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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Sigh. Wish I had an edit function. “Paying attention” of course, “not paying intention.”
Willis to me (8:31):
Independent? Well, if you cannot see that GDP depends on population, or that energy used depends on GDP, or that CO2 emissions depend on energy used, then I fear that I cannot help you.
Strangely, in your very next reply (8:32 am, to John Moore), you acknowledge these relationships of dependence. You seem to be unclear in your own mind what “independent” means.
Earlier, I challenged you to practice what you preach by quoting the interpretation of the Kaya Identity that you’re arguing against, and all you could produce in response was the Identity itself together with the interpretation that you made up in your own head. That won’t do.
Here is Pielke’s interpretation, from the article cited in the head post:
carbon dioxide emissions = population x per capita GDP x energy intensity x carbon intensity.
This interpretation, not the one you invented, is what is on the table — particularly because this conversation is supposed to be about Pielke’s work. Respond to it. Show that it’s problematic if you can. But don’t make specious claims based simply on the fact that the math works out. (The equation would be wrong if the terms didn’t cancel!)
Dr. Doug : “You seem to be unclear in your own mind what ‘independent’ means.”
I wish I had your superior powers of reaching through the internet and discerning clarity, or lack, in another person– not that being clear is correct.
In the world of mathematics it is indeed pretty clear.
If X = A B C, and A can be specified whatever you like, and B can be specified whatever you like, and C can be specified whatever you like, then A B C are independent, not only of the answer but of each other.
Now then if B depends on A, then it should be stated as some coefficient times A.
X = A *2A * C
If this equation is reflecting something “real world” then a dependency may exist that is not specified or captured in the equation. If the dependency CAN be revealed, then it ought to be revealed with suitable coefficients of whatever variables are actually independent.
If it is only partly dependent, then it ought to be factored into a dependent factor some coefficient of the independent variable, and the other independent variable capturing the independent part.
In this context, if GDP really is a dependent variable, then it need not be identified separately. If everyone’s contribution to GDP is $1,000 then you don’t need the whole GDP/population thing, just use the value and merge it into population: $(1000P) /Energy
But that’s math.
I could be wrong, but I am not uncertain. I appreciate everyone’s zeal in trying to explain this. I’ve never seen anything so simple be so difficult.
Willis (8:32 am):
Willis, before you purport to explain what the Kaya Identity can’t do, you really need to show that you know something — anything will do at this point — about how Pielke or others actually use it. Please consider it possible that experts in a field may have found some use for it that has not crossed your mind. If you want to parse and criticize what Pielke or others have done, fine, check it out. But don’t draw conclusions before that.
Now, as I and others have said before, an identity in itself indeed can’t prove or establish anything about the real world, but it can provide a useful analytical and accounting framework. If you disagree with that, then you really need to argue the point. You had the chance in the two threads that you yourself started and then abandoned. You have the chance now as well.
As for your ‘one ratio of interest’, you begin to show a little common ground with Pielke. He divides his analysis into two parts: GDP (=pop x GDP/pop) and your ratio, CO2/GDP, which Pielke notes can be further divided into the energy intensity of GDP and the carbon intensity of energy. So Pielke does give some emphasis to what you find of interest, but he also finds it useful to (1) discuss what GDP is going to be and (2) discuss two roads to reducing CO2/GDP.
We don’t “need the Kaya identity”, as you put it, if all we need to do is push some “reduce CO2” button. But if we want to think seriously about reducing CO2 (which, granted, you don’t), then a bit more analysis is useful.
As I said, if you take the formula out of context and ignore how they define their terms, then yes, the whole discussion amounts to “the formula as written in this report is misleading”. But the only way that could happen is if you didn’t read the accompanying text. That would be a pretty dumb mistake.
Oh look, Willis defines his terms as well:
Why doesn’t he refer to the accompanying text when he defines his terms? It looks like he didn’t even read the text. Could that be it? No, he includes the original definition in his July 9th post. Why didn’t he continue to use the original definition in his later post? Maybe he just glanced over the definition, and was careless? Then it should have been trivial for him to figure out where he went wrong and correct his mistake. But I guess he was out for blood, and not all that interested in facts. Yes, science can be a “bloodsport”, but it doesn’t have to be. This “bloodsport” idea, this kind of egotism and intellectual alpha-dog behaviour, is holding humanity back.
It does look like more people are starting to get it. Willis is a victim of his education system – self taught.
