As many readers know, there was quite a hullaballo over the Kaya Identity last week, two posts by Willis Eschenbach here and here created sides seemingly equally split on whether the equation is useful or not.
One of the most strident critics was Dr. Roger Pielke Jr., and in the spirit of keeping an open mind on the issue, I offered him space on WUWT. Here is my email and his response, reprinted with his explicit permission.
On Mon, Jul 14, 2014 at 9:52 AM, Anthony xxxxxxx@xxxx.com wrote:
Hello, Roger Jr.,
I’d like to direct you to a comment on WUWT that challenges your calculations using the Kaya Identity.
http://wattsupwiththat.com/2014/07/12/the-beer-identity/#comment-1685623
I provide it only for your information.
I know both of you have issues with the current state of discussion on WUWT regarding that equation/identity/relationship, and I’m certainly OK with that.
I think that much of the dissent over it has to do with the difference in viewpoints between science and engineering. I and many others look at the Kaya identity equation more from the engineering perspective, and expect it to perform as many other calcs do, but it seems that it doesn’t act as a hard equation, but more like a soft one, that generally defines the relationships of terms. A number of commenters have approached it from the engineering viewpoint, and find themselves puzzled as to why the numbers they get don’t seem sensible.
I puzzle over that also.
To that end, and because you’ve been highly critical, agreeing with such statements as “breathtakingly ignorant”, therefore, given the critical comment above, I’d like to offer this, first raised in another comment:
http://wattsupwiththat.com/2014/07/12/the-beer-identity/#comment-1684325
Perhaps Anthony could give equal time to Pielke in defense of the Kaya identity?
I’m more than happy to do so should you be so inclined; not just for my own education on the topic, but for the hundreds, if not thousands of others that suffer from the same doubts that the equation isn’t as well thought out as some claim it to be. Or, if it was never intended to produce real world numbers accurately, but serves only to illustrate the relationship of the variables, explain that clearly so that the engineering types understand it better.
If you wish to make a submission, MS Word with embedded images works best. Any equations you might want to use in MS word’s equation editor don’t translate to WordPress well, so they will be converted to images. Or, you can optionally use LaTex, which is supported directly in WordPress.
I would appreciate an answer, no matter if it is a yes or a no. Thank you for your consideration.
Anthony Watts
=========================================================
Roger’s response Tuesday, July 15, 2014 6:59 AM (published with permission)
Hi Anthony-
Thanks for your email. Apologies for the delay in responding, as have been off email while traveling.
If you’d like to help your readers better understand the use of the Kaya identity, which I think is the most important tool for analyzing actual and proposed carbon policies, then I would recommend that you introduce them to this paper (open access);
http://iopscience.iop.org/1748-9326/4/2/024010
The mathematics are simple. Of course, there is a more in depth discussion in my book, The Climate Fix.
Finally, for those who’d prefer a lecture format, here is me at Columbia Univ last summer explaining the significance of the Kaya Identity for climate policy analysis:
Thanks, and all the best,
Roger (Jr.)
==============================================================
I agree with Roger that: “The mathematics are simple.”
In fact I think it is that simplicity that lends itself to being criticized as not being fully representative of a complex system. Willis described the Kaya Identity as being “trivially true” while Roger in his book and video treats its with the same respect as some physical law equation. My take is that the truth is somewhere in the middle between those viewpoints.
Whether it is best used as a political tool or as a physical science tool is still an open question in my mind, though I tend to think it leans more towards political usefulness. Whatever your viewpoint is, let’s thank Roger Pielke Jr. for taking the time to respond and to offer his view here.
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July 20, 2014 at 12:01 pm
Yes you are.
Take an example; imagine that the World had had 1 Billion fewer people than today. Well there would be emitted less carbon from the breathing from 1 billion fewer people, but food for 1 billon people would not have been produced. That means that the farms of the world would not have captured the carbon for food for 1 billion people. The less carbon capture on the farmlands equals the less emissions by exhaling CO2. This means that it is a zero sum carbon budget.
There would probably be more wilderness and less farmland, but the carbon captured in the wild plants is released when the plants rotten. That is also a zero sum budget.
/ Jan
bushbunny says:
July 19, 2014 at 8:43 pm
“O/T Do you reckon any of these so called climate change bullshit artists,….”
=============
What do you have against artists ?
Jan Kjetil Andersen says:
July 20, 2014 at 1:55 pm
Yes you are.
