Not Spaghetti

Terry - you say "use of the ambiguous term "energy flow" raises the issue of what is meant by "energy flow."" - WHAAAATTT??

Energy is perhaps the most fundamental quantity in physics! More fundamental than mass. More fundamental than any particular particle or atom or physical system in itself. Energy is exceptionally well understood and central to essentially all of physics. How on earth can you call the term "energy flow" ambiguous? It is not in the least. And the diagram labeled "global energy flows" is absolutely accurate in calling those things energy flows, because they are the fluxes of energy through Earth's atmosphere, which mediates the interactions between Earth's surface, the Sun, and the rest of the universe. Radiative energy is a form of energy, quantifiable as such. Heat is defined as an exchange of energy between systems at thermal equilibrium. Heat is derivative, radiation intensity is derivative, energy is fundamental.

And the "applicable conservation principle" is the first law of thermodynamics, that energy is always conserved (so that in a steady state system, with constant temperature, net flow has to be zero, or where net flow from the universe to the surface is positive, temperature has to increase - global warming...). So of course "heat" and "radiation intensity", as pieces of the energy flow around our planet, are part of that same conservation principle. Your conclusions and extrapolations on this are absurd.

Terry, yes, of course back-radiation is a radiative energy flow ("radiation intensity" if you wish) - by definition it cannot be "heat" because heat requires thermalization (redistribution among degrees of freedom at a given temperature), and the radiation is not thermalized until it is absorbed at the other end. So in transit it is most certainly not "heat", but radiative energy flow. And from Kirchoff's law (as well as the second law) the net radiative energy flow which determines the actual heat exchange between the two sides must be from hot to cold. That's very straightforward. Perhaps UCAR mislabeled a diagram (though I don't actually see any such mis-labeling in the page you pointed to), but there's no question that back-radiation is definitely a radiative energy flow which is only one side of a heat exchange - the name says "radiation" for one.

Your "problem for this interpretation" as a radiative energy flow is completely illogical. For one, the most recently updated Kiehl-Trenberth diagram which I linked to earlier in this discussion is not balanced - there is net heat increase of about 1 W/m^2 on the surface. The cause of the imbalance is humanity's enormous increase in greenhouse gases in the atmosphere, which is sort of the whole point of this discussion. It is not balanced.

Of course it is close to being balanced (and the earlier iteration with less precision was numerically balanced) - but all that means is that the Earth is in close to a steady state, not heating or cooling. G&T's call for some sort of "conservation principle" is hilarious - the "conservation principle" in question here is simply the conservation of Earth's temperature. If Earth's temperature remains fixed, then no net heat is flowing to our planet, and incoming and outgoing radiation flows must balance. If there is an imbalance (as there is right now) then Earth's temperature must increase. Really, there's little more that needs to be said about their (and apparently your) misunderstanding of the whole problem.

Dear Mr. Staples:

Thanks for taking the time to comment!

I'm not focused on the AGW controversy but rather on a foundational issue for climatology. This issue is whether or not the Kiehl-Trenberth type of diagram is fundamentally flawed. If it is fundamentally flawed, this would have far reaching implications for climatology.

If it is flawed, this flaw is obscured by an ambiguous and confusing use of language in climatology. Under this language, the separate concepts of "heat," "work" and "internal energy" are described by the single word "energy." Additionally, a heat flow is confused with a radiation intensity. The confusion results in the need by climatologists to employ the neologism which they call the "net heat flow" to avoid violations of the second law of thermodynamics. For climatologists, the second law does not apply to a heat flow but rather to a "net heat flow." This is a non-standard and confusing usage of technical English. In technical English, the notion of a "net heat flow" does not exist.

In making the following remarks, I use standard technical English. Thus, my "heat flow" is the equivalent of the "net heat flow" of climatology. Also, unlike a climatologist, I distinguish between the concepts of heat flow and radiation intensity

According to one UCAR publication, the entity that flows through a Kiehl-Trenberth diagram is energy. According to another UCAR publication, this entity is heat. If it is heat, then the Kiehl-Trenberth diagram is invalidated by the violation of the second law of thermodynamics by the heat flow which UCAR calls the "back-radiation."

If an energy flow is not a heat flow, then it seems to me that it must be a radiation intensity. However, there is a problem for this interpretation. The Kiehl-Trenberth diagram implies there is a balance of energy flows. This implies there is a balance of radiation intensities. However, in their paper "Falsification...," Gerlich&Tscheuschner point out that the notion of a balance implies the existence of a conservation principle. However, they state, there is no such principle for radiation intensities. They state that to assume there is such a principle is the "cardinal error" of climatology.

I'm left with the conclusion that, whether an "energy flow" is interpreted as a heat flow or as a radiation intensity, there is something fundamentally wrong with the Kiehl-Trenberth diagram.

