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.
Scott Wilmot Bennett says: “An identity is true for all values of the variables.”
I sit corrected and have learned something new tonight.
If it slides, slithers, swims, scurries, scuttles, slips, creeps, crawls, climbs, dips, dives, hops, hobbles, jumps, jives, walks, wades, waddles, flys, flaps, flounders, flutters, frolics or f**ks – is outside the Kaya thing, unless of course it is on menu in a Chinese restaurant and becomes a part of GDP.
Matthew R Marler says:
quote: “The terms on the RHS are to be determined by statistical analyses of states and regions. ”
Well, why not ? But this is *not* what you claimed before. You claimed that *the decomposition of the Kaya identity* was strongly supported by macroeconomic facts. So, where are those facts ? And how your RHS-statistical-analysis could *justify* the decomposition ? Please explain.
quote: “All it says is how much change in the LHS can be effected by changes in the terms on the RHS.”
No. The kaya identity itself cannot say that. Whatever your statistical analysis, any change on RHS cannot “affect” LHS because all the terms are, by construction of this tautology, completely interdependent and redundant. It is strictly equivalent to LHS = 1 * 1 * 1 * LHS. Please explain how a change in the decomposition of 1 could provide information on LHS ?
I agree with you that if by chance you get, maybe by the way of statistical analysis, other (external) physical relationships between some terms, measured separately and reliably, then you could reduce some degrees of freedom. But definitively, this would be *no more* this Kaya-thing. It would become some (more useful) equation. For the moment it is not.
Dan Metal says: “I dare say you have no inkling as to the depth of your ignorance.”
That’s easy. The upper limit of ignorance is infinity, as ignorance is simply 1/knowledge. As knowledge goes down, the reciprocal of it, ignorance, rises to an asymptote and then becomes undefined.
The other limit is zero. 1/everything-that-can-be-known is zero or very close to it.
Michael 2 says:
July 14, 2014 at 12:00 am
[…]
http://www.manicore.com/anglais/documentation_a/greenhouse/kaya_equation.html
As you can see, many people (including right here) think it’s great to have algebra that cancels out but somehow still has meaning. THAT is entertainment!
*********************************************************************
It would be entertaining if it wasn’t so depressing. That’s some real garbage you dredged up with that link.
James Gibbons at July 13, 2014 at 2:50 pm
posted this link: http://climatemodels.uchicago.edu/kaya/
This is an equation that works (no comment on validity) though it is not very clean as the “watt year” term cancels.
I have argued against the M&M analogy:
M = P * M/P
and the distance analogy:
d = d/t * t
I will abandon the quest here. If I have missed any corrections or counter arguments to anything I’ve said I’m sorry about that. The comments are much too many to navigate any longer. I wish everyone well.
Oh brother. Here I was wondering all night what all the fuss is about. Turns out most can’t even grasp the simple fact that (number of a per unit of b) times (number of b) equals (number of a).
And the main criticism still holds. You can use (number of a per unit of b) as a parameter in an equation; and (number of b) as a variable, in which case you have some sort of (linear) “model”, but to use the KAYA identity in such a fashion is still a travesty. Because it’s an oversimplification: 4 lousy variables, and no inter-dependencies.
If Willis had said that in the first place, we might have had a fruitful discussion. Now this site has become the laughing stock of everyone who knows elementary algebra.
Sorry Matthew, it seems that the first claim “supported by macroeconomics facts” was made by Pete Brown, not you. But my comments above hold anyway, as you were, as I understand, completing Pete’s views in your comment, and the 2nd claim is from you.
Prof Yoichi Kaya first proposed his relationship (subsequently labeled as an identity) in the 1980s and published it in the mid 1990s. It eventually was utilized by the UN / IPCC.
As an economic and industrial conception his relationship does not appear to have been made to order for the alarmist ideology of CAGW.
John
John Whitman says:July 14, 2014 at 12:57 am
As an economic and industrial conception his relationship does not appear to have been made to order for the alarmist ideology of CAGW.
