Guest Post by Willis Eschenbach
There is a more global restatement of Murphy’s Law which says “Nature always sides with the hidden flaw”. Parasitic losses are an example of that law at work.
In any heat engine, either natural or manmade, there are what are called “parasitic losses”. These are losses that tend to reduce the temperature differentials in the heat engine, and thus reduce the overall efficiency of the engine. In general, as a percentage parasitic losses increase rapidly with ∆T, the temperature differences in the engine. In the climate system, two main parasitic losses are the losses from the surface to the atmosphere by way of conduction and convection (sensible heat), and the losses from surface to atmosphere by way of evaporation and transpiration (latent heat). Both of these parasitic losses act to reduce the surface temperature with respect to the overlying atmosphere, by simultaneously cooling the surface and warming the atmosphere … nature siding with the hidden flaw to reduce the overall system efficiency. So I decided to see what the CERES data says about parasitic losses. Figure 1 shows the parasitic losses (the sum of sensible and latent heat losses), as a percentage of the total surface input (downwelling longwave plus shortwave).
Figure 1. Parasitic losses (latent and sensible heat loss) from the surface to the atmosphere. Percentage of parasitic loss is calculated as the sum of sensible and latent loss, divided by the total surface input (downwelling shortwave plus downwelling longwave).
I was most interested in how much the parasitic loss changes when the total surface input increases. Figures 2 to 4 shows that situation:
Figures 2-4. Scatterplots, parasitic loss in watts per square metre (W/m2) versus total surface input (W/m2). Parasitic loss is loss as sensible and latent heat. Gold line shows the loess smooth of the data. Red dots show land gridcells, which are one degree square (1°x1°) in size. Blue dots show ocean gridcells.
I was very encouraged by finding this result. I’ve written before about how at the warm end of the spectrum, parasitic losses would increase to the point where most of each new additional watt striking the surface would be lost as sensible and latent heat, and that little of it would remain to warm the surface. These graphs bear that out entirely. Here’s why.
The slope of the gold line above is the rate of increase in parasitic loss for each additional degree of warming. As you can see, the slope of the line increases from left to right, although the rate of increase goes up and down.
In order to understand the changes, I took the slope (change in parasitic loss divided by the corresponding change in surface input) at each point along the length of the gold line for both the land and the ocean separately. Figure 5 shows that result.
Figure 5. Change in parasitic loss (in W/m2) for each additional W/m2 of surface input. “Wobbles”, the looped parts in the two graphed lines reflect subtle changes in the loess smooth, and can be ignored.
Now, what are we looking at here? Well, this is how the parasitic loss changes as more and more energy is input to the surface. Where there is little surface input, the loss is low. In fact, at the South Pole the situation is reversed, and the net flow of energy is from the atmosphere to the surface. This is the result of huge amounts of energy being imported from the tropics.
The key point, however, is that as we add more and more energy to a given gridcell the amount of parasitic losses rises, in perfect accordance with nature siding with the hidden flaw. And at the right hand end of the scale, the warmest end, for every additional watt that is added, you lose a watt …
Is this relationship shown in Figure 5 entirely accurate? Of course not, the vagaries of the smoothing process guarantee that it isn’t a precise measure.
But it clearly establishes what I’ve been saying for a while, which is that parasitic loss is a function of temperature, and that at the top end of the scale, the marginal losses are quite large, close to 100%.
Now, as you can see, nowhere is the parasitic loss more than about 30% … but the important finding is that the marginal loss, the loss due to each additional watt of energy gain, is around 100% at the warm end of the planet. Here is the parasitic loss for the planet as a whole versus total surface input as shown in Figure 2:
Figure 6. Change in parasitic loss (in W/m2) for each additional W/m2 of surface input, as in Figure 5, but for the planet as a whole.Change in parasitic loss (in W/m2) for each additional W/m2 of surface input. “Wobbles”, the looped parts in the two graphed lines reflect subtle changes in the loess smooth, and can be ignored.
