# the Air Vent

## Because the world needs another opinion

• JeffId1 at gmail dot com

Everything you need to know about Climategate. Now available at Amazon.com

 philjourdan on In the News Brian H on Sausage the Deer Classical Values… on In the News Brian H on In the News Brian H on In the News omanuel on In the News gallopingcamel on In the News omanuel on Sausage the Deer CoRev on Sausage the Deer Robert Austin on Sausage the Deer Robert Austin on Sausage the Deer omanuel on Sausage the Deer Jeff Id on Sausage the Deer Fred Harwood on Sausage the Deer 4TimesAYear on Reader Background
• ## Follow Blog via Email

Join 129 other followers

## Fixing the basic AGW calcs II

Posted by Jeff Id on December 20, 2010

This comment was left in the thread of Judith Curry’s blog.  It is an explanation of the problems introduced when the simple black body sphere estimate for basic forcing is not used.  While Tomas makes the point that the solution is nonsense, these things can still be estimated and do have uses so I’m not as dismissive as he of the idea, however on the complexity of the problem we agree.  So when people say 33 C from global warming gasses, you have to wonder where they got their facts or if they understand them.  The 33C value is just an estimate which is likely to be a poor quality one.
-

Judith just look at how bungled this “sensitivity” concept is .

(1) F = ε.σ.T⁴(definition of emissivity)
dF = 4.ε.σ.T³.dT + σ.T⁴. dε => dT = (1/4. ε.σ.T³).(dF – σ.T⁴. dε)

Ta = 1/S . ∫ T.dS (definition of the average temperature at time t over a surface S)

Now if we differentiate under the integral sign even if it is mathematically illegal because the temperature field is not continuous we get :

dTa = 1/S . ∫ dT.dS

Substituting for dT
dTa = 1/S . ∫ [(1/ 4.ε.σ.T³).(dF - σ.T⁴. dε)] . dS

Now this is a sum of 2 terms :

dTa = { 1/S . ∫ [(T/ 4.ε) . dε].dS } + { 1/S . ∫ [dF/4. ε.σ.T³].dS }

The first term is due to the spatial variation of emissivity.
It can of course not be neglected because even if the liquid and solid water has an emissivity reasonably constant and near to 1 , this is not the case for rocks , sable , vegetation etc . It is then necessary to compute the integral which depends on the temperature distribution.
E.g same emissivity distribution , different temperature distributions give different values of the integral and different “sensitivities”.

The second term is more problematic.
Indeed the causality in the differentiated relation goes from T to F . If we change the temperature by dT , the emitted radiation changes by dF .
However what we want to know is what happens with T when the incident radiation changes by dF.
This is a dynamical question whose answer can not be given by the Stefan Boltzmann law but by Navier Stokes (for convection) , the heat equation (for conduction) and the thermodynamics for phase changes and bio-chemical energy.

OK as we can’t answer this one , let’s just consider the final state postulated as being an equilibrium.
Not enough , we must also postulate that the initial and final “equilibrium” states have EXACTLY the same energy repartition in the conduction , convection , phase and chemical energy modes.
In other words the radiation mode must be completely decoupled from other energy transfer modes.
Under those (clearly unrealistic) assumptions we will have in the final state dF emitted = dF absorbed.

Now comes the even harder part . The fundamental equation (1) is only valid for a solid or some liquids so the temperatures and fluxes considered are necessarily evaluated at the Earth surface.
If we took any other surface (sphere) going through the atmosphere , all of the above would be gibberish.

Unfortunately the only place we know something about the fluxes is the TOA because it is there that we will postulate that radiation in = radiation out.
This is also wrong (just look at the difference between the night half, the day half and the sum of both) but this is the basic assumption of all and any climate models sofar.
So what we postulate at some height R where the atmosphere is supposed to “stop” is :
FTOA = g(R,θ,φ) with g some function.
From there via radiative transfer model and assuming known lapse rate, we’ll get to the surface and obtain F = h(R,θ,φ)] with h some other function depending on g (note that h , so F depends also on the choice of R e.g the choice where the atmosphere “stops”)
Last step is just to differentiate F because we need dF in the second integral.
dF = ∂h/∂θ.dθ + ∂h/∂φ.dφ

Now substitute dF and compute the second integral . The sum of both gives dTa , e.g the variation of the average surface temperature.
We can also define the average surface flux variation :
dFa = 1/S . ∫ dF.dS

It appears obvious that {∫ [(1/ 4.ε.σ.T³).(dF - σ.T⁴. dε)] . dS} / ∫ dF.dS
(e.g dTa/dFa) will depend on the spatial distribution of the temperatures and emissivities on the surface as well as on the particular form of the h function which transforms TOA fluxes in surface fluxes.
It will of course also change with time but this dynamical question has been evacuated by considering only initial and final equilibrium states even if there actually never is equilibrium.

A careful reader will have noted and concluded by now that it is impossible to evaluate these 2 integrals because they necessitate the knowledge of the surface temperature field which is precisely the unknown we want to identify.
The parameter dTa/dFa is a nonsense which can only have a limited use for black bodies in radiative equilibriums without other energy transfer modes.
The Earth is neither the former nor the latter.

1. ### Oliver K. Manuelsaid

Yes, the AGW story is filled with flaws.

But the most basic flaw are

a.) Ignoring well-documented variations in Earth’s heat source – the Sun – and

b.) Earth’s orbit inside the outer layer of the Sun – the heliosphere.

The next most serious flaw probably arises from the obsolete Standard Solar Model model of Earth’s heat source
[“Why the Model of a Hydrogen-Filled Sun Is Obsolete”} http://arxiv.org/pdf/astro-ph/0410569v1

Oliver K. Manuel

2. ### DeWitt Paynesaid

Tomas Milanovic makes the same mistake as Gerlich and Tscheuschner. He appears to think that if you can’t solve a problem analytically, you can’t solve it at all. That is, of course, not true. I bet he’d really freak if he ever looked at temperature profile measurements by satellite microwave emission measurements. That’s another problem that can’t be solved analytically. Worse, it’s ill-posed, as are many inverse problems. You solve these problems iteratively by first making a best guess and then putting in other constraints like continuity and smoothness.

The 33 degree number is for a sphere at uniform temperature. But you only have to be fairly close to uniform for the error in the average temperature to be no more than a couple of degrees. The high heat capacity, rapid rotation rate and air and water circulation of the Earth makes the surface temperature close enough to uniform that the error is going to be less than 5 degrees. In other words, good enough.