—————————————————————————————————————————
No, I am not wrong – but let’s not get in a trivial tit for tat contradictory argument.
The carbon cycle is called a cycle for a reason – all the CO2 that gets consumed or sequestered will eventually return to gaseous CO2 it started at, it’s just a matter of how long that takes.
In a simple breakdown of the level of concentration of CO2 in the atmosphere, it does not matter where it came from, what matters is whether the rate of emission of CO2 is greater than the rate of absorption. The sources of emission consist of natural (including ‘natural’ emissions from humans) or anthropogenic (from fossil fuels). Considering that the anthropogenic sources are exclusively from fossil fuels it can be conclusively demonstrated that the current level of CO2 in the atmosphere is most probably due to our consumption of fossil fuels and the resultant emission of CO2. I say ‘most probably’ because if you make an assumption that the natural processes are at equilibrium for emission and absorption of CO2 from the atmosphere then the only source of increase is from the burning of fossil fuels – the spigot in Pielke’s bathtub. Unfortunately, the assumption that natural sources are at equilibrium is false.
Your example of a 1 billion person drop in the population resulting in a zero sum budget is also false. Disregarding the fact that most of the CO2 removed from the atmosphere is done by microscopic plankton, farms that do not grow food are still teeming with plant life so there is not a net reduction in the plant life capturing carbon. As far as wild plants releasing their carbon when they die and rot, i recommend you study how fossil fuels were formed.
“..Considering that the anthropogenic sources (CO2) are exclusively (coal fired power plants!!!)from fossil fuels…” What about the other GHGs, methane, etc. What about contemporary HC fuels, ethanol, bio-gas methane, wood, bagasse,…..
“…assumption that the natural processes are at equilibrium…” I do not consider this a valid assumption. There are plenty of good reasons to believe that for a dynamic earth equilibrium does not exist, does not last. CO2 could be ramping up because of gradual warming driven by solar cycles or ocean floor (nobody knows what’s going on down there.) volcanic vents independent from man’s activities (coal fired power plants). Just because we don’t know the answer doesn’t mean we can just fill in man, even though he is the divinely inspired, created, centerpiece of the cosmos. The earth will adjust and accommodate. If we don’t really know why a volcano erupts does tossing in virgins (coal fired power plants) help?
Got carried away. Forgot to mention there is a significant agricultural component to CO2 emissions.
Wow, what a bunch of fuss over something that is pretty simple. The Kaya identity is a way of demonstrating variances – the general, necessary impact of messing with one or more of its terms. For that, I think it’s pretty good. If you want to use it to calculate exactly how much of this or that you need… well… see the last paragraph below. Oh, and don’t get hung up on whether or not CO2 causes the earth to melt, or whatever – that isn’t the point of the KI.
The Kaya identity is best understood if you *don’t* cancel out the various numerators and denominators. I think everyone is getting hung up on the obvious fact that if you cancel them all out, you get C = C. That is true, but it is a feature, not a bug. This is no different from a trigonometric identity, except that seeing the numerators and denominators side by side triggers old middle school algebra instincts to cancel. Don’t do that – it just confuses things.
So let’s reformulate it:
E = q*Ei*Ci
q = quality of life – i.e. GDP/population is sort of a measure of this. For policy purposes, it’s a lot more interesting than GDP.
Ei = Energy intensity – don’t worry about what it is made of, for now
Ci = Carbon intensity – don’t worry about what it is made of, for now
We can easily see that decreasing emissions requires (Ei and Ci held constant) a decrease in the quality of life – GDP/capita.
So, if we don’t want to decrease the quality of life, just mess either Ei or Ci.
And, we can do that.
And that’s the point of the KI.
Some have argued that it isn’t precise. In one sense, that’s false – it is, by definition, an identity. But in another sense, it’s true – you can’t really hold some variables constant in the real world. And, of course, there are non-linearities.
However, this shouldn’t matter. It isn’t meant to be a precise way of tuning policy. In fact, if you are trying to precisely tune a policy, you are committing the fundamental error of progressivism – the idea that you can actually tune things exactly.
So, this provides a way of *demonstrating* sensitivities, which is useful for explaining the most important policy conclusion: you cannot significantly reduce emissions without either hurting quality of life, or making dramatic *independent* improvements in Ei or Ci, and you need to thus look at the likelihoods of those improvements and their (invisible in this identity) impact on GDP/P.
John Moore says “The Kaya identity is best understood if you *don’t* cancel out the various numerators and denominators. I think everyone is getting hung up on the obvious fact that if you cancel them all out, you get C = C. That is true, but it is a feature, not a bug.”
