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Discussion > Can Trenberth do sums?

Kevin has calculated that heat has gone missing and is looking for it in the deep ocean. Is he perhaps mistaken? He has demonstrated his mathematical abilities by the calculations that give the component parts of what he considers to be the Global Energy Flows. You can see these graphically here;

The most striking feature to me is that there are 184 W/m^2 of solar radiation reaching the surface but a much larger quantity, 396W/m^2 leaving it as radiation and 333W/m^2 returning as back radiation. Why striking? Because it suggests that if I was standing in that graphic, the radiation from the Earth and the back radiation from the clouds would both be twice as effective in heating me up as the Sun was. In the real world, I have not experienced that at any time of year: energy flowing from the ground and back from the atmosphere four times more than I feel from the sun!

So if his calculations are correct then they must be wrong-headed. He calls them energy flows. But are they? I can feel the obvious one from the sun but not the much larger other two. Back to the graphic: if I ignore that which I can't detect, 356W/m^2 and the 333W/m^2 I get something believable and the total incoming and outgoing have not changed at all.

It couldn't be that he has mixed up his energy flows (radiated energy from a surface with a temperature above absolute zero) with energy transfer (radiated energy from a hot body to a colder one) could it?

And that missing heat.....

Sep 2, 2013 at 6:17 PM | Unregistered Commenterssat

Trenberth's nonsense falls at the first hurdle, 341 Wm-2 of insolation. Insolation is 1366 Wm-2. For anybody who doubts this please check it yourself.

Average planetary surface temperature is the metric of choice of the "climate scientists". In order to calculate this properly requires the correct spherical integration of the planetary temperature field, by calculating the temperature at every point by taking the fourth root of the absorbed radiation at that point, and then averaging the resulting temperature field across the planet's surface (in other words accounting for Holder's Inequality). NOT the way that Trenberth and the IPCC do it! NASA Diviner's empirical data from the Moon demonstrate this point beyond a shadow of a doubt.

This is something that is obvious to anyone with a degree in physics, mathematics and/or many branches of engineering. Trenberth at al are trying to account for an "AGW signal" of order 1 Wm-2, when they can not get even the basic mathematical physics correct. These are the clowns that tell you that the GHE is 33K. It is a travesty that this nonsense has persisted for so long.

As for his missing heat.... somewhere past Alpha Centauri.

Sep 2, 2013 at 7:28 PM | Unregistered CommenterRoger Longstaff

Not only that, Roger, but when they do that sum they compare radiation from the surface (and clouds and GHG) with their fanciful 'global average temp' which is derived from air temperature. Anybody who accepts the old 33K story is somewhat of a victim of deception either by intent or laziness.

Sep 2, 2013 at 8:47 PM | Registered Commenterrhoda


If KT is wrong about everything then it is up to (handsomely paid) science to correct that. But to suggest that I will roast just by being on the surface of this planet (even at night) is plainly absurd. If the man can overlook the absurd then I feel safe in ignoring the dangers of his calculated missing heat.

The only missing heat I can see is the difference between projected temperatures and measured ones.

Sep 2, 2013 at 9:28 PM | Unregistered Commenterssat

Over on the main site (Sea level rise & PDO) there has been a discussion about physics that is perhaps more appropriate here. While there is agreement about the 33K nonsense, there is disagreement on another issue:

Alec M says: "CO2 is the working fluid in the heat engine that regulates atmospheric temperature"

I would disagree - I think that H2O is the working fluid that regulates average planetary surface temperature (minimises entropy rise), with CO2 being an insignificant player.....

Anybody want to join in?

Sep 14, 2013 at 9:08 AM | Unregistered CommenterRoger Longstaff

Anybody want to join in?"

I would if you don't mind my ignorance. First off I believe that the main regulator of our planetary surface temperature is water too. For that I offer my oft repeated, but never challenged, observation that diurnal temperatures in dry arid regions can swing by 30C to 40C, while humid areas they seldom vary by more than a few degrees.