Of course not. As sais above (but nobody reads all the posts of course) the identity emerged out of a quest to identify the main driving forces of CO2 emissions. That’s all.
And others started “abusing” it as if the KAYA identity is some sort of mathematical model.
John Whitman:
Your post at July 14, 2014 at 12:57 am says in total
Prof Yoichi Kaya first proposed his relationship (subsequently labeled as an identity) in the 1980s and published it in the mid 1990s. It eventually was utilized by the UN / IPCC.
As an economic and industrial conception his relationship does not appear to have been made to order for the alarmist ideology of CAGW.
So what?
Svante Arrhenius first proposed his proposal that increased atmospheric CO2 concentration would cause global warming in the 1890s and published it in the mid 1890s.
(ref . Philosophical Magazine and Journal of Science. Series 5, Volume 41, April 1896, pages 237-276.) Margaret Thatcher elevated it to be a political issue in the 1980s. It eventually was utilized by the UN / IPCC.
As an economic and industrial conception his hypothesis does not appear to have been made to order for the alarmist ideology of CAGW.
Richard
dp says:
”
July 13, 2014 at 2:06 pm
“As said many times before, and by many: the formula is only a tautology, CO2 = 1 * 1 * 1 * CO2″
This pretty well sums up the complete lack of understanding of what an identity is. Well done.”
”
Thank you. But we are not talking about the abstract definition of what identities should be. We are talking about the usage of this specific “Kaya identity” to define real world policies. I do not try to prove that this Kaya-thing is *not an identity*, I argue that it contains *no information* whatsoever about CO2, population, GDP or whatever.
If you can find any *non trivial piece of information* in this formula, please share.
If you are just satisfied by the fact is an identity without contest, well, I have nothing to add.
Johan says:
July 14, 2014 at 12:50 am
Oh brother. Here I was wondering all night what all the fuss is about. Turns out most can’t even grasp the simple fact that (number of a per unit of b) times (number of b) equals (number of a).
********************************************************
a = a/b * b is what you are saying?
I hope not because this is an identity and requires you to know “a” ahead of time.
Let a = number of grains of sand on the beach,
Let b = number of cubic cm of sand on the beach,
Then a/b = (number of grains of sand on the beach) / (number of cubic cm of sand on the beach)
or Let a1 = number of grains of sand in 3 cubic cm,
Let b1 = 3 cubic cm.
I would not attempt a/b. That can only be found if a is known.
It makes more sense to solve for a useful rate: a1/b1, what say 100 000 gos / 3 cm^3
a1/b1 = 33 000 or so gos/cm^3
a = 33 000 gos/cm^3 * b
this is a heck of a lot better than a = a
Will says: July 14, 2014 at 1:26 am
a = a/b * b is what you are saying?
For Pete’s sake, if you can’t grasp that 10.9 kg CO2/gallon x 1.18 gallons = 12.8 kg CO2; then obviously this whole discussion is a complete waste of time.
Even the ancient Babylonians knew more of algebra than some commenters here.
Johan says:
July 14, 2014 at 1:40 am
Will says: July 14, 2014 at 1:26 am
a = a/b * b is what you are saying?
For Pete’s sake, if you can’t grasp that 10.9 kg CO2/gallon x 1.18 gallons = 12.8 kg CO2; then obviously this whole discussion is a complete waste of time.
Even the ancient Babylonians knew more of algebra than some commenters here.
********************************************************
I would not dis the ancient Babylonians.
But I guess I am missing your point. If you meant a = a/b * b is meaningful then you miss the fact that a on the left is different that a on the right, your example, a on the right = 12.8 and a on the left is 10.9, illogical. Not to mention the value of b is 1 and 1.18 respectively.
If you didn’t mean that then well, I guess we are in agreement.
Will says: July 14, 2014 at 1:56 am
But I guess I am missing your point. If you meant a = a/b * b is meaningful then you miss the fact that a on the left is different that a on the right, your example, a on the right = 12.8 and a on the left is 10.9, illogical. Not to mention the value of b is 1 and 1.18 respectively.