Note also that across the main part of the range, which is to say in most of the planet except the tropics and poles, about half of each additional watt of energy increase doesn’t warm the surface … it simply goes into parasitic loss that cools the surface and warms the atmosphere.
Best to all,
w.
PS—If you disagree with what I’ve said please quote my words. That lets all of us know just exactly what you disagree with …
In other words Willis I was laughing at your claim so hard I was making light of it,
if what you are saying is true, then after years working on keeping heat on and off things using insulation I wouldn’t be asking myself how you can even conceive it being true, firstly,
and then,
when I tried to think of something that would reveal the hilarity of your claim
I thought of how everything reveals the hilarity of your claim about “radiant loss predominatiing”
and I thought ”It might be hard to express it not trying to sound like I’m joking.”
Well it did sound like I was laughing Willis but I’m not joking.
I’m trained in thermodynamics to work professionally in thermal management and know for a fact that your claim is false.
But how to prove that to Joe Sixpack reading your claim?
Simply ask everyone two things: if what you are saying is true, then why is it that firstly we know that all through history the management of air flow through an area determines it’s temperature much more powerfully than it’s radiative capability
and the “A” portion of it is ” why don’t we all know, of many myriad ways to manipulate and maximize the radiative heat loss of everything we have? ”
The answer of course is they’re so minimal in everyday applications
“B” is “why do we all instead know of many myread ways to manipulate and maximize the convective and conductive heat loss of things?”
The answer to which is because it’s what predominates since the beginning of time and today,
And if what you are claiming is real then where are all the products that show that mankind knows this and has been manipulating it as predominate method for heat removal for – everything ?
We should be able to go to any field and see the highly predominating radiative heat loss augmentation products,
and see a very minor section for the convective/conductive products.
But of course everybody reading your hilarious claim knows, it’s exactly the opposite of your claim.
All over the world in every field,
convection and conduction are the go-to heat removal methodologies exploited
where radiative heat removal is way down the list.
LoL Willis you need some training in foundations of thermodynamics.
Jones can ‘lose’ his original data and forget what all of the ‘adjustments’ were.
Manniacal can ignore requests for data and code
Others insist that the warmth is ‘hiding’ and tell everyone AGW is warming the earth but they just don’t know where the energy snuck off too.
Mostly they earn a lot of money using the classic shell game all singing “watch the pea”.
Willis: This type of research (your CERES articles) are where CAGW meets it’s demise. As long as the fakers hid their data, jumbled word definitions, pal’d their way to published papers and used non scientific descriptions they were able to keep clamor for real science at bay.
But science is advancing and has left the alarmists dancing as fools.
You may not be willing to actually publish papers, but you are seeding a lot of thoughts and ideas on fertile ground Willis! Remember to properly attribute Willis folks!
Say what?
Perhaps you meant to write the formula as (D=R*T)/2?
Or, after you shoot the laser at the moon you’re also waiting at the moon to observe it’s arrival? Not an unusual type of claim for many of the CAGW crowd; just not your normal stance.
Not a closet AGW believer. Just a believer, so long as the model has had all of it’s components certified and verified!
Yeah, that silly little requirement that model output is validated by observations! Validation that is replicated by any interested enough to try.
I don’t think this is issue for most of us. The issue is the dodgy application of models to CAGW chicanery. Many who mention why they’ve found WUWT, Bishop Hill, JoNova, Climate Audit is because of the shameful actions and claims of the alarmists and the inability of the models to show any accuracy or semblance to reality.
Virtually none of your flights of fancy make any sense, least of all what you think Willis posted.
Settle down, write exactly what CERES is showing, list all calculations and then highlight where you think you can help the discussion. Otherwise you’re just mouthing trash talk.
James, you are making Willis’ argument for him. The argument that you cannot augment radiative heat transfer to nearly the extent that you can for conductive/convective transfer is different from claiming that radiative transfer is not significant. Engineered heat transfer systems exploit the fact that you can augment conductive/convective transfers with pumps and fans, etc. to use these mechanisms primarily.
