30 from the cloud tops, if I read the cartoon correctly.”Correct and so does just about every other published global heat budget more or less.So the question yet again arises. What does Miskolczi include in that 60 W/m^2? More of the latent heat (total ~80 W/m^2) than the ~50 W/m^2 (~62.5%) that typically downwells (according to the mainstream literature)? Doesn't seem at all likely as that only occurs during rain or ice formation and Miskolczi's measurements are purported to get a much narrower variability range of E_D:A_A. So, what about the only thing which appears in that famous cartoon – using T,F&K09 (say) the ~333 W/m^2 'Back Radiation' (E-D in Miskolczi formalism):333 + 60 – 40 = 353 ~ 356 (i.e. A_A)353/356 = 0.992 ~ 1.00So, I return to my question. Is Miskolczi so clever that he has defined S_T as that which strictly is not absorbed between BOA and TOA BUT also includes that which is reflected off the bottoms of clouds to be incorporated into his E_D and hence not all of his S_T departs TOA (as part of OLR) despite his own cartoons?It's a reasonable proposition (albeit at odds with hsi cartoons). If as he insists A_A=E_D and it is critical to his theory (which it is), maybe this is where Miskolczi explicitly (and legitimately?) departs from all the mainstream literature global heat budgets, which as Zagoni recently noted have A_A/E_D ~ 1.08 typically ranging 1.00 at clear sky though 1.11 at total cloud cover).I always though Miskolczi did himself a big disservice by lumping all his (supposedly non-radiative) unknowables into that horrible K term. This is yet more evidence for that – and even raises the possibility of a forgotten truly radiative term within K.

“Miskolczi is correct when he says that the Virial Theorem requires the ratio of potential energy per degree of freedom (in his case z) of kinetic energy to be 2:1.”But he didn't say that in his paper; he said:“The atmosphere is a gravitationally bounded system and constrained by the virial theorem: the total kinetic energy of the system must be half of thetotal gravitational potential energy.”Of course, this comes back to the unsolved mystery of that these fluxes have to do with PE and KE anyway.

Miskolczi claims in his correspondence on the thread at The Air Vent that he was referring to just the kinetic energy in the z direction. He quoted an email from Toth to that effect.

“…..Regarding the final clause in my paper, I found it important to stress that the degrees of freedom must be considered, while at the same time, I did not wish to actually criticize Ferenc’s paper. A good thing, too, because in his latest e-mail, Ferenc made it clear that he did account for the degrees of freedom, he just did it differently (rather than accounting for it in his expression of the virial theorem, he only considered the kinetic energy per the vertical translational degree of freedom to begin with.) I do find this a little confusing (I don’t think this is clearly explained in his paper) but the result is correct, and that’s what matters in the end…”

If that's what me meant to say rather than what he actually said, and I'm willing to give him the benefit of the doubt on that, then we should drop the virial theorem argument and concentrate on the real unsolved mystery which is indeed as you stated.