Applying elementary rules of algebra:
a = a x 1 = a x (b / b) = a x [b x (1/b)] = a x [(1/b) x b] = [a x (1/b)] x b = (a/b) x b
In my example 12.8 kg CO2 is a; 1.18 gallons is b and 10.9 kg CO2/gallon is (a/b).
So of course 12.8 doesn’t equal 10.9; for the simple fact that 12.8 = a and 10.9 = (a/b).
Since when is a = (a/b), if b is not equal to one (and for the sake of convenience one might also assume b is different from zero) ???
The utility of the Kaya identity would be revealed by establishing its universality for a consistent set of parameters. It is a — possibly useful — linearized decomposition of the dependence of the rate of CO_2 production on population.
So one has to look at the various parameters. CO_2/energy is hardly universal — it is one of the parameters we are supposed to be trying to vary in order to reduce the rate of CO_2 production. CO_2/energy for nuclear power plants or solar cells is essentially zero. For methane-based generation it is one value. For an efficient modern coal plant it is another. For a wood based fire in a fireplace it is another. Different countries have very, very different mixes of energy generation, with first world (redefined as the wealthiest 33%) predominantly “efficient” (comparatively less CO2/joule), with the third world (the poorest 33%) predominantly “inefficient” (burning animal dung and charcoal on open fires to cook), and the second world in between.
Then one has the next few parameters, although I don’t completely understand why. One could just jump to energy/population and then multiply by population instead of going through energy/gdp, gdp/population as intermediaries. I suppose the point they are trying to make is that some countries are relatively efficient in the energy they consume per unit of “wealth” as measured by gdp, but this is already reflected, as noted, in CO_2/energy. Again, it is hardly a set of universal values. It cannot be. Different parts of the world have different baseline energy requirements just to stay alive, and have very different sources of “wealth” that go into their GDP. Antarctica, for example, has a negative GDP and a huge energy requirement just to have a human population exist there. Parts of the world have no wealth or resources for generating wealth. Other parts have climates suitable for agriculture, or massive collections of natural resources. This all sorts out in the first, second, third world decomposition once again — Kuwait is enormously wealthy with a huge GDP/population, and yet it is almost irrelevant to the average economic profile of the rest of the world — tiny population, small country, and nearly 100% of its wealth derived from a single valuable resource that is present in abundance. On the other end of the spectrum are the tiny island nations of the south pacific — no natural resources of any value, tiny populations, no need for most of the trappings of modern civilization and no way to pay for them if they needed them. There isn’t even homogeneity within countries — India is wealthy and industrialized and dirt poor neighborhood by neighborhood as one wanders about in the country.
In the end, the lack of universality makes the identity useful primarily as a political oversimplification. Here’s an easy way to show that. Forget CO_2. Suppose we want to relate population to energy consumption directly. That is, after all, the name of the game. We can easily go through all of the countries of the world, tally their populations, and add up all of their sources of energy. What, exactly, is the advantage of adding the the GDP step in that? We learn a bit from GDP/population times energy/GDP that we didn’t already know from energy/population, but not much, and what we do learn isn’t likely to be universal or describable in functional form. It’s gangbusters useful for political argumentation, though…
rgb
Thomas says:
July 13, 2014 at 11:57 am
“ [Willis quote] “If I burned that exact amount of gasoline in a furnace to make a tool, that would add to the GDP. But I didn’t. I burned it in an activity that does not add to the GDP.”
You are using a definition of GDP that is not the common definition. GDP is the sum of *consumption*, investment, government spending, and net exports (from Wikipedia).”
—————–
Your stated “common definition” of GDP does not negate Willis’s above statement simply because you are misunderstanding your stated GDP definition which should read, to wit:
“GDP is the sum of *consumption spending*, investment spending, government spending, and net revenue from exports ”
Thus, his purchase of gasoline was “consumption spending” which added to the GDP ….. but he “burned” it without producing anything of value ….. thus NO increase in GDP.