Also, most people underestimate how much radiative transfer is going on, even when temperature differences are relatively small. When temperature differences are large, the fact that radiative transfer is related to the difference in the 4th power of temperatures means that these transfers predominate.
When talking about the earth in space, the near-absolute-zero effective temperatures of space mean that radiative transfers would predominate even if there were stuff out there to conduct/convect to. There is a reason that astronauts’ space suits have seven layers of radiative insulation.
Curt you tried. So did AtheoK. A+ for willing to say anything for the cause, F for factual reality awareness. The reason the space programs of the world use reflective insulation is because the heat from the sun can’t escape till things overheat.
Good try but factually reversed so not so good at understanding who’s telling the truth here bud.
In other words Curt you thought it was cold in space and that’s why space programs insulate everything with that shiny insulation?
No, the reason they have those highly insulated surroundings on themselves and all the equipment is because in space where there is no atmosphere to cool the surfaces of objects,
the heat travels through the solid objects building up until the equipment overheats. Not because it’s cold out there. Where there’s an atmosphere the air washes off heat that causes equipment to fail in space for that reason.
James, you simply do not know what you are talking about. Inside an astronaut’s spacesuit, there are seven layers of aluminized mylar, each one providing a layer of radiative insulation, with the plastic mylar itself keeping the aluminum layers from conducting to each other.
The reason for this is that the human body produces about 100 watts through its metabolism. But the surface of the body radiates away close to 500 watts. Without the “back radiation” we are used to on the earth’s surface, without excellent radiative insulation, the astronaut would very quickly freeze to death when out of the direct line of the sun.
And I note that you did not address my larger point about your confusion between the ability to augment some types of heat transfer in an engineered system and their relative magnitudes in a natural system. I should point out that their is a reason (beside style) that many metal shells of electronic devices are black anodized – it does significantly enhance radiative transfer to ambient.
No Curt that isn’t correct actually about the space suits.
“Temperature
To cope with the extremes of temperature, most space suits are heavily insulated with layers of fabric (Neoprene, Gore-Tex, Dacron) and covered with reflective outer layers (Mylar or white fabric) to reflect sunlight. The astronaut produces heat from his/her body, especially when doing strenuous activities. If this heat is not removed, the sweat produced by the astronaut will fog up the helmet and cause the astronaut to become severely dehydrated; astronaut Eugene Cernan lost several pounds during his spacewalk on Gemini 9. To remove this excess heat, space suits have used either fans/heat exchangers to blow cool air, as in the Mercury and Gemini programs, or water-cooled garments, which have been used from the Apollo program to the present.”
From N.A.S.A. : How SpaceSuits Work:
Parts of a Spacesuit
NASA spacesuits have many pieces and parts. Learn about the parts and why each piece is important.
Primary Life Support Subsystem
The PLSS is worn like a backpack. It provides astronauts many of the things they need to survive on a spacewalk. Its tanks supply oxygen for the astronauts to breathe. It removes exhaled carbon dioxide. It contains a battery for electrical power.
The PLSS also holds water-cooling equipment, a fan to circulate oxygen and a two-way radio. A caution and warning system in this backpack lets spacewalkers know if something is wrong with the suit. The unit is covered with protective cloth layers.
Layers
The spacesuit arm has 14 layers of material to protect the spacewalker. The liquid cooling and ventilation garment makes up the first three layers. On top of this garment is the bladder layer. It creates the proper pressure for the body. It also holds in the oxygen for breathing. The next layer holds the bladder layer to the correct shape around the astronaut’s body and is made of the same material as camping tents. The ripstop liner is the tear-resistant layer. The next seven layers are Mylar insulation and make the suit act like a thermos. The layers keep the temperature from changing inside. They also protect the spacewalker from being harmed by small, high-speed objects flying through space. The outer layer is made of a blend of three fabrics. One fabric is waterproof. Another is the material used to make bullet-proof vests. The third fabric is fire-resistant.
