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.
Discover more from Watts Up With That?
Subscribe to get the latest posts sent to your email.
RobertInAz
nevermind – i figured it out – the equation is simple stuff – the method is bafflingly new to me
–john eyon
“That’s not my game. It’s yours.”
#################
I have nothing to do with it. But to convince yourself that implementation of the KI works nothing like the way you are using it, visit http://forecast.uchicago.edu/kaya.html and give it a try. Then view the page’s source. There you will find all the math and data. The calculator is implemented in easy to read JavaScript. Really bright people are using the Kaya Identity all the time because they don’t make a grade school error in the implementation.
“Jan Kjetil Andersen says:
July 22, 2014 at 12:59 am
Michael 2 says:
“Let’s cut population in half. It’s in the numerator and denominator — no change!
Michael 2, the Kaya identity does not work that way.
The Kaya Identity starts with the working assumption that each of the ratios remains constant”
Let’s be precise here – the Kaya identity does work perfectly fine the way Michael2 suggests: it just requires that a halving of population of requires that the total GDP doesn’t change and the total energy used doesn’t change. Since GDP is generated by people and the energy is used because people need it/want it, the idea that these things wouldn’t change is *highly* unrealistic. If you could change the population without changing the energy demanded, Michael would be right. We don’t live in that universe though(as far as we can tell).
RobertInAz says:
July 22, 2014 at 4:43 am
“The last term is CO2 per unit of energy. It is the CO2 efficiency of energy production. Interpreting the last term as total CO2 over total energy is what leads to the C=C conclusions. People can certainly do that since that was the formula in the text, put that is not Kaya. It is something else.”
I’m not sure what you’re looking at specifically but I agree with Michael2 here. If your total units of CO2 are 1000tons and your total energy usage is 1000MWh gives you 1ton of CO2 per MWh as CO2 efficiency on energy production. It has to work this way for Kaya to be an identity (or equation or whatever you would rather call it).
There’s nothing wrong with Michael2’s argument(about changing population) per se – you can *with the right assumptions* construct a world where changes in one factor are not reflected in changes in others. The problem is, those assumptions are not realistic. In the real world, population, GDP and energy usage are all related to one another.
Cheers, 🙂
Michael 2 says:
July 22, 2014 at 9:24 am
So you use the somewhat unfamiliar “E” for electric potential in volt.
Well, anyway the current “I” can also be expressed as Power (P) divided on E or I= P/E
The resistance “R” can be expressed as E*E / P
You then get E = (P/E) * (E*E/P) which cancels out to E=E
No that is not what it does. It is used as a tool to divide the big challenge of reducing CO2 emissions into smaller and more manageable units.
If we set a target of for instance reduce the CO2 emissions by 50% in 2050 we can do this by either
1. Hope that the world population will be reduced by 50%, which is obviously not going to happen.
The population will probably increase to 10 billons before it levels out.
2. Strive to reduce the average GDP per capita. Some people think that we can accomplish something by cutting rich peoples luxury use, but it will not amount to much. On the contrary we should strive to increase the per capita GDP because that is the best way to fight poverty. Hopefully the per capita GDP will have doubled or more by 2050.
3. We can reduce the amount of energy used per dollar of value created. This is already happening and has done so for decades, but on a very slow rate.
4. We can reduce the amount of carbon emitted per Kilowatt hour produced.
This can be done with various techniques from carbon capture to more nuclear and renewable energy.
Those are the four elements in the Kaya identity. It is trivial to reduce it to C=C. As you say any 8th grader can do that. I think even Bart Simpson could recognize it and saying something like: “those scientists must be awful stupid not to have seen that”.
The somewhat more complex thing is to recognize that it is useful to divide the problem of controlling the carbon emissions into these four factors.
/Jan
while i think Kaya is a valid method – and it’s useful in limited ways – i have to sympathize with Willis – while acknowledging that he didn’t grasp the identity’s function – nor did many of us
Kaya Identity is an analytical tool new to many of us – obviously – and it works a little differently – we can’t manipulate it in traditional ways
i never had to use sophisticated forms of math in my jobs – so i’ve never encountered a formula where the result on the left is identical to just one element of the righthand side – and that element is manually plugged in
it should have been obvious from that – that we aren’t generating the figure on the left – instead – we’re using that figure like a beam to hang the factors on the right – so that the results of tweaking the factors on the right side – can be seen in the right side
Michael 2 says:
July 22, 2014 at 10:03 am
“In this case I detach “GDP” from resources. Malthusian limits have nothing to do with the labeling of resources with dollar values. GDP will rise simply because of inflation if for no other reason, it is a measure of *activity* and not of resources. It’s artificial and a poor metric of anything long term because its “basis” changes. I recognize that you normalize GDP to a standard dollar and I appreciate your recognition of the importance of doing so.”
