A conversation with Dr. Roger Pielke Jr. on the Kaya Identity

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.


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:


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);


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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I don’t have 90 minutes for a “simple” explanation. I’m raising points I have raised before. Why is it all about “fossil” fuels and not the non-“fossil” hydrocarbon sources of CO2? ethanol? bio-gas methanol? wood? And where in the equation are the natural CO2 sources? Or is it as I have posed elsewhere anthrocentric – all about man?

Daniel G.

Why is it all about “fossil” fuels and not the non-”fossil” hydrocarbon sources of CO2? ethanol? bio-gas methanol? wood?

It includes that too.

Vanishing Point

Another version of Kaya identity
2 + 2 = 5 ±1
and just as useful. Post modern science at work. In addition to peer review now we have to redefine maths too.

Willis Eschenbach

I’m on the road with little time at the moment, but I wanted to thank Dr. Pielke for providing his viewpoint. I may not reply for a few days until I get back, but I greatly appreciate his willingness to discuss the issue.
Best to all,


The meaning of the word equation: both sides are equal. There is no such thing as a soft equation. Either two things are equal, or they’re not. The climate models are more accurate than that ridiculous so-called equation.

Don’t fudge. Willis was not just wrong, but snarky wrong. And you published it.
[we are giving your opinion on the matter all the consideration it deserves -mod]


If the Kaya Identity is useful for climate policy analysis, as Dr. Pielke says, then it would be concerned with human sources of CO2 only. Climate policy has little or no effect on natural CO2 sources. Such policies would also have little effect on human emissions that are due to acts of war, criminal behavior, or unintended accidents, such as wild fires, burning coal seams, etc. It would be mostly concerned with everyday human activity that can be influenced or controlled through climate policy. If it is used to educate or make recommendations, I’m all for it. But I’m 100% against using it to control people through carbon taxes, onerous regulations, or any other non-optional use of the law.

I always get very excited when experts and scientists, Dr. this or that, doesn’t seem to be able to wrap their minds around something simple. In his video he uses a bathtub as an illustration for explaining the challenge of stabilizing the Carbon Dioxide (CO2) level. This is how i understand it, – written in very simple english; The effect of Carbon Dioxide (CO2) is almost as high it can be, simply because the effect of adding more Carbon Dioxide (CO2) decreases as the level of Carbon Dioxide (CO2) increases, and the level is close to saturated in the atmosphere already, a further increase of the amount of Carbon Dioxide (CO2) will only give a theoretical (approx. 1 degree Celsius that are most likely to be dwarfed by other variables), non measurable temperature increase.
In other words, if you’re in the bathtub – all submerged in a completely full bathtub – to continue to add water will not make you any wetter. It’s the same with Carbon Dioxide (CO2) – it doesn’t rise temperature.
Read more; http://wattsupwiththat.com/2010/03/08/the-logarithmic-effect-of-carbon-dioxide/

One more equation.
We put spending per hectare and
environmental and tax red tape per productive sector,
and a particular population in DC and its bureaucracies,
and then we balance it all with a molecule on the other side.
Which molecule shall we balance this Eris tocratic force with? Something really avoidable, like arseno-legislentium. Really we cannot have levels like this in our capitals. Sorry.


Hopefully people who have been trying to use the identity as a formula will stop doing that and follow the example in Dr. Pielke’s link. A good test is to use current values and calculate the necessary rate of change in each parameter to realize a predetermined level of CO2 emissions by some predetermined date. The U of Chicago calculator does this using their selections but does quickly let the visitor explore the impact of these changes.

Mark Bofill

Thanks Dr. Pielke. I’m looking forward to reading and viewing this this weekend.

Ian W

CO2 emissions do not vary in direct ratio with GOP. As stated above CO2 has a logarithmic effect (if any overall effect in the real atmosphere) and that effect is close to, if not at, saturation. This is another example of simplistic linear projection based on false assumptions. It is useful but misleading in discussion with those with low information such as politicians, it’s target audience.


FYI: In the video, Dr. Pielke introduces the Kaya Identity just past 18 minutes in, and he begins to explain the parts that make up the identity at 20 minutes in.