Of course it is a feature. *I* wouldn’t use it, but what do I know about persuading billions of people that I am a brilliant scientist?
It makes no difference if you cancel or don’t cancel
Suppose 10 = 7 * (6/7) * (5/6) * (10/5) (the numerator in the fourth term on RHS must be the same as the LHS term). In fact, it doesn’t make the slightest difference what numbers you use along the way so long as you remember that the numerator of each term is the denominator of the next.
Obviously, if you have actually *measured* something, then feel free to insert it, at which point it ceases to be the Kaya Identity.
John Moore says: July 20, 2014 at 7:03 pm
nicely said,.
Dr. Roger Pielke Jr.
Please answer me this question: What is the half life of CO2 in the atmosphere?
I think I should also do a followup question: Do you believe that any CO2 released into the [atmosphere] remains in the atmosphere?
Greg Cavanagh says: July 20, 2014 at 7:35 pm
Dr. Roger Pielke Jr.
Please answer me this question: What is the half life of CO2 in the atmosphere?
Not relevant to the Kaya discussion, Outside his area of expertise.
I think I should also do a followup question: Do you believe that any CO2 released into the [atmosphere] remains in the atmosphere?
Hmm, the presence of CO2 in the atmosphere makes the answer to this trivial. Perhaps you want to rephrase.
p.s. I’m not Dr. Pielke.
RobertInAz quoting a question from Greg: “Do you believe that any CO2 released into the [atmosphere] remains in the atmosphere?”
Robert says “Hmm, the presence of CO2 in the atmosphere makes the answer to this trivial. Perhaps you want to rephrase.”
Trivial and yet you choose not to declare your answer.
“p.s. I’m not Dr. Pielke.”
No doubt. I suspect he would say that any particular molecule of CO2 is eventually going to be taken up in some way — such as turned into a carbonate rock or into plant cellulose.
All this blah blah about how much CO2 is or remains in the atmosphere is orthogonal to the subject at hand.
John Moore — the subject at hand had changed. In a few minutes it may change again. Indeed, you have already changed it from a discussion of how LONG does CO2 remain in the atmosphere to how MUCH is or remains in the atmosphere.
@Willis “According to the Kaya Identity, what happens to the amount of CO2 emitted from doubling those variables?
Well … nothing. No change in the slightest. The population and the GDP and the energy used all appear in both the numerator and the denominator, so they cancel each other out. ”
Willis, you failed to note that total energy appears in two terms, not just one. That means that your numbers require the carbon intensity of energy production to be reduced by the increase in total energy.
So, after you plug in the numbers, go back and look at the values of each of the four ratios and you will see this.
The key to using this is to NOT cancel things out in the equation, and to look at the final values of the four ratios, not just the final value of each side, which will, of course, be equal to E.
And that is why the identity is useful: Plugging in the numbers shows these interdependencies.
And if CO2 has no meaningful impact on global warming or ice caps melting or sea levels rising or hurricanes blowing or people sweating it’s all a bunch of moot gum flapping.
“And if CO2 has no meaningful impact on global warming or ice caps melting or sea levels rising or hurricanes blowing or people sweating it’s all a bunch of moot gum flapping.”
If everybody believed that, you would be right. They don’t.
John Moore: You take the liberty of holding some ratios constant; I’ll take the liberty of holding some of Kaya numbers constant: If the GDP grows twice, everything else being constant, CO2 production does not. change. If the population doubles, everything else being constant, CO2 production does not change.
Does it make sense? Of course not, even though it is mathematically true. The issue is that in the real world all parts of the identity influence each other – holding selected numbers or ratios constant does not make sense. If Kaya identity nudges you in that direction, better check twice.
The equation doesn’t address GDP – it addresses GDP per person. If you want to play with the GDP, note that the carbon emission only holds constant (for constant population) if you halve the energy usage per GDP. And if you do that, it does make sense.
If you don’t do that, the equation shows that emissions go up. And that, also, makes sense.
Put another way, the equation shows that to double the GDP while holding emissions constant, you have to halve the Energy/GDP. And that’s the whole reason that it’s valuable – it shows that the Energy/GDP is a big constraint on your ability to hold down emissions while increasing GDP.
Note that for the above analysis, to make explanation simpler, I assumed that P is constant and Ci is constant. This sort of holding variables constant is normal in multivariate analysis. In the real world Ci and Ei are closely tied together, but my point holds.