GDP isn’t a perfect measure but global GDP *in constant dollars* is growing pretty steadily(constant dollars are the only way GDP works as a comparison). If Malthusian limits were important, this would become increasingly harder to do which does not seem to be the case. For limits to matter, they will have to show up in measures of activity like GDP eventually. Resources are generally getting less important over time (Google Julian Simon wager) for a more indepth discussion of these issues.
“Consider Norway — abundant hydropower. That entire nation is practically disconnected from the Kaya Identity. Population? Irrelevant. GDP? Irrelevant. CO2 production per Kilowatt? Nil.”
I’m not sure where you got your ideas about Norway but per wikipedia’s list of CO2 per capita, Norway is #32 on the list CO2 per capita and its CO2 usage per capita has increased by ~18% over the last ~20 years. Norway is probably pretty close to 0 population growth so the increase is probably mostly due to increased GNP(partially offset by
“It seems trivially easy to portray the *intention* of the Kaya identity in a way that does not expose it (and its advocates) to ridicule. Why do so many people not see this? Some here have attempted that very thing but it’s not “sticky”. Once you make a Kaya formula “rational” it is rather mundane and obvious — leaving the spotlight on the absurdity.”
Well, it is rather mundane and obvious, but that doesn’t mean it is useless. If you take your Norway example, instead of just asserting that population and GDP growth are irrelevant, one can test this for Norway say and, confirm that, in fact, they are not. I would know a mundane but true fact than think I know an interesting but false. 😉
Cheers, 🙂
JEyon says: July 22, 2014 at 10:33 am
…..
The key point is the formula Willis cites is not Kaya. It disagrees with the immediately preceding text which does describe Kaya.
Going back to Willis’s reference on page 12: This text is good:
CO 2 emissions can be expressed as the product of four inputs: population, GDP per capita, energy use per unit of GDP, and CO 2 emissions per unit of energy:
This formula, immediately following the text, is deeply ambiguous. Hence the beer identity thread.
CO 2 emissions = Population x (GDP/Population) x (Energy/GDP) x (CO 2 /Energy)
——————————————–
A formula that better matches the text would be something like:
CO 2 emissions from energy production = Total Population x (GDP/Person) x (Energy/Unit of GDP) x (CO 2 /Unit of Energy). With this formulation, which better matches the description, the terms do not just cancel out.
Nor does this require holding one term constant in order to analyze carbon abatement.
RobertInAz says:
July 22, 2014 at 11:17 am
“A formula that better matches the text would be something like:
CO 2 emissions from energy production = Total Population x (GDP/Person) x (Energy/Unit of GDP) x (CO 2 /Unit of Energy). With this formulation, which better matches the description, the terms do not just cancel out.”
I’m not following the precise point you are making but the factors in your version of Kaya are equal to the ones that Michael was using. GDP/Person=Total GDP/Total Population, Energy/Unit of GDP=Total Energy/Total GDP …
Cheers, 🙂
Shawnhet says: July 22, 2014 at 12:18 pm
“I’m not following the precise point you are making but the factors in your version of Kaya are equal to the ones that Michael was using. GDP/Person=Total GDP/Total Population, Energy/Unit of GDP=Total Energy/Total GDP ….”
The point is when the proper equation is used, then the CO2 variable on the left is a dependent variable that can be calculated from the terms on the right rather than trivially derived from CO2=CO2. People analyzing these things use the correct formula to think through the implications of varying the factors on the right:
– Total Population
– Per person GDP
– Energy efficiency of GDP
– CO2 efficiency of energy production.
The fact that a useful equation (Kaya) can be transformed into a not useful equation (not-Kaya) does not detract from the usefulness of the useful form.