As for Trenberth's diagram I agree with Roger that the Sun gives us 1366Wm2. The explanation for the 341 at the top of the atmosphere is that the sun is shining on a quarter of the earths surface area at any given instance. While I can understand that in that case at any instance 3/4 of the world won't be receiving the incoming radiation from the Sun I have yet to grasp why that radiation should be divided by 4, unless of course there is a temporal aspect to the calculations, which I can't see. Having said that nobody from the sceptical science side of the debate has challenged this assumption, so clearly I'm missing something.

Having said that, still unchallenged by the sceptical science community, is the precision of his mathematics and what has to be a very dynamic scenario he's come up with a figure of 0.9Wm2 retained heat which has to be well and truly in the noise for a system that (a) is stochastic (More cloud, less cloud randomly) and (b) even if not stochastic we're talking about 494Wm2 incoming radiation and 493Wm2 outgoing radiation. I simply don't believe there is the instrument that can measure the OLR to 0.18% accuracy. Could be wrong though so I'll have a look at CERES.

The most likely explanation for the "missing" heat is it didn't get here in the first place, but that would bugger up the whole CAGW meme., or if it did, it returned to space.

Sep 15, 2013 at 12:38 PM | Unregistered Commentergeronimo


I like to imagine the flux when considering this conundrum. The starting point is that, in equilibrium, incoming must equal outgoing. The next thing that has to be accepted is that the solar spectrum includes all of the infra-red wavelengths. That some of the gases in the atmosphere are radiative is, of course, a given.

If we take the last two together the first conclusion is that those radiative gasses add to albedo – they will reflect some of the incoming solar directly out to the sink of space without adding energy into the atmosphere: we accept that fact for clouds, at least for the visible spectrum. Adding small amounts of these gases will therefore reduce incoming and by extension, outgoing radiation. As the added amounts are small then so is their effect on increasing albedo, but it is there.

All radiative gases therefore reduce the flux through the system. When/if they condense, the effect is magnified as they interact with frequencies other than in their absorption bands. The dominant radiative gas in Earth's atmosphere is water vapour and the dominant albedo gas is its condensed form – cloud.

Solar radiation not reflected by this albedo excites these gases, raising their energy state which the law of entropy then requires them to forego. They forego either by re-radiating or in collision with non-radiative gases and/or with solid/liquid surfaces. It is the collision with the non-radiative gases that, for want of a better term, is the greenhouse effect.

Those gases have been warmed, not by contact with surfaces but without that contact having been made: they have parasitically warmed at the expense of the surfaces. There is no additional energy in the system as outgoing energy will not have changed.

Those are the interactions with sunshine but now, Earthshine. This occurs both at night and day but is more easily observed at night when reflection of sunlight is absent. In a dry dessert, temperatures fall rapidly as earthshine escapes to the sink of space whereas in areas where the humidity is higher such as oceans and more habitable land, temperatures fall more slowly. This difference is entirely an atmospheric effect and relates only to the quantities of water vapour (even in the absence of clouds). Carbon dioxide, methane etc. concentrations are equal in both scenarios. This demonstrates the reduction in flux from the surfaces caused by the presence of radiative gases. It is however, an entirely local effect as the planet remains in equilibrium. Sunshine – albedo = Earthshine.

It is the parasitic warming of the atmosphere that changes global average temperature. Earth with an atmosphere only of non- radiative gases (yes, I know) would show an entirely different average. That Earth would radiate to space only from its surfaces whereas this Earth does so also from its atmosphere. The radiative gases have an effect directly proportional to their concentrations and spectral bands. Adding to the concentration of any one will have a directly proportional response.

That Earth would have an atmosphere warmed only by convection whereas this Earth has an atmosphere warmed by convection and radiation. Whether the difference would be 33 degrees is irrelevant, that there would be a difference is the important point for me, a non-scientist of the climate kind. Specifically, the difference my adding carbon dioxide to the atmosphere by my love of accessible energy from fossil fuels. I accept that the result (from above) is to reduce the diurnal temperature difference and also the non-controversial fact that it makes plants more productive which in my book are both benign. But will that action, carried out by all my co-inhabitants, ultimately lead to a climate that turns nasty? Well no because of two well known facts: the absorption bands of carbon dioxide become saturated placing a limit on its effect and that it is and will remain, a trace gas because of sinks for it that will endure if not in fact increase.