Oh, and don’t get hung up on whether or not CO2 causes the earth to melt, or whatever – that isn’t the point of the KI. – John Moore
= = = = =
The “identity” is built on the very premise that our CO2 emissions are warming the planet dangerously, and thus must be limited. The truth value of that premise does matter. 17+ years of accelerated emissions but no warming is not a problem for you? It is healthy and scientific to be “hung up” on falsification of the hypothesis by the real world, because a false hypothesis is not one you would want to cling to or agonize over for the rest of your life. What a tragic waste of time that would be.
“If everybody believed that [CO2 did not have a meaningful impact], you would be right.” – John Moore
= = = = =
Wrong. Truth is not established by consensus: truth is established by the real world, not by its representations or representatives. The real world, despite popular beliefs, indicates “no meaningful impact” for CO2.
Mike Tremblay says:
July 20, 2014 at 4:10 pm
Thank you for the answer Mike, but I do not follow you in this.
We all know how fossil fuels where formed, that is trivial. The thing is that only a tiny fraction of the plants and animals are sedimented and form fossil fuels. The overwhelmingly bigger part rot and release the carbon when the plants die.
However, one part that do not rot and release carbon is the one that is used for making food. The Carbon in that part is released when we breathe, but it makes no difference in the carbon budget since microbes in the rotting process would have released if that food had not been made.
/Jan
Here’s my problem with the Kaya Identity. To refresh my tired memory, here is the identity again.
Suppose we put in the actual numbers of today for population, GDP, CO2 emitted, and the rest. This gives us the current amount of CO2 emitted today.
Now, suppose that the population doubles and the GDP doubles and the energy used doubles. That seems like a very probable change, that in the future we’ll have more people using more energy and producing more stuff.
According to the Kaya Identity, what happens to the amount of CO2 emitted from doubling those variables?
Well … nothing. No change in the slightest. The population and the GDP and the energy used all appear in both the numerator and the denominator, so they cancel each other out. As a result, the conclusion has to be that a doubling of the population combined with a doubling of the GDP and a doubling of the energy used will have no effect on CO2 emissions.
Does anyone believe that doubling the population and doubling the GDP and doubling the energy used will NOT change CO2 emissions? Yet that is exactly what the Kaya Identity says.
What am I missing here? As an identity the Kaya Identity is assuredly true, but how is this useful in the real world?
w.
Jan Kjetil Andersen says:
July 20, 2014 at 9:32 pm
—————————————————————————————————————————
Simply put Jan, the rotting process does not return all the carbon to the atmosphere in the same amount of time as consumption by people, and as such it acts as a carbon sink compared to human consumption. To give an example, somewhere in the past I remember someone saying that it takes 1 acre of farmland to feed 1 person for 1 year. Now, given that nearly 100% of CO2 absorbed from the atmosphere by that acre will be returned to the atmosphere by the consumption of the food produced from that acre within the same year, there will be a zero net change in the atmospheric CO2 concentration over the course of one year for that acre.
Now, the fact is that in order to create one acre of farmland, one acre of undeveloped land must be converted to farmland, and since the undeveloped acre is not used to produce food, and because the process of decay is much slower, the time to return 100% of the CO2 sequestered by that same acre is on the order of tens of years for grasslands, hundreds of years, in the case of forests, or millions of years, in the case of swamps and jungles. All of this means that any undeveloped land, when developed into farmland, is removed from the negative CO2 balance into the zero CO2 balance and effectively becomes a net CO2 increase – in other words, before the land is developed it is removing CO2 from the atmosphere, and after it is developed it is not , even though it is not emitting CO2, so effectively all the CO2 produced by the human dependent upon that acre of farmland is being added to the balance of CO2 in the atmosphere.
If we expand this to the whole biologically related balance of CO2 production and consumption, and make another false assumption that the non-biological/non-anthropogenic CO2 balance is in equilibrium, (ie. CO2 emission from volcanic sources is in equilibrium with CO2 absorption by metallic ions), you can see that any increase in the CO2 producing (animal) populations has to be matched by an increase in the CO2 consuming (plant) populations in order to maintain zero increase in the CO2 concentrations in the atmosphere. In fact, in real terms this population matching is rarely achieved, with constant ‘boom and bust’ cycles in the living populations of both plants and animals. Thus, we see in the geological record, and in the present Keeling curve, natural cycling of the CO2 concentration curves – and this provides a possible explanation of the increases and decreases in CO2 concentrations in the past that cannot be provided by man’s consumption of fossil fuels.
