Sunday, September 07, 2014

On the Kaya Identity

Now that two of the three bunnies Eli considers most annoying on the INTERNET have spit the dummy on the Kaya identity, Eli thinks he might have a word.

\text{Global CO}_2\text{ Emissions} =(\text{Global Population})\left ( \frac{\text{Gross World Product}}{\text{Global Population}}\right )\left ( \frac{\text{Gross Energy Consumption}}{\text{Gross World Product}}\right )\left ( \frac{\text{Global CO}_2\text{ Emissions}}{\text{Gross Energy Consumption}}\right )

Dr Roy sees nothing wrong with , but really does not see why it is useful, Willis E says it's an identity, CO2 emissions equal CO2 emissions, who cares?  Roger Jr. says the mathematics are simple, therefore all is good.  Eli will take his word on that.  Oh yes, Roger doesn't like Paul Krugman's take.  Perhaps the math was too complicated?

But, dear bunnies, Eli is here to defend the Kaya identity.  Measuring current, past or future CO2 emissions is not trivial.  The Kaya identity allows one to look at four different factors which may be more easily and perhaps exactly estimated and/or measured.  Three of the factors are ratios.  While we may not be able to measure or estimate the numerators or denominators exactly, we can perhaps get a handle on the ratios. For the last two terms estimates can be gotten by looking at a range of known component systems and trends.

The Kaya identity is useful in that it provides a handle on something we cannot necessarily measure directly, future CO2 emissions (and to an extent past ones).  In this it is very much like engineering thermodynamics which allows us to quantify things we cannot directly measure by providing relationships with things that we can.  Maxwell's equations are useful for other things than bedeviling junior chemistry majors.

16 comments:

Anonymous said...

It's a good reminder that population is growing more slowly and efficiency is increasing more rapidly than was thought decades ago.

Dikran Marsupial said...

It is a bit like the chain rule for differential calculus, it is just an identity, but it is is a useful one in breaking up a derivative into terms that may be individually meaningful (and hence help to get an intuitive understanding of the maths) or more easily calculated (in which case it is computationally useful).

At the end of the day, if an idea has been widely used and/or cited and you can't see the point in it, then it is rather more probable that you have missed something, than that the research community has not noticed that the identity they had been using was not useful.

palindrom said...

I'm reminded of the Drake Equation, which estimates the number of communicating civilizations in the Galaxy as the product of a number of factors. In that case, each of the factors is wildly uncertain, so the answer is even less certain, but the equation provides a framework for thinking about the problem. Here the factors are a lot better known, though obviously still rather fuzzy.

Anonymous said...

Willis was actually much more confused than your short synopsis... he claimed, "It is an identity. I can substitute in Gross Beer Production, and the identity will claim that if I improve beer-making efficiency, I can reduce global CO2 emissions proportionally", thus proving that he is clueless about the equation, and fails to engage with any of the commenters who try to educate him about it.

-MMM

Fernando Leanme said...

I read Pielke's piece and it sounds very reasonable. Given Krugman's weak background in engineering he may be glossing over the energy efficiency and carbon intensity figures.

One reason I try to engage with you guys is the unreal approach you have to engineering issues. The climate thingy tends to be reasonable, although the climate histrionics are a bit trying. The key is that I wouldn't want to ride a bike built by Paul Krugman and friends. We don't need a fleet of Space Shuttles, nor can we afford to waste the time heading that way.

J Bowers said...

It's all about Roger. It's always about Roger. It can never not be about Roger. And Roger isn't an engineer, either. Just sayin', Nando. How are you doing with the principles of heat transfer, by the way? Does the pool still feel cold on a hot day and acting as an analogy for Arctic waters?

Thomas Lee Elifritz said...

We don't need a fleet of Space Shuttles, nor can we afford to waste the time heading that way.

And of course Fendandino thinks he speaks for 'we' (aka us). Troll alert. You invited it, now you need to learn to ignore it. Or at least try to ignore it. (Hint : in the future, don't invite idiotic, opinionated, innumerate trolls to a special discussion of advanced topics.)

Marion Delgado said...

Thank you for this.

It's a real service to the general public that Eli Rabbett explains what each part is derivable from and useful for.

But what excuse do the people he's citing have? They're supposed to be "experts" and yet they turn on the disingenuous sham at every opportunity.

yes it's an identity or what we tend to call a reformulation. All reformulations are identities. Every step in every proof is an identity.

Anonymous said...