The elephant in my room, some would say, is the effect that my action has in total and which will promote a change in excess of what I have outlined, by a positive feedback – a trend away from the benign to the dangerous. This feedback is reported to be calculated from an effect caused by a slight increase in energy in the system creating a greater proportion of water vapour in the atmosphere. It is true that warmer air can hold more water vapour, a radiative gas which therefore reduces the diurnal temperature difference but it also condenses to cloud which increases albedo – a negative feedback. We should therefore experience both a lower diurnal range and a lower diurnal average. In effect, a self-regulating mechanism within an overall unchanging flux and entirely bestowed by water vapour. To answer your question: carbon dioxide is a midget compared with its compatriot both in concentration and effect.

So what about these calculations? My original post was about the ability of mainstream climate science to do sums; sums that produce answers that go against reason: calculation based on an assumption of positive feedback. Theirs is no more than a what-if scenario and which observations are and will continue to show is irrelevant.

Sep 15, 2013 at 1:57 PM | Unregistered Commenterssat

Sorry to have dropped out for a few days - I am a long way from home. I'll get back to this at the weekend.

Sep 18, 2013 at 4:40 PM | Unregistered CommenterRoger Longstaff

geronimo: " I have yet to grasp why that radiation should be divided by 4".

I think it goes something like this - the division by 4 is the ratio of the surface area of a sphere (4*pi*r^2) to the area of a disc (pi*r^2). The crazy notion being that the normal insolation of a disc of Earth radius equates to the energy intercepted by the planet, which in turn can be equated to a uniformally insolated sphere, at one quarter actual insolation. The physics collapses on many points - no rotation, no correction of Stephan Boltzmann physics to account for spherical geometry, etc. In my first post I referred to NASA's Diviner data for the Moon - this proved that the correct use of geometry and physics gives the same answer as that obtained by measurement and modelling. This science is settled, and Trenberth and the IPCC are wrong!

As for your oft stated observation "diurnal temperatures in dry arid regions can swing by 30C to 40C, while humid areas they seldom vary by more than a few degrees" please carry on repeating it! After a while people will begin to understand....

ssat - I agree with all that you say. When it is combined with geronimo's observations of the differences between deserts and the humid tropics we can infer the contributions of H20, Co2, etc. And remember - the IPCC talk about average planetary surface temperatures - it seems to me that doubling CO2 would have a negligabe effect, and that a negative feedback effect of H20 (increased albedo) would dominate.

But I just wish they would admit they got their sums wrong, If I am wrong, why can Richard Betts not come here and briefly explain why? It really is not that complicated and it has been bugging me for a long time.

Sep 20, 2013 at 9:21 AM | Unregistered CommenterRoger Longstaff

I like geronimo's point regarding water vapour. I believe that a lot of "the warming" is as a result of night-time temperature increases. So if there has been an increase in atmospheric water vapour content then night-time temperatures will be raised. If we're talking about a figure of 1 Wm-2 then I wouldn't have thought that much change in water vapour levels would be required to add a significant amount to "the warming".

I am quite happy to be put right on this line of thought,

Sep 20, 2013 at 2:31 PM | Unregistered CommenterSandyS

What's with the observation about night time desert temperatures? Apart from being an interesting pub quiz type of factoid, are you suggesting it proves or disproves anything? It must have been common knowledge to climate scientists and physicists for a century or more, including to Arrhenius himself. What have they all missed?

Sep 20, 2013 at 3:43 PM | Unregistered CommenterChandra Banerjee

"What's with the observation about night time desert temperatures?" and " What have they all missed?"

Chandra, I think that the answers you seek lie in the data. How have arid desert min/max temperatures altered as atmospheric CO2 has increased? How have diurnally averaged temperatures altered?

Sep 20, 2013 at 4:45 PM | Unregistered CommenterRoger Longstaff

I have no idea, how have they changed?

Sep 20, 2013 at 7:12 PM | Unregistered CommenterChandra Banerjee

You must seek the answers yourself, only then will you begin to understand.

Sep 20, 2013 at 7:19 PM | Unregistered CommenterRoger Longstaff

Where would I look?