As far as your other commentary Curt I’m happy to remind you everyone already understands you’d only be confused about the above matter if you were utterly unable to grasp what we’re talking about.
So thanks for the invitation to chat about your belief space suits have giant heaters inside.
I’ll pass.
James, I invited you to provide numbers, references, or citations to back up your claims. To date you have provided nothing.
Onwards to your main claim, which is that humans increase the heat loss of objects by building fins or installing fans. This is for a simple reason. It’s hard to increase heat loss from radiation. As you say you are in the business, perhaps you could list for us some possible ways to increase radiative cooling.
Now, of course the obvious one is to paint the radiator black. Because Kirchoff’s Law says that emissivity = absorptivity, that will make the object nearer to being a blackbody, so it will cool by radiation. That’s why automobile radiators are painted black, for example..
And make no mistake, engineers definitely use that method of cooling, changing the surface characteristics. It’s used e.g. in solar cells, to radiate away the heat from the back side. But once you’ve done that, how else can you increase the radiation? I know of no way to do that. According to Stefan-Boltzmann, radiation is the SB constant times emissivity times T^4 … which doesn’t leave a whole lot other than emissivity to mess with.
Once we move away from radiation, of course, we find that there are a host of ways to increase the physical removal of heat from a solid object through conduction/convection/evaporation. We can put fins on it. We can put a fan on it. We can spray water on it and let the water evaporate. We can use a heat pump, or a heat pipe, to remove the heat. The possibilities are endless … which is why as you point out almost all of the engineering work on cooling goes on in areas other than radiation.
Whether radiation or conduction/convection predominates in any given situation, however, is a function of the situation. For example, the earth loses 100% of its energy by way of radiation, and 0% by either conduction or convection … which shows that there are no general rules. You can’t depend on theory, you have to look at the actual measurements of the radiation and of the conduction/convection to see which one predominates in any given situation.
Now, all of the observations and measurements and scientific estimates I know of say that conduction/convection is about a fifth of the total surface heat loss. If you think different it is YOUR JOB to come up with the links to the OBSERVATIONS and MEASUREMENTS and SCIENTIFIC ESTIMATES to back up your case.
Because until then, you’re just flapping your gums, and nobody’s gonna believe your unadorned word in the face of lots of evidence. This is a scientific site, come up with evidence to support your claims or forget it.
w.
Willis says:
“And if you still can’t understand how we are analyzing the individual flows, then go buy a text on radiative energy exchanges.”
Thanks, but I got the highest grade in my Heat Transfer and the course was very comprehensive and the professor VERY demanding. We had to solve (and understand) all of the problems (some very difficult and tricky) from our textbook before even thinking of taking the exam.
Of course you can analyze the individual flows, my point that it can be confusing and misleading. It seems to me that it misled you to think that the atmospheric radiation is a surface input. The direction of radiative heat transfer at the surface is surface -> atmosphere, and it’s a surface output, together with the non-radiative surface cooling fluxes (convection and evaporation or sensible and latent heat). The input is the absorbed solar energy (by the surface).
Alternatively, the net radiation (Rn = SW + LW, where LW = LW↑ + LW↓) can also be viewed as a surface input (available energy) and I can accept that too (the way it is in climatology). It makes no sense to me to regard SW + LW↓, without the LW↑, as the surface input.
Willis you’re the first human being in my entire adult working life
dealing with sophisticated thermodynamic principles
who had the nerve to try to tell me
“metal is different from other things so the reality of convection predominating in nature is by that assertion evaded.”
You’re
Willis Eschenbach says:
March 27, 2014 at 12:59 am
“Flapping gums etc”
You’re free to stay here and talk about gum flapping Willis it’s your venue; but you are obviously not trained in any field related to thermodynamics, formally, or you’d realize the gross malfeasance exemplified in trying to claim refined man made materials lose and gain energy differently than those very same elements embedded raw in ore.