The annual average TOA emission has been measured as a function of latitude and it’s fairly flat. (Figure 1.1 Grant W. Petty, A First Course in Atmospheric Radiation, Second Edition) compared to the incident radiation absorption as a function of latitude. You can use this data to calculate meridional heat transfer. It’s quite large, about 5 PW at the peak near 40 degrees latitude. The range in emission is about 150 to 270 W/m2. That corresponds to temperatures of 227 and 263 K compared to 255 K for a sphere at uniform temperature radiating an average of 239 W/m2. Note that the plot is by latitude which exaggerates the magnitude of emission from high latitudes.

3. ### Steve Fitzpatricksaid

DeWitt #2,

You are for sure right about this, but that diagram would be a lot more convincing if the total areas of surplus and deficit were equal…. the diagram suggests a continuous net loss of energy, which is non-sense.

4. ### Steve Fitzpatricksaid

Dewitt,
forget my earlier comment; the units are watts per square meter, and the number of sqaue meters falls with increasing latitude. The diagram would be better if they somehow normalized to have the total areas (positive and negative) equal.

5. ### Ryan Osaid

In the end, many of those complexities don’t matter when looking at the whole picture. The only significant energy source is the sun. The only way for the earth to dissipate energy to space is via radiation. So if the earth is the system under consideration, ignoring convection and conduction is correct. Convection and conduction are internal processes that redistribute the energy within the system, but the only escape for the energy from the system is radiative.

6. ### Brian Hsaid

#5
Doesn’t that beg the question of just how fast and by what means this “balancing” occurs? Someplace in these explanations, the assumption is always slipped in that this occurs on relevant time scales. And, of course, no actual moment of actual equilibrium ever occurs, locally or globally. And there are energy sinks and sources which have nothing to do with solar radiation in the game.

As for the “close enough” temperature gradient observation above, Sahara/Antarctica ranges might be something like )/-50°K out of a total in the 270K range. Tropics are dynamically and actively kept COOLER than the nearby sub-tropics by convection and circulation (by a lot more than 5°). Etc.

All this “close enough for government work” stuff is really stretching it. Hand-waving is one thing; mole-whacking is quite another.

7. ### Brian Hsaid

mod: typo above: +/-, not “)/-”.

8. ### Carricksaid

SteveF:

forget my earlier comment; the units are watts per square meter, and the number of sqaue meters falls with increasing latitude. The diagram would be better if they somehow normalized to have the total areas (positive and negative) equal.

Dang it. I was just getting ready to convert that curve into text value, then do the integral including the cos(theta) factor.

Ryan O:

Convection and conduction are internal processes that redistribute the energy within the system, but the only escape for the energy from the system is radiative

Not sure I entirely agree here. Convection affects the height at which you get the “free radiation” condition (it’s responsible for the environmental lapse rate of 7°C/km), which in turn affects the net surface warming.

Brian H: One can start with the assumption of a uniform temperature, then use first-order perturbation to compute the correction due to the nonuniformity of the temperature in some regions of the planet. Don’t forget that the oceans have a relatively smoothly varying temperature with latitude. So corrections from extreme environments will not make a huge difference in the answer.

I’ll mention that Arthur P Smith has a fairly complete description of the physics at work here.

He doesn’t address the details of how one treats irregular globe, that would be a simple extension of his work.

I’d be interested in what people think of his arguments.

9. ### Ryan Osaid

Carrick,

Yep, but the energy cannot escape the earth via convection or conduction. It must escape via radiation. Convection certainly has an important influence on what happens to the surface, but does not change the amount of energy escaping the earth (at least once near-equilibrium is reached).

10. ### Ryan Osaid

I should specify something. From the perspective of a simple model, with no feedbacks, you can calculate what changes in the optical depth will do to surface temperature at equilibrium fairly easily. With a little more effort, you can calculate the transitory response. This is the first-order approximation. You don’t need to know all the stuff that he thinks you need to know to do this. Stefan Boltzmann is sufficient.

Now, when you start adding in the other complexities, things do, indeed, get hairier. But is argument that the situation is intractable (even as an approximation) is not true. While an exact answer cannot be obtained, an estimate can, and depending on the data quality, confidence intervals can be placed on that estimate (not that this is done properly, but that’s a separate issue). He is presenting the reasons why models must parameterize, not why an estimate of sensitivity cannot be obtained.

11. ### Dustersaid

Ryan O said
December 20, 2010 at 4:41 pm

“… But [the] argument that the situation is intractable (even as an approximation) is not true. While an exact answer cannot be obtained, an estimate can…”

The problem with an estimate is that the model solution will diverge from empirical conditions over time. The existing models seem to have diverged fairly rapidly. Lorentz regarded long range modeling as probably intractable and he’s the guy who first discovered “strange attractors” while trying to model weather.

12. ### Ryan Osaid

Duster,

By “model”, I don’t mean GCM. I mean mathematical simplification that makes the problem calculable. And yes, the time frame over which you forecast is important.

13. ### Ryan Osaid

Also . . . you seem to be implying that models will always diverge and are thus useless. First, this is not always true. Second, this is tantamount to saying we ought not to bother to calculate anything, since the act of reducing a problem to a set of equations always involves a model to a certain extent. Always.

14. ### RBsaid

We sort of went over this chaos and predictability recently. My read of this is that the assumption is that expected change due to CO2 will overwhelm natural variability over the centennial timescale and therefore even though climate is chaotic at all timescales, you can neglect that over the next 100 years. It is probably a circular argument if you only use the recent temperature record for sensitivity estimates and believed that most of the record is explainable by natural variability.

15. ### David in Londonsaid

I’m no scientist but it fascinates me when I see them debating complex equations behind global warming all over the internet, which tells me the only thing I need to know:

The science is clearly not settled.

If you can all easily disagree and dismantle virtually every theory from either side then why don’t the IPCC do it (no need to answer, I know why, but ask yourselves though).

16. ### DeWitt Paynesaid

I’d be interested in what people think of his arguments.

I’ve done much the same thing, but in a my usual cruder, brute force style. You can get the lunar curve looking more like the real thing if you use a diffusive model for heat transfer into and out of the surface (not that I did, but you can). That way the temperature rises and drops faster at sunrise and sunset. An axis of rotation that is not perpendicular or parallel to the orbital plane will also make some small difference. Meridional heat transfer by air circulation probably makes the most difference at the highest latitudes. In theory with no atmosphere and a perpendicular axis of rotation the poles have a temperature of absolute zero or at least the CMB temperature. It only takes a tiny amount of heat transfer to raise that temperature a lot.