Whereas, if he had “burned” it to produce a “tool”, … then the sale of said tool would have garnered more “consumption spending” and/or an increase in “net revenue from exports” ….. thus an increase in GDP.
Willis is “right as rain” ……… so quit picking on him.
Cheers
Shawnhet says:
July 13, 2014 at 5:05 pm
Ian W says:
July 13, 2014 at 4:26 pm
Shawnhet says:
July 13, 2014 at 10:39 am
Ian W says:
July 13, 2014 at 10:11 am
“You are wrong of course.”
Your arguments against it working *now* are all based on stuff that hasn’t happened yet or is probably too small to make a significant difference. I’m not sure what the PR guys would say about that 😉
France gets 75% of its power from Nuclear energy – and you say that is ‘stuff that hasn’t happened yet’?
The base assumption of this ‘identity’ breaks down to the ‘green’ PR battle based on 3 weak points:
Claim 1 — GDP requires energy generation and
Claim 2 — Energy generation is equivalent to CO2 generation and
Claim 3 — CO2 generation is something bad.
——- therefore reduce GDP
Energy generation is NOT equivalent to CO2 generation – see France, and I am sure there are other examples and there will be more in the future. There are also non-industrial inputs to GDP that require no energy source.
There is also no proof that CO2 does any harm in the real world but considerable evidence that it does good in greening the deserts and increasing crop yields.
The three level argument does not then support the claim that GDP growth is a ‘bad’ thing.
This ‘identity’ is just a subtle way of introducing Holdren’s favored de-development and de-industrialization as otherwise there will be more of the demon gas CO2.
rgbatduke:
You conclude your post at July 14, 2014 at 4:53 am saying
Yes!
I have been saying that for days. For example, at July 11, 2014 at 7:55 am in one of my posts on the other thread I wrote
Richard
Well, it can be. Or not. It can also be used as a means of pointing out that there is a real difference between Kuwait, India, the United States, China, Ukraine, Viet Nam, and Nigeria. Kuwait has a huge GDP/population because it is a desert country sitting on top of a single valuable resource. That resource requires little energy to produce, and so the energy/GDP reflects a reasonably affluent populace living in a hot dry climate with no particular industrial base. India, on the other hand, has a huge population and hence a comparatively low GDP/population, even though objectively it has far greater “wealth” than Kuwait. It is also very mixed in its economy, with substantial agriculture (sufficient to feed a billion people and export the remainder), a large and growing industrial base, and substantial natural resources. Its energy generation is a very mixed bag, though, and its delivery of both energy produced and the social benefits of that energy (clean water, sewage systems, cheap and universally available electricity) is enormously uneven — so much so that the notion of “energy/GDP” is nearly useless, as is (really) “GDP/population”. India is in some sense two or three countries in one, certainly compared to a Kuwait that would comprise a single smallish state in India.
The point is that it is all well and good to study the economics of things like CO_2 production if one thinks that it is an important parameter that human civilization might should be worried about. That is, even though I disagree about the evidence supporting CO_2 linked CAGW/CACC, I think that there are enough benefits to tracking down and understanding the global energy ecology/economy to warrant this sort of study. The problem arises when one writes down oversimplified equations like this. This “identity” (decomposition) is too low resolution and two few dimensions to be useful to any actual economist or to anyone seeking to “solve” the hypothesized CO_2 problem. This is overwhelmingly evident in the case of large countries like China, India, Russia, the United States, Canada, and most of the larger, wealthier countries with a highly mixed economic base. Energy/GDP isn’t comparable between wealthy/mixed countries and averages over all of the detail, and it is the DETAIL that matters. In the case of smaller, less economically varied countries, it is downright misleading.
rgb
No – we are all gathered here because Willis reviewed a paper and misunderstood the math (http://wattsupwiththat.com/2014/07/09/diving-into-the-deeps-of-decarbonization/). He then started this second post to better explain his claim. He shifted slightly from his original misstep but did no better here because he still doesn’t understand the math and as Mosher pointed out, is unrepentant in the matter. The formula in the quote above demonstrates Willis is not alone. So the conversation has been to solve the problem of people not understanding the math. It was the identity, not the application of it that Willis parsed to his great amusement to CO2 emissions = CO2 emissions. The problem is these are two different things which invalidates his mathematical cancellations in the original post. You should find out what they are.
