The Tyranny of Tautology

A response to A conversation with Dr. Roger Pielke Jr.

Guest essay by Scott Bennett

Willis Eschenbach described the Kaya Identity as being “trivially true”, his opinion is uncontested by Dr Pielke Jr., whose only retort in its defence was, ‘the math is simple’.

The Kaya is a simple Identity, used as a tautological instrument. To deny this, would be to deny the very heart of its utility. The algebraic cancellation and isolation of its terms is de rigueur for its use.

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Fig. 1. The “Kaya Identity” as depicted in the lecture by Dr Roger Pielke Jr. : Climate Policy for a High Energy Planet4

I really wanted to understand how the Identity was actually applied, both mathematically and as a “tool” of policy discourse. To that end, I spent several days grappling with Kaya, as demonstrated by Dr Pielke Jr. .

When I felt I fully understood its application, I turned to the real world, from whence the model was presumably derived.

It doesn’t take very long to see why the Kaya is being used as an instrument of policy. Examining the real world, makes it abundantly obvious, just what a stake-to-the-heart, reality is, for policy wonks!

The Kaya’s real value is in its use, as a claim to authority. It is a construct, designed to frame the debate and thus isolate and compartmentalise contradiction.

Everywhere I looked, the terms as factors of total emissions where erroneous. But how could this be, I wondered? It seemed reasonable to suppose that the factors as given in the Kaya, according to Dr Pielke Jr., are the ‘only levers available in the tool box’.

I spent some time gathering data and comparing real places. More and more I began to see, that there was a fundamental factor missing. How is it possible that emissions weren’t a direct measure of the energy intensity of GDP and the efficiency of its energy production? Clearly there was a missing factor that was making the proportionality of the Kaya’s terms aberrant. Some hidden input was providing efficiencies that oddly, reduced the size of real world terms, making their ratios, counter intuitive!

But before I reveal what it is, I will tell you why it was left out! It was censored because it exposes the fact that the relationships of the Kaya are not universally applicable (Across the countries of the world). The inclusion of this important term renders the Kaya impotent as a tool of national policy.

Truly, the phrase “one size does not fit all” could never be ascribed more applicably than to the Kaya Identity!

Land area1 is the missing term and including it makes it very difficult to compare economies directly, and at the same time keep a straight face!

Ratios like, population density and emissions per km, would seem to be, essential aspects of any genuine and realistic analysis. Without this quantity it is irrational to compare national emissions and their individual contribution to the global total.

Singapore, with the world’s highest population density, is 11,000 times smaller than Australia. Australia’s land area represents 5% of the Earth’s surface, while its emissions are just 1% of the global total. The entirety of Europe2 fits inside Australia with room to spare.

Singapore’s population is 4 times smaller than Australia, its GDP is 5 times smaller, its emissions are 3 times smaller and its total energy usage is 45 times smaller. Yet, using the ratio of Emissions/GDP3, we find that Singapore produces 1.7 times more CO2 emissions for every dollar of GDP than Australia. This isn’t a real mystery, when you realise that not all GDPs are equal, of course!

It is probably safe to say that the resources in Australia’s vast land area, something Singapore lacks, is the missing factor in this case. The numbers are also strongly at odds with the assumptions spruiked by Kaya devotees, because Singapore produces all its electricity from natural gas while Australia is coal fired!

It is also probably not a surprise, that with such a small land area, Singapore produces 3,500 times the CO2 per km compared to Australia’s tiny contribution of just 5.5 kt/km.

This is the weakness of the Kaya. It can’t be universally applied. As soon as you compare figures across countries you discover the logical fallacies inherent in it.

Australia’s ratio of, emissions to GDP, is just double that of France. If emissions per square kilometre are compared however, France emits 12 times that of Australia.

It is clear why governments around the world aren’t rushing to embrace the logic of the Kaya. They understand, that they would be ill advised to do so. The Kaya is a tool of the global minded, useless for national policy, that reveals with perfect clarity, the hubris of groupthink and the latent stupidity of collectivist ambitions.

=============================================================

Notes:

1. Absolute values are given here, rather than “Real Land Area” which is of less relevance to the geography of climate.

2. Western Eurasia excluding Asia and Russia. The West or Western Europe.

3. This ratio is demonstrated in Dr Pielke’s lecture! The intent here, is to highlight that its “usefulness” also extends to invalidating the relationships between all four terms of the Kaya itself 😉

4. https://www.youtube.com/watch?v=QTUE5Ue6Z38

UPDATE: Dr. Roy Spencer has a nice simplification of the terms cancelling issue here in The Kaya Identity Crisis

UPDATE2: Elevated from a comment.