17. ### Geoff Sherringtonsaid

Ryan,

Although the overall balance might be there, the sub-components are important. It’s because of sub-components that we have emphasis on greenhouse gases. In a round about way, we now have early estimates of GHG contributions (day 1850-1920) being calculated from early guesses or proxies for (say) aerosols. The difference between two poor, opposing numbers is still a poor number.

The poor numbers enable political argument.

18. ### BillyBobsaid

I asked myself, how much is of the earths surface temperature comes from the core?

This site suggest some areas can be heated at 350mW/m2

http://geophysics.ou.edu/geomechanics/notes/heatflow/global_heat_flow.htm

19. ### Concernedsaid

Jeff, a new smear campaign against global warming skeptics seems to have started here:

http://globalwarmingsuperheroes.com/

The domain was registered in the UK at:

Registration Service Provider:
Fasthosts Internet Limited, domains@fasthosts.co.uk
+44.8708883600
+44.8708883760 (fax)
http://www.Fasthosts.co.uk

Note the registration date: Record created on 14-Oct-2010
===

You can try contacting the owners of globalwarmingsuperheroes.com here:

https://rr-n1-tor.opensrs.net/wp_mailer/

Just paste in globalwarmingsuperheroes.com, fill in the captcha, and you’ll get a form to contact the globalwarmingsuperheroes.com admin.

===
globalwarmingsuperheroes.com
Globalwarmingsuperheroes.com is a domain controlled by three name servers at livedns.co.uk. All three of them are on the same IP network. The primary name server is ns1.livedns.co.uk. Incoming mail for globalwarmingsuperheroes.com is handled by one mail server at globalwarmingsuperheroes.com themselves. globalwarmingsuperheroes.com has one IP number (213.171.218.7).
You might also be interested in administrator.globalwarmingsuperheros.com.
Search for globalwarmingsuperheroes.com.
===

Any way for UK readers to find out who is behind this?

20. ### DeWitt Paynesaid

I found my old spreadsheet. Here’s the graph of total power in Watts by latitude corrected for area. The problem with this graph is you lose the connection to effective temperature that you get with W/m2 compared to just W. It does show that you have to get fairly far from the poles to get much total power. Considering I digitized more or less by eye, it’s almost a miracle that the incoming and outgoing power are only 2% different.

21. ### AusieDansaid

The problem is that you are not taking real account of the chaotic nature of the climate.
You are all working in an assumed equiblimrium seeking system.
All the sub sysrems on the earth play catchup, but never make it.
But above all that, the sun itself is chaotic, so the incoming amount of heat and probably more importantly, the magnetic flux, the cosmic ray count, cloudiness etc are forever fluctiating.
But not necessarily fluctiating around some mean.
Periodically, there is, not just a step change, but a complete change in circumatances and all the forces are different.

Some think we may have reached such a stage with the switch from cycle 23 to 24.
That will take some years to become clear.
Your calculations do not encompass what may or may not be happening.

And the effect, if any, of CO2 cannot rise above these forces.
CO2 emissions are just part of the internal system, not outside it.

22. ### berTanya Jawabsaid

Thanks the info Mr..
This blogs is beautiful

23. ### plazaemesaid

I agree with 21. It was un interesting point at Curry’s place, not enough explained (at least for me). I find this “extra” commentaries quite informative.

Thanks.

24. ### scienceofdoomsaid

Jeff Id:

I’m not sure what exactly you are claiming – or posing as a problem.

In the article you say “So when people say 33 C from global warming gasses, you have to wonder where they got their facts or if they understand them. The 33C value is just an estimate which is likely to be a poor quality one.

And in Judith Curry’s blog you say: “I also wouldn’t be surprised to find out that warming from doubling of CO2 even with no feedback has been incorrectly estimated. I haven’t found a good reference for the 1C calculation as yet.

Two different problems. Both with their own issues.

Then there is a link to a comment:
Tomas says:
Now if we differentiate under the integral sign even if it is mathematically illegal because the temperature field is not continuous we get..

Who has demonstrated that the temperature field is not continuous? I’m sure it is continuous. We might not know it completely but that’s a very different problem.

I agree with DeWitt Payne, comment #2.

Well, not being sure what your point is:

1. The 33′C “greenhouse” effect is only a “headline” value.

a) if there were no “greenhouse” gases the climate would be quite different. Colder for sure, but there would be feedback effects which are not quantified.
The surface would – on average – radiate the same amount as absorbed solar radiation. But the absorbed solar radiation would change with the colder temperature (albedo changes at least). As described in The Hoover Incident.

b) if the absorbed solar radiation was exactly the same as now, the surface radiation would be 239 W/m^2. This equates to an average temperature of -18′C if the temperature has little variation. But the larger the variation the lower the surface temperature. So 33′C change is a minimum result in this case.

2. The no feedback doubling of CO2 value is only a “no feedback all other things being equal” value. If all other things are equal it isn’t so difficult to work out this value.

All other things won’t be equal. With overall negative feedback the number will be lower. With overall positive feedback the number will be higher.

The “no feedback” value is simply calculated by assuming that the lapse rate and water vapor stay the same. After all, they are feedbacks (the lapse rate being a believed negative feedback and the water vapor being a believed positive feedback).

So in a different question, what is the usefulness of the “no feedback” number? It gives a magnitude of the effect that would be caused by CO2 doubling if the climate didn’t react.

3. Tomas statement appears to try to demonstrate that no problems are soluble if you don’t have perfect knowledge of the continuous values of the variables in question.

Maybe he can explain what it is he is really claiming to demonstrate.

If temperature – in the places we don’t measure it – goes to some discontinuous value like 100,000K or 7,600K or 0K – then he is probably right that current methods are problematic. In this case, we have more pressing problems to worry about..

25. ### huntersaid

Ryan O,
You keep underscoring that energy only escapes via radiation, but are you forgetting some large heat sinks: Earth and Ocean?

26. ### Mark Fsaid

24:
Well, it wouldn’t be escaping, then, would it? Sigh.

27. ### steveta_uksaid

Hunter #24

Heat cannot escape via a heat sink – it’s temporary storage that once it reaches equilibrium cannot absorb any more.

However, heat can be lost via the boiling of the top of the atmosphere into space. That must make up some almost-measurable loss that’s not been included!