I'll end with a bit of speculation. A balance of heat flows is a valid concept. Perhaps, climatologists have fooled themselves into thinking there is a balance of radiation intensities by their failure to distinguish between a heat flow and a radiation intensity.

Sean Casten and I have been discussing all this quite a bit further over at Grist (see the link in Sean's comment above). There are several issues with what I've written in this article that probably should be corrected, though I'd like to see the numbers in some alternate sources for confirmation. The basic substance of my article, though, is still, as far as I can tell, perfectly correct. Here are the issues for further investigation/correction, if I get a chance!

(1) The Oak Ridge report very likely was talking about "real" CHP combined-cycle gas turbines (CCGT's) when they discussed those - total installed CCGT capacity in the US is stated by Sean to be about 230 GW, so the 45 GW listed by the Oak Ridge report is just 20% of that. However, these plants are really CHP only just barely (for regulatory/tax purposes), and "optimized for electric production". I.e. they are hybrids of E-CHP and R-CHP (topping systems) with the R-CHP component corresponding to a small fraction (a little over 10%) of the total fuel consumption of the system. In any case, many of the benefits that the report touts from switching to more CHP for electric production still look from the numbers to come more from the good electric conversion efficiency and natural gas use of CCGT (E-CHP) systems rather than any of the "waste heat recovery" true R-CHP components.

(2) Sean seems to use a cost/benefit metric for CHP installations (bottoming or topping) that assumes the cost or value of heat is a constant that can be factored out. For some economic modeling that's probably not a bad assumption - as I said here, these plants can deliver real benefits from making use of energy that would otherwise be just wasted. But what the thermodynamics tells you is that for low-temperature heat you can do much better than 100% - and that means there's a huge competitive window to lower the cost of heating at those low temperatures. So I don't believe long-term it's a good assumption to make economically, but short term it probably is about as good as any other. In any case, the problem with production of two incommensurate products (heat and electricity) is that there never can be a single metric that captures everything you need to know. Much depends on the circumstances. But the thermodynamics really does matter, in the end.

I have now studied both the article and Kramms pdf-document closer.

I was also quite confused because you state right under equation 6 that the effective quantities you define by equation 7 and 8 are planetal averages. Reading your comment "Why are some people so easy confused" solved it for me however. While equation (7) is a true average for for T^4 the same does not hold for equation 8. But I fully understand what you mean in the context.
If one plugs in definitions (7) and (8) to equation 9 one recovers equation 6, just as expected.
It is vital to realise what you state "effective radiative temperature in this discussion, the particularly useful value corresponds to the uniform temperature that would given the same Stefan-Boltzmann emissions as the given temperature distribution under uniform emissivity" if one wants to understand this.

I think the confusion could have been avoided if you had used another expression after equation 6. If one makes standard averages as Kramm does (and the text kind of suggests) then equation 9 does not hold.

Best regards
Søren Rosdahl Jensen

Your article makes a number of fairly common mistakes, largely around confusing thermodynamic efficiency with the efficiency as perceived by our wallets and environment. The two are similar, but not identical. If I install insulation in my home, I can stay just as warm with less marginal fuel use, giving me (on the margin) comparable useful energy with less fuel consumption. What's the marginal fuel efficiency of that investment? Zero divided by a negative number is meaningless from a thermodynamic perspective, but very real from an environmental and economic one. Similarly, cogen doesn't have to violate the second law of thermodynamics to effectively achieve first-law level fuel-to-electric efficiencies on a marginal basis.

Have a look here for a more fulsome explanation: http://www.grist.org/article/chp-primer-fun-with-thermodynamics

One other point to keep in mind. Thermodynamic balances on systems are wonderful tools, but all have an innate assumption that you are dealing with a closed system, within which all energy inflows and outflows are known with precision. Outside of a controlled laboratory environment, it's very hard to find such systems. This can create neat ancillary effects whereby CHP (or other efficiency measures) lead to apparent violations of the first law as well by lowering system losses that are not normally quantified. A common example I have often found in the ~70 odd CHP projects I've personally built is that industrials often overdesign their processes to use higher temperature thermal energy than they need to maintain safety margins. When a decision is later made to install a CHP plant, they suddenly see that bias for safety margins as an explicit trade off against their bottom line. This results because a decision to supply high temperature heat from a CHP facility is a conscious decision to generate less electricity, lowering overall fuel efficiency (your suggestion that high temperatures = higher efficiency is exactly backwards in every way that matters economically and environmentally). As such, operators suddenly have an incentive to lower the temperature of heat supply to process, lowering radiative losses throughout their thermal networks and in some instances leading to marginal electric out / marginal fuel in efficiencies in excess of 100%.

This is not to say that CHP is a silver bullet, any more than any other technology can uniquely provide all of the solutions to our environmental challenges. But it doesn't suffer from the limitations you cite.

Actually I don't even remember a turbulence argument. I don't particularly want to reread it - if you do have a specific question from it let me know.