Sep 20, 2013 at 8:05 PM | Unregistered CommenterChandra Banerjee

Chandra, I can only suggest the internet. I have looked briefly (but now out of time) and I can not find evidence of any changes over the last few decades. In this case, if all else is equal, does this not suggest that the 30% increase of atmospheric CO2 over the last 50 years (all from memory) has had little or no effect on temperature, in the absence of any major contribution from water? If this is indeed the case, does it not suggest that over the whole planet CO2 will have a negligable effect on temperature?

Sep 20, 2013 at 8:20 PM | Unregistered CommenterRoger Longstaff

Roger, it has been bugging me too. I keep returning to the diagram and decided to check it. To prove mainstream climate science as it currently stands, wrong, we have to start somewhere.

The basic is that CO2 absorbs and emits radiation – it is a radiative gas unlike say, nitrogen or oxygen which aren't. This is uncontested. Other radiative gases include water vapour and methane. It is however, the action of radiative gases in the atmosphere which leads to doubt in the current theory pursued by mainstream climate science. This theory requires greenhouse gasses to increase surface temperatures by radiating back to the surface the energy that would have escaped directly had they not been present. Climate science has constructed a diagram to illustrate that and it can be found here in the link in the headpost of this thread

The quantity of 333 Watts per square metre is the stated measure of that “back radiation”. This is a puzzle to logic because heat energy transferred by radiation is always from the hotter body to the colder and easily understood by warming your hands by a fire. Yet, in that diagram we see energy travelling in both directions between the same two places – surface and atmosphere showing 333 coming down and 356 going up. These numbers are greater than that shown for sunshine at the surface of a mere 161. The 333 and 356 look entirely out of place in the company of the sunshine and could not have been measured by the same instrument, if one was used.

It is possible to calculate energy transferred by radiation using a physical law enshrined in the Stefan Boltzman constant. Again uncontested. Using that constant we can extract information from the claimed 333 and 356 Watts per square metre;

For 333, T^4 = 5873015873 degrees Kelvin and therefore T atmosphere = 277degK
For 356, T^4 = 6278659612 degrees Kelvin and therefore T surface = 282degK

Those results are for 'perfect black bodies' which the atmosphere and surface are not* and both will therefore be a little warmer but the size of the difference will remain approximately the same (average surface temperature is around 288 degrees K). (*They are grey bodies but their actual attributes are imprecisely known.)

From this, we have established that the climate science diagram accepts that the atmosphere is colder, on average, than the surface. But this says nothing about the flow of energy which is what the diagram has claimed to do. Here, the first and second laws of thermodynamics prevail – heat flows only from a hotter to a colder body. This allows us to make sense of the diagram in terms of its stated Global Energy Flows;

Energy from surface to atmosphere 356-333 = 23. Add to that the 1 that is the claimed result of those flows and which is shown in the diagram as the net absorbed in the surface = 24.

Let's check that;

Surface only: Incoming absorbed by surface, 161, less lost by thermals of 17, by evapotranspiration, 80 and by direct radiation, 40. Total =24

Atmosphere only: The combined 199 emitted from the atmosphere less the incoming absorbed by atmosphere of 78, less absorbed by thermals of 17, less evapotranspiration of 80 = 24.

We can see that the 1 Watt claimed to be the product of greenhouse gasses in the atmosphere is in fact the result only of a calculation performed using the Stefan Boltzman constant but with no physical method of delivery to the surface because of the laws of thermodynamics. What is true is that both the 333 and 356 would be the approximate quantities of energy radiated to the sink of space which is close to absolute zero (~2 degK) but the difference between them of 23 is the actual energy transferred and in the direction of surface toward atmosphere, when considered within the confines of this energy flow diagram.

For the avoidance of doubt let me state this another way: the 1 Watt per square meter stated as being additional energy imparted to Earth's surface due to the effect of radiative gases in our atmosphere is derived only from *imprecise mathematics and incorrect application of physical laws. The balance between incoming energy and outgoing is not affected by the removal of the spurious energy flows identified here.

Conclusion: The greenhouse effect does not exist in the manner claimed by mainstream climate science.