RobertInAz says:
July 22, 2014 at 12:47 pm
“The point is when the proper equation is used, then the CO2 variable on the left is a dependent variable that can be calculated from the terms on the right rather than trivially derived from CO2=CO2. People analyzing these things use the correct formula to think through the implications of varying the factors on the right:”
I would sort of agree except that I would say that the benefit of Kaya is that you can separately *measure* the right hand factors to help understand *why* CO2 is changing and, from there, what the practical implication of trying to change CO2 levels might be.
Cheers, 🙂
RobertInAz says:
July 22, 2014 at 12:47 pm
The “proper equation”? My friend, I quoted the EXACT EQUATION that was used in the paper I was analyzing, called “pathways to deep decarbonization”. The equation was and is:
Suppose we double the population. A logical expectation is that the GDP would also about double, and that the energy used to produce twice the goods would be about twice the energy needed for the smaller population.
This leads to the following equation:
In other words, despite the population doubling, and the GDP and energy used to produce the GDP doubling … the Kaya Identity says that the CO2 emissions are UNCHANGED.
According to you there are four factors that can vary independently:
But that is a misconception. You cannot just vary, for example, the energy efficiency of the GDP, because the underlying independent variables (GDP and energy) appear in two of the other variables. You do not have the options of independently “varying the factors on the right”, because they are not independent variables.
As a result, the Kaya Identity does NOT represent the real world. Nobody believes that if we double the population, double the GDP, and double the energy used, that the CO2 emissions will stay the same … but that is what the Kaya Identity says would be the result of varying the INDEPENDENT factors on the right hand side of the Identity.
This means, of course, that the Kaya Identity cannot add to our knowledge of what is going on. It is true, no question about that … but it is trivially true. It is certainly instructive, as you point out, to look at the individual factors. But the KI as a whole just leads to meaningless conclusions, like the idea that emissions won’t change if we double the population, the GDP, and the energy needed to produce that GDP.
w.
PS—For another look at the KI, you might consult the “Statistician To The Stars”, Matt Briggs …
“In other words, despite the population doubling, and the GDP and energy used to produce the GDP doubling … the Kaya Identity says that the CO2 emissions are UNCHANGED.”
Wrong – in your example, that is true but because you also doubled the carbon efficiency of energy production.Thus, in order to hold the CO2 emissions constant with doubling of population, in your case, the equation shows that the carbon efficiency of energy production must be doubled.
That is exactly why this identity is useful: it forces you to recognized what changes are necessary in light of other changes.
The same would hold true if you wanted to halve the C emissions: if all other ratios are held constant (like you did), the carbon efficiency of energy production would have to double.
Regarding Briggs… he’s a really smart guy. But this identity seems to do the same thing to smart guys as the Monte Hall statistics problem: half of the smart folks looking at it get cross-eyed. Also note that Briggs is rigorously formal about causality, and if one tries to impute causality from this equation, one gets in trouble.
A more substantive criticism of the identity is that it isn’t numerically true if you vary the numbers by much – it doesn’t predict. But, that also begs the point – the identity is useful in that it forces folks to think a bit more carefully about management of carbon (which, whether we think they are right enough, is a big deal).
To me, the biggest problem with the identity is that people look at it the wrong way and then get hung up on it. The identity (and it truly is an identity) is meant to be a simple way of showing relationships between important variables in the economic and energy system. It fails at that the way it was expressed, exactly because smart people over-think it.
I think that if the identity were simply presented as C = P*GDPp*Eeff*Ceff, without showing the ratios, it would work a lot better.
All that based on a false hypothesis by James Hansen, that the law the atmosphere operates on – the Ideal Gas Law – had been replaced by a ”green house gas law” due to the power of computing LoL.
Willis Eschenbach says: July 22, 2014 at 3:18 pm
The “proper equation”? My friend, I quoted the EXACT EQUATION that was used in the paper I was analyzing, called “pathways to deep decarbonization”. On page 12 of the paper you cite you have two different formulas. One half inch above the formula you repeatedly side is this text: CO 2 emissions can be expressed as the product of four inputs: population, GDP per capita, energy use per unit of GDP, and CO 2 emissions per unit of energy: Throughout the paper, they apply the correct form of the equation. The form of the equation you apply is not Kaya.
Using your example (unrealistic): Suppose we double the population. A logical expectation is that the GDP would also about double, and that the energy used to produce twice the goods would be about twice the energy needed for the smaller population. Using the correct equation
Pop*2 * (per capita GDP-unchanged)*(energy per GDP Unit – unchanged) * (CO2 efficiency of energy – see discussion). Discussion: if the CO2 efficiency of energy is unchanged, then CO2 doubles. If the CO2 efficiency is doubles (half the CO2 per unit of energy) then CO2 remains constant.