The problem with the Kaya identity is in its application, not in its arithmetic or ability to produce a bit of understanding about the real world. It is being used to help generate policy; long term policy that will be around for decades. It is being used to generate a meme; a way of thinking that will influence decision makers for many years to come.

The Kaya identity begins with the assumption that CO2 emissions MUST be reduced. RPjr stated in his video that it wasn’t even worth talking about the science of climate change anymore. He implied that there was absolutely no point in even discussing climate sensitivity to CO2 emissions and that such discussions are actually harmful. (I was gobsmacked!) The Kaya identity is part of the meme that proclaims “The science is settled!” He argues that it doesn’t matter what the science says about CO2′s impact. The Kaya identity is valid regardless. While that may be true for the identity, it is just stupid to carry that thinking over to the process of making policy. There is nothing more important than the science in making good policy decisions.

The Kaya identity ends with disaster. It is inherently linear in every aspect. The world is inherently non-linear in every aspect. The Kaya identity gives an illusion of knowledge and wisdom to decision makers; convincing them that they will be making good choices. In reality, there is a near zero chance that policies resulting from the use of the Kaya identity will be positive. The outcomes from such policies will range from bad to disastrous.

The Kaya identity gives decision makers the idea that they actually have a control knob. A half turn to the right gives a certain result every time. A half turn to the left gives another result, but just as predictable and dependable as the half turn to the right. This is a complete illusion!

Using the Kaya identity to make policy is like deciding to paddle your raft with two strokes on the right, followed by two strokes on the left, for the entire duration of your trip down the Colorado river. Such a strategy will not get you very far and may actually kill you. They way to paddle your raft down the Colorado river is by constantly assessing your current situation and deciding the best possible paddle strokes for that moment.

The same is true for climate change policy. There is no need to implement solutions today that will solve all climate change problems for the next 100 years. In fact, that would be impossible, and any attempt to do it would almost certainly cause more harm than good. In order to make good decisions, those decisions should be focused on the short term, and the main objective should be the strengthening of the position of future decision makers. That means the current policies should promote adaptability in all areas while enhancing the financial strength of future generations to deal with their issues; issues that they will certainly understand far better than we do today. It means the science is constantly assessed, along with the current state of the population and their needs. It means the UN should be concentrating on potable water for all of humanity today and not on the average global temperature 100 years from now.

The use of the Kaya identity rationalizes the bad decision making process. It allows decision makers to ignore the vital importance of adaptability and weaken the financial strength of future generations. It is the height of hubris and the antithesis of wisdom to use the Kaya identity in the manner it is being used by the United Nations and other bureau-crazies; and apparently promoted by Roger Pielke, Jr; a man I admire and respect, but strongly disagree with on this topic.

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July 24, 2014 1:28 pm

Anthony:
At July 24, 2014 at 10:36 am you write concerning the Kaya Identity

REPLY: Actually, yes, I’m pretty well done with it. I found the whole exercise an interesting study in perceptions, much like the global warming debate itself. I’m prepared to leave with the identity being trivially true for science to true for political purposes.

I write to respectfully request that you continue to provide posts on such matters on WUWT.
The predictions and projections of anthropogenic (i.e. man-made) global warming (AGW) have failed to occur and – very importantly – no successor Treaty to the Kyoto Protocol has been achieved or seems possible. In these circumstances it seems likely that in several countries bureaucratic methods will be used to achieve the policy aims of the AGW-scare. I refer anybody who doubts this to peruse, for example, actions of the US EPA in its declaration that CO2 is pollution.
Such bureaucratic activities need justification in the absence of empirical evidence for discernible AGW and lack of international policy agreements. And propaganda tools such as the Kaya Identity provide the required justification for the bureaucratic activities. As can be seen (for example, in this thread) arguments concerning options suggested by the Kaya Identity can displace discussion of need for any actions.
Hence, in my opinion, exposure of the function of such propaganda tools is important
Richard

JamesNV
July 24, 2014 1:32 pm

Jim Clarke says:
July 24, 2014 at 6:46 am
The Kaya identity begins with the assumption that CO2 emissions MUST be reduced. RPjr stated in his video that it wasn’t even worth talking about the science of climate change anymore. He implied that there was absolutely no point in even discussing climate sensitivity to CO2 emissions and that such discussions are actually harmful.