That’s what’s called absolute evidence of lack of formal thermodynamical comprehension Willis, it’s what people are tested for when they take beginner classes in the field, much less more sophisticated ones requiring algebraic calculation etc.
You’re just an obviously, not formally educated man, trying to bullshoot professionals. You’re coming across a bumbler because the errors you’re making are extreme in their nature.
I’ll leave the “Space is cold that’s why astronauts wear space suits” and “4/5ths of all energy emitted by natural and man made material is is through radiant transfer” crowd to your discussion and you can justify your assertions without even being bothered having me do it to you, all over again.
Good night and as I say I like your roving south seas guitar player stories. One thing I can recommend to get you into the real thermodynamic analysis field is take some courses and get yourself a degree of some kind in physical sciences and instrumentation if you’re going to talk about our fields. It’ll help you get along with us a lot better by being able to understand what the foundational principles are.
And Willis you and I both know, there’s no fundamental difference in the ways man made vs natural materials emit energy.
So you really need to recognize trying that kind of infantile insanity in a discussion about physical matter, is as low rent intellectually as it gets.
It’s outright, unrecoverable confession just how profoundly out of contact with the essentials of matter and energy, you are each time you make it.
If you want to you’re free to go ahead and claim yet again
you think “metal emits energy differently when it is ore, than when it is refined,”
and that “refined material uses different laws of physics to emit energy than natural”
it’s your right to state it : but any trained technical personnel in any field of matter and energy handling who sees you say it recognizes it instantly as revelation of profoundest ignorance.
Profoundest ignorance Willis I seriously can not imagine that you say that and don’t know what a torpedo to anyone believing anything you ever say afterward, to claim you think refining material makes it emit energy according to different laws of thermodynamics. Ouch Willis. That’s… that’s simply said Willis unforgivable error in physical understanding.
The simplest chemical engineering minor student in a Jr College Willis, knows this to be utterly ridiculous and yet you say it to me
like you expect to say it and not be somehow flagged as utterly remiss, in even the foundations, of physical science. It’s the kind of thing one would mark-off a 16 year old for putting on a test, on energy and matter.
“Matter that is refined and graded through handling by man emits energy according to
the same laws of physics in matter as unrefined ore.”
True
False
It’s a sixteen year old class question and you’re arguing with people who have actual careers managing energy in matter, about their not understanding how it can really be true.
No Willis. You really need to get some authentic education in thermodynamics so you can join the people who actually know what we’re talking about relative to atmospheric energy.
Sorry bro but the public needs to be protected from you if you can’t even be bothered to realize refined ore and unrefined ore, emit energy according to the same laws of thermodynamics.
That protection comes from having other people point out that the things you’re saying don’t even pass the judgement required in a test for a 16 year old Willis, because those of us who have some education and working functioning credentials, know far better and want others to know just how far what you’re saying has slipped into the realm of “and from that point on not a single word he said made much more sense than that statement.” The one about how refined ore emits energy according to different laws of thermodynamics than raw ore in the ground.
Willis just because you don’t have anyone call you to a halt with your misleading of laymen campaign doesn’t mean you aren’t harming the perception of people about atmospheric energy;
and if you can’t be bothered to say things that actually make functional sense, you need to stop arguing that the professionals who come by seeing you slaughter the laws of physics
deserve to go educate them or our selves.
You’re the one without the education and career in thermodynamics
insisting
refined man made material
emits energy
according to different laws of thermodynamics,
than raw ore
lying on the ground.
That’s not just intellectually incompetent it’s outright insult to expect people to come by and not object to it’s being touted as a scientific possibility:
much less a reality.
I’ll leave you and bid you good night – but you need to think about the claims you make to people Willis.
And no I don’t need to hear about how catching you claiming “unrefined ore, and refined ore emit energy according to different thermodynamic mandate”
means because of some chant or invective, I was the one who got caught making such bizarre claim.