28. ### Steve Fitzpatricksaid

DeWitt #19,

I think the best way to make the heat balance versus latitude graph both have incoming and outgoing heat equal, and preserve information about rate of loss per square meter area, is to maintain the y-axis values as in the original graph, but adjust the x-axis scale to compensate for how the total area available for transfer declines with increasing absolute latitude. That is, the displacement of each data point along the x-axis from 0 should be proportional not to the latitude angle but to sine of that latitude angle, with the full range of the x-axis then being from -1 (south pole) to +1 (north pole). So, the units on the x-axis just change change from latitude to sin(latitude), and the extremes of the data (high latitudes) get compressed along the x-axis and so represent less area under the curve, even though the y-axis values continue to show the net loss per square meter.

29. ### stansaid

Jeff,

This is totally off topic, but perhaps some “lazy” day you will put up a thread on it. P Gosselin has some of the questions and answers of an interview Hans von Storch gave in German http://notrickszone.com/2010/12/21/hans-von-storch-on-media-politics-climate-science-and-activists/

Money quote —
Q: What has to improve with the public communication of anthropogenic climate change and what has to happen so that it gets better?
HvS: More openness to questions and skepticism; more skepticism with respect to the alarmists (i.e. the ones who have the more interesting “stories” for the media and politics); more resistance to attempts at using single events as proof that supports far-reaching statements (like on the irrelevance of the man-made greenhouse effect) on climate dynamics; caution in the argumentative use of the latest scientific findings ( much in Nature and Science later turns out to be in need of revision); evaluating scientific results from the methodical points of view, and less from the point of view of political application.

“Much in Nature and Science later turns out to be in need of revision”

For me, climate science often appears to be an exercise in incompetence on steroids. Of all the garbage that leaves me scratching my head, this is the one aspect that has me scratching the hardest. “Scientists” with a track record of screwing up their statistics put out a new study that supposedly changes scientific understanding. It hasn’t been audited or replicated. Yet EVERYONE, alarmist and skeptic alike, immediately treats the announced conclusions of the study as if they are solid.

HvS is right, but he doesn’t go far enough. Climate scientists (perhaps scientists in general) come off like a bunch of unquestioning Chicken Littles. They’ll believe anything. Not only will they believe anything, they will extrapolate the shaky conclusions of a single, untested study even further. [Maybe it's the "science" culture. Look at the history of all the announcements about what is good for our health, oops -- bad for our health, oops -- good for our health again.] I’d have a lot more respect for the whole bunch of them if they were capable of saying “maybe, could be, interesting possibility, needs a whole lot more work.”

30. ### DeWitt Paynesaid

Like this? That does look better.

31. ### Steve Fitzpatricksaid

DeWitt #29,

Yes, perfect. Much more informative; thanks. Now here is what I take away from the modified graphic:

1. The peaks of net emission fall near the limits of the tropics, but with greater peak emission in the north due to the desert bands (high emitting.. warm, few clouds, low absolute humidity) mainly in Africa.

2) The drop in emission near the equator (compared to surrounding low latitudes) suggests some positive feed-back for tropical moisture/clouds.

3) The lowest emission in the tropics is slightly north of the equator…. lying over the Amazon basin and central tropical Africa, where heavy daytime and early evening clouds, along with very high absolute humidity, reduce IR emission. There is a corresponding dip in the solar absorption curve at the same north latitudes, but not quite as large, suggesting that increasing albedo from thunderstorms does not quite balance the reduced IR emission due to clouds/moisture.

4) The extremely low emissions over Antarctica are consistent with the very low temperatures there, but in addition, indicate that the very low Antarctic temperatures are in large measure due to the thermal isolation of the continent from lower latitude heat by the cold Southern Ocean… very different from the Arctic.

Now an interesting (well to me!) graphic would be the plot of black-body temperature calculated for the emission rates vs sine(latitude). If subtracted from the average surface temperature versus latitude, you would have a green-house effect versus latitude graphic.

32. ### Jason Calleysaid

Ryan O said on December 20, 2010 at 1:25 pm:
“In the end, many of those complexities don’t matter when looking at the whole picture. … Convection and conduction are internal processes that redistribute the energy within the system, but the only escape for the energy from the system is radiative.”

True, radiation is the only way out for the energy, but convection and conduction still make a difference. A radiating sphere (that’s us!) with hot and cold spots will radiate more total energy than a sphere with the same heat evenly smeared out. The hot spots (since radiation is a T^4 function) will radiate an extra amount that is greater than the loss from the cooler spots. Also, if the hot spots are accompanied by massive atmospheric upwellings (like in a thunderhead)there will be an increase in radiative efficiency by moving the hot air closer to the upper atmosphere where IR transparency is higher.

Radiation is the only way out, but radiation is modulated by convection.

33. ### Doug Proctorsaid

Planetary average temperatures by definition are a time-averaged value over a geographical, topological and albedo varying object in a non-circular orbit around a slightly intensity-varying sun. The NASA data showing temperature variations by hemisphere and month show great differences, but if you go deeper into the time and location data, the variability becomes greater. We have multiple varying factors non-entirely linked, at least not in unique solution ways. All this considered, what is the 60 year or greater natural variability in insolation and planetary albedo? The varying factors are not in lockstep with each other. So: we say the total GHG give us a 33K boost over simple black/gray body radiation, but what is the +/- in terms of the insolation & albedo variations?

The assumption in CAGW is that the world is in a steady-state equilibrium, a static equilibrium. I doubt that very much. I expect the world to be in a dynamic equilibrium like all other physical and biologic systems on the planet. If true, then the 33K boost this year may be the 33.7 boost next year, and the 32.3K boost the year after. Or on a decadal sense. Or 60 year period.

In this case it is not the error bar that is important, but the natural variability of two contradicting parameters (themselves functions of other, numerous semi-independent variables): insolation and albedo. The non-cirularity of Earth’s orbit at 1.6% means a 3.2% change in insolation or 13.6 W/m2, and at an albedo of 0.296, an absorbed variation of 9.6 W/m2. A 2% change in Earth’s albedo equates to about 1.4 W/m2 and said to be equal to the CO2 radiative reduction with a doubling of CO2. With just those two variables considered, we can see 11.0 W/m2 surface and atmospheric heating variation must reasonably occur. That, according to the IPCC, is about enough to heat or cool the planet by 3-5K. Since we don’t see such changes year to year, there must be feedback, dampening or a governor involved, but why do we assume (warmist assume, that is) that the effect is reduced to a 0.1-0.2K variation? And is this variation the only one? What about a +/- of 0.3K on a larger scale, or +/1.0 on an even larger scale?

We are lost in the minutae of climate variation, right down to the weather in southern Devonshire. But what can we say about a 0.6K temperature rise over 30 years if we don’t even have a +/- insolation & albedo dynamic variation? The IPCC image of a static world at a planetary scale doesn’t make sense to me. If we lived in a static world we would have climate and no weather.