I think you sort of answered your own question earlier when you say:

It is being used to help generate policy; long term policy that will be around for decades.

My take is that Pielke is observing that long-term policy is being generated right now. In the minds of many policy makers, the debate is over. Given that, somebody has to make the situation understandable to policy makers so they can see, that given their assumptions, a) just how difficult it will be to reach their CO2 targets, and b) what “knobs” they should touch, and which “knobs” they should not touch. In my mind, he is working on damage control.

There is nothing more important than the science in making good policy decisions.

Well, yes. Except the only problem is that we are dealing with imperfect beings who believe the science is already settled. And they are generating “long term policy that will be around for decades” right now. If you had the ears of policy makers, would you continue to argue about uncertainties (and quickly lose the ears of policy makers) or would you try to mitigate some of the damage they were about to do?

July 24, 2014 1:35 pm

Johan (1:06 pm):
Sorry, what natural resources affects is economic structure, which is already well reflected in the Kaya Identity.
Regarding your “Scott Bennett Identity”:

CO2/GDP = (L/GDP) * (P/L) * (GDP/P) * (E/GDP) * (CO2/E)

The first three ratios on the right-hand side all cancel out together. In other words, you have a circular argument embedded in the equation. This does not make for useful analysis.

Joseph Murphy
July 24, 2014 1:44 pm

Dr. Doug says:
July 24, 2014 at 1:01 pm
However, in applying the Kaya Identity to the future, it’s necessary to make projections of future GDP, and that requires making projections of population.
——-
It is only necessary because those variables are in the Kaya identity. I posted an identity just as valid as the Kaya identity without population. You could do the same for GDP if you wish. There is no magic in the Kaya identity, nothing empirically needs to be in there.
CO2 emissions = CO2 emissions is just as valid as the Kaya identity. And it also simplifies the policy decisions! Let’s make some more.
CO2 emissions = Energy use x (CO2 emissions per energy use). Now we have dropped population and GDP. We could of course add more variables in if we like.
CO2 emissions = Houses x (people per house) x (Energy use per person) x (CO2 emissions per energy use). Now, if we can only cut down on the number of people per house.

sinewave
July 24, 2014 1:49 pm

Johan says “For what purpose? Just read the book he co-edited.” Yeah, that’s the most sensible thing to do. I still wonder if he has anything to say about this current discussion / debate since the book is 17 years old.

July 24, 2014 1:55 pm

Joseph (1:44 pm), you’re repeating Willis’s ‘Beer Identity’, which was well refuted on that thread. GDP is close to an encompassing measure of energy-using activity. Houses are not.

July 24, 2014 2:02 pm

Dr. Doug says: July 24, 2014 at 1:35 pm
natural resources affects is economic structure, which is already well reflected in the Kaya Identity.
Reflected yes, but not “well” reflected. GDP = GDP1 + GDP2, where GDP1 stands for the “primary sector”, and GDP2 for all the rest (secondary and tertiary). All I am doing is singling out the primary sector. Set L = GDP1, and we have
CO2/GDP = (GDP1/GDP) * (P/GDP1) * (GDP/P) * (E/GDP) * (CO2/E)
So, GDP1/GDP would simply the the share of “primary sector” in total GDP; and (P/GDP) the population per unit of output in the primary sector. Those are values than can easily be looked up.
As for canceling out, well, it is written as an identity. Try
CO2 emissisons per unit of GDP = output of primary sector per unit of GDP * population per unit of output of the primary sector * GDP per capita * energy intensity * CO2 emissions per unit of energy
GDP1 and GDP would both be expressed in monetary units, but I still don’t see why you can’t say 0.14 dollars of primary sector output per 1 dollar of total GDP.

Duster
July 24, 2014 2:21 pm

Dr. Doug says:
July 24, 2014 at 11:27 am
Duster (10:21 am):
How again is the Kaya identity informative?
The Kaya Identity is informative to the extent that one can plug in informed numbers for the ratios in the identity. Pielke does so, showing, for example, that Britain’s energy policy cannot plausibly achieve its carbon-reduction goals.

Well, that does seem to be what people say, but all the variables except the CO2 emissions cancel, which would seem to mean they have no effect on the value of CO emissions: CO2 emissions = CO2 emissions.