John Moore says:
July 23, 2014 at 12:17 pm
Thanks, John, as always you manage to bring sense to the matter. Again I have no objections to anything that you say.
As to further decomposing the CO2/gdp into energy/GDP and CO2/energy, here’s the current reality:
So while we can play at the margins of CO2/energy, we don’t have a “no CO2” option in the real world. The planet runs on fossil fuels, and will do so for quite a while longer.
In addition, there is no country that has managed to drop its CO2/GDP ratio until it has reached an advanced stage of technological development. Here, from the brilliant Gapminder site, is the record of some of the countries:
As you can see, most countries are still well below the level when their CO2/GDP starts to drop … and the big countries, India and China, show no signs of slowing the increase. The graph is linked above, and it’s live, you can go and change the settings, look at other countries.
All the best,
w.
Willis, we are in agreement about the actual CO2 situation. I also am very skeptical of the warmist conclusions – i.e. of the accuracy of warming predictions, although I do agree that adding CO2 will increase the temperature trajectory of earth’s surface temps.
My only reason for entering this thread was to attempt to clear up some of the confusion on interpreting the KI.
John Moore says:
July 23, 2014 at 3:54 pm
And you’ve cleared it up very well, in my case at least.
Thanks,
w.
Michael 2 says:
July 23, 2014 at 9:12 pm
“If it is only partly dependent, then it ought to be factored into a dependent factor some coefficient of the independent variable, and the other independent variable capturing the independent part.”
In those terms, GDP is only partly dependent on energy but regardless of whether it should be broken down into a dependent factor and an independent factor – this cannot be done currently. We don’t understand what causes GDP to change well enough. We know that many of the things that show up in GDP take energy to do them but it does not thusly follow that, for instance, using twice as much energy will double the size of the economy.
Cheers, 🙂
Michael 2 says:
July 23, 2014 at 9:22 pm
“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.”
I don’t think anyone insists that the ratios don’t change, it’s just that the don’t change assumption is the simplest and most realistic in the absence of *specific* information to the contrary. In any case, you continue to miss the actual math of the situation.
I’ll refer you back to my previous posts on this subject, but at base a comparison of the doubling ratios will simplify to CO2(2)=XCO2(1) where X is the ratio of CO2(2) to CO2(1) and 2 refers to the doubled situation and 1 refers to the non-doubled situation not CO2=CO2 as you assert.
IOW, the hypothetical you are arguing for is where
P2=2P1
GDP2=2GDP1
E2=2E1
CO2(2)=CO2(1)
I’m not sure why you’re having trouble with this but you’re obviously not the only one but just to make it clear – in this hypothetical you are assuming that GDP will double if the population doubles – this doesn’t have to be true. Likewise, you are assuming that energy demand will double if population does – this also doesn’t have to be true.
When you get to the last line, you *assume* that CO2 doesn’t change but somehow refuse to notice that this also *doesn’t have to be true*!! It is entirely possible that the changed CO2 doubled or halved.
When you get to this point, you will realize that it is the assumptions that make the difference here. I would suggest that the best assumptions would be those that are grounded in reality somehow.
Cheers, 🙂
Michael 2 says:
July 23, 2014 at 9:31 pm
Michael 2
Calculus is widely used with all kind of multivariable functions in for example economy.
Your argument does not make sense, and I think it is absolutely silly to insist that a concept like the Kaya identity shall mean something else than what the creator defined it to be.
/Jan
Jan says: “I think it is absolutely silly to insist that a concept like the Kaya identity shall mean something else than what the creator defined it to be. ”
You are so correct! I will henceforth ignore everyone’s opinion of what it means except that of Kaya himself. (or maybe not, this has been an interesting discussion).
Shawnhet said:
July 23, 2014 at 9:59 pm
I am genuinely trying to follow this thread and I do feel the pain of those who are arguing for the formulaic nature of the Kaya. Therefore, it is extremely frustrating trying to follow any of these arguments if folks don’t show simple working examples.
I have set out your “formula” quoted above and given it values.
Can you please tell me, how you are actually using it.
I am not being sarcastic or frivolous, I genuinely want to see your thoughts explicated.
IF
CO2(2) = A
CO2(1) = B
X = A/B
THEN
CO2(2)=XCO2(1) = A = A/B * B
CO2(1) = B = 500
CO2(2) = A = I0
X = A/B = 10/500
[CO2(2)=XCO2(1)] = [A = A/B * B ] = [A = 10/500 x 500] = [A = 0.02 x 500] = [A= 10] = A = A
However, I think you are saying, that instead of ratios, you see constants such as the “C” (The speed of light) in E=MC2.