Pielke stated:

"Because halting economic growth is not an option, in China or anywhere else, and because technological innovation does not occur via fiat, there is in practice no such thing as a carbon cap"

This is clearly bollocks. The point is that carbon caps don't have to halt growth. Yes, there is a level at which a carbon cap would be unrealistic, but, for example, the EU ETS is a cap and it exists, so, um, proof that Pielke is wrong? (yes, the EU ETS price is really low, but it is non-zero, so the cap is binding) (and in other places, taxes have been implemented, and for any given carbon price or gas tax, there is a cap quantity that would produce an almost identical effect)

-MMM

ps. Krugman isn't an engineer, but Pielke can simultaneously manage to be really condescending and totally wrong - remember the Megan the undergrad fiasco? I'm still not sure that Pielke actually understands where he went wrong (he certainly never apologized): http://scienceblogs.com/deltoid/2008/05/19/pielke-train-wreck-continues/

turboblocke said...

...technological innovation does not occur via fiat... Looks like a straw man to me. Technological innovation does occur if there is an incentive.

Gator said...

Pielke jr. When someone points out the equation is multiplicative, not additive, and that you can make a realistic scenario where the economy grows, but carbon doesn't, he replies: "Sure, you can jigger the numbers many different ways."

And Fernando thinks Pielke is an engineer?? LOL.

Pielke is an expert victim bully. That's about all I can see. "For years, Krugman has called me names and hid his critique behind vague allusions to my moral turpitude."

He's worse than useless. He's useful to the people fighting an effective evaluation of the problem and potential policy approaches.

Jim Prall said...

The Kaya identity is genuinely useful in unpacking what you need to consider in asking how we might cut carbon emissions, and how quickly.
Some people fixate on stopping population growth (first factor; would help if you could; demographers have pretty tight estimates of expected future growth and slowing rate).
Some people focus on economic growth - rising GDP/capita. If that rises/plateaus/falls with all else held equal, then CO2 also rises/plateaus/falls in lock step. There are a few Luddites and anti-capitalists saying we actually "need" the 'end of capitalism' and global trade to save the climate.
The last two factors are more pertinent and illuminating. We can study the energy efficiency of economic production - how much energy does each type of useful economic task actually require, and can we do each one with less energy than we have? There is steady progress on this front, driven by economic self interest that energy costs money, so wasting it is worse than using it efficiently.
Finally there is the carbon intensity of energy. This is the one we can zero in on, and say that it is entirely conceivable that this would decline to zero in the future. We can drive EVs charged from renewables, power a grid with PV, wind, tidal, geothermal, hydro plus storage, and we can heat and cool buildings (with superior insulation to require the least conditioning load to start with) also using renewables, passive solar, geothermal, etc.
Knowing there are these four factors that you multiply together, we can grasp what foreseeable changes in each one must do to the final output.

William T said...

Knowing there are these four factors that you multiply together, we can grasp what foreseeable changes in each one must do to the final output.


The problem is that we can't be sure that the terms are independent - the only one which is sure to have an effect is burning less fossil fuel...

Susan Anderson said...

Jim Prall, I wouldn't dismiss those who feel we cannot continue with a model of continuous expansion as luddites. You might call us realists. Conservation and avoiding waste will be necessary. Letting marketing run our lives in pure idiocy under the circumstances. One of the necessary wedges in making urgent cutbacks to fossil fuels is conservation and efficiency.

Marion Delgado said...

I agree with Susan Anderson.

Thomas Lee Elifritz said...

I agree as well. Just changing the methods we use to convert energy is not going to change the way we use that energy, which is a bigger short term problem than the longer term carbon dioxide problem.

That being said, I'm all for better ways of converting and conserving energy. I'm particularly interested in the fundamental condensed matter physics of energy conversion.

In that respect, Susan, PW might be interested (or not, who knows) in something that just came up that might change the landscape. One of the big problems in understanding here is quantum coherence at high temperatures. One of the ideas that has been floating around for a while is electronic Bose-Einstein condensation. I know PW has been a big 'single electron' theorist in the past, but that alternative scenario of strong electron pairing has not been able to gain much traction due to a perception of impossibility among theorist. That is looking to change with a new experiment that has found a second hole pocket in the cuprates where the math indicates that for this to occur there must be a decoupling of the CDW order from the pseudogap, in other words, the pseudogap mechanism itself is not equivalent to the CDW, but some other mechanism of spectral weight transfer across the high energy charge transfer gap. This can only be Philip Phillips predicted charge 2e virtual boson, or from the hole perspective a pair of excitons along with some paired composite quasiparticles. I'm trying to work this out right now but it puts 'Mottness' into a new light. Since these virtual bosons don't really exist, when the composite quasiparticles can no longer participate in conduction they degenerate into the CDWs and the broad incoherent mid infrared spectrum as a result of the fluctuating nanoscale phase separation and the domain walls. There is some exotic physics occurring around these domains which will certainly be useful in for new energy conversion methods.