Guest Post by Willis Eschenbach
It’s morning here in Reno, and I thought I’d write a bit more about the Kaya Identity and the Beer Identity. My last post about the Kaya Identity was controversial, and I wanted to see if I could clarify my point. On the last thread, a commenter did a good job of laying out the objections to my work:
Sorry but I think you’ve all entirely misunderstood the point of the identity. The Kaya identity is a means of communicating the factors of which CO2 emissions are comprised, in order to explain the physical levers that are available if one wishes to control an economy’s CO2 emissions.
These are analogous to mathematical factors, for e.g. 6 = 3 x 2. This illustrates that 2 and 3 are factors of 6. This doesn’t prove anything mathematically – it’s just an identity. But it is informative nonetheless. It tells you that 6 can be broken down into factors of 2 and 3. In the same way, CO2 emissions can be broken down into factors of population, GDP per population, energy per population, and CO2 emissions per energy.
That is a very clear and succinct description of what the Kaya Identity is supposed to do. The only problem is … it doesn’t do that.
Let me take another shot at explaining why. To start with, the Kaya Identity states:
where “CO2 emissions” are the CO2 emissions of say a given country; “Population” is the population of that country; “GDP” is gross domestic production of the country, which is the total value of all the goods and services produced; and “Energy” is energy consumed by the country.
The Beer Identity, on the other hand, states the following:
Where all of the other variables have the same value as in the Kaya Identity, and “GBP” is gross beer production by the country.
I think that everyone would agree with those two definitions. They would also agree that both of them are clearly true.
Now, as the commenter said above, when we write
6 = 3 x 2
it tells us that six can be broken into factors of three and two. Not only that, but we can say that for example
(6 * 0.9) = 3 x (2 * 0.9)
That is to say, if we change one of the factors by e.g. multiplying it times 0.9, the total also changes by multiplying it by 0.9.
But is that true of the Beer Identity? Suppose we get more efficient at producing beer, so that it only takes 90& of the energy to make the same amount of beer. Will this decrease our CO2 production by 10%, such that
Well … no. It’s obvious that changing our beer production to make it 10% more energy-efficient will NOT reduce CO2 emissions by 10%. In other words, despite it being unquestionably true, we have no guarantee at all that such an identity actually reflects real world conditions. And the reason why it is not true is that it doesn’t include all of the factors that go into the emission of the CO2, it only includes the beer.
Now, I can hear you thinking that, well, it doesn’t work for gross beer production, but it does work for gross domestic production.
And up until yesterday, I was convinced that the Kaya Identity doesn’t work for GDP any more than it works for GBP … but I couldn’t figure out why. Then yesterday, as I was driving along the Lincoln Highway on my holiday with the gorgeous ex-fiancee, I realized the factor that is missing from the Kaya Identity is … me, driving along the Lincoln Highway on my holiday with my gorgeous ex-fiancee.
The problem is … I’m burning energy, and I’m emitting CO2, but I’m not part of the GDP. I’m not producing anything with that energy—no goods, no services, nothing. My CO2 emission is a part of the total, but it is not included in the Kaya Identity anywhere.
So in fact, the Kaya Identity does NOT tell us the “factors of which CO2 emissions are comprised, in order to explain the physical levers that are available if one wishes to control an economy’s CO2 emissions” as the commenter said.
And that to me is the problem with the Kaya Identity. It’s not that it is false. It is that it gives a false sense of security that we’ve included everything, when in fact we haven’t. And because it looks like mathematical truth, we have folks who take it as gospel, and object strongly when it is questioned or laughed at. Steven Mosher thinks I was wrong to laugh at the Kaya Identity, and I do respect his and the other opinions on the matter, his science-fu is strong … but in fact, the Kaya Identity is no more complete than the Beer Identity, which is why I laughed at it.
So that’s my objection. It’s not that the Kaya Identity is false. It can’t be, by definition its true.
It is that it gives the false impression of mathematical certitude, the impression that it represents the real world, the idea that it identifies the “factors of which CO2 emissions are comprised” … but it doesn’t. This false certainty, because people think it’s “mathematically demonstrable”, leads people to not question whether it applies to the real world.