Wow, scary stuff in print.
The excuse a politician needs to implement population reduction strategies under the guise of building a better world.
Where have we heard that before?
And the excuse? “It’s mathematical. To save the planet, we must take active measures to reduce the population.” All the factors in the equation have the same end. Reduce population, reduce GDP (standard of living), reduce energy consumption. Fact is, energy consumption has been an integral factor in current longevity. (Think refrigeration to keep food cold to keep bacteria from growing.)
For those thinking we aren’t already taking active measures, look at Obamacare;
Driving up the cost of healthcare makes it less available.
Open border without sending ill people to quarantine?
Escalation of costs in food and energy?
I never thought I would see such things in my day.
Willis Eschenbach says:
July 20, 2014 at 9:48 pm
What am I missing here? As an identity the Kaya Identity is assuredly true, but how is this useful in the real world?
————————————————————————————————————————-
As I understand how Dr. Pielke presented it, it is useful if you want to establish an emission goal and want to know what the consequences will be for the GDP, Population growth, and energy consumption. To me, it obviously fails if you want to establish zero emissions – which is the purported goal – unless you commit to the absolute conversion of all energy sources from carbon based to non-carbon based energy sources.
IMHO, since it was created by an economist, it is very similar to the obsession that economists had with reducing the deficit (carbon emissions) while ignoring the fact that as long as there was a deficit the national debt (CO2 concentrations in the atmosphere) was increasing. You can’t stop the national debt from increasing until you reduce the deficit to zero, and you can’t reduce the national debt until put the deficit into a surplus – something that in terms of CO2 concentrations, will never be achieved in our lifetimes, the lifetimes of our children, nor the lifetimes of our grandchildren.
My take is the Kaya Identity is correct and useless. Here is my Pop Identity:
Population = Males + Females
It is correct and useless for forecasting purposes because it does not tell me how many males and females in any given year in the future. But it is accurate in any given year in the past.
I see that this blog fudges the difference between an equation and an identity.
The difference is simple at first sight: the sign for an equation is “=” but for an identity is 3 horizontal bars.
You prove an identity to be true using mathematics. In mathematics identities can be solved or not. If solved they are true. If not solved they may be true or not. Maybe somebody else can solve and identity I cannot solve. If an identity is true it is true because of the tautological nature of mathematics.
You don’t prove an equation by mathematics. In fact, if an equations sets out a law of nature or your theory how nature works, you can never prove it to be true. You may or may not be able to show that it is false. If the relationship is not capable of being proven false, then it is not science.
The method of showing a relationship to be false is: the hypothesized relationship becomes unsatisfactory for explaining the observations of interest. You need a new theory.
So Newton’s laws of motion were not false for Civil War artillery 150 years or so ago . But the same physics do not explain many phenomenon related to GPS satellites and their receivers which use the theory of special relativity developed by Einstein a little over 100 years ago..
The Kaya Equation describes a theory about the behavior of nature. Whether or not it will be falsified depends on whether or not it explains observations better than some other theory. If the Kaya Equation is not satisfactory for the purpose it was put forward we will say that it has been falsified.
The question was asked, Why all the fuss about the difference between emissions from fossil fuels and other fuels? Or, why did Dr Murray Salby lose his job?
Murray Salby is a leading climatologist, author of a leading university textbook in atmospheric physics a new edition of which is on my bookshelf. Dr Salby was fired from Macquarie University. reason. We do know that he had given a lecture in which he claimed that most of the CO2 in the atmosphere was not generated from fossil fuels but from other sources.
We have a new paper by multiple authors that you can read for yourself on this subject because it is open source (free).
Simulating the integrated summertime ?14CO2 signature from anthropogenic emissions over Western Europe, D. Bozhinova, M. K. van der Molen, I. R. van der Velde, M. C. Krol1,, S. van der Laan, H. A. J. Meijer, and W. Peters. Atmos. Chem. Phys., 14, 7273-7290, 2014, URL: http://www.atmos-chem-phys.net/14/7273/2014/
Abstract: “We find that the average gradients of fossil fuel CO2 in the lower 1200m of the atmosphere are close to 15 ppm at a 12 km×12 km horizontal resolution.”
My comment: The significance of this is that total CO2 in the atmosphere is usually taken as about 400 ppm now and 280 ppm before the onset of the industrial age.