In this case, perhaps you might write a “formula” like this:
[A = K * B ]
WHERE
A = Pay ($)
K = Rate of Pay ($/hr) = 50
B = Hours worked (hr) = 500
A = K x B
A = 50 x 500
A = 25000
Units are not dealt with by formulas explicitly, the result is expected to be in the correct dimension. A formula is not properly constructed if its units don’t balance though!
So, of course your pay is in ($) units because the units of (hr) cancel* 😉
* The values of the variables don’t cancel, only the units in this case because the value of K is independent of B it is not the quotient of A/B and B is not the reciprocal of K.
Is this how you see the Kaya being implemented?
Scott Wilmot Bennett says:
July 24, 2014 at 2:30 am
Ok, so let us take it from the beginning.
Kaya identity as described by IPCC 2007:
The Kaya identity is a decomposition that expresses the level of energy related CO2 emissions as the product of four indicators:
CO2 = CI * EI * GDB/cap * P
CI = Carbon intensity, i.e. the amount of carbon emitted per unit of energy produced.
CE = Energy intensity, i.e. the amount of energy used per dollar GDP created
GDP/cap = how many dollars GDP each citizen of the planet produce on average per year
P = the world population
To find the numbers for the indicators above we calculate CI as:
CI = CO2/TPES where:
CO2 = Total energy related carbon emission per year
TPES = Total primary energy supply per year
We calculate CE as:
CE = TPES/GDP
Where GDP = Total annual GDP
GDP/Cap is calculated as GDP /world population
The Kaya identity is therefore sometimes described little imprecise by substituting the original indicators by how we calculate those indicators. Then the Kaya identity becomes:
CO2= (CO2/TPES) * (TPES / GDP) * (GDP/P) * P
However, this somewhat imprecise meaning should not cause any confusion if you pay any attention to how the identity is used and explained.
The four original indicators are the free variables in this identity, not the numerators and denominators used to calculate the identities.
Some people here insist that the numerators and denominators should be the free variables.
That is what this is all about.
/Jan
Scott Wilmot Bennett says:
July 24, 2014 at 2:30 am
“CO2(2)=XCO2(1) = A = A/B * B
CO2(1) = B = 500
CO2(2) = A = I0
X = A/B = 10/500
[CO2(2)=XCO2(1)] = [A = A/B * B ] = [A = 10/500 x 500] = [A = 0.02 x 500] = [A= 10] = A = A
However, I think you are saying, that instead of ratios, you see constants such as the “C” (The speed of light) in E=MC2.”
First off, the context of the quote I have provided was to deal with the folks (e.g. Willis and Michael2) who think they have demonstrated that Kaya says that CO2 emissions can’t change. Your math shows how that is not so – we just don’t have enough information to calculate X (or A/B) using Kaya alone. If, however, you make an assumption about how *specifically* CO2 will change, you can do so.
I don’t believe that anything is a constant, I believe that predicting a change in CO2 requires that we *assume* how the factors that affect CO2 will also change in response to a hypothetical change in another. These assumptions can either be grounded in reality if you want realistic predictions or not grounded in reality if you don’t care about how your predictions turn out.
At the end of the day, it is easier to think of the variables in Kaya being the ratios themselves (mathematically this is not necessary but it is a much simpler way to think about it). If, over the next 30 years, if a country doubles its population, GDP and demand for energy, is it historically plausible for CO2/E to drop to half its current value? This remains a valid question regardless of whether you want to think of Kaya in terms of its ratios or not.
Cheers, 🙂
Shawnhet says “deal with the folks (e.g. Willis and Michael2) who think they have demonstrated that Kaya says that CO2 emissions can’t change.”
While the rest of your comment is reasonable, do at least please get this part correct. I have not written that CO2 cannot change, rather, I have written that you can make CO2 anything you want because all other terms cancel. It is true that CO2 doesn’t change *because* of changing one of these other self-cancelling terms.
The usual response is to explain that each term is actually a ratio and Population in the first term probably isn’t Population in the second term, and GDP in the second is not GDP in the third, and so on. IF you use the same numbers then it makes no difference whether you calculate the ratios first and then multiply, or cross cancel and multiply. But if you don’t use the same numbers well then anything goes!