Finally, in closing let me repeat something I said in the comments on the first thread, which likely didn’t get seen because it was somewhere down around the five hundredth comment.
l hear rumblings that people think that Anthony shouldn’t have published this piece of mine, or should disavow it in some fashion. This totally misunderstands both what Watts Up With That (WUWT) does, and Anthony’s position in the game. The strength of WUWT is not that it is always right or that it publishes only the best stuff that’s guaranteed to be valid.
The beauty and value of WUWT that it is the world’s premier location for public peer review of climate science. On a personal level, the public peer review afforded by WUWT is of immense use to me, because my work either gets falsified or not very quickly … or else, as in this case, there’s an interesting ongoing debate. For me, being shown to be wrong is more valuable than being shown to be right. If I’m right, well, I thought so to begin with or I wouldn’t have published it, and it doesn’t change my direction.
But if someone can point out my mistakes, it saves me endless time following blind alleys and wrong paths. And my opinions on the Kaya Identity may indeed be wrong.
There is much value in this public defenestration of some hapless piece of bad science, whether it is mine or someone else’s. It is important to know not only which ideas are wrong, but exactly why they are wrong. When Anthony publishes scientific claims from the edges of the field, generally they are quickly either confirmed or falsified. This is hugely educational for scientists of all kinds, to know how to counter some of the incorrect arguments, as well as giving room for those unusual ideas which tomorrow may be mainstream ideas.
So it is not Anthony’s job to determine whether or not the work of the guest authors will stand the harsh light of public exposure. That’s the job of the peer reviewers, who are you and I and everyone making defensible supported scientific comments. Even if Anthony had a year to analyze and dissect each piece, he couldn’t do that job. There’s no way that one man’s wisdom can substitute for that of the crowd in the free marketplace of scientific ideas. Bear in mind that even with peer review, something like two-thirds of peer-reviewed science is falsified within a year, and Anthony is making judgements, publish or don’t publish, on dozens of papers every week.
So please, dear friends, cut Anthony some slack. He’s just providing the arena wherein in 2014 we practice the blood sport of science, the same sport we’ve had for a few hundred years now, ripping the other guys ideas to bits, also known as trying to scientifically falsify another person’s claims that you think don’t hold water. It is where we can get a good reading on whether the ideas will stand up to detailed hostile examination.
It is not Anthony’s job to decide if mine or any other ideas and expositions and claims will withstand that test of time … and indeed, it is often of value for him to publish things that will not stand the test of time, so that we can understand exactly where they are lacking.
So please don’t fill up the poor man’s email box with outrage simply because you think a post is not scientifically valid enough to be published. Send your emails to the guest author instead, or simply post your objections in a comment on the thread. Anthony is just providing the boxing ring. It is not his job to predict in advance who is going to win the fight. His job is to fill the fight cards with interesting bouts … and given the number of comments on my previous post about the Beer Identity, and the huge popularity of his website, he is doing it very well.
Regards to each and all of you, my best to Mosher and all the folks who have commented, and my great thanks to Anthony for the huge amount of work he does behind the scenes to keep this all going. I’m on the road again, and my highway CO2 emissions are still not included in the Kaya Identity …
w.
As Always: If you disagree with something that someone has said, please have the courtesy to quote their exact words. It avoids much confusion and misunderstanding.
kabend says:
July 12, 2014 at 10:53 am
To rephrase it and expose the subtlety:
The equation:
V = I / R
Expressed simply as an identity:
V = R * ( I / R ) * ( V / I )
Then verbosely expressed as a dimensionless identity,
units of voltage = units of resistance * (units of current / units of resistance ) * (units of voltage / units of current )
defines a dimensionless unit (of voltage) on the LHS and nothing else. It does not resolve to a value expressed in this form.
V = I/R produces a quantity expressed in volts where variable I is a quantity of current, and the variable R is a quantity of resistance
This has been quite the can of worms. If you want to consider the flaring of wells as outside the Kaya identity. then isn’t most, like 96%, of CO2 outside the identity?