A second conversation has to do with the value of the Kaya Identity to inform policy. I’m with the majority on that in that I think it is a very course tool with poorly defined parameters. There is too much going on behind the curtain for a proper skeptical inspection. It doesn’t help that Dr. Kaya himself is focused on renewables which is another way of saying the emerging world economies deserve nothing better than expensive mediocrity. Imagine if renewables had been mandated in the Marshal Plan – Europe would still be digging themselves out of WWII.
Time to move on from here and follow his excellent travelogues which he always gets right.
– – – – – – – – –
This seems conceptually straight forward and not slanted toward any climate tribe ‘sides’.
That said, I must point out, however, Pielke jr’s position does illogically beg the question of an incorrect premise that fossil fuels are a net climate liability.
John
Sakoku Village, USA
Sakoku is a small isolated fictional village in which 100 people live, work, and recreate using only food and electricity for energy consumption where there’s neither surplus production nor unsupplied want/need (a truly magical place). The village is nestled beside a lake which supplies 1,000 kWh of hydroelectric power to the village. The village also has a coal fired plant producing 100,000 kWh. The hydroelectric power produces 0 CO2↑ per kWh of electricity while the coal fired plant produces 1 Ton of CO2↑ per 100 kWh. On average each person in Sakoku uses 500 kWh of electricity every day for personal use. Commerce within the village consists of a brewery using 5,000 kWh, a bakery using 10,000 kWh, a general manufacturing plant/store using 10,000 kWh, farms using 5,000 kWh, and everything else (including the diner) using 20,000 kWh in all producing $1,000,000 worth of goods and services (including the electricity being generated).
On average the village CO2↑ per kWh = (1000 Tons CO2↑ / 100,000 kWh) 99,000 kWh – (0 tons CO2↑ / 1,000 kWh) 1,000 kWh = 990 Tons CO2↑/kWh
In 2009 the village elders (Gilligan, Skipper, Professor, Ginger, Mary Ann, Mr. and Mrs. Howell) were visited by three ghosts from 350.org, showing them the 10:10 video. They were so scared of being blown to bits they decided to reduce the village’s CO2↑ by 10% in 2010. The professor immediately went to research the problem and came back with: According to the Kaya “Identity” the village could reduce its CO2↑ by A) reducing the population, B) decreasing standard of living, C) increasing production efficiency, D) reducing the CO2↑ intensity of its energy production, or E) some combination thereof. He continues …
Current situation:
Population = 100
GDP = $1,000,000 (value of goods and services produced)
GDP/Population = $10,000 per capita (standard of living)
Energy/GDP = 0.1 kWh/$ (production efficiency)
CO2↑/ Energy = 990 Tons / kWh (CO2↑ intensity of energy)
CO2↑ = 100 people x ($10,000 per capita) x (0.1 kWh/$) x (990 Tons CO2↑/kWh)
= 99,000,000 Tons CO2↑
10% of CO2↑ = 9,900,000 Tons CO2↑
2010 Emission Goal = 89,100,000 Tons CO2↑
Plan A) Reduce population to 90 people:
CO2↑ = 90 people x ($10,000 per capita) x (0.1 kWh/$) x (990 Tons CO2↑/kWh)
= 89,100,000 Tons CO2↑
Plan B) Decrease Standard of living to $9,000 per capita:
CO2↑ = 100 people x ($9,000 per capita) x (0.1 kWh/$) x (990 Tons CO2↑/kWh)
= 89,100,000 Tons CO2↑
Plan C) Increase production efficiency to attain 0.09kWh/$ Energy per GDP:
CO2↑ = 100 people x ($10,000 per capita) x (0.09 kWh/$) x (990 Tons CO2↑/kWh)
= 89,100,000 Tons CO2↑
Plan D) Reduce CO2↑ intensity of Energy production to 891 Tons CO2↑/kWh:
CO2↑ = 100 people x ($10,000 per capita) x (0.1 kWh/$) x (891 Tons CO2↑/kWh)
= 89,100,000 Tons CO2↑
Plan E) Attain 0.095 kWh/$ and 940.5 Tons CO2↑/kWh (5% ↑ in prod. Eff. and Energy ↑ intensity each)
CO2↑ = 100 people x ($10,000 per capita) x (0.095 kWh/$) x (940.5 Tons CO2↑/kWh)
89,347,500 Tons CO2↑
Surprised that a five percent reduction in two factors isn’t equivalent to a 10% reduction in one factor?