July 24, 2014 2:22 pm

Johan (2:02 pm),
Sorry, the first three ratios on the right-hand side of your identity are interdependent. You can’t change one without simultaneously changing one or more others in a way that exactly offsets your change. The equation does not allow for “ceteris paribus”:
CO2/GDP = (L/GDP) * (P/L) * (GDP/P) * (E/GDP) * (CO2/E)
If you raise L while leaving GDP and P constant, then the rise in L/GDP will be offset by the fall in P/L. If GDP rises as well as L, then P/L and GDP/P will offset each other. There is no way around it.
And yes, including L is double-counting, because L unavoidably affects the structure of GDP and thus the E/GDP ratio.

July 24, 2014 2:28 pm

Dr. Doug says: July 24, 2014 at 2:22 pm
The equation does not allow for “ceteris paribus”:
Well, the whole point being, neither does the original KAYA identity. But for whatever reasons, you are totally unwilling to accept that.

Mark Bofill
July 24, 2014 2:29 pm

JamesNV says:
July 24, 2014 at 1:32 pm
—————————
I don’t follow Dr. Pielke closely, but +1 anyway. I’d like to think that anyway. 🙂

July 24, 2014 2:37 pm

Johan (2:02 pm again):
I’ll grant that It could certainly be useful to treat L within the category of GDP. You could model differing economic structures (resource intensities) and their implications for the E/GDP ratio. But you can’t break out L apart from GDP.
(Johan 2:28 pm): The fact that KAYA indeed allows for “ceteris paribus” (i.e., holding other things equal) was firmly established by consensus after long discussions in the preceding threads. I won’t reopen that can of worms here.

Tommy
July 24, 2014 3:18 pm

I don’t see how land area can be a useful “lever in the tool box”.
Consider a swimming pool with kids in it.
P = Kids * (refreshments/kid) * (liquid/refreshment) * (P/liquid)
If I want less P in the pool, I can reduce the # of kids swimming, or give them less refreshments, or give them refreshments with less liquids, or use liquids that result in less P (what would that be, olive oil?)
Does it matter how many kids are in the shallow or deep end? Whether most are in the shallow, or deep, or equal, or whatever, I still get the same amount of P in the pool.
Likewise, let’s say Singapore purchases the western parts of Australia where almost nobody lives. Now we’ve dramatically changed the land area of both countries but changed nothing about the CO2 emissions.
What am I missing?
(Note: Don’t get me wrong… a little P in the pool doesn’t actually bother me, and I realize some CO2 in the atmosphere is good for the environment whether it comes from people’s machines or not)

July 24, 2014 3:51 pm

Dr. Doug,
Defending the Kaya Identity as a useful tool, without understanding the diabolical purpose of it, is what worries me, unless you are part of the soft sell team that does this sort of thing. If you actually think this was designed as a useful tool for understanding things, then there is an old label coined early in the last century by political philosophers of the same stripe that rhymes with useful tool. Making benign-looking frameworks like this for shaping policy thinking a generation or so down the line while indoctrinating the next generation in classrooms is the way to do it.

garymount
July 24, 2014 3:54 pm

This is my one and hopefully only comment on the Kaya Identity. When Willis posted the original article I had a read through and because of my mathematical background I quickly came to the same conclusion as Willis, and I moved on to other topics of the day. I was surprised to find later that there were a lot of comments on that post. Then there was another post, then another and another.
Yesterday, before this latest and perhaps last post on the Kaya topic, I was sitting in the coffee shop looking at the parking lot and it reminded me of the posts on the Kaya Identity. Why might you ask, because technological advancements don’t seem to be part of the identity. And indeed technological advancements don’t seem to get much mention throughout media discussions of all sorts of topics.
So why a parking lot? It has to do with computer advancements and the coming revolution in autonomous vehicles. The parking lot I was looking at, and am looking at now is 1/3 full. There is a neighboring parking lot that is 2/3 empty serving a restaurant. Then there is the other neighboring parking lot serving the grocery store, and the Costco parking lot across the street and so on and so forth.
The autonomous or self driving vehicle is a topic I have been researching since about 1996. One reason I think about this topic is because of the car accident that put my twin brother into a coma for 40 days and his agonizing slow multiyear recovery learning to walk and talk all over again starting in 1981 at the age of 21. One of my sisters was also in a vehicular accident when the van she was a passenger in with 13 others followed the van in front of them off the road in a snow storm in Québec. She was luckier than some with only a smashed leg requiring metal rods and pins to repair and years of healing and further surgery.
Anyway, onto the economics of the potential change this technology could wrought. Imagine no more car accidents and no more grid lock. No need for police to check for drunk driving, speeding, using a smart phone. No need for truck drivers and the deliveries could be make outside of the rush hours.
And those parking lots that are empty at night. Cars can drop you off at the front door of businesses then go park themselves in community parking lots. Land consumed by parking lots could be considerably reduced.
Then there’s the thousands of lives saved, the fuel saved from not idling in traffic, and so on. None of this technological advancement seems to make up any of the components of the Kaya.