Not sure what version of the rebuttal you saw, but yes a version should be published in coming months. Haven't heard a date though yet.

To add to your points in favour, if the fuel cell technology that this is based on has the potential to switch to other fuel sources in the future (eg hydrogen) then it is an even better step in the right direction. It builds expertise and promotes economies of scale in the fuel cell business which should lower costs for future infrastructure in this area.

Thanks for the quick reply Arthur.
I did already read that post as wells as Kramms pdf I linked to. It seems like he is confusing your definitions.
I just asked aobut the turbulence stuff because I am a little bit rusty in that but I am going to look at this soon.

I agree that the surface integral issue is quite straight forward.

I have another question that might be off topic, but however:
I have seen the rebuttal paper to Gerlich and Tscheuschner, I would like to know if it was accepted for publication or if it will be?

Thanks for your time,
Søren R. Jensen

Response to: Thu, 02/25/2010 - 14:15 — apsmith "Terry, you cannot just "assign nil to PHot -PCold". Those photon flows do not cease just because you've added some air. What happens in the limit where the air density gets very small?"

Arthur:

Thank you for taking the time to respond. The effect of your deletion of the major portion of my submission is to create a strawman argument that obscures a violation of the second law of thermodynamics on the speculative grounds that the radiative component of heat transfer may not be nil. This argument fails on several grounds. One is that the second law violation stands independent of whether the radiative component is nil.

The major issue under discussion is whether UCAR errs in implying that heat flows from colder matter in Earth's atmosphere to hotter matter in Earth's surface thus warming Earth. It certainly does err, for this heat flow violates the second law of thermodynamics. By this error, UCAR creates a "greenhouse effect" that does not exist. According to UCAR, this "greenhouse effect" is THE greenhouse effect. As a proposal is on the table to spend about 500 trillion dollars on CO2 abatement to address an alleged greenhouse effect, it seems to me that this issue is worthy of discussion in your blog.

As UCAR plays a prominent role in climatological research, it would be well if we could explain to UCAR what is wrong with its thinking. To accomplish this task, we would need to have an accurate picture of UCAR's thinking. I don't have such a picture. However, I do have some ideas. One is that UCAR's thinking is clouded by failure to distinguish among the concepts of energy, heat and work. Another is that UCAR is confused about the mechanism by which heat leaves Earth's surface.

In relation to the question of the mechanism, a limitation of the literature on heat transfer arises. One is that the literature on convective heat transfer makes the tacit assumption that the radiative contribution to the heat transfer is negligible. Once this assumption is made, a picture arises that explains how a greenhouse really works. It works by thickening the hydrodynamic and thermal boundary layers at Earth's surface thusly increasing the resistance to heat flow from Earth's surface. Trapping of radiation by the greenhouse glass is not a factor in warming the portion of Earth's surface that lies under a real greehouse. This conclusion is consistent with the experimental findings that are reported by G&T.

In the partially deleted post, I take the radiative contribution to the heat transfer from Earth's surface to be nil. I do this for the purpose of linking a description of the mechanism of the heat transfer to the literature on heat transfer. G&T address the appropriateness of this approximation in their paper. On page 15, they state that "...Alfred Schack...showed that the radiative component of heat transfer of CO2, though relevant at the temperatures in combustion chambers, can be neglected at atmospheric temperatures." On page 77, they state that "...Alfred Schack pointed out in the twenties of the past century that the infrared
light absorbing fire gas components carbon dioxide (CO2) and water vapor (H2O) may be responsible for a higher heat transfer in the combustion chamber at high burning temperatures through an increased emission in the infrared." I gather from the two quotes that neither CO2 nor water vapor contributes signicantly to the heat transfer at atmospheric temperatures.

Whether G&T are right or wrong in their assertion is immaterial to the issue of UCAR's second law violation. If G&T are seriously in error, the only effect is to complicate the mechanism of heat transfer such that the literature of heat transfer does not provide an accurate description of it. Such an error does not permit UCAR to violate the second law.

Arthur:
Do you have a response to the note from Gerhard Kramm about the notational disagreements?
http://www.gi.alaska.edu/~kramm/climate/Arthur Smith and the basic rules of calculus.pdf

Especially on his comments about the use of your notation in turbulence?

Ah, you need to take a look at the Kiehl-Trenberth diagram: http://chriscolose.wordpress.com/2008/12/10/an-update-to-kiehl-and-trenb...

Net average heat flow from surface to atmosphere for Earth is 23 W/m^2 by radiation, 17 W/m^2 by convection, and 80 W/m^2 via latent heat flow (conduction is, as I suggested, negligible on the real Earth). There's an additional 40 W/m^2 of radiation that leaves Earth and goes directly into space - that number would be higher on clear nights, as you note. So total net radiative cooling of Earth's surface (the PHot - PCold term discussed above) averages to 63 W/m^2, or a little under 40% of the total heat flow.