Sheesh. Mr. Kaya must be laughing his ^%$* off at how seriously everyone is taking his equation. The thing is nothing more than a political statement masquerading as a scientific formula. It deserves ridicule, not serious thought.
I’m exhausted with this two part Kaya post. I have this strange, surreal feeling that I’m watching a Bill Murray movie. . . I just can’t figure out whether it’s “Groundhog Day” or “What About Bob?”
Cheers, enjoy the WC consolation match!
Dan
I may be missing the higher point about the Kaya identity equation, but I agree with Willis it is practically useless. In order determine a value, we must already know so much about energy consumption, GDP, and CO2 emissions and their relationships it would be more direct to just use total fossil fueled power consumption and the rate of CO2 per unit of power consumed (gas, oil, coal)? Also, Kaya implies that for any society or country the rate of non-GDP power consumption will be the same. Comparing for example China and in the U.S., the Kaya calculation of CO2 would skew the numbers favorably to the U.S., because although not included in the GDP, power consumed (and thereby CO2 emitted) for personal auto use, home heating, recreational uses, etc.) per GDP would be much higher in the U.S. than in China. Of course, the power used in producing the energy is included in GDP, but the potential energy in the fuels burned is not. I think that with the huge amount of data already available about the hot-potato issue of CO2, concepts such as the Kaya identity have no practical or scientific value.
Reply to Kate Forney.
There is a HUGE difference. In your formula none of the items reduce out of the equation. I’m amazed that people don’t get this.
If you said “bankbalance = myweight * (bankbalance / myweight) you would have an equivalent to the Kaya equation. The equation is certainly true and the result would be bankbalance but – and here is the whole point – the value of myweight does not affect the outcome.
So it is with the Kaya equation.
Do it yourself to see. Plug in arbitrary values into the formula. No matter what values you put in, the result can only be the value of CO2.
No matter what values are put into the equation for Population, Energy and GDP, the result will ALWAYS be CO2.
In order to consume a car, insurance, gas, sandwiches, beer, sunglasses, and the road you’re driving on those goods must first be produced. The total value of goods produced must equal total expenditures. You can calculate GDP by adding up either one (or incomes for that matter).
Willis, your driving around consumes energy and provides you are your ex-fiancé some pleasure sightseeing, but seeing pleasant (or otherwise) sights is not part of the GDP. In other words you have emitted CO2 without changing the GDP. That falsifies the original equation.
Several people above (lots actually) have said that buying gas means adding to the GDP. Well, the service portion of it does. The raw fuel does not as it originated outside the US, probably. So what? The main point is that 100% of the CO2 from that gasoline is producing nothing of ‘benefit’ and all of the ‘correctors’ admit that it contributes to the GDP a bit at least. Energy consumed, CO2 emitted, disproportionally small GDP increase, no product. You could have purchased the gas and not burned it so the purchased is added to the GDP, but the CO2 may or may not have been emitted, and no productive work was accomplished. More falsification of the concepts behind the Kaya equation.
These facts demonstrate a couple of things: GDP is not necessarily related to the useful application of energy sources that produce CO2, after all the GDP did not rise ‘efficiently’. One can easily think of ways to emit CO2 without providing any GDP increase such as burning a forest or breaking windows to demonstrate the broken window fallacy. And lastly one can show that an increase in population that wastes more energy driving around for no GDP gain is not working in the formula as mooted..
CO2 Total = CO2 per something where the number of somethings is finite and countable + CO2 per something else where the number of something elses is finite and countable + CO2 per additional thing where the number of additional things is finite and countable . As you correctly and reasonably point out, putting the CO2 both above and below the line is silly – it don’t add up. Why? Not just because the CO2’s cancel (if the fractions are multiplied) , but because the units are not in agreement.
Tons of CO2 = Dinosaurs per Tuesday * Tuesdays per Dinosaur * CO2 in tons
That doesn’t demonstrate anything. It is logically and mathematically true, but examined rationally it is pointless.