Well it ain’t (not according to the Kaya identity anyway):
0.95A x 0.95B = 0.95AB NOT 0.9AB
So what about a 10% reduction in 2 factors:
CO2↑ = 100 people x ($10,000 per capita) x (0.09 kWh/$) x (891 Tons CO2↑/kWh)
= 80,190,000 Tons CO2↑ which is equivalent to a 19% reduction from original not a 20% reduction from original.
So what about a 10% reduction across the board:
CO2↑ = 90 people x ($9,000 per capita) x (0.09 kWh/$) x (891 Tons CO2↑/kWh)
= 64,953,900 Tons CO2↑ which is equivalent to a 34% reduction from original not a 40% reduction from original.
So, according to the kaya identity the village is better off putting all its efforts into one of the factors to get the most bang for the buck. This doesn’t seem to jive with the Law of Diminishing Marginal Returns but what the heck, it’s just Climate “Science”.
The professor being a level headed sort of person recommends calling the Ghost Busters, exercising their right to keep and bear arms to protect themselves from anyone that might want to blow them to bits for any reason, and not worrying about their insignificant CO2↑.
steverichards1984 (July 13, 2014 at 7:31 am) says:
You say the Kaya is mathematically sound.
On what basis can a formula such as A = A be sound?
I say it is mathematically sound because it is true for all possible values of A by definition. The Kaya expression is also mathematically sound for the same reason because it is derived from the similar statement CO2 = CO2 that is likewise universally true by definition.
Yes LHS = RHS but what is the point of such an equation when its usefulness is limited to demonstrating that LHS = RHS?
This is a different question. Just because a mathematical statement is true that does not mean it is necessarily useful or has a point. The statement LHS = RHS may be pointless and useless depending on the situation to which one is applying it, but if it is nevertheless true then it would still be mathematically sound, would it not?
If its alleged use is to find the amount of CO2 somewhere, then it fails miserably because it always gives you whatever answer you want.
The Kaya equation appears to have been derived from the fundamental identity CO2 ≡ CO2 by the judicious addition of self-cancelling fractions to the RHS. This is a standard pure mathematical technique in common use. So the Kaya expression is sound from the standpoint of pure mathematics because its inherent mathematical integrity has been preserved at every step of the way.
Nevertheless, from the standpoint of applied mathematics it still “fails miserably” as you say. As I’ve already explained, I think it does so because the fractional variables that it ultimately derives on the RHS cannot be measured independently of their primary components which have been defined in the pure mathematical derivation and which all cancel one another out. In the end it just reduces back down to the original tautology CO2 ≡ CO2 and so leaves us none the wiser.
But I think this currently-inescapable dependence on the primary components of its fractional variables is its critical flaw. Ways to measure the fractional variables independently of their primary components need to be found before the Kaya function can become the effectual tool of global environmental science and economics that it is made out to be.
John West,
You were doing really, really well there until you said:
0.95A x 0.95B = 0.95AB
In fact, 0.95A x 0.95B = (0.95x 0.95) AB = 0.9025 AB
So it’s just short of a 10% reduction.
To get a 10% reduction you need to use the square root of 0.9 = 0.94868…
That is, you need to reduce two factors by 5.13% each.
Then, as you say, diminishing returns may well suggest this route is more effective than a single 10% reduction. (Assuming, of course, you believe reducing CO2 is an effective way of scaring off ghosts.)