Main text:
“Radio carbon dioxide (14CO2) can be used to determine the fossil fuel CO2
addition to the atmosphere, since fossil fuel CO2 no longer contains any 14C.”
Figure 4(B) on page 7281 shows the maximum observed fossil fuel CO2 (ffCO2) as 50 ppm.
My comments:
For densely-populated Western Europe the study recorded only 3.75% as the average fossil fuel CO2 in the lower 1200 meters (4,000 ft) of the atmosphere and only about 12.5% as the maximum before diffusion.
Vertical diffusion of CO2 above 1200 meters has the effect of reducing the average percentage of fossil fuel CO2 percentage because only 15% of the mass of the atmosphere is below 1200 meters, while about 60% of its mass is between 1200 meters and top of the troposphere (about 10,000 meters). In addition, lateral diffusion takes place west to east and north to south.
The average percentage of fossil fuel CO2 in the atmosphere must half or less the average below 1200 meters in Europe and even lower for the whole globe.,
Willis Eschenbach says:
“Suppose we put in the actual numbers of today for population, GDP, CO2 emitted, and the rest. This gives us the current amount of CO2 emitted today.
Now, suppose that the population doubles and the GDP doubles and the energy used doubles. That seems like a very probable change, that in the future we’ll have more people using more energy and producing more stuff.
According to the Kaya Identity, what happens to the amount of CO2 emitted from doubling those variables?
Well … nothing. No change in the slightest. The population and the GDP and the energy used all appear in both the numerator and the denominator, so they cancel each other out. As a result, the conclusion has to be that a doubling of the population combined with a doubling of the GDP and a doubling of the energy used will have no effect on CO2 emissions.”
CO2emissions = pop*GDPpc*EnergyIntensity*CO2Intensity
If both population and GDP double, that means GDP per capita is unchanged. If both GDP and energy use double, that means energy use per unit of GDP (energy intensity) is unchanged. Assuming the same CO2 emission intensity (CO2 emissions per unit of energy unchanged), CO2 emissions will exactly double in your scenario.
Edim says “Assuming the same CO2 emission intensity (CO2 emissions per unit of energy unchanged), CO2 emissions will exactly double in your scenario.”
How about just assuming that the Kaya Identity is useless? You cannot just “assume” the fourth term is unchanged and still call it mathematics.
If you double energy in the third term (2E/GDP), you must also double it in the fourth term (CO2/2E) and the net effect is that the doubling of the numerator, divided by a doubling of the denominator, is “1” or unchanged.
You are quite right, as is everyone else here that refuses to process an algebraic equation as an algebraic equation but do please understand all the people that DO process algebra using the rules of algebra. What is this world coming to when sometimes an equation isn’t an equation?
After a all of this commentary, Willis still declines to read and understand the text accompanying the ambiguous formula.
Willis continues to repeat his initial misunderstanding.
Sad.
RobertInAz says “Willis continues to repeat his initial misunderstanding. Sad.”
And you continue to repeat yours (and I, mine, etc). Not sad! I haven’t had this much engagement in quite a while. I had no idea how few people can work ordinary algebra, or lay something out that deliberately looks like algebra but we are assured that it isn’t (you could, of course, lay it out differently so that it means what you seem to think it means).
Willis Eschenbach says: July 20, 2014 at 9:48 pm
Now, suppose that the population doubles and the GDP doubles and the energy used doubles. That seems like a very probable change, that in the future we’ll have more people using more energy and producing more stuff.
According to the Kaya Identity, what happens to the amount of CO2 emitted from doubling those variables?
For this toi play, the CO2 efficiency of energy production doubles. So if today, a KW of energy production emits 100 KG of CO2 – in the doubled population/GDP/Energy scenario, it will emit 50 KG of CO2. Kaya tells us this type of progress is implausible.
In Willis’s thought problem, Population doubles, GDP per person stays the same, Energy per dollar GDP stays the same, so the CO2 efficiency of energy production must double to keep total CO2 constant.
Willis, if you cancel everything out, of course you get CO2emissions = CO2emissions, but that’s not the Kaya Identity anymore. Furthermore, it doesn’t mean “no change in the slightest”, it means:
CO2emissions(after your doublings) = CO2emissions(after your doublings)
It may be undetermined, but it’s correct.
However, if you use the Kaya Identity and its factors, then you can calculate the emissions if you know the factors (pop, GDPpc, EnergyIntensity, CO2Intensity).
Edim dear, Robert dear, put numbers directly in Kaya. Willis is right.