Wouldn’t one need to know all of the inclusions that go into calculating GDP before they could exempt their activity from the equation? Likewise, the Kaya equation places value on economies that can create higher GDP with lower CO2 emissions which both presently and unfortunately incentivizes paying more than we should for energy. The US political risk on coal should cause its price to plummet so keep building those coal plants China your ROI can only get better.
Matthew R Marler says:
July 12, 2014 at 10:16 am
By the usual rules of English, “grue” and “bleen” could be words, it just happens that they are not.
Sorry to disagree with you but “grue ” is a valid english word old fashioned but still in the dictionary meaning ” a shiver or shudder; a creeping of the flesh” origin middle english also a part of gruesome
Look carefully at GDP. It is a B/S number. (Google DJIA and GOLD) In the USA, Magically it has increased over the last 5 years. Why has it increased? Because of Quantitative Easing. If you look at GDP for the USA in terms of GOLD or any other hard currency, it is NOT increasing. The fed has been pumping close to a 100 Billion Dollars a Month into the USA, devaluing the Dollar and giving the FALSE impression that the GDP is increasing. Even the DJIA is not worth what it was in ounces of GOLD ten years ago. HOW is this factored in the equation. How does the equation correct for Government Meddling of the inputs to the equation? A valid “Identity” would eliminate inflation from the factors.
What is going to happen to the USA, in the real world, when the cost of energy “Necessarily Skyrockets” and it becomes to expensive to manufacture anything in the USA (as is beginning in many countries that have pushed this green agenda further than the USA)? Yes, CO2 emissions in the USA may go down, but what about India and China when they start making everything the USA consumes? What is going to happen the GDP of the USA then?
Arthur says:
July 12, 2014 at 12:54 pm
====
Well, yes, actually they do.
And, in your example, if indeed I could independently ascertain myweight and the ratio bankbalance/myweight (call it “rho”), where rho could be read directly (i.e. without reference to bankbalance or myweight), instead of indirectly (by dividing bankbalance/myweight), then the identity is useful, because your independently-read rho, when multiplied by your independently-determined myweight, should give your independently-read bankbalance.
For example, it’s possible to estimate mean density without calculating both mass and volume and dividing, even though “density=mass/volume”. So if I had my estimate of density, then measured mass and volume, and my estimated density did not equal my estimated mass divided by my estimated volume, I would know that I had a problem.
On the other hand, if you determine rho by dividing bankbalance by myweight, or estimate density by dividing mass by volume, then you are right, you’ve gained nothing by proceeding with the reconciliation.
Now, NB, I’m not saying that there IS a way to directly read rho, but have just posited such for the purpose of argument.
Just as in my post above, were it possible, through some hitherto-unknown technology, to read directly (or, compute, via some variables that do not include either GDP or total co2 emissions), the term (co2 emissions/$GDP), which I termed “dollar-of-gdp-specific co2 emissions”, but serves the same illustrative purpose as my “rho”, above) then the identity co2 emissions = GDP * (dollar-of-gdp-specific co2 emissions) would be useful. However, since we must determine dollar-of-gdp-specific co2 emissions by dividing co2 emissions by GDP, we do not achieve anything useful by carrying out the exercise.
Again, I’m not saying it’s possible to directly come up with the gdp-specific co2 emissions. In fact, the only known way of doing that is to carry out out the division. So, irrespective of any algebraic cancellation, *were it possible* to get independent measures of any (most, actually) of the terms in the Kaya identity, then it would be useful. I leave it as an exercise for the reader to determine if any of the factors can be read without measuring the numerator and denominator and dividing.
I certainly don’t *believe* per-capita GDP can be determined without separately determining GDP and population, neither do I *believe* energy used per dollar of GDP can be determined without determining total energy used and total GDP. Maybe co2 emissions be unit of energy can be approximated without measuring aggregate co2 emissions and aggregate energy consumption, but I would question how accurately.
Thus, in my little world, I don’t see how the Kaya identity can be of particularly much benefit as each of the ratios must be determined by division — there is no other means available, and thus the cancelling problem that you describe is manifest.
I apologize if my previous, rather more brief, explanations were somewhat cryptic.