Shawnhet says “If, over the next 30 years, if a country doubles its population, GDP and demand for energy, is it historically plausible for CO2/E to drop to half its current value?”
Irrelevant for a formula. Kaya Identity says that is exactly what will happen. It is unlikely to actually happen, but you are using a math equation to use the past 30 years (which Kaya doesn’t), to predict the future (which Kaya also doesn’t).
If you go nation by nation then this question can be answered more precisely by ditching Kaya and just examining the various factors. Ultimately the thing that produces CO2 is everything that produces CO2.
Automobile average mileage has increased dramatically in 30 years in the United States.
http://www.infoplease.com/ipa/A0004727.html
From an average of 14.3 mpg in 1960 to 20.2 mpg in 1990.
So the answer is yes, it is plausible to halve the CO2 per capita. Unlikely, but possible, and Kaya is no help in deciding this question. In other words, so many assumptions are built into Kaya that it just seems useless — the big assumption being that human beings have the fuel to burn to keep doing “business as usual”.
I suppose I should say that since I’m not a climatologist I have no say in the matter. Climatologists obviously have a private language, technical jargon, which at times seems silly to outsiders. After all, in my line of work the people that use a computer are called “users” but that word also used to mean someone that used recreational drugs (might still mean that).
But I am a taxpayer and voter. So climatologists must decide whether to stay confined in their ivy halls vying for grants from NSF or try to communicate in ways that is still effective but not obviously silly in the eyes of the public.
“Kaya Identity part II – and a ‘diamond law’?
Posted on July 25, 2014 by Ruth Dixon
http://mygardenpond.wordpress.com/2014/07/25/kaya-identity-part-ii-and-a-diamond-law/
“Are some apparent CO2 emission reductions ‘too good to be true’? In this post, I discuss how the Kaya Identity leads to what might be called the ‘diamond law’ of CO2 emissions. This ‘law’ (in fact just chemistry) allows us to check the plausibility of apparent dramatic CO2 reductions.”…………..
Conclusion:
“I have no idea what caused the discrepancy in the CO2 emissions for Singapore from the two sources. But I am sure that the World Banks’s numbers are ‘chemically impossible’ while the IEA’s numbers give Singapore a CO2 intensity of fossil fuel of just over 2, consistent with the ‘diamond law’. This ‘law’ – derived entirely from the chemistry of carbon – therefore provides a useful check on the plausibility of reported CO2 emissions data.”
Michael 2 says:
July 25, 2014 at 12:57 pm
“I have not written that CO2 cannot change, rather, I have written that you can make CO2 anything you want because all other terms cancel.”
I must say that I find your writing to be confused. You did, in fact, state that CO2 cannot change (per Kaya) in your July 23, 2014 at 7:36 am post.
July 25, 2014 at 1:07 pm
Shawnhet says “If, over the next 30 years, if a country doubles its population, GDP and demand for energy, is it historically plausible for CO2/E to drop to half its current value?”
“Irrelevant for a formula. Kaya Identity says that is exactly what will happen. It is unlikely to actually happen, but you are using a math equation to use the past 30 years (which Kaya doesn’t), to predict the future (which Kaya also doesn’t).”
No, it doesn’t say that. Kaya itself doesn’t tell you how its factors are going to change(BTW your argument here is disagreeing with your previous post). For you to claim that historical studies of how the factors of an expression are irrelevant is just wrong.
“Automobile average mileage has increased dramatically in 30 years in the United States.
http://www.infoplease.com/ipa/A0004727.html
From an average of 14.3 mpg in 1960 to 20.2 mpg in 1990.”
What is wrong with this example – let me count the ways.
1. It does not demonstrate the CO2/E falling by 50% in 30 years.
2. It is cherry picking – you took the best possible period to demonstrate your case – the final 15+ years of your own data show almost no change in mileage per gallon
3. This is only for one technology not for all technologies that produce CO2
Cheers, 🙂
The paper The British Climate Change Act: a critical evaluation and proposed alternative approach by Roger A Pielke Jr addresses the energy poverty faced by individuals that did occur as a result of (quixotic) energy policy.
Although Dr. Pielke used the Kaya equation to underscore his prophetic analysis, Willis Eschenbach did point out that the equation does reduce to CO2 = CO2, and that similar equations could be created for anything of insignificance.
Do not understand Anthony’s concerns.