34. ### Ryan Osaid

Geoff,

I agree with you 100% (and everyone else who mentions that conduction and convection play an important part). What I am trying to say is that it is a trivial task to obtain a first order approximation assuming no dynamical responses using only Stefan Boltzmann. This indicates that the “simple physics” dictate a temperature increase at equilibrium with an increase in C02. While not always true, the simply physics often indicates the direction the system will take due to the perturbation, albeit not necessarily the magnitude of the response.

From there, everything becomes much more complex. But given that the simple physics says increase in CO2 = increase in surface temperature, the argument that the feedbacks are so complex and incalculable that we can never even estimate what the magnitude of the increase will be simply doesn’t hold any water for me.

With that being said, people who propose that any particular range of climate sensitivities have been “ruled out” are either intentionally misleading or hopelessly myopic. If even one or two of the known (and who knows about any unknown ones?) differ significantly from what is assumed to be true based on other simplifications and parameterizations, then that climate sensitivity number could change a great deal.

What I’m saying is that arguments like Tomas’ serve to highlight the uncertainty in the sensitivity numbers that warmists pretend don’t exist, but they do not prohibit estimates of the numbers from being obtained, nor do they prohibit assigning likelihoods to those numbers.

35. ### Dan Hughessaid

I can be wrong, but I think the first order, simple physics does not identify the constitutes of the radiatively interacting media that surrounds the planet. Realistically, the materials that are responsible for the reflectivity ( albedo ) of these simple models of the planet are the phases of water. At the same time that the reflectivity is introduced, accounting for the outgoing long-wave radiative energy is typically omitted. An inconsistency, IMO, because the same constitutes responsible for the reflectivity are radiatively interactive with the outgoing long-wave radiative energy.

Those equilibrium radiative energy balances are only half an energy conservation equation.

A pure black body, without an interacting surrounding media, gives are equilibrium temperature of about 280 kevins. If an emissivity of 0.87 is assumed for the planet surface, the temperature is about 288 kevins.

A few calculations are summarized in the files linked here and here.

Corrections will be appreciated.

36. ### BillyBobsaid

BOOM!

SORCE satellite data: It was the Sun after all.

“Now, however, boffins working at Imperial College in London (and one in Boulder, Colorado) have analysed detailed sunlight readings taken from 2004 to 2007 by NASA’s Solar Radiation and Climate Experiment (SORCE) satellite. They found that although the Sun was putting out less energy overall than usual, in line with observations showing decreased sunspot activity, it actually emitted more in the key visible-light and near-infrared wavelengths.

These shorter wavelength forms of radiated heat penetrate the atmosphere particularly well to heat up the Earth’s surface – just as the same frequencies get in through car windows to heat up its interior. The hot seats and dashboard – in this case the seas, landmasses etc – then radiate their own increased warmth via conduction, convection and longer-wave infrared, which can’t escape the way the shortwave energy came in. This is why the car, and the planet, become so hot.

Thus the Sun, though it was unusually calm in the back half of the last decade, was actually warming the planet much more strongly than before.”

http://www.theregister.co.uk/2010/10/07/solar_as_big_as_people/

via

http://chiefio.wordpress.com/2010/12/21/sorce-says-sun-did-it/

37. ### Ryan Osaid

Dan,

Unless the mere presence of additional CO2 changes the other constituents of the radiatively interacting media surrounding the planet, the first order effect is, indeed, warming. Changes to the amount and phase of water vapor are a response – not to the presence of additional CO2 through some chemical or quantum mechanical interaction – but to warming.

If your point is that calculations typically used to estimate the amount by which our atmosphere warms the surface make some unjustified simplifications, I do not have an argument against that. My point is that the first order effect can be calculated, and, based on the properties of CO2, the effect is, indeed, warming.

38. ### kuhnkatsaid

Mark F #25,

I think the sink point is that we DO NOT know whether the sinks are gaining or losing at this point so don’t know if there is no problem or it is WORSE THAN WE THOUGHT!!

Ryan O,

Do you know if additional CO2 in the Stratosphere drives out water vapor? This is one of many issues of atmospheric chemistry that I think are still open. Another question I have never had answered is how much anthropogenic CO2 increases the partial pressure of CO2 in the atmosphere inhibiting the natural release of CO2 from the oceans. Maybe these are trivial and do not deserve answers. I do not know.

39. ### DeWitt Paynesaid

I think the dip near the equator represents the average position of the ITCZ. Lots of clouds so you’re looking at mostly cloud top temperature rather than surface temperature.

I thought this one was interesting as well.

40. ### Steve Fitzpatricksaid

DeWitt,

Thanks again. An eye-ball analysis suggests that the ‘greenhouse’ warming (surface temperature less effective emitting temperature) is ~35-40C in the tropics, but drops to very low values (certainly <10C on average) near the poles.

The ocean heat looks to me like it is mainly driven by orbital eccentricity (~7% more intensity in January than in July), although the difference in (higher albedo) land mass north between north and south hemispheres probably also contributes.

41. ### Mark Fsaid

36 – gaining, losing, not the issue. In 24, Hunter cited heat escaping into oceans etc. Golf balls escape my house through the doors, and if they choose to hide in the cellar, they aren’t escaping, they’re being stored. Storing for future escape, perhaps, but most certainly not escaping from the house if they remain IN the house. A concept perhaps easily missed by a mind undergoing entropy, wherefrom disordered thoughts may escape.

42. ### kuhnkatsaid

Mark F,

Storage implies it can not go anywhere and stays in place. This is ONE of the false concepts that warmers tried to promote with CO2 STORING energy or preventing the energy from leaving the system. Energy will always be seeking a balance so there is no “storage” unless energy is expended to create a storage area. The expended energy then takes the place of the entropic flow being stopped within the storage area.

In 24 he is referring to energy fluxes. The flux can be positive or negative. In 24 it is positive for the oceans and negative for the OLR. This would NOT be a permanent state, but, it is also one of the arguments of the warmers that energy is building in the deep ocean. As we do not have decent measurements of it again, we do not know. IF it were happening it would be show as a lower energy at TOA!!

You golf ball really doesn’t encompass the issue.

43. ### Georgesaid

“Yep, but the energy cannot escape the earth via convection or conduction. It must escape via radiation.”

But convection allows the point where the radiation occurs to change. Heat can be absorbed at the surface and radiated at altitude. Most of the cartoons I have seen assume that heat absorbed at the surface is radiated from the surface. That isn’t the real world here on planet Earth.