Your misunderstanding comes from misreading. It is “Kaya Identity”, not “Kaya equation”. There have been multiple examples given of what identities are and now they differ from a mathematical formula, but this is not being understood by the identity deniers. (I say, that’s a joke, son)
The Kaya identity if perfectly valid as a mathematical tool when used correctly. Whether it is useful for analyzing the import of CO2 to GDP growth, population growth, and rate of energy consumption is certainly debatable. The difficulty thus far has been the lack of scope of the variables, GDP, population, and energy. Even if scoped there is still the disagreement of the validity of the scope. In the PNAS and Roger Pielke Jr. analyses the scopes have been identified but with no consensus, but that does not prevent discussing the results. As a visualization tool it is perfectly suited to what-if’ing a problem where ranges of reasonable data are tested.
The calculator here is buggy but does give you a sense of impact the variables impose on the results.
http://forecast.uchicago.edu/kaya.html
For example, set the end population to the current population, 6 billion (population does not change over time) the result is just what you expect – a flat line. That is an unrealistic value, though, unless there is a pandemic or catastrophic world war. Reasonable best, and worst case values can be plugged in to see what happens over the period of analysis.
It may not be obvious, but the analysis is done over the time period 1900 – 2100, and observed is shown by red dots ending at Y2K, and the errors are obvious though the trends are close.
Damn typo:
Kabend 10:53 says
“V is proportional to (I/R),” which is NOT true.
Being a New Yorker, I felt it incumbent on me to write something obnoxious like, “The proportionality constant is R*R, which is a constant, as those little lines someone drew around the circumference of my resistors tell me.” But then, a light bulb went off in my head: I doubled my thinking intensity, but the flow of ideas increased by only 25%! Sincerely, thanks for a great idea for helping my students understand that V = IR is not a complete statement of Ohm’s Law.
Now, this brings us to use of Kaya-Beer and the use of GDP as a surrogate for carbon dioxide emissions, or, for that matter, tree rings for temperatures. As noted above, the nonlinearities and excluded variables kill you. I never did like the Chain Rule anyhow. Fortunately (?), the UN realizes that a “carbon” tax based on GDP is a non-starter, as the PRC is still a developing nation, and would never go for it. Unless Kerry was a better diplomat around the time of his Jakarta speech than he was a Climate Scientist.
Matthew R Marler says:
July 12, 2014 at 10:16 am
Willis Eschenbach: And that to me is the problem with the Kaya Identity. It’s not that it is false. It is that it gives a false sense of security that we’ve included everything, when in fact we haven’t.
If you could come up with some examples of such false sense of security, you might have a case.
OK, so my neighbor and I, both driving the same model new car that we bought last Thursday, go on a 500 mile (each) trip. We each burn close to the same amount of fuel and emit close to the same amount of CO2.
But, I bought gasoline from an entirely US company, gas that came from US wells and was refined in the US. My neighbor bought gasoline from Citco – oil from Venezuela.
How, then, could we both be considered having equal impact on the US’s GDP?
Just wonderin’.
For purposes of understanding the relationships, assumed values of GDP and population can be used. For purposes of policy actual values should be used. If actual values are not available then the process is invalid except as an exercise.
Astonishing. The number of people and comments taking this kaya-thing seriously. And I suspect it was the objective of this tautology: do not think about logical or physical reality of the thing (it has not), just react to the usual keywords as GDP, energy, efficiency, etc… and focus on the agenda they have put straight into the equation. And it works.
Here is another “identity” along the lines of what dp and John West were explaining
G = M / MPG
where G is gallons of gasoline consumed
M miles in trip
MPG vehicle mileage in miles per gallon of gas consumed
Which when you look at the terms
(Gasoline consumed) = (miles traveled) / (miles traveled per gallon consumed)
Whoopie, we now have
(Gasoline Consumed) = (Gasoline Consumed)
So, the “identity” tells us that the gasoline used for a given trip is the gasoline used for a given trip. Big whoop.
I put “identity” in quotes since this is really a DIMENSIONAL EQUATION that lets me determine how much gasoline I will need for the 230 mile trip from my place in Southern California to Las Vegas. (I know what kind of MPG my car gets.) You can argue all you want about how useful the equation might be if you have no clue as to how you get MPG for your car. I know what MY car gets in fuel economy.