Thing is Willis I don’t even dislike you: I just recognize you as an utterly untutored wannabe in so far over your head you can’t even begin to dream how swiftly the laughing starts.
You don’t deserve some free pass to publish bull*** even a sharp 15 or 16 year old would catch and you’re not going to get one from the very people whose fields you couldn’t pass into
if asked if natural and man made material emit energy
according to the same set of thermodynamic laws.
If you were trying to get a job as a high school dropout who wanted to install fire alarms you might well run into the test question “Refined ore and unrefined ore obey the same set of thermodynamic laws: true/false.”
You would be viewed as too scientifically illiterate to give the correct answer to that. Do you think you’re enhancing your legacy by suggesting to readers they get an education when they catch you peddling all this as reality based science?
For shame,
for real.
You should really ask yourself how many perfectly correct and honest well meaning people you’ve unleashed this torrent of fantasy physics onto Willis because I have no doubt if you’ll try it on me you’ve done it scores of times before.
It’s just a shame what utter lack of conscience about what one will publish will bring to a man.
For shame.
I’m not quite sure I follow you on the ‘parasitic loss analogy’ here, Willis. Aren’t the convective processes (conduction/convection/evaporation) simply the mechanism by which the heat moves through the system (the troposphere), from where the heat enters (surface) to where it exits (ToA)? And aren’t they simply getting stronger the more powerful the surface heating becomes and weaker the lesser the surface heating?
They’re not reducing the efficiency of the heat engine, they’re the result of the efficiency of the heat engine: surface heating, lapse rate -> temp difference between the two endpoints + atmospheric weight.
The true ‘hidden flaw’ here lies in treating the atmosphere as a second provider of energy to the surface, as if it adds an extra INput.
In the real world, the warm body (the surface) receives no energy from the cold body (the atmosphere) at all. It delivers energy to it.
Radiation (in the form of EM waves) is of course being emitted in all directions, but the FLOW OF ENERGY between two bodies at different temperatures (not to say the least, where the one body actually heats the other one), ALWAYS and ONLY goes one way, from hot to cold.
This seems to be a very hard concept for people to grasp. Much easier then to naively imagine two opposite and distinctly separated ‘highways’ set up between the two bodies where energy in the form of ‘light particles’ can be transported back and forth.
No, simply compare it with an electrical current or a flow of air (wind) between a high pressure and a low pressure. It’s all about gradients/differences in POTENTIAL.
Individual electrons naturally fly around in all directions, but the CURRENT moves only one way. Driven by the voltage across the circuit. Likewise, individual air molecules naturally fly around in all directions, but the FLOW of air, the wind, moves only one way. From high to low pressure.
The size of the difference in potential, the gradient between high and low, whether it’s represented by voltage or pressure … or temperature, determines the strength of the flow (resistance disregarded).
Follow the HEAT through the system. It’s all that matters. Everything else is just confusing the matter.
165 W/m^2 worth of HEAT comes IN to the surface (from the Sun) and 165 W/m^2 worth of HEAT goes OUT from the surface (to the atmosphere (and space)). 68% of the outgoing heat loss from the global surface comes through convective processes, only 32% through thermal radiation (of which only about 62% goes to the atmosphere whereas about 38% goes directly to space). But the real situation is much more lopsided than even this. Radiation is not transporting energy through the troposphere, up from BoA to ToA. Convection is. As soon as surface IR is absorbed by the air immediately above it, the air is warmed, grows less dense and buoys up. It happens instantaneously, naturally, automatically. The only thing radiation works towards within the atmosphere after this is progressively cooling it to space.
James Rollins Jr says, March 26, 2014 at 9:48 pm:
“Simply ask everyone two things: if what you are saying is true, then why is it that firstly we know that all through history the management of air flow through an area determines it’s temperature much more powerfully than it’s radiative capability
and the “A” portion of it is ” why don’t we all know, of many myriad ways to manipulate and maximize the radiative heat loss of everything we have? ”
The answer of course is they’re so minimal in everyday applications
“B” is “why do we all instead know of many myread ways to manipulate and maximize the convective and conductive heat loss of things?”