July 24, 2014 4:23 pm

garymount (3:54 pm):

because technological advancements don’t seem to be part of the identity

Gary, if you read Roger Pielke Jr.’s work (linked in the previous post), you’ll see that technological advance appears twice within the Kaya framework: (i) in the energy intensity of GDP, E/GDP, and (ii) in the carbon intensity of energy, CO2/E. Technological advance generally reduces both of these ratios.

July 24, 2014 5:43 pm

Gary Pearse (3:51 pm):

Dr. Doug,
Defending the Kaya Identity as a useful tool, without understanding the diabolical purpose of it, is what worries me, unless you are part of the soft sell team that does this sort of thing. If you actually think this was designed as a useful tool for understanding things, then there is an old label coined early in the last century by political philosophers of the same stripe that rhymes with useful tool. Making benign-looking frameworks like this for shaping policy thinking a generation or so down the line while indoctrinating the next generation in classrooms is the way to do it.

Gary,
I’m sure that the Kaya Identity, like almost anything, could be abused for a diabolical purpose, but I think it important to affirm the distinction between use and abuse. “Abusum non tollit usum”, as the ancient saying goes. It is important to claim (or reclaim, as the case may be) every tool that is valid in itself. Even if the Identity is abused, it hardly makes sense to avoid using it properly, and thus letting uncommitted observers (and your schoolchildren) see an obviously proper tool supporting only the wrong side of an argument. “Why should the devil have all the good music?”, as early evangelicals put it.
In truth, I don’t think the KI has a diabolical purpose — certainly not as Pielke uses it! Give me evidence if you would convince me otherwise. I am well aware of the ‘useful idiots’ among the see-no-evil left who supported Lenin, Stalin, Mao, Castro, and Chavez. And I am not part of the “team that does this sort of thing”.

Greg Cavanagh
July 24, 2014 5:51 pm

I think the whole argument is about trees, while completely missing the forest.
If the resident time for CO2 in the atmosphere is 5 to 7 years, then who cares what the emissions are. It’s gone in 5 – 7 years anyway.
If the current rise in CO2 is caused by the warming of the oceans, and that humans contribute 3% of the total. Then it’s a pedantic exercise (using something that’s not even an equation?).

Ted Clayton
July 24, 2014 6:21 pm

The Problem with Citing or Referencing a so-called Kaya Identity
At the top of this post is a link to A conversation with Dr. Roger Pielke Jr., a previous WUWT post by Dr. Pielke Jr., et al. At the top of his remarks, the Professor recommends that to understand the Kaya Identity, we refer to his published paper elsewhere; The British Climate Change Act: a critical evaluation and proposed alternative approach.
This paper is Dr. Pielke Jr.’s well-known & well-received rebuttal of the British national response to AGW. He says that he critiques their efforts, using the Kaya Identity. In his Methodology section, he begins:

The methodology employed here draws upon Waggoner and Ausubel (2002) who argue that understanding the ability to influence environmental outcomes through policy requires `quantifying the component forces of environmental impact and integrating them’. For carbon dioxide the relationship of forces leading to emissions has been called the Kaya identity …

However, the title of Waggoner & Ausubel (2002) is; A framework for sustainability science: a renovated IPAT identity [emph. added] Proc. Natl Acad. Sci. 99 7860–5. This is the PNAS paper that I cited & linked above, in Ted Clayton says: July 24, 2014 at 11:03 am. I copy my (full content) link, to the title here.
The problem is, Waggoner & Ausubel are talking about a construct called the IPAT identity (or I = PAT). They are emphatically not discussing the Kaya Identity.
IPAT and KAYA are quite similar. But IPAT was created & developed by other people, not by Yoichi Kaya. The basis of Professor Pielke Jr.’s presentation is not the work of Yoichi Kaya, as one would infer, but of others who are not being clearly credited.
The original creators of IPAT are Barry Commoner, Paul Ehrlich and John Holdren. Waggoner & Ausubel cites them thus (with 13 others):
1. Commoner, B. (1972) Bull. At. Sci. 28, 17, 42–56.
2. Ehrlich, P. R. & Holdren, J. P. (1972) Bull. At. Sci. 28, 16–27.
IPAT predates Kaya by 21 years, and by major scientific figures. Yet Dr. Pielke Jr. does not mention IPAT, or any of the people behind it, although it is the basis of his analysis, and his leading Methodology citation.