Robert in Calgary

Has this link been posted here recently?
Main page http://climatemodels.uchicago.edu/models.html
Specific page http://climatemodels.uchicago.edu/kaya/


It kinda makes sense, however given the softness of the parameters any hope of accuracy must go out of the window. Having said that, accurate or not, it will provide guidelines to the politicos as to whether they can reach their targets. More importantly, from my point of view, including the GDP/head of population makes it explicit to the politicos that any mistakes that are made in their assumptions will have a price to pay in the GDP/head of population. All too often these mitigation strategies are developed with lots of arm waving and it will be “alright on the night” this at least tries to show the interaction between mitigation and economic welfare.
It is not Schroedingers Wave Equation, or Kirchoff’s Laws, that’s for sure, but a reasonable attempt at telling the whole story. The politicos should have some backcloth against which to make their decisions.


who cares about co2?
those who want to tax your breath, is who.
what’s the kaya incantation good for?
parasites to befuddle their victims while they catherize a main vein is what.
the science is ‘how to bleed you out’
it’s a cookbook!

Curious George

Let’s simplify the problem: We will concentrate only on CO2 generated by cars:
[Cars identity] CO2 = (Number of cars) * (average CO2 generated by a car)
Now I take a liberty of twisting Dr. Pielke’s statements (I have changed “population” to “Number of cars” and “economy” to “cars”) in http://iopscience.iop.org/1748-9326/4/2/024010 to apply to this equation:
According to the logic of this relationship, carbon generated by cars and accumulating in the atmosphere can be reduced only by reducing (a) the number of cars, or (b) the carbon intensity of a car. Most proposals advanced by governments and in international negotiations focus on actions that will lead to the reduction of the carbon intensity of the car (whether or not they are explicitly presented as such), which in this paper is referred to as ‘decarbonization’. Policies
to reduce the number of cars or that result in economic contraction are not generally considered by governments as a strategy of emissions reductions. Thus, the [Cars identity] provides a
straightforward and useful basis for evaluating the proposed and actual performance of policies focused on decarbonization and which are typically called mitigation policies.
What does [Cars identity] really tell us? Nothing. It is only a thinly veiled definition of an average:
(average CO2 generated by a car) = CO2 / (Number of cars)
There is absolutely no insight here, deep or useful. The [Cars identity] brings nothing new to the table. Yes, you can reduce car emissions by limiting the number of miles driven, or by building more efficient engines, or hybrid cars, or electric cars – but all of it comes from our knowledge of cars, not from the [Cars identity].

Michael 2

Ian says:”and that effect is close to, if not at, saturation.”
Saturation would be 1 million parts per million. We have a long, long way to go.

Michael 2

Dr. Pielke is a man I respect. Not strident; well reasoned in his arguments.

Robert in Calgary

Okay, went from 18:00 to about 46:00
For me, the most interesting parts were the Dungeness B comparison at around 39:00 and the 3rd runway/China example at 43:00.
While I appreciate that Roger finds Kaya useful in his work. To me in the real world, it’s still garbage.
I’d rather see an identity factoring in CO2 hysteria and Deep decarbonization hysteria.

Michael 2

“An extremely powerful tool for policy analysis.”
C = C

Of all the discussion topics, I have no idea why anyone is making a big deal out of this.
Who was making a big deal out of Willis’s original post?

john robertson

Perhaps what is truly interesting here, is that these soft “sciences” have gotten away with impersonating actual science for so long, that they now believe these kind of methods can produce useful information.
There is an obvious failure to communicate at play in both of Willis’s posts.
This Kaya thing, is a mockery of empirical measurement and reproducible results.

Sorry couldn’t watch after he endorsed weepy Bill ;>(


From the Transcript button of the YouTube video: [needs work!]

so forget about all this nonsense about targets and timetables for emissions
its its it’s a sideshow it’s it’s a about the path to insanity
number one but it’s also I unlikely to bear fruit from a policy standpoint that
the question we ought to be asking
is how are we going to generate 90 percent-plus
afar energy from carbon-free sources at the same time we
double triple quadruple global energy supply

Thanks a lot for shearing this. Wish to get this type of article again and again.
Wish to Get such article again again


I’m with Anthony, it’s in the middle, but it really depends on your purpose. If you want to understand the basics of your “policy levers”, the equation is mostly inoffensive. But if you want to really understand, or better yet predict, the GHG emissions of an economy/society (as if that will really have much impact on actual climate!) then I think it fairly crude and useless.

Michael 2

I should not have been so snarky. I’ll watch the entire show and see how it goes (when I have that much unscheduled time).
I see two entirely distinct things under this umbrella — one is a reasonable approach to estimating total CO2 emissions, and the other is “C = C” which doesn’t seem very useful.