Sep 20, 2013 at 9:17 PM | Unregistered Commenterssat

Roger, come on don't tease. When you said in reply to Geronimo:

As for your oft stated observation "diurnal temperatures in dry arid regions can swing by 30C to 40C, while humid areas they seldom vary by more than a few degrees" please carry on repeating it! After a while people will begin to understand....
don't tell me that you can find no evidence showing this factoid to be significant!

Sep 21, 2013 at 7:39 AM | Unregistered CommenterChandra Banerjee

"What's with the observation about night time desert temperatures? Apart from being an interesting pub quiz type of factoid, are you suggesting it proves or disproves anything? It must have been common knowledge to climate scientists and physicists for a century or more, including to Arrhenius himself. What have they all missed?""

They haven't missed anything, both water vapour and CO2 are GHGs, nobody is denying that, what I'm pointing out is that in the absence of water vapour there is very little heat retained by CO2 on its own. If you have an explanation for that let's hear it that's what this blog's all about.

ssat: The diagram has a number of facets that make it dodgy. First of all my reading of the TOA is that it is in, for want of a better term, energy equilibrium, 341W/m2 in, 341W/m2 out. At the surface he has 494W/m2 in and 493W/m2 out, which I believe accounts for his 0.9W/m2 of retained heat. To get to the TOA figure it is assumed that 30% of the incoming radiation is reflected by albedo, I'm left to wonder how they can have fixed albedo when both clouds and sea ice can vary widely. Clouds and soil are the key to all this according to Dyson Freeman because they are both "known unknowns". Personally, I don't believe that the stochastic nature of the albedo can be modelled and that this diagram is a good starting point if you don't want accuracy.

Sep 21, 2013 at 8:06 AM | Unregistered Commentergeronimo

"don't tell me that you can find no evidence showing this factoid to be significant!"

Here's one who's not understanding Roger.

Sep 21, 2013 at 8:10 AM | Unregistered Commentergeronimo

geronimo, what may be obvious and significant to you and me is clearly not to Chandra. We must find a better way to explain it. I will try to think of a better form of words - unless you can first.

Sep 21, 2013 at 8:27 AM | Unregistered CommenterRoger Longstaff

Geronimo/Roger, you assert that, "in the absence of water vapour there is very little heat retained by CO2 on its own", but fail to demonstrate it. The temperature of space is 2K. The tropical deserts come nowhere near that.

"If you have an explanation for that let's hear it" - there is nothing to explain that is not already clear. The desert lacks water vapour. If it also lacked CO2, it would get colder.

Sep 21, 2013 at 8:37 AM | Unregistered CommenterChandra Banerjee

ssat, while your forensic examination of Trenberth's numbers continues to show the absurdity of his calculations, I am afraid that I can take none of them seriously as they are all meaningless, for the following reason:

In Trenberth's fantasy universe the sun has gone out, the Earth has stopped rotating and the microwave background has been replaced by isentropic radiation giving 341 W/m2 at TOA, with everything in thermodynamic equilibrium. In the real universe the Earth rotates and faces a 5000K black body in one direction and 2.7K in all other directions (ignoring the Moon). The surface and atmosphere of the planet are NEVER in thermodynamic equilibrium, primarily as a consequence of rotation.

Furthermore, all of the points made above (Holder's Inequality, fourth power relationship between flux and temperature, the empirical evidence from the Moon, etc.) apply to show that all of his calculations are not only incorrect, they are barking mad! As I have said before, if you get the first step of a calculation wrong all that follows is nonsense. But this is even worse - if you get the entire premise of a calculation wrong all of the calculations that follow MUST produce meaningless nonsense.

Sep 21, 2013 at 8:54 AM | Unregistered CommenterRoger Longstaff

Chandra, look at Mars, which has no water. The lapse rate can be explained entirely by its' insolation, the mass of its' atmosphere and its' gravitational field.

Sep 21, 2013 at 8:58 AM | Unregistered CommenterRoger Longstaff

Forget Mars, please justify your assertion: "in the absence of water vapour there is very little heat retained by CO2 on its own". Also please drop the apostrophes on "its" ;-)

Sep 21, 2013 at 9:11 AM | Unregistered CommenterChandra Banerjee