The answer to which is because it’s what predominates since the beginning of time and today,”
We could also ask people why humanity still tries its utmost to perfect the capture of solar energy but NOT the capture of ‘back radiation’ energy. Why do we waste our time and effort on building solar power stations and not on ‘atmospheric back radiation’ plants? The energy flow from the atmosphere to the surface after all allegedly provides it with 345 W/m^2 whereas the Sun can only muster 165 W/m^2, the former flux being more than twice as intense as the latter one.
James, do you really not understand that metals have near-zero emissivity in the long-wave infrared, but virtually all natural substances, including metal ores have near-unity emissivity in the LWIR? Seriously?
Edim says, March 26, 2014 at 12:57 pm:
“Willis, it’s not my crazy theory. The only surface input is the absorbed solar. This input is balanced by the surface outputs: evaporation, convection and net surface LW radiation.
http://science-edu.larc.nasa.gov/EDDOCS/images/Erb/components2.gif
The downwelling LW is only one ‘side’ of the LW radiative heat exchange at the surface – the net LW flux is upwelling and is a surface output.”
Somewhere along the way Climate ‘Science’ managed to corrupt basic physical principles to such an extent that people today walk around believing this utterly fundamental and childishly intuitive truth to be false, that the solar flux is NOT the only energy INput to the surface of the Earth.
I weep for humanity.
Hehe, what on earth is ‘childishly intuitive’? Skip the ‘childishly’ term from the above.
Willis Eschenbach says, March 26, 2014 at 12:35 pm:
“For example, we know (from measurements) that the ocean constantly loses about 400 watts per square metre (W/m2) of radiated energy.”
Again with this nonsense, Willis?! This has been shown so many times to be false and still you’re regurgitating it.
We haven’t MEASURED the 400 W/m^2. We have CALCULATED it by imagining that the earth’s surface emits into a vacuum at 0 K, by splitting the radiative heat transfer equation into two separate Stefan-Boltzmann equations. You can’t do that. That is, you can do it mathematically, but then you’re no longer describing reality. The only thing we MEASURE, Willis, the only REAL energy flow here is the P/A term (the ‘heat’) in the former equation.
I didn’t read all of the comments but it seems one would also need to measure any changes in reflected SW to determine all the gains/losses over time.
Willis, the Bejan et al. modeling has been extended since the first publication in 2005. The most recent version of which I am aware has appeared in at least three places as follows:
Clausse, M., Meunier F., Reis, A.H. and Bejan, A. (2012) ‘Climate change, in the framework of the constructal law’, Int. J. Global Warming, Vol. 4, Nos. 3/4, pp.242–260. https://dl.dropboxusercontent.com/u/26966144/Climate%20change%2C%20in%20the%20framework%20of%20the%20constructal%20law%20.pdf
http://www.earth-syst-dynam-discuss.net/2/241/2011/esdd-2-241-2011.pdf
Earth Syst. Dynam. Discuss., 2, 241–270, 2011 http://www.earth-syst-dynam-discuss.net/2/241/2011/ doi:10.5194/esdd-2-241-2011
http://www.earth-syst-dynam-discuss.net/2/C243/2011/esdd-2-C243-2011-supplement.pdf
M. Clausse, F. Meunier, A. H. Reis, and A. Bejan, Climate change, in the framework of the constructal law
https://dspace.uevora.pt/rdpc/bitstream/10174/6817/1/Using%20the%20Constructal%20Law%20to%20predict%20climate%20changes.pdf
F. Meunicr, M. Clausse, A. H. Reis and A. Bejan, Using the Constructal Law to Predict Climate Change versus Atmospheric Properties, Proceedings of the Global Conference on Global Warming 2011, 11-14 July, 2011, Libson Portugal.