The bathtub analogy is oversimplified. In practise if the inflow is increased the water level will rise only until the increased inflow matches an increased outflow, due to the increased hydraulic pressure of water at the outflow orifice. A new equilibrium will be established at a slightly higher water level. Similarly if a person gets into the bath the level will immediately rise, but outflow will increase and the level will drop until the same equilibrium level is again achieved, but now with less physical water in the bath. In the climate system more CO2 stimulates more photosynthesis, the planet gets greener and a new equilibrium at the slightly increased CO2 level develops. Nature has a way of compensating, in this case to the benefit of living things.


One of the challenges with someone who is smart but largely self-taught is they may over look or be surprised by ideas that have been developed and accepted by others.
The idea of a mathematical identity seems to be one of those.
Here is an excerpt from the definition for “Identity”:
“What are identities used for?
They are used in simplifying or rearranging algebra expressions. By definition, the two sides of an identity are interchangeable, so we can replace one with the other at any time.
For example, suppose we are working an algebra problem and we have We recognize this as one side of a familiar identity* So we can replace it with the thing on the other side of the identity:
In summary, an identity says that two things are equivalent. If you see one, you can replace it with the other.
*Important Identities are only useful if you know them, since only then will you recognize that a replacement is possible. But there are a lot of them (see trig identities below). Get a feel for the common ones and have a quick reference handy to look them up. ”
That excerpt is from
Which is the identity section of the Math Open Source Dictionary.

The “Kaya Identity” stating CO2_emissions = Population * GDP/Population * Energy/GDP * CO2_emissions/Energy has a duality:
1: It says CO2_emissions = CO2_emissions
2: It says that factors favoring increase of CO2, such as increase of population, increase of per-capita GDP, and decrease of energy efficiency, contribute to increase of CO2.
I propose a temporary decrease in the birth rate, to the extent our planet’s ability to comfortably and healthfully sustain its human population is being stressed. This means no need for people to die until they do so from old age. And, I favor mandates for increased energy efficiency of appliances, vehicles, homes, lighting, etc. to an extent as great as possible that allows consumers to pay less overall. I see a very large number of small savings there, and I see this as significant.
What I don’t like is restriction of energy consumption from the supply side, unless significant “conspicuous consumption” becomes significant. That is a possible issue, due to income inequality decreasing over the past 40 years, and one metric set there is median/mean ratio of incomes of individuals and families as determined by the US Census Bureau. Another is how the 5 “fifths” of US population fared for income. I worry about the top-20% or an upper fraction of that, which has a majority of USA’s disposable personal income, feeling free to add demand (and accordingly upward price pressure) to limited natural resources that are necessary for everyone else.
There is another matter: I don’t think CO2 is the best reason to encourage energy efficiency. I think that decrease of energy demand via increased energy efficiency allows allows the limited fossil fuel supply to last longer, and allows people who work for a living to pay less for the energy that they need to live their lives. This also allows solar and wind more time to become competitive, and for nuclear power (including a largely renewable form and another form both having great supply and lack of usefulness for making bombs), to be more accepted.
Japan failed to consider that both they are prone to earthquakes, and that there was significant chance over a time scale of decades for an earthquake worse than any of the previous 100 years.
I don’t see Japan’s failure to design a nuclear power plant to withstand an earthquake having intensity only one order of magnitude greater than “likely to occur within 100 years” as an argument against nuclear power. Instead, I see that as a fault of how Japan handles things new to them in the past several decades.
Furthermore, I see all-too-often poor civil engineering in USA, due to consideration for “100 year” floods as being “rare”, and on-average hitting 1% of USA every year. This gets compounded by flooding trends being altered (largely for the worse) by land-use changes that result mainly from population growth. My point here is that civil engineering having shortfalls is an argument to improve civil engineering, catastrophic disaster consideration in power plant design, and/or to reduce the birth rate, rather than to roadblock nuclear power.
Nuclear has its power generation mechanisms not generating CO2, and its track record is better than coal, and probably also both oil and gas, for risk rate of dying prematurely or spending time being disabled. This applies to those working in the nuclear power industry (as opposed to fossil fuels), and it also applies to everyone else, even in the likely event fracking is not as bad as its opponents claim it is.

Mike McMillan

Pervasive ignorance.
Questioner at the end saying the Tea Party is funded by the rich capitalists is like saying Lincoln was bankrolled by the slave holders. The Chamber of Commerce, big business, and establishment political parties have spent in the hundreds of millions against Tea Party primary challenges. Pielke Jr doesn’t question the premise.
Further comments self-snipped.


Gee. I am stunned you guys don’t get it. Instead of focusing on the CO2 terms, plug in real world numbers for the other terms and see what you get.
I have not followed the threads, but Willis gets it wrong with his very first statement when he says “where “CO2 emissions” are the CO2 emissions of say a given country; “Population” is the population of that country; “GDP” is gross domestic production of the country, which is the total value of all the goods and services produced; and “Energy” is energy consumed by the country.”
And then he basically says he can perform a trivial dimensional analysis to show the identity is meaningless. I guess the same type of analysis applied to Newton’s Law’s of Motion:
http://en.wikipedia.org/wiki/Newton's_laws_of_motion. Or how about JKeplers lay of planetary motion: http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion. Or consider the law of gravity: http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation.
Go back to high school physics Willis. Every equation in physics cancels out in the same way – the dimension on the left will equal the dimension on the right be it joules, watts, or KG CO2. It is the stuff in between that is relevant.
Now, lets go back to the identity (I am doing this from memory and a brief refresher on the equation)
On the left we KG CO2 emitted by the entity.
On the right we have total population in people of the entity
We have GDB (dollars) per person of the entity
We have energy (watts)/dollar of GDP of the entity
We have KG CO2/watt of energy of the entity
Each of these terms describes something that is of interest and measurable. IMHO, it requires a unique form of obtuseness to not be able to figure out the applicability of this identity.


This one is for you Anthony:
“I agree with Roger that: “The mathematics are simple.””
Well duh – Step 1: go back and review all of those incredibly complex equations you learned in high school physics again.
“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.”
See step 1. Trivially true identities are the basis of all modern engineering.


As formulated, the Kaya is ridiculous, but focusing on that is to worry about the trivial. Why bother?
It’s either a mistake , or we should reformulate the thing to have a more useful discussion. Here is one version that might be more useful.

co2em =  totCO2emissions * EconEnergyEff * perCapitaGDP * Population
units:      CO2/GW           GW/GDP         GDP/person	     Persons

(I hope the format doesn’t totally suck. It started out looking good.)
In this version the units cancel out to something slightly more interesting. But that part I realize could be very valuable is the Economic Energy Efficiency. In other words, how much raw energy does it take to produce our GDP? How have we done historically? How do we compare to other nations? I’m working on some of those figures now.
As an aside, I updated my understanding of GDP versus GNP. I had thought the GNP only included balance of trade, but no, it also includes all foreign business activity of Americans and removes foreign business activity here. And surprisingly (at least to me), our GNP is much higher than our GDP. The economic benefits of foreign trade make the trade deficit appear to be much less of a worry. However, we should remember our federal debt is equal to our current GNP.
I wonder what it really means when our domestic economy is apparently so weak and our companies involved in foreign trade are doing seemingly very well. Something seems seriously wrong about that. That current buzzword “sustainability” comes to mind. I also wonder how much our government is interested in our well being, since it is getting much more revenue from sources other than US citizens (as income tax). Could we ever reach what should be an impossible state in which the government needs nothing from its citizens? Then what will make it continue to work in our best interests?


Oops, I should have changed the energy units to TWh.


Hmmm forgive my ignorance Dr P. But what has mathematics got to do with the weather. We have had snow in New England (Australia not the USA) And it is colder here that it has been for nearly 103 years. Although we are 3,500 ft about sea level, we are surviving well. I just don’t understand how some climate scientists relay the planet is warming when we have two hemispheres and so many micro-climates within them that we can’t make one decision or hypothesis to cover all. Cutting greenhouse gases when 95% is water vapor, is an impossible dream. The physics does not support any of the predictions about climate change being forced by human activity, unless you are referring to UHI effects known in big urban and city environments which is not typical in smaller or rural communities. Australia has diverse environments including that nearly 2/3 of our land mass is classed as desert. Yet Alice Springs right in the centre is experiencing night time temps of minus and daytime temps up to 20 C. A typical arid environment or desert temperature fluctuations.

RobertInAz – Willis got it right. The equations are circular logic.
Let me explain. You say:
“On the right we have total population in people of the entity
We have GDB (dollars) per person of the entity
We have energy (watts)/dollar of GDP of the entity
We have KG CO2/watt of energy of the entity”.
Total population – we know that (to reasonable accuracy).
GDP per person. We don’t know that directly. The way we get it is by estimating total GDP and dividing it by total population.
Energy per dollar of GDP. We don’t know that directly, we get it by dividing total energy usage by total GDP.
Kg of CO2 per unit energy. We know that for each form of energy, but to get the average over all energy, we total the CO2 and divide by total energy.
So the exact same number that goes into the ‘top’ of one equation goes into the ‘bottom’ of the next equation. Hence the equation really does say “C=C”. It’s therefore circular logic – it ends up with what it started with.
Sometimes, equations like this can be valuable. That’s when the various factors are obtained from different sources, and hence provide something new when combined. That’s not the case here.

Dr. Roger Pielke Jr:
Kaya Identity huh? That’s the current gimmick name?
Looks like unlabeled pie chart value using mathematic symbols and fancy sciency letters and numbers.
Every position in the formula is filled with a variable; estimated variables that is. Every assumed variable produces a different ratio series.
Must be cool to tie into some flows of continuous metrics and then animate with the resulting scrolling values. Sort of like watching call/put or bid/sell values during a busy market day. Just as useful for long term decisions too, though it does take a lot of imagination.
Kaya may be decent for an explanation, for that moment only as any variable input into formula will change before the formula is run.
What Kaya fails to accomplish is to establish a start/fini/zero/even bar that allegedly relates GDP, population to any third substance whether it is water, CO2, money, beer, flatulence…
Maybe it’s a formula Mann can use?

Read the paper, skipped the video.
What the paper seems to be saying is that the UK Climate Change Act seeks an 80% reduction in CO2 emissions over a given time frame, and that this is impossible to achieve on the basis of “decarbonization” of the economy. In other words, the Act is DOA unless the government is willing to destroy the economy or reduce population, or both.
I have to agree with Dr Pielke on that matter.
However, I don’t think you need a fancy formula to make that case. Nor can the formula be justified by observing (which the paper does) that certain economic patterns have not happened in the past, so can’t be expected to happen in the future. That’s just not a quantifiable argument that can be incorporated into an equation.
The basic premise though, that “decarbonizing” the economy is not possible while maintaining population and standard of living is what skeptics for the most part have been arguing all along. We just don’t need something like the Kaya identity to make that case. 1,000 people carrying 100 lbs each can’t move freight as far, or as fast, as a single semi-trailer. They could not do in a month what the semi can do in a few hours. Figure out what that does to the cost of the truck load of goods. Pray it isn’t produce, because it would never even get to destination before going bad or being consumed by the porters. That’s all you need to understand to know that the “decarbonized” version of our economy would collapse of its own weight.


So what does this identity thingy do when the world cools?


geronimo says (at 7:49 pm):
“The politicos should have some backcloth against which to make their decisions” …
about how we will live, and how much we will pay. As usual, we get no say.
The “Democracy Identity” – you’re standing in it.

And if CO2 in fact has no effect on temperature then what? How does CO2 explain the Maunder minimum? The sun is the more likely cause.


That is a good question Kim. A lot of people won’t like it.
ANd yet, the world really is due for cooling, and it is now in a circa 30 year meridional cooling pattern, according to the UN FAO. The Zonal warming pattern, according to the U.N, was due to end around 2004. http://www.fao.org/docrep/005/y2787e/y2787e03.htm
Interesting that the UN forecast concords with not only “the pause,” but the meridional excursions of the polar vortex over the formerly glaciated U.S. regions, great lakes and Niagra freezing, etc. (I think the modern adjusted records stink – especially 2010.)

Every position in the formula is filled with a variable
I can do that. F=ma

Khwarizmi says:
July 18, 2014 at 11:02 pm
Habibullo Abdussamatov says we will see noticeable cooling in 2014.

This is a statistical calculation that indicates that ocean cycles and solar activity can explain most of climate. CO2 explains nearly nothing.

I do not know if the Kaya equation is valid or not, but his video was a real eye opener, and it shows that most governments do not have a clue when it to energy production and emission reductions.


Kim – the Kaya identity deals with decarbonizing the economy and has nothing to do with with temperatures. It was created by an advocate of renewable energy. It doesn’t offer many pragmatic ways to reducing CO2, but that never stopped an alarmist. I’ve decided it is the perfect tool for Planned Parenthood to use to leverage climate change hysteria in promoting their services.


Thanks, dp. All together now, sing Kumkaya.