44. ### Mark Fsaid

43 and others. THe earth includes the atmosphere, which is implicit in all of the sane statements in this thread. I really don’t give a hoot whether radiation takes place from the surface, or from the last atom or molecule at the edge of space, wherever that is, it’s the only mechanism for energy escape from that system. It may move around, it may take place at different wavelengths. It’s still just radiation.

45. ### DeWitt Paynesaid

Here’s another plot for completeness:

Albedo vs sine(latitude)

46. ### curioussaid

45 DeWitt – please can you clarify what the source data and conditions are for that albedo plot? For example – is it averaged from measured data inc. clouds? Are angle of incidence effects relevant? Thanks

47. ### scienceofdoomsaid

#33 – Doug Proctor:

But what can we say about a 0.6K temperature rise over 30 years if we don’t even have a +/- insolation & albedo dynamic variation?

Take a look at The Earth’s Energy Budget – Part Four – Albedo. You can see the albedo changes over time.

48. ### David in Kingsburysaid

Wow, if all the brains and energy went into providing clean water around the world or clearing up the plastic island in the Pacific we could really change the world. Yet you all seem to prefer devoting your clearly incredible intellects to different weather patterns possibly happening at an unknown and impossible to witness date in the future outside our own lifetimes. It is clearly a truism to state many academics are so caught in their minds they can’t see the wood for the trees. The money spent on trying to reduce CO2 so far (with no success at all) could have solved at least one of the aforementioned problems along with malaria as there is only one supply of money and research time and that has been spent on trying to reduce an essential and most probably totally harmless trace atmospheric gas. As an outsider to the discussion I find all your obsession totally beyond reason.

49. ### Samsaid

Wow, if all the brains and energy went into providing clean water around the world or clearing up the plastic island in the Pacific we could really change the world. Yet you all seem to prefer devoting your clearly incredible intellects to different weather patterns possibly happening at an unknown and impossible to witness date in the future outside our own lifetimes.

If this were entirely theoretical, then you are right. It obviously isn’t, since governments all over the world are attempting to use this very science in order to make very real changes. These changes affect both those with a high intellect and those without. Spending time understanding an issue is not wasted time.

It is clearly a truism to state many academics are so caught in their minds they can’t see the wood for the trees.

It is clearly a truism to state many middle-aged bloggers from London suburbs can’t understand science so they ridicule others for trying. Nothing is easier than stating clear truisms.

As an outsider to the discussion I find all your obsession totally beyond reason.

As an outsider to your blog I found your discussion of subjective, philosophical nonsense totally beyond reason.

Your unit of measure is unimportant. Don’t be presumptuous.

50. ### curioussaid

48 David in Kingsbury – I find your comment a bit offensive. How do you know what other issues people who blog here also put their time and energy into? Sure – there are lots of problems in the world large and small, but I don’t see how people coming together to share their knowledge and expertise in order to openly figure out what has been presented as a catastrophic medium term threat to mankind can be a bad thing.

51. ### DeWitt Paynesaid

It’s primarily derived from Fig. 1.1 that I posted in comment 2 above. Petty does not reference the data source. I calculated albedo based on the difference between TOA annual average insolation by latitude and the energy absorbed curve. I have a large spreadsheet page with insolation by latitude and day of year. It took a while to assemble. You get one month’s data for a given latitude. For 5 degree latitude steps, that’s over 400 separate calls, assuming that varying longitude doesn’t make a difference for averaging purposes. If I had sufficient R-fu, I could probably have automated the process, but it probably would have taken me as long to figure out the code as it did to just brute force manually download and copy.

52. ### curioussaid

50 – Thanks DeWitt, comments noted and appreciated. I had a look at the NASA page you link in 50 and it seems to be a calculator not a measured data reporter?

Sorry to ask for more but please can you clarify the 400 calls?

I can see you need 24 * 15deg latitude sectors for a complete month’s values (if I’ve understood this is calculated material I hesitate to call it data) for any given latitude band. For your figure of greater than 400 calls, are you saying that each 5deg latitude band is then made up from (say) 20 calls of 0.25deg intervals per 5deg latitude band?

Thanks in advance for any clarification.

53. ### Steve Fitzpatricksaid

DeWitt,

I asked for the revised curves to allow an estimate of the ‘resistance’ of the atmosphere of transport of heat as a function of latitude.

The difference between the absorbed and emitted energy curves is (of course) heat transported out of or into each latitude by atmospheric circulation and ocean currents. The difference between the surface temperature and the effective emission temperature is a measure of the ‘delta-T’ required to transport the net absorbed energy (that is the absorption less any heat carried away) to where it can be radiated to space at each latitude. That ‘delta-T’ divided by the net absorption at each latitude (total absorption less any heat carried way by the atmosphere or ocean) should give a measure of the atmosphere’s resistance to heat transport (degree delta-T/watt/M^2). So in the tropics, the ‘delta-T’ looks like about 41C, while the net absorbed radiation is equal to the emitted radiation… about 255 watts/M^2.. and resistance = 0.161 degree per watt/M^2. If the average arctic surface temperature is ~256K, the average arctic emission temperature is ~242K, and the average absorbed energy is ~95 watts, then the atmosphere’s resistance is about 0.147 degree per watt/M^2… almost the same as in the tropics!

So, it looks like moist convective heat transfer between the surface and upper troposphere in the tropics mainly compensates for IR absorption by water vapor… surface temperature is everywhere roughly a delta-T above the local radiative emission temperature, with that delta-T roughly proportional to net solar absorption locally at that latitude.

Of course, at high latitudes, the emission temperature is increased by substantial transport of heat from the tropics…. which keeps high latitudes much warmer than they would otherwise be. Adding GHG’s will apply pretty much uniform radiative forcing everywhere, but much of this added forcing in the tropics will be transported from the tropics to high latitudes (which have much lower total surface area!), so warming from added GHG’s should be substantially greater at high latitudes than at low… but we already knew that.

So double CO2 (3.71 watts/M^2). In the tropics, assume transport of 20% of that goes to high latitudes, and you will get about 0.8 C (blackbody) plus ~(3.71 * 0.8 * 0.161)= 0.48, and about 1.28C total surface temperature increase. At very high latitudes the increase would be up to 3+ times this, but since the area involved is small, the global average would remain ~1.6 degrees increase per doubling.

Interesting (well, to me at least).

54. ### curioussaid

52 Steve – do you think that Ryan et el’s findings on Antartic trends conflict with the theory of polar amplification?

55. ### Steve Fitzpatricksaid

%53,

I don’t know. I do know that Antarctica is very much more isolated (in a weather sense) compared to the Arctic (you can see how low it is in emissions). I suspect more isolation would mean less amplification, at least compared to the Arctic.