Anyway, the “Kaya Identity” is NOT an identity but a DIMENSIONAL EQUATION. And the REAL question is: How do you measure CO2 emissions per GDP? (And is that even a worthwhile measurement?)
Are there any factors in this equality from natural CO2 sources or is it assumed that only man’s contributions really count? How would that look? .95 natural components and .05 anthrocentric components?
dp says:
July 12, 2014 at 1:38 pm
For purposes of understanding the relationships, assumed values of GDP and population can be used. For purposes of policy actual values should be used. If actual values are not available then the process is invalid except as an exercise.
===============
Why yes, thank you for that, although that is of only tangential bearing on my argument, except to illustrate that there is no way of ascertaining the ratios without first ascertaining the principal quantities and dividing, unlike, say density, mass and volume: It is possible to estimate density without first measuring mass and volume and then dividing. If you do so, then the tautology/identity/definition of density=mass/volume becomes a useful tool for you to check on the correctness of your three estimated quantities.
It’s useful. It’s an analogy to the DuPont identity in finance.
http://www.investopedia.com/exam-guide/cfa-level-1/financial-ratios/return-equity-dupont-system.asp
For example one use was exposing Chinese plans to DOUBLE CO2s in their 5YP by rabbiting on about “intensity.” Looking at the factors IS useful.
In your example, driving increases energy per unit of GDP for the economy as a whole. If there is more “recreational” energy use, that increases energy intensity.
Well MY problem, with granting the “Kaya Identity”, with any credibility at all, is that ANYBODY can simply write his own product of factors; each of which is some ratio, that all conveniently, cancel via the Willis math; and simply concoct an illusion that some factor is a significant issue in climate.
Take “Energy / GDP ” for example. What evidence is there that this is an important climate phenomenon. ??
For starters, The USA is a big energy user; but we also have a big GDP; well we used to pre-Obama. We also don’t have that large a population, in World terms. So why is the USA the whipping boy in the pollution sweepstakes. and the USA is a net carbon sink, because of our agriculture and forestry. In fact we are the only large (land) one on the planet. Also, the USA spends vast amounts of its resources, which are energy intensive, on defence. much of that is to provide defence of others, who spend little of their own resources for their own defence; relying on the USA to bail them out.
How do you compare the GDP and population, and petroleum based US economy, with the GDP. population, and cow dung fuelled economy of some other country.
If energy consumption per GDP is an important factor to minimize, then PV and wind solar should be abandoned immediately. Natural gas and petroleum, are much more efficient at GDP production.
No I put the Kaya Identity at about the same place as the Drake Equation (identity), as something to sit up and take notice of; pretty much idle nonsense.
And that is a personal opinion. No great climate significance should be assigned to my opinion.
g
This is silly. Every single factor in both equations is cancelled out except for CO2 emmissions. For example you multiply by population, then divide by population. Population divided by population is one. Ever factor in the equation is treated that way except CO2 emmissions, so there is no handle to grab.
I wasn’t very good at math but I think that if you write X= Y*z/y*w/z*x/w
The ys,zs,and ws all cancel each other, and all you are left with is x=x . You can substitute any terms you want and it doesn’t make any difference. So you have CO2 emissions= CO2 emissions. So what we know that.
The z/y and w/z and x/w are just representing ratio variables.
Again, I will invoke the M&M’s example:
You have crates (C crates), inside those crates there are boxes (B boxes). Inside those boxes, there are M&M’s packages (P packages), and of course, there are M&M’s (M M&M’s) inside of those.
The number of M&M’s can be found by multiplying the number of crates by three rations: boxes per crate, packages per box, M&M’s per package. Those ratios can be represented by B/C, P/B, M/P
Then:
M = C * (B / C) * (P / B) * (M / P)
Is this identity too trivial? Useless?
The factors are population, gdp per capita, energy intensity of the economy and co2 intensity of energy. They are not all 1.
Willis Eschenbach wrote:
Fuel is included in the gdp, duh.