You do not have the options of independently “varying the factors on the right”, because they are not independent variables. In the not-Kaya version of the equation you and others enamored of the beer identity apply, you sort of have a point. The population, energy and GDP terms all have to move in the same direction. However, even in the not-Kaya form, you can tweak population independently of energy independently of GDP. Then you insert the correct value of CO2 on the right to reflect the new CO2 efficiency of energy production and viola, you have a new value for CO2 on the left from before you started tweaking the independent variables on the right. However, as you and all of the other beer-identity lovers point out, in order to derive the CO2 efficiency of energy production, you have to know the total CO2 answer already.
I think that if the identity were simply presented as C = P*GDPp*Eeff*Ceff, without showing the ratios, it would work a lot better. Which is exactly what the sentence one half inch above the flawed formula on page 12 of “pathways to deep decarbonization” says. And it is exactly how all of the beer-identity haters think of Kaya.
John Moore says:
July 22, 2014 at 4:14 pm
“…that is true but because you also doubled the carbon efficiency of energy production.”
Yes, that is they way to interpret it.
“But this identity seems to do the same thing to smart guys as the Monte Hall statistics problem:”
A great brainteaser. I remember when Marilyn Vos Savant wrote that one up in the Sunday supplement, and lots of credentialed people, including a professor from MIT, wrote scathing letters to her telling her she was wrong. That was a lesson I took to heart: don’t put your public reputation on the line for something trivial. You might be precipitous, and end up looking very foolish.
John Moore says:
July 22, 2014 at 4:14 pm
Say what? There is no independent variable called “carbon efficiency of energy production”. I have calculated the results if I change the population, the GDP, and the energy used. These are the independent variables. You see the result.
w.
Willis,
First, I think it important to use the KI as an explanatory tool and nothing else. Anyone trying to use it to fine tune some policy is foolish (but then, fine tuning any economic variable is a fools errand). Also, accept that it is not exact as soon as one changes any variable, but for explanatory or teaching purposes, that is a second order concern and not initially important. Finally, recognize that the domain of usage is one where we assume, whether we believe ourselves it or not, that carbon releases are important.
Finally, accept that, like any identity, it is tautological. You can always cancel terms and end up with C = C, but that is not more relevant here than it is in trig identities (which can also be expressed in a way that you can cancel terms).
The point of the KI is to demonstrate rough relationships between important variables: total population, GDP per capita (far more interesting than GDP), Energy needed to have that GDP (TE/GDP), and the carbon efficiency of energy production (a quantity of great significance if one is interested in the game of modifying carbon emissions).
The problem is getting hung up on the” independent variables”. Forget about them except as how you use them to calculate ratios! Treat the ratios as the variables and it works just fine. The C/Te is the carbon intensity of energy production. Use it as if it were named gamma or something, and don’t look inside. These ratios are meaningful things in themselves.
Thus, write the equation as C = P*Wc*Egdp*Ceffic
Then plug your numbers into the following (note, for now assume C as a proxy for greenhouse emissions):
P = population
Wc = GDP/P ~= Economic welfare per capita
Egdp = Energy/GDP = energy intensity of economy
Ceffic = C/Energy = Carbon intensity of energy production
Then watch how the ratios (Wc, Egdp, Ceffic) change. It then becomes clear that, all other things being equal, halving C emissions requires either: halving the carbon intensity, halving the carbon intensity or halving the economic welfare. Note that any of us who have been paying attention already know this, and we don’t need the KI to tell us this – but again, that’s not what it is for.
This is a useful thing to be able to show people if you are trying to get them thinking a bit more clearly, and a bit more quantitatively about this issue.
Obviously, we could get more complex – halving C means varying more than one ratio. Or whatever. But the point is that you have to vary the *ratios* (or the population) – nothing else is interesting.
Finally, don’t expect the results to be exact. The identity is linear, but the real world isn’t.
John Moore says “The problem is getting hung up on the” independent variables”. Forget about them except as how you use them to calculate ratios! Treat the ratios as the variables and it works just fine.”
That’s what I thought, too, and it does eliminate the tautology. But the underlying math still works — see my response to Shawnhet above — if you double population ONLY, it makes no difference whether the “2P” is in the denominator of the second term or you calculate it “offline” — every person gets half the GDP and CO2 emissions is unchanged, never mind whether you can now actually calculate it because you’ve eliminated the tautology.