Joseph Murphy
July 24, 2014 6:24 pm

Dr. Doug says:
July 24, 2014 at 1:55 pm
Joseph (1:44 pm), you’re repeating Willis’s ‘Beer Identity’, which was well refuted on that thread. GDP is close to an encompassing measure of energy-using activity. Houses are not.
————–
Yes, that is the point. The kaya identity does not demonstrate a relationship between the variables, it is the correct way of representing them if they do have that relationship. The identity is true with any variables, the output will be total carbon emissions. That is why it is trivially true. If you are going to argue that population and GDP are important variables in dealing with and lowering climate emissions, you still have to make that argument. The kaya identity doesn’t make it for you. It has no predictive power, you need to punch in the correct values for it to work. It does not tell you what will happen to carbon emissions if you adjust the variables. That was the point Willis was making and it was not refuted. That is what the identity is. If you know total carbon emissions, you can create the variables and the equation will be true. With that being said, RPJR is making the argument that these are the correct variables for this to have some predictive power, he is making the argument that these are the ‘knobs’. Although, I don’t know to what precision and I have seen no predictions verified. That is what is frustrating. The identity tricks people into thinking it is an equation that demonstrates a relationship. It tricks people into thinking it is an equation with predictive power. It is not.

July 24, 2014 6:28 pm

The rather obvious omission for me is that climate affects energy consumption. Here in Australia, even though we don’t have large differences in climate across the country, household energy consumption in the cooler states and territory is double that of the warmest state.
http://www.abs.gov.au/ausstats/abs.nsf/Lookup/4670.0main+features132012
Were a climate factor to be introduced into the equation, it would show, that for most of the developed world, increasing CO2 emissions would result in declining demand for energy. A rather inconvenient truth for the Warmists.

July 24, 2014 7:04 pm

Dr. Doug says:
July 24, 2014 at 5:43 pm
I’ve grown tired reading most of the comments on the three articles related to the Kaya identify; so I’ve run out of steam and haven’t read all your comments.
But I must say I fully agree with your most recent comment (cited above). In particularly, there seems to be a subset of Kaya objectors who reject it mainly because they feel that it can be abused by the warmists. Also, it’s one thing to be a skeptic and another to be paranoid.
Thanks for your thoughtful post.
Dan

krischel
July 24, 2014 7:14 pm

Units are not variables.
Say it again:
Units are not variables.
The “Kaya Identity” is actually:
V CO2 = W Population × X (GDP/Population) × Y(Energy/GDP) × Z(CO2/Energy)
Note the units properly cancel, so that the result on the RHS is the same units as the LHS.
Note that there is nothing about this that is an identity – without units, it looks like:
V = W * X * Y * Z
V varies for any change in W, X, Y or Z.
You cannot construct this “identity” algebraically:
V = V

V = W * X * Y * Z ???
Please, for those people that want to write out the “Kaya Identity”, stop omitting the variables.

mjc
July 24, 2014 7:38 pm

I would call things like Population a constant and not a unit.
Same with GDP and the rest.

July 24, 2014 7:48 pm

krischel says:
July 24, 2014 at 7:14 pm
Wow, a couple of cogent comments, the most recent by krischel (cited above). All of this hullabaloo because someone decided to “dumb down” the Kaya identity with a dimensional representation using non-mathematical, sophmoric nomenclature.
Taking Krischels comment one step forward, a rational use of this equation might be to take the total differential of V using the chain rule to show the individual influence (via partial derivatives) of each RHS variable. This would provides a localized and linear set of sensitivity parameters, telling how V is influenced by W, X, Y, and Z independently . . . and also allow what-if analyses.
Is it decisive in resolving the climate scientific and policy debate. . . no! But can the method provide insight. . . possibly so as has be done for similar zeroth and first order equation used in engineering.
Dan