56. ### RBsaid

Curious #53, I think what Gavin had to say regarding Antarctica might be relevant.

57. ### curioussaid

55 Thanks RB – I followed the link Gavin gave to Miller et al:

http://pubs.giss.nasa.gov/docs/2006/2006_Miller_etal_2.pdf

but I don’t feel I have the skills to evaluate how it relates to temperature. I think figure 11 graphic o) shows observed pressure fluctuations of magnitude of low single digit millibars. From a quick skim of the paper I didn’t grasp to what magnitude this is expected to effect temperatures. The paper seems more of an abstract discussion of model qualities.

I haven’t put any time into the other link he gave to the Shindell and Schimdt 04 paper. It starts with this sentence:

“While most of the Earth warmed rapidly during recent decades, surface temperatures decreased significantly over most of Antarctica.”

which doesn’t tally with my understanding of the graphic Ryan posted showing non significant trend areas greyed out.

58. ### DeWitt Paynesaid

Yes it’s a calculator, but given the relative constancy of TSI at the TOA, a calculation should be very accurate. The site has links to files on the details of the calculation.

5 degree steps from -90 to +90 latitude is 37 separate latitudes, since you have to count the end points. 37 times 12 months is 444. I could eliminate some of the calls at high latitudes in winter because TOA insolation there is zero. The final data array has dimensions 37×366 (I picked 2008, a leap year)

59. ### DeWitt Paynesaid

In the tropics, assume transport of 20% of that goes to high latitudes, and you will get about 0.8 C (blackbody) plus ~(3.71 * 0.8 * 0.161)= 0.48, and about 1.28C total surface temperature increase.

That may be an underestimate of the transfer of heat and an overestimate of tropical warming. For constant relative humidity, it takes a lot more joules to warm moist air by 1 degree C than it does cold dry air. I believe the evidence is that during warmer periods when there were no polar ice caps and boreal forests existed in Antarctica, it wasn’t very much warmer in the Tropics than it is now. Of course you have albedo feedback playing a part too.

60. ### kuhnkatsaid

DeWitt,

It would appear the incoming energy distribution has changed with less UV and more Visible and IR, although a little UV did not decline!

http://www.nasa.gov/topics/solarsystem/features/solarcycle-sorce.html

61. ### kuhnkatsaid

Mark,

” I really don’t give a hoot whether radiation takes place from the surface, or from the last atom or molecule at the edge of space, wherever that is, it’s the only mechanism for energy escape from that system. It may move around, it may take place at different wavelengths. It’s still just radiation.”

But when is an issue. The whole AGW issue was a small amount of energy that gets delayed so that it piles up to a point that the atmosphere was unable to radiate it fast enough!!

62. ### DeWitt Paynesaid

The problem is that exposure to UV radiation tends to damage optics in a way that reduces sensitivity in the UV more than in the visible and IR. I’m with Judith Lean on this. We need independent confirmation.

63. ### curioussaid

57 Thanks DeWitt – that clarifies. However I think I’m still missing something – are you working on a surface segment at 0deg longitude?

For example if I do a calc for this month at 0deg longitude I get this result:

Daily Insolation Parameters

Latitude: 0.000 Longitude: 0.000
Time Zone: Greenwich Mean Time (Longitudes -7.5 to 7.5)
Local Standard Time is used, not Daylight Time.
For Daylight Time add 1 hour to times reported in table below.

Sunlight
Weighted
Daily Cosine
Average of
Sunlight Zenith
Date Sunrise Sunset (W/m�) Angle
—- ——- —— —— —–
2010/12/01 5:45 17:53 415.45 0.729
02 5:46 17:53 415.14 0.728
03 5:46 17:53 414.85 0.728
04 5:46 17:54 414.57 0.727
05 5:47 17:54 414.31 0.726
06 5:47 17:55 414.06 0.726
07 5:48 17:55 413.83 0.725
08 5:48 17:56 413.62 0.724
09 5:49 17:56 413.42 0.724
10 5:49 17:56 413.24 0.723
11 5:50 17:57 413.08 0.723
12 5:50 17:57 412.94 0.722
13 5:50 17:58 412.81 0.722
14 5:51 17:58 412.71 0.722
15 5:51 17:59 412.62 0.721
16 5:52 17:59 412.56 0.721
17 5:52 17:60 412.51 0.721
18 5:53 18:00 412.48 0.721
19 5:53 18:01 412.48 0.721
20 5:54 18:01 412.49 0.721
21 5:54 18:02 412.53 0.721
22 5:55 18:02 412.58 0.721
23 5:55 18:03 412.66 0.721
24 5:56 18:03 412.75 0.721
25 5:56 18:04 412.87 0.721
26 5:57 18:04 413.00 0.721
27 5:57 18:05 413.16 0.721
28 5:58 18:05 413.33 0.721
29 5:58 18:06 413.53 0.722
30 5:59 18:06 413.74 0.722
31 5:59 18:07 413.98 0.723

If I do the same calc but at 90deg longitude I get this:

Daily Insolation Parameters

Latitude: 0.000 Longitude: 90.000
Time Zone: Bangladesh Standard Time (Longitudes 82.5 to 97.5)
Local Standard Time is used, not Daylight Time.
For Daylight Time add 1 hour to times reported in table below.

Sunlight
Weighted
Daily Cosine
Average of
Sunlight Zenith
Date Sunrise Sunset (W/m�) Angle
—- ——- —— —— —–
2010/12/01 5:45 17:53 415.53 0.729
02 5:46 17:53 415.22 0.729
03 5:46 17:53 414.92 0.728
04 5:46 17:54 414.64 0.727
05 5:47 17:54 414.37 0.726
06 5:47 17:55 414.12 0.726
07 5:48 17:55 413.89 0.725
08 5:48 17:55 413.67 0.725
09 5:48 17:56 413.47 0.724
10 5:49 17:56 413.28 0.723
11 5:49 17:57 413.12 0.723
12 5:50 17:57 412.97 0.723
13 5:50 17:58 412.84 0.722
14 5:51 17:58 412.73 0.722
15 5:51 17:59 412.64 0.722
16 5:52 17:59 412.57 0.721
17 5:52 17:60 412.52 0.721
18 5:53 18:00 412.49 0.721
19 5:53 18:01 412.48 0.721
20 5:54 18:01 412.49 0.721
21 5:54 18:02 412.52 0.721
22 5:55 18:02 412.57 0.721
23 5:55 18:03 412.64 0.721
24 5:56 18:03 412.73 0.721
25 5:56 18:04 412.84 0.721
26 5:57 18:04 412.97 0.721
27 5:57 18:05 413.12 0.721
28 5:58 18:05 413.29 0.721
29 5:58 18:06 413.48 0.722
30 5:59 18:06 413.69 0.722
31 5:59 18:07 413.92 0.722

Not a big diference but it is a difference and I wonder if it matters or is relevant?

Anyway – time to get on with Christmas! Seasons Greetings to all, and best wishes for a peaceful, prosperous, healthy and happy New Year. C

64. ### Kevan Hashemisaid

The surface of the Earth is close to a black body: water is opaque to infrared light, and so are most rocks and dirt. If the atmosphere were transparent to both short-wave and long-wave radiation, it would be uniformly cold all the way through. That’s a clear starting point from which to estimate the effect of greenhouse gases.

If you dispute the uniform coldness of a transparent atmosphere, then have a look at the following argument, which shows that a temperature drop across the atmosphere in the absence of heat flow is a violation of the Second Law of Thermodynamics.

Once we accept that a transparent atmosphere would be uniformly cold, we calculate the surface temperature of the Earth for a transparent atmosphere in the manner you have all proposed. But you don’t have to worry about changing surface temperature because most of the Earth has a uniform temperature during the cycle of the day: it is ocean.

http://homeclimateanalysis.blogspot.com/2010/12/surface-cooling.html

Subtract your calculation from the observed Earth temperatures, and that’s the best estimate we can come up with for the greenhouse effect. Perhaps it is latitude-dependent. But we don’t have to get involved with non-black bodies.

If we want to estimate the effect of CO2 doubling, things are more complicated. We need some source of gas spectra, such as this one:

We have to divide the atmosphere into layers so we can analyze the absorption and radiation of heat by these layers. I have obtained the spectra for the various layers:

http://homeclimateanalysis.blogspot.com/2010/07/earths-atmosphere.html

I also provide a simple program you can run on the spectra to determine the total power radiated for different temperatures and concentrations. But the temperature rise as you descend to the Earth is the result of the near-adiabatic compression of descending gas as part of the convection cycle that carries heat up from the surface. Venus is an extreme example.

http://homeclimateanalysis.blogspot.com/2010/10/venus.html

So, all this to say, the average daily heat from the sun at a particular latitude in a particular season should allow us to calculate the transparent-atmosphere temperature of the surface, and thus by subtraction the season- and latitude-dependent greenhouse effect.

65. ### Steve Fitzpatricksaid

DeWitt,
“I believe the evidence is that during warmer periods when there were no polar ice caps and boreal forests existed in Antarctica, it wasn’t very much warmer in the Tropics than it is now.”

As best I can figure from internet references, Antarctica has been glaciated for at least 30 million years. Prior to that it was not surrounded by ocean, was connected to Africa and Australia, and was located considerably northward of it’s present position. So the presence of boreal forests would not in themselves prove that the world was much warmer… although it probably was at least somewhat warmer. What does seem clear is that glaciation is a strong negative feed-back, due to increased albedo. Once glaciation begins to build considerable altitude as an ice sheet, the surface temperature would gradually fall, stabilizing/promoting further glacial growth.

66. ### DeWitt Paynesaid

South America, not Africa. It wasn’t very much further north (see Fig.1 here). In the Eocene there were no ice caps at either pole. There was no Antarctic bottom water. The benthic foraminifera d18O record shows that the deep ocean was quite warm until about 15 Mya. While an ice cap formed on Antarctica ~33 MYa, it apparently melted again about 25 Mya and didn’t form again for another ~10 Myr. 65 Myr of Climate Change.

All that is irrelevant to whether tropical temperatures on a warmer planet were similar to current temperatures. This reference says that late Eocene sea surface temperatures were similar to current temperatures at low latitudes.

Our results, in conjunction with published data from other paleoclimate studies (using other types of proxy data and from other sites), imply that the low-latitude, late Eocene coastal ocean was characterized by warm surface temperatures (>26C in nonupwelling regions). On the basis of these data we infer late Eocene open ocean temperatures were similar to modern at low latitudes.

They then go on to irrelevant hand waving about how this was all due to greenhouse warming.

67. ### DeWitt Paynesaid

are you working on a surface segment at 0deg longitude

Yes.

I’m assuming that it all averages out over a year and if it doesn’t, the difference is small. Besides, there was no way I was going to download data for different longitudes as well as latitudes.

68. ### Steve Fitzpatricksaid

DeWitt #65,

You are right about Africa; it was South America. I remembered a diagram incorrectly.

http://www.exploratorium.edu/origins/antarctica/ideas/gondwana2.html

As to the opening of the Southern Ocean, it appears that there is some uncertainty. For sure the circulation of the Southern Ocean is important to isolate Antarctica thermally.

69. ### Eli Rabettsaid

Thomas Milanovic gets it very wrong.

1. The temperatures, emissivities and albedo used in these simple calculations are effective radiative ones, as in “effective radiative temperature”, Teff e.g. the temperature that would be calculated for an isotropic, isothermal earth in radiative balance with the solar input. Arthur Smith shows how this is done. TM claims that this cannot be done, but, in fact it is both definable and these effective parameters can and have been measured.

2. Hoelder’s inequality shows that the temperature calculated from an area average over the surface, Tave would be less than the Teff.

3. In the simplest models of the greenhouse effect Teff (no atm) is calculated for an Earth without an atmosphere, and compared to an observed Tave. The 33K difference is a lower limit to this difference because Tave (no atm) must be lower than Teff (no atm).

4. Smith shows how, you can add complication, a rotating earth, a variation of T(X,t) with latitude, etc, and find Tave(no atm). You can, of course, also add convection, and more complicated models do this, so the question is what do you gain in understanding at what cost.

The S-B temperature used to describe the Earth with and without the greenhouse effect in the simplest models is calculated from balancing the solar energy flux flowing in and the IR energy being emitted. These are definable quantities put together for use in a simple model which can, and have been measured, mostly from satellites to a fair degree of accuracy. Oh yeah, Eli thinks the temperature field is continuous, at least as far as fluid dynamics goes.

70. ### raindropsaid

IN Control runs the IPCC models still warm without any changing values, they have an in-built warming regardless of co2 rising – could this be the 0.9w/m2 warming the ocean a little each year raising temps? Is this then attributed to man and co2 when mixed with the effect of rising co2 – mmmmm one wanders!