What I have been seeing is that advocates, on seeing this obvious problem, insist that GDP tracks population, that if you double population you also double GDP, and necessarily Energy but you cannot halve the CO2 produced by energy generation.
AS IT IS USED, the Kaya identity ought to just be written:
CO2 emissions = population * co2-per-person.
Let’s see if anyone argues with THAT. If everything tracks population then you don’t need those other terms.
Michael 2 writes:
No, this is using the identity incorrectly. If you double population, you double population. If you don’t touch any other ratio, the identity suggests (since it isn’t exact with this big a change) that the GDP/capita has to go down 50% to keep carbon stable.
and
That is true, because it is an identity. But it is also only useful in the case where you are willing to hold the other two terms constant. In other words, the KI separates the CO2 emissions into four factors, and shows (roughly) how they interact. And that’s all it does, but that is more than the more simplified formula above.
John Moore in response to Michael 2: “No, this is using the identity incorrectly. If you double population, you double population. If you don’t touch any other ratio, the identity suggests (since it isn’t exact with this big a change) that the GDP/capita has to go down 50% to keep carbon stable.”
Actually it goes down the instant you put “2P” in the denominator, but yes, I have written this result several times. I realize it is a stampede of commentary here. I have even written that Kaya is correct in the case of abrupt transitions where society cannot catch up — a suddenly doubling WILL produce its impact in the next term, GDP/population, cutting everyone’s GDP in half — except of course the impact won’t be uniformly distributed, and to a small extent I believe that is exactly what is happening. The rich are in no danger of becoming poor and that portion of GDP that actually relates to energy will not be uniformly distributed.
The implications ought to be obvious — CO2 mitigation strategies are likely to hit the poor first and hard.
In this present instance, what had been happening in these arguments is “assumptions” and you know how to spell assume.
Writers insisting that the ratios don’t change (when in fact they DO), and to do that, if you double P you must then double GDP and then you double Energy at which time the math says you’ve instantly cut CO2 per energy in half. That’s what the math says, but of course, then you have to actually DO it and until the the math “is wrong” because doubling energy is going to double CO2 but Kaya has no mechanism for doubling CO2. It ALWAYS simplifies to CO2 = CO2.
If you do NOT “daisy chain” the doubling’s down the chain, then whichever ratio you stopped this process is going to be cut in half — maybe it was GDP per person, maybe it was energy per GDP. Of these, actually cutting GDP per person is more possible, so is reducing population as several nations have done that on a rather large scale (Cambodia, Lenin/Stalin Soviet Union).
If we come to an agreement of which form of the relationship is Kaya and which is not-Kaya, then we might want to discuss why Kaya does not apply to the notion of deep decarbonization.
Several posters have mentioned this. The “variables” on the right are only mathematically independent. In the real world, they impact one another. So changing one by more than a few percentage points will have a measurable impact on the others. So to get to even a 50% reduction in CO2, IMHO, Kaya provides only coarse insight as to what will happen along the way. It does, of course, provide great insight into what the other terms must be to get to the goal once you start varying, say, population.
RobertInAz says:
July 22, 2014 at 4:54 pm (Edit)
Willis Eschenbach says: July 22, 2014 at 3:18 pm
On page 12 of the paper you cite you have two different formulas. One half inch above the formula you repeatedly side is this text: CO 2 emissions can be expressed as the product of four inputs: population, GDP per capita, energy use per unit of GDP, and CO 2 emissions per unit of energy: Throughout the paper, they apply the correct form of the equation. The form of the equation you apply is not Kaya.
You can name the combined independent variables if you wish, Robert. However, the fact remains that I used the same exact actual equation that they show. Here is a screenshot of their equation, from page 12 of their study (8 Mb PDF).
Note that is identical to the equation I am using. I don’t care what they might call the combinations of independent variables. In fact, you could combine any number of the terms and give them names … doesn’t change a thing.
The fact is, I AM using the proper equation, it is the equation that contains the independent variables, and it is the equation they used.
w.
Bart says:
July 22, 2014 at 4:56 pm
I doubled the population, the GDP, and the energy used. The Kaya Identity says if you do that, the “carbon efficiency of energy production” will automatically double, and the CO2 emitted will stay the same.
Do you believe that?
This is the problem with naming the combinations of independent variables, and then treating the combinations as if they were actually the independent variables. They are not. We can’t just change say the GDP/energy, because it affects the others.
w.
Willis writes:
‘I doubled the population, the GDP, and the energy used. The Kaya Identity says if you do that, the “carbon efficiency of energy production” will automatically double, and the CO2 emitted will stay the same.
Do you believe that?”
You are misinterpreting it. The identity says that the carbon efficiency of energy production must be doubled in order for the CO2 emitted to be the same. In other words, it says that, somehow, you must double the carbon efficiency of energy production. In no way does it say this the carbon efficiency magically doubles!! Give the guys a little credit – they aren’t idiots. This is a matter of interpretation – of knowing what the KI is for and how to use it.
John Moore says: “You are misinterpreting it.”
It’s math. How can it be misinterpreted?
“The identity says that the carbon efficiency of energy production must be doubled in order for the CO2 emitted to be the same.”
There is no “must”. If you double the denominator you have just halved the value of the term.
“Give the guys a little credit – they aren’t idiots.”
They are very clever. Has any other topic attracted this much attention?
John Moore says:
July 22, 2014 at 4:14 pm
“I think that if the identity were simply presented as C = P*GDPp*Eeff*Ceff, without showing the ratios, it would work a lot better.”
Maybe it would help to spell it out clearly:
CO2_Emissions = population X per_capita_GDP X Energy_use_per_unit_of_GDP X CO2_Emissions_per_unit_of_Energy
Willis Eschenbach says: July 22, 2014 at 5:10 pm ….and it is the equation they used.
As in (from page 13)?
This is the result of a combined 60% reduction in the energy intensity of GDP (Energy/GDP)
and 70% reduction in the carbon intensity of energy (CO 2 /Energy) compared to their 2010 levels.
How about table 5-1 on page 23?
How about para 6.5.2 on page 32? On average, the CO 2 intensity of power production is reduced by 94%, from 617 gCO 2 per kilowatt-hour (kWh) in 2010 to 34 gCO 2 per kWh by 2050 (Figure 6.9).
The document is an exercise in fantasy. However, I did not find a single instance where they used the not-Kaya form. Over and over again, they rely on decreasing the carbon intensity of energy production – that being the independent variable of particular interest to these writers.
Willis Eschenbach says: July 22, 2014 at 5:13 pm The Kaya Identity says if you do that, the “carbon efficiency of energy production” will automatically double, and the CO2 emitted will stay the same.
Not quite. Kaya says that if you double population, GDP and energy, and do nothing with to CO2 intensity of energy production, then CO2 emissions will double. Applying the not-Kaya form and demanding it act as a mathematical identity is what leads to the beer-identity view of things. If Kaya were an identity in the mathematical sense (Johan convinced me it is not) then the CO2 terms in the not-Kaya form must be the same because they are the same variable. That is way I no longer refer to it as the Kaya identity. The term identity has a precise meaning in mathematics.
However, in the Kaya form proposed by Willis above C = P*GDPp*Eeff*Ceff, and in the text of “pathways to deep decarbonization” immediately before the not-Kaya form of beer-identity fame, then C on the left is a dependent variable calculated from the four “independent” terms on the right. [See my comment July 22, 2014 at 5:03 pm for why independent is in quotes]. This is how Kaya is used throughout “pathways to deep decarbonization”.
RobertInAz — Thanks! Make it a formula or function: “proposed by Willis above C = P*GDPp*Eeff*Ceff.”
Kaya and “pathways to deep decarbonization. The united States discussion starts on P. 180. Table 1 shows the economy in 2050. On page 184 we see:
“….reductions in the final energy intensity of GDP (-74%) …. In other words, by 2050, in their minds, it is possible the economy will produce $4 of economic output for the same amount of energy that produces $1 now. Similarly ….and the CO 2 intensity of final energy (-80%)….
There are people out there who believe this stuff is possible. Now, because they use Kaya, it is possible to compare what they hope might happen to what actually has happened, Dr. Pielke covers this ground well. Then we can go spend our spare dollars on adaptation.
Kaya and “pathways to deep decarbonization” 2. They mention in passing the notion of CO2 intensity of GDP but never calculate it. In the US example above, a reduction of energy intensity of GDP of 74% and and CO2 intensity of final energy of 80% implies a reduction of CO2 intensity of GDP of 95%. Showing my work
(Energy/Unit of GDP) * CO2/Unit of energy = CO2/Unit of GDP
energy/unit of GDP = .26
CO2/unit of energy = .20
therefore CO2/Unit of GDP = .26 * .20 = .052
In other words, the CO2 required to produce $1 of GDP will be reduced by 95%.
If you believe that is possible by 2050, or even 2100, I have something to sell you.
To RobertInAz says: July 20, 2014 at 7:52 pm
I asked ” Please answer me this question: What is the half-life of CO2 in the atmosphere?”
You reply “Not relevant to the Kaya discussion, Outside his area of expertise.”
But it is relevant. There is a carbon cycle involving oceans, soils, animals, vegetables, and the atmosphere. From what I understand of this Kaya Identity, You’re attempting to balance an equation of human activity to carbon dioxide release into the atmosphere. So, for a new carbon dioxide molecule becoming airborne, how long under normal conditions, will it remain in the atmosphere before being taken up in the ocean, animal life or plant life?
My impression of the equation was what spurned my second question.
“Do you believe that any CO2 released into the [atmosphere] remains in the atmosphere?”.
Because it could only matter if the carbon dioxide has a long half-life in the atmosphere. I’ve read many people claim it’s about 5 to 7 years. Which for me, makes the Kaya Identity equation redundant? (Because it’s the heating of the oceans that is increasing the CO2 in the atmosphere, not human activity).
And for my first question to be outside of Roger’s or your own expertise, or the fact that neither of you even considered the questions, makes me think the entire enterprise is playing with only half the information you need.
Willis Eschenbach says:
July 22, 2014 at 3:18 pm
First off, I completely agree that your expression of Kaya is the same as RobertinAz’s – you are right about that.
“In other words, despite the population doubling, and the GDP and energy used to produce the GDP doubling … the Kaya Identity says that the CO2 emissions are UNCHANGED.”
No, the Kaya identity doesn’t say that – you assume that – the reason you say that CO2 emissions are unchanged is that you’ve **assumed** they are unchangeable. Think about it. You start by using reasonable assumptions namely that if population were to double, so would GDP and energy demand, then your final assumption is that CO2 will not increase no matter how much we increase energy demand. This has nothing to do with Kaya. With Kaya and three out of 4 variables, you can calculate the fourth. If you define all four variables, you can make the expression come out however you want.
If I say that mass is density times volume, and you say that a liquid has a density of 5 and volume is 2, I can calculate that the mass is 10, if, however, you assume (unreasonably) that the mass is fixed, you can assume that no matter how much of the liquid you have at whatever density, the mass will always be fixed. You can’t blame the expression for being unreasonable – it is just the assumptions you are applying to it that make the answers come out to what they do.
If, OTOH, you assume that the carbon intensity (the ratio of CO2 to E) stays constant (which is fairly reasonable) – you will calculate the CO2 under doubled population to also double. IOW, reasonable assumption – reasonable result, unreasonable assumption – unreasonable result.
Cheers, 🙂
Shawnhet says: “(Willis:) ‘In other words, despite the population doubling, and the GDP and energy used to produce the GDP doubling … the Kaya Identity says that the CO2 emissions are UNCHANGED.’ No, the Kaya identity doesn’t say that”
Indeed it does. All terms except the fourth are null and void in the formula as usually written.
EVEN IF you take the position (as all warmists do) that each ratio is intended to be pre-computed before inserting, so that there’s no nasty little numerator/denominator thing, it does actually sort of still work that way because if you double the population, then you must also double the population in the GDP per Capital computation. So whether you ‘cross cancel’ in the Kaya Identity or effectively do the same thing by separate computation it is the same.
What I see is that warmists instinctively double *everything* if P doubles. That’s okay but you have to be a bit more clear about it. Saying “double the population” implies ONLY the population. Kaya then reveals that everyone gets half GDP and CO2 emissions stay the same.
THAT is what Kaya says! Everyone gets half GDP if population doubles. If you go beyond that, well then you’ve gone beyond.
Shawnhet says “If, OTOH, you assume that the carbon intensity (the ratio of CO2 to E) stays constant (which is fairly reasonable) – you will calculate the CO2 under doubled population to also double.”
Well then just make it a constant and all this hullabaloo goes away. 🙂
We don’t need no steenkin constants: