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.

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

  1. 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?

  2. 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.

  3. 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.

  4. 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,

    w.

  5. 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.

  6. 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]

  7. 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.

  8. 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/

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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!

  15. 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].

  16. 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.

  17. 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.

  18. 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?

  19. 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.

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

    54:30
    so forget about all this nonsense about targets and timetables for emissions
    54:33
    reductions
    54:35
    its its it’s a sideshow it’s it’s a about the path to insanity
    54:39
    number one but it’s also I unlikely to bear fruit from a policy standpoint that
    54:44
    the question we ought to be asking
    54:46
    is how are we going to generate 90 percent-plus
    54:50
    afar energy from carbon-free sources at the same time we
    54:54
    double triple quadruple global energy supply

  21. 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.

    Cheers,

  22. 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.

  23. 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.

  24. 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

    http://www.mathopenref.com/identity.html

    Which is the identity section of the Math Open Source Dictionary.

  25. 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.

  26. 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.

  27. 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.

  28. 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.

  29. 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?

  30. 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.

  31. 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.

  32. 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?

  33. 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.

  34. 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.

  35. 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.

  36. 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.)

  37. 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.

  38. 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.

  39. maybe it’s a “soft’ equation cuz – unlike 6=2*3 and E=MCsquared – the Kaya factors – population, gdp per capita, etc – are cherry picked to “guide” policy makers – the righthand side doesn’t emerge from a rigorous set of equations leading up to them – instead someone used common sense to produce them – or used their agenda

    the usefulness of this equation is that it shows policy makers how tweaking any of the chosen factors will effect the lefthand side of the equation – and that’s why the equation is so simple – it shows only the cherry picked factors – and allows them to be tweaked – it can be said to almost state the obvious

    i don’t know if alternate factors can be found to make a new and improved guide for policy makers – Kaya kinda works as long as it is never used in isolation – policy makers need to know effects outside of co2 output

  40. M Simon says: (July 18, 2014 at 11:13 pm) “This is a statistical calculation that indicates that ocean cycles and solar activity can explain most of climate. [link]“. It’s pretty, but it’s only a statistical calculation, and it has only been tested over the ~160yr period that was used to derive it. ie, it hasn’t really been tested. The real-world climate has proved to be a graveyard for hypotheses that work for a while but then collapse. (As the IPCC and others keep saying, it’s a complex coupled non-linear system). It will be interesting to see how this one goes over the next few decades – and more. At least it’s going a bit better than the CO2 hypothesis, which looks like it’s well on the way to collapse (rising CO2, not-rising temperatures). If solar activity and the ocean cycle fall together, I fervently hope that it fails!

  41. Mike Jonas says: July 18, 2014 at 10:39 pm
    “RobertInAz – Willis got it right. The equations are circular logic.”

    In which case, every identity that forms the basis of modern physics is circular logic.

    You make the same error as Willis when you say: “So the exact same number that goes into the ‘top’ of one equation goes into the ‘bottom’ of the next equation.” The correct description is: “The units of the variable at the top of one term of the equation are the same as the units of the bottom of the next term of the equation. In physics, we confirm our equations are right when the units on the right cancel out to equal the units on the left.

    Let’s break down Willis’s wildly incorrect description of the identity term be term: the entire statement was “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.”

    1. where “CO2 emissions” are the CO2 emissions of say a given country;. CO2 Emissions on the left are the CO2 emissions of, say a given country The CO2 emisiions term on the right is the CO2 emission for a given unit of energy production. The CO2 term on the right is much smaller. Both terms can be expressed as KG CO2 – the basis of the confusion,
    2. “Population” is the population of that country; This is true for the first term. Population in the second term refers to a single person. Again, these are entirely different things that have the same unit of measure – people.
    3. “GDP” is gross domestic production of the country: Again, true for the first appearance of the term. For the US, this is trillions of dollars. For the second appearance of the term, it refers to a single dollar. Again, the units are the same (dollars) but the terms refer to completely different things.
    4. “Energy” is energy consumed by the country.”. Same store, the first use of the term is a really big number (terrawatts), the second use of the term is a single watt. Once again, the units are the same but the meaning of each appearance of the term is different,

    I see the ambiguously framed equation is on 12 of the report Willis referenced. It should have been written like this:
    Total CO2 = Total Population * (GDP (dollars)/Person) * (Energy (watts)/ dollar GDP) * (Gram CO//Watt)

  42. That said, if you insist on wrongly interpreting the Kaya identity as did Willis, then you will reach the same conclusion – it is uninteresting,.

  43. In defense of the report, the description immediately before the ambiguous equation was correct:
    “we simply refer to them as CO 2 emissions. 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: “

  44. JamesNV says (at 11:46 pm):
    I hear people saying that skeptics are acting like alarmists. Or are skeptics and alarmists acting like… people?

    http://www.nytimes.com/2011/06/15/arts/people-argue-just-to-win-scholars-assert.html

    = = = = = =
    Some people argue just because they don’t enjoy living in a world of extraordinarily popular delusions, with the ruling caste of “movers and shakers” and “opinion makers” always herding us into their shearing sheds or abattoirs. Some people argue for the opposite reason, of course, and they have the loudest voices.

  45. Let me try again:
    1. where “CO2 emissions” are the CO2 emissions of say a given country;. CO2 Emissions on the left are the CO2 emissions of, say a given country The CO2 emisiions term on the right is the CO2 emission for a given unit of energy production. The CO2 term on the right is much smaller. Both terms can be expressed as KG CO2 – the basis of the confusion,
    2. “Population” is the population of that country; This is true for the first term. Population in the second term refers to a single person. Again, these are entirely different things that have the same unit of measure – people.
    3. “GDP” is gross domestic production of the country: Wrong! First appearance is GDP for a single person. For the second appearance of the term, it refers to a single dollar. Again, the units are the same (dollars) but the terms refer to completely different things.
    4. “Energy” is energy consumed by the country.”. Wrong! First appearance is Energy per dollar of GDP, the second use of the term is a single watt. Once again, the units are the same but the meaning of each appearance of the term is different,

  46. That said, if you insist on wrongly interpreting the Kaya identity as did Willis…

    Because that happened the rest of Willis’ initial article had to be accepted as uninformed. It never got better from there. As strange, his misunderstanding seemed to be the prevalent take on the identity. Not many got it right. It’s happening again in this thread, too.

    I do question the value of the entire enterprise given that the presumption of it is more CO2 is bad. We don’t know that, yet.

  47. Khwarizmi, that’s a nice sentiment. But it is clear from recent nasty infighting, that as a group skeptics are no less human than the warmists. As a whole, I wonder how much this kind of primitive behaviour holds humanity back.

    I remember how disappointed I was by Roy Spencer’s unfair attacks on Willis. Sigh.

  48. Donald L. Klipstein:

    You make two proposals in your post at July 18, 2014 at 9:55 pm and the first is

    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.

    I have repeatedly pointed out that rhis is what the Kaya Identity is really about. In the previous thread I wrote at July 14, 2014 at 5:40 am in this post.

    Yes!
    I have been saying that for days. For example, at July 11, 2014 at 7:55 am in one of my posts on the other thread I wrote

    The equation as presented – as you say – pretends and “is intended to illustrate” that reduction of CO2 emissions requires fewer people or poorer people. It is an excuse for Malthusianism. This evil is screened by being accompanied with assertions that similar effects may be achieved by more efficient energy production or more efficient energy use, but those efficiency improvements will happen as a by-product of normal economic activity if no interference is adopted.

    And your claim that this “means no need for people to die until they do so from old age” is disingenuous because it would ensure they dies of “old age” at a younger age.

    The matter is explained in my rebuttal of Malthusianism which is here. I ask you to read it.

    Richard

  49. V= s/t or F=ma or etc. are not like the Kaya’s identity. These equations are at their simplest form, and relate different QUANTITIES. The Kaya’s identity is NOT at it’s simplest form; when it is, it is a tautology, A=A. It says nothing. As analytic philosophers say “it is meaningless and should never have been uttered.”

    Dimensional analysis is not made with UNITS and it is not made with QUANTITIES. Dimensional analysis is made with QUANTITIES DIMENSIONS (see Wikipedia “List of Physical Quantities”).

    In dimensional analysis, V= s/t (and all other correct equations), after you replace quantities with the quantities dimensions, must yeld the same dimension on each side of the equation or, to be simple, must be tautological to be dimensionally sound.

    Simplifying Kaya’s identity to get a tautology is simplifying an equation, not dimensional analysis.

    Otherwise, anyone can write nice innovative equations which also are meaningless.

    Speed = exp(log(Speed)) * (Trains / Boats) * (Boats / Cows) * (Cows / Trains)

    Sorry. As I said before, I did this when I was ten to amaze friends.

  50. The most fundamental question, taken as a given assumption by the KId, is that reduction of man’s CO2 emissions can effect global temps. That is specified by RP Jr., that 450ppm =’s +2C by 2100. And that that 50 ppm, above todays 400ppm, comes from man, and thus can controlled by man.

    My retort is simple, BS. The sun and its irregular rhythms, the ocean-atmosphere cycles, and their nonlinear feedbacks, with the biosphere and ocean chemistry responses means that man’s ifluence is secondary or tertiary. Natural climate varibility due to factors beyond our control most likely swamp those things within our control. Thus decarbonization of world economies is a fool’s game.

  51. It seems that atmospheric CO2 concentration is a proxy for wealth and growth. No wonder the watermelons don’t like it.

  52. The problem is most people don’t seem to realize that 6=(6/2)*2 is as much an identity as is y= (y/x)*x; where 6 and 2 are obviously just “numbers”; and where y and x are “variables”. In other words, an identity does not have to contain variables !
    The KAYA identity is trivially true when using “historical values” (i.e. “just the numbers”) for CO2 emissions, population, GDP per capita, energy consumption per unit GDP and CO2 emissions per unit energy.

    The real problem begins when KAYA is used as y = x1 * x2 * x3 * x4, where y = CO2 emissions, x1 = populaton, x2=GDP per capita, x3 energy consumption per unit GDP and x4 is CO2 per unit energy; AND where y, x1, x2, x3 and x4 are now all treated as variables. It does not take a genius do understand this is NO LONGER an identity! You cannot take an arbitrary value of y (CO2 emissions), and expect that for whatever values of x1, x2, x3 and x4 the LHS = RHS.

    Once you consider y as an independent variable, and x1, x2, x3 and x4 as dependent variables, you are treating the KAYA “equation” as some kind of “model” that allows you to calculate future values of y, based on some “assumed” values of x1, x2, x3 and x4. But such kind of model is totally detached from reality, for a number of quite obvious reasons. Firstly, it’s an oversimplification (just 4 variables to describe a very complex reality!). Secondly, and more importantly, none of those variables on the RHS are independent of each other (e.g. GDP per capita would more likely than not be some kind of function of Population; not to say that Population in the long run might as well depend on GDP per capita). And accepting that there are dependencies between x1, x2, x3 and x4, there are absolutely no reasons to expect that those dependencies would have to be linear, on the contrary!

    In conclusion. The KAYA identity used with historical values is trivially true; KAYA used as an equation to “predict” or “prognosticate” future values of CO2 emissions is an abomination.

  53. To invert Forest Gump’s famous maxim, “Intelligence is as intelligence does”.
    In that spirit, the process through which a number of posts have materialised here, from either side of the ‘argument’, could best be described by the cautionary phrase, “Ready, fire, aim!”

  54. Great if people can use it (kaya) as a mental crutch or whatever, to remember that (co2=emissions=energy=money=production)*p/p
    Kaya also tells us there where no people on earth 300 years ago.
    I guess Occhams razor no more is as sharp as it used to be.

  55. JEyon says:
    July 18, 2014 at 11:32 pm
    “maybe it’s a “soft’ equation cuz – unlike 6=2*3 and E=MCsquared – the Kaya factors – population, gdp per capita, etc – are cherry picked to “guide” policy makers – the righthand side doesn’t emerge from a rigorous set of equations leading up to them – instead someone used common sense to produce them – or used their agenda”

    Well, you’re sort of right about this. The way the right hand side stuff is measured leaves it open to many sorts of errors, but if it was actually flawed we could test it out by double checking against the actual physical measurements of CO2 emissions. This is the step that critics of Kaya never seem to get to which is how the Kaya actually performs (the answer seems to be not perfectly but not bad either).

    When I first heard about Kaya my gut instinct was that it couldn’t be very useful but it seems that it does do a reasonable job of modelling CO2 emissions, to my surprise. If, for example, the GDP per capita was unrelated (or inversely related) to CO2 per capita – Kaya would not work in the real world whether or not the units of one side of the equation match the units of the other side of the equation.

    Cheers, :)

  56. Since Anthony pointed out this post, I think it is worth discussing in a bit of detail.
    “http://wattsupwiththat.com/2014/07/12/the-beer-identity/#comment-1685623″
    “1. If
    c= 2, g=20, p=4, e=8.
    Then
    RHS = p x (g/p) x (e/g) x (c/e) = 4 x (20/4) x (8/20) x (2/8) = 4 x 5 x 0.4 x 0.25 = 2
    Therefore CO2 Emissions = 2 if c= 2, g=20, p=4, **e=8**.
    2. If
    c= 2, g=2000, p=4, e=8. (Increasing g)
    Then
    RHS = p x (g/p) x (e/g) x (c/e) = 4 x (2000/4) x (8/2000) x (2/8) = 4 x 500 x 0.004 x 0.25 = 2
    Therefore CO2 Emissions = 2 if c= 2, g=2000, p=4, **e=8**”. Emphasis mine.

    As you can see above, this approach is based on saying you can have whatever GDP you want providing you can increase GDP without increasing energy (e remains 8). The problem with this is that it can’t be done in the *real world as it exists currently*. For now, if I want to buy a toaster (and increase GDP by doing so) it takes energy to acquire the materials to make, energy to manufacture it, energy to move it to the store and energy for me to move it back from the store to my kitchen.

    This example doesn’t reflect the real world.

    Cheers, :)

  57. M Simon says: I can do that. F=ma

    That sounds good until you mix it with politics and everything goes wrong. I have an example.

    In the UK we have a 12 ft.lbf legal limit on the permitted power for an unlicenced pneumatic rifle. The accepted formula for calculating muzzle kinetic energy is velocity squared times projectile mass in grains, avoir dupois, all divided by the magic number 450240 and there lies the rub. Obviously to convert pounds mass to pounds force you have to stand somewhere and drop something. To get 450240 you have to stand somewhere where gravity is 32.16 ft/s/s. Beats me.

    Obviously science disagrees with the accepted norm. Try to decide which is correct and you end up having Pilates’, “What is truth?” argument. If you are programming for MKE do you want to spend eternity explaining why you are right and 450240 is wrong? No, you use 450240.

    If this Kaya thing is for policy makers perhaps we simply render unto Caesar that which is Caesars’ and agree even though it is complete bunkum and tosh.

    I tend to infuriate people, if this post infuriates you I apologise, I will try to understand but it is difficult for me, please define your precepts.

  58. Dr. Pielke is a man one can respect. He is not strident and is well reasoned in his arguments. However in this instance, he is also wrong.

  59. What really beats me, even none other than IPCC itself admit that at best,KAYA can only be used to organize discussions of the primary driving forces of CO2 emissions

    [QUOTE] While the Kaya identity above can be used to organize discussion of the primary driving forces of CO2 emissions and, by extension, emissions of other GHGs, there are important caveats. Most important, the four terms on the right-hand side of equation (3.2) should be considered neither as fundamental driving forces in themselves, nor as generally independent from each other. [/QUOTE]

    http://www.ipcc.ch/ipccreports/sres/emission/index.php?idp=50

  60. One problem I see with the equation is that the terms are statistics, not physical variables. GDP/population, for example, is a statistic called Per capita income (from wiki: total resources/total population) It is the mean or arithmetic average domestic production per person. If you read any statistics book you’ll realize that you can only use means or averages if you can prove that the values being studied follows a normal (or Gaussian) distribution. Only in the Gaussian distribution case you can apply the Central Limit Theorem.

    This is obviously not the case since the average domestic production does NOT follow a normal distribution, Not in the USA, not in China, and more obviously not in the world. Some people produce a lot and make a lot of money falling into the outlier category. That breaks the normal distribution. And since the distribution is skewed, the arithmetic mean does not properly describe the population.

    The same can be said about Energy/GDP or CO2emissions/Energy. They are not physical variables, they are arithmetic means of values that you cannot prove that follow a normal distribution and therefore these statistics don’t properly describe the distributions.

    Also, the Kaya identity reminds me of the Drake equation. Both are invalid under the scientific point of view because none of them are derived from empirical data, Not Drake equation, nor Kaya indentity. The relationships among terms used in both equations are not based on physical experimentation. You do not know if the correlations are linear, quadratic, logaritmic or mixed with saturation, like Michaelis-Menten kinetics or relativistic velocity.

  61. There is no good reason to write down the Kaya identity, because given values for the terms on the right hand side, calculating the CO2 follows from a trivial application of algebra which we expect anyone over the age of twelve to be able to do. It certainly does not merit a grandiose name. The only reason to write it down and give this trivial algebraic identity a name is to give the illusion that the variables contained in it are fundamental, like mass and time and similar in physics equations. Equations from physics, of course, are not mere algebraic identities.

  62. Drake’s equation, although entirely made out of unknown functions of unknown values, has a definitive advantage over Kaya’s: the terms don’t cancel out. And the LHS, defined, quantity is not present on the RHS too.

    Though, miraculously, I read a comment somewhere here that sheds some light /sarc/ on it: the quantities with the same name “above the line” are not the same as the quantities with the same name “below the line”, so they don’t cancel. Oh, wonder.

    I also read another comment saying something like, if you increase GDP, it makes the population vary, so actually, even though GDP cancels out, the change in population will make a change. (This, I guess, is because the population “above the line” is something completely different from the population “below the line”). How didn’t I think of it? /sarc/

    I have been showing the Kaya thing to my colleagues, but I can’t write here what they said about it. I wonder if economists use algebra in a different way than the usual guy does, and recent world events suggest it might be so.

    This concludes my interest in this Kaya erm… thing, except for comedy purposes.

  63. Shawnhet says:
    July 19, 2014 at 2:55 am

    You can put any values you like into any variables and “c” will equal the value you gave it.
    Just do the Math yourself, as Dr Rodger Pielke Jr recommended, over and over.

  64. The sea levels are not rising, the ice sheets are not melting, the weather has not become more extreme, the temperature trends are disputed, What/where is the equation that connects CO2 concentrations and catastrophic climate change? Without that connection this discussion about modeling mankind’s contributions to CO2 is a tale of sound and fury told by you know whom.

  65. Looks to me like the sort of “equation” that only an ologist would find indicative of anything at all.

    Talk about oversimplification…

  66. Thanks to Dr. Pielke for his post.
    In a conversation it is good to know what the definition of words and terms are.
    What an identity is, and is not, seems to be at the heart of Willis’s concerns.
    If we can define identity, perhaps we can move forward past this.
    This seems to be a reasonable definition of “Identity” as used in mathematics:

    http://www.mathopenref.com/identity.html

    Here is an excerpt from that definition that seems to applicable to our conversation:
    “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.”

    I think Dr. Pielke is owed an apology.

  67. I’m a mathematician. Willis is right and Pielke is wrong. Here is my attempt at an explanation.

    The climate change economics community would like to have a useful equation that shows how changes in things like population would affect things like carbon dioxide levels. No such equation has been derived from controlled experiments, so they posit a theoretical relationship between the variables of interest, and use this as a tool to describe potential outcomes to politicians. This is all well and good.

    Problems arise when you compare their equation with something like F = ma (Newton’s 2nd law of motion). This too is a theoretical relationship linking force, mass and acceleration. This “law” is just a very good approximation of the physical world – special relativity is needed for an improved understanding. However, F = ma can be used to solve real and important problems. In order to put men on the moon, NASA knew how much acceleration was needed, and then designed rockets with different mass and force configurations that would (hopefully) attain the acceleration. This IS rocket science, and without F = ma the moon landings would very probably not have happened.

    Compare this with the Kaya identity. Supplying values for global population, gross domestic product and gross energy consumption gives you absolutely no new information. You haven’t solved a problem. It doesn’t matter if the values are accurate current estimates, or if they come from an idealised scenario. You end up knowing that the carbon dioxide emissions are equal to the carbon dioxide emissions.

    Unlike (say) physics and chemistry, economics and climate science are full of “models” which can’t be used to solve any actual problem. This isn’t the fault of the disciplines: no-one is going to test an economic model involving (say) minimum wages by increasing them $10,000 per hour and seeing what happens, and there simply isn’t another planet that we can test climate models on by removing all the humans. So they have to invent mathematically and scientifically sub-standard “models” like the Kaya identity to make any progress. It only becomes a problem when they believe their own hype, and start thinking that these “models” encapsulate some scientific truth.

  68. Josualdo says: July 19, 2014 at 3:53 am
    I have been showing the Kaya thing to my colleagues, but I can’t write here what they said about it. I wonder if economists use algebra in a different way than the usual guy does, and recent world events suggest it might be so.

    No,Josualdo, economists use the same kind of algebra. What we’re witnessing here is a complete failure to understand the difference between identity and equation.

    x4 = x1*(x2/x1)*(x3/x2)*(x4/x3) is obviously an identity [namely an equation which is true regardless of what values are substituted for any variables (if there are any variables at all].

    z1 = z2*z3*z4*z5 is an equation (namely a mathematical sentence built from expressions using one or more equal signs), but it is obviously not an identity. All identities are equations, but not all equations are identities.

    What Pielke Jr. and others are doing is treating z2, z3, z4 and z5 as independent variables in an equation (not identity !) that allows you to calculate the dependent variable z1. Although called “independent”, their contention is that policies can somehow change the values of those variables, or certainly of some of them (e.g. higher carbon taxes would mean lower CO2 emissions per unit energy, through a change in energy mix, e.g. coal plants being replaced by wind turbines). Problem is, the latter is not obvious from their equation. In fact, very little is.

  69. The formula/equation/identity provides only one way to reduce CO2 to the level necessary to save the earth.
    Reduce people.
    Nothing else goes far enough.
    But first, you have to believe in the identity.
    You have to know it is the only answer.
    (2+2=5 you see that, don’t you Winston?)
    What do you see?
    cn

  70. Mike Jonas says:
    July 18, 2014 at 11:45 pm

    FWIW Habibullo Abdussamatov and David Evans come to similar conclusions both by different methods.

    If you look at the radiation bands CO2 affects – they are saturated (mostly). Thus zero effect for CO2 is not an absurd conclusion. It may in fact be the correct conclusion i.e. the CO2 effect – if any – is down in the noise.

    I’m still waiting for an explanation of Maunder, Dalton, etc. Once the CO2 hysteria dies I think we will start looking at the sun to explain those periods. And when I say sun I do not mean just TSI.

    What is interesting to me is that the alarmists and a LOT of sceptics are on the same page when it comes to CO2 – there is an effect. They just differ on the amount.

    I am – OTOH – on a different page. And thus take it from “both” sides.

  71. Here’s my identity:

    political policy acceptance = baffle them with bull sh*t

    In plain English: the more you bullsh*t people the better chance of your politics being accepted.

    I believe that also applies to climate “science”.

  72. If we include climate sensitivity and earth’s current temperature in the identity we should be able to calculate how much we need to reduce GDP to get a desired temperature decrease.
    These guys think of everything. I like it.
    cn

  73. This discussion reminds me a bit of training I was given at GM a few years ago, before I retired. The training was mandatory for management. We were trained on the critical importance of RONA, return on net assets. We were given a number of multi-term formulas to calculate RONA. Someone asked the trainer: “Since RONA reduces to profit divided by assets, why wouldn’t managers simply sell off assets to improve RONA?” The reply was simple: “Don’t be silly. Managers aren’t that dumb. Doing that would bankrupt the company.”

    Hmmmmm?

  74. Tom in Florida says:
    July 19, 2014 at 5:48 am

    Here’s my identity:

    political policy acceptance = baffle them with bull sh*t

    Here’s an identity I’ve discovered over my 60 years of living, let’s call it the Kaka Identity:

    Politician = Bullsh*t Artist

  75. I could not help but notice that some commenters, apparently those with their feet solidly grounded in engineering, seem to mock economists and environmental scientists for the KAYA identity.

    But the biggest irony of all is that prof. Kaya, father of the so-called “identity” named after him, is an engineer. I will shout it, so that everyone may notice it, an ENGINEER !

    The so-called “identity” was the result of a discussion regarding the main drivers of global anthropogenic CO2 emissions, and Kaya and his fellow engineers came up with 4 (four!) driving forces, namely:
    P = global population
    g = global GDP per capita
    e = energy intensity of world GDP
    f = carbon intensity of energy

    And so it came to be that they wrote the “equation” (I tell you, equation):
    F = P*g*e*f, where the variable F = global CO2 emissions from human sources, and the variables P, g, e and f as defined above.

    Now, I ask you, my engineering friends, is F = P*g*e*f an IDENTITY ????? Is it, if you know that in mathematics identity means an equation which is true regardless of what values are substituted for any variables? So, is this what engineers are saying: 20 = 2 * 5 *7 * 2.4; or maybe 34 = 9 * 2.7 * 30 * 0.1 ???

    Is it the fault of economists that apparently a professor in engineering can’t tell the difference between an identity and an equation? :)

  76. Managers aren’t that dumb. Doing that would bankrupt the company.
    ======================
    Obviously never watched Gordon Gekko / Wall Street. Raid a company. Buy up the stock with junk bonds. Sell off the assets. Make billions.

  77. Dr Pielke shows in his video that human emissions of CO2 jumped from 1% to 3% annual growth in 2000 (15 min in). Yet, when we look at CO2 at Mauna Loa, there is no corresponding jump in CO2 accumulation.

    If the bathtub model of atmospheric CO2 levels is correct, with humans as the source for increase, why does Mauna Loa not show a corresponding jump in the rate of increase? Doesn’t this argue strongly that the increase in CO2 is not directly tied to human emissions?

  78. And, once more, what is the connection between CO2 and climate/weather especially the catastrophic kind?

  79. F = P*g*e*f

    You can start with what is known from observation and calculate the unknowns. Global CO2 emissions, for example, are approximated. Global GDP is approximated, and global population is known to an acceptable value. Global energy consumption per capita is probably known with low accuracy but we’re talking politics here – close enough for government work, etc.

    Now you have a starting point. This means you can begin what-if’ing by creating a time series of varying rates of change for each of the knowns (P, g, e, f) and how that affects F. This can be plotted and given to a Senator or Congressman as supportive evidence of your agenda.

  80. “If the bathtub model of atmospheric CO2 levels is correct, with humans as the source for increase, why does Mauna Loa not show a corresponding jump in the rate of increase? Doesn’t this argue strongly that the increase in CO2 is not directly tied to human emissions?”

    The identity does not address atmospheric CO2 levels – it is focused on the CO2 emitted by an economy.

  81. Pielke’s “Iron Law” of Climate Policy
    In practice, this means that efforts to make dirty energy appreciably more expensive will face limited success.

    http://thebreakthrough.org/archive/yalee360_pielkes_iron_law_of_c

    ===============
    And then in the same breath the author contradicts himself and proposes a carbon tax as a solution. The justification being that the tax will be used to fund innovation.

    This ignores the lessons of history. Innovation is not something that can be purchased by governments. On the contrary, governments have an incredibly poor record of picking winners and losers.

    The problem is that the author has a conflict of interests. Academics and universities rely on government funding. So of course they will see taxation and research funding of their work as the solution.

    The rest of us, the ones living in the real word, that don’t have our snouts berried in the public trough, know when someone has their hand in our pockets.

  82. The identity does not address atmospheric CO2 levels – it is focused on the CO2 emitted by an economy.
    ===========
    I’m watching the video of Dr. Pielke’s presentation. There is a general rule in logic. No matter how correct your conclusion mathematically, if your premises are wrong then your conclusions are wrong.

    I’m questioning the premises behind the Kaya Identity, because if the premises behind the Identity are wrong, then no matter how correct the mathematics, the conclusions of the identity will be wrong.

  83. The unstated premises of the Kaya Identity are:

    1. increased atmospheric CO2 levels will lead to warming greater than 2C, which will lead to harm
    2. increased atmospheric CO2 levels can be controlled via human CO2 emissions.

    The contradiction between Dr. Pielke’s video (15 min) and Mauna Loa CO2 argues that premise 2 is wrong.

  84. There appears to be a group of posters who still parrot Willis’s original misunderstanding of the meaning of the equation. This is from the document he linked.

    The simplest way to describe the deep decarbonization of energy systems is by the principal drivers of energy-related CO 2 emissions—for convenience, since the focus of this chapter is on energy systems, we simply refer to them as CO 2 emissions. 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:

    CO 2 emissions = Population x (GDP/Population) x (Energy/GDP) x (CO 2 /Energy)

    Unfortunately, the equation is poorly framed and thus ambiguous.

    Johan above proposed re framing it. ( Johan says: July 19, 2014 at 2:03 am ) similar to this

    T-CO2 = (T-POP) * (GDP-POP) * (WATTS-DOLLAR) * (CO2-WATT) where the terms are defined as above. If the article had done something like this, then Willis would not have found the equation remarkable.

  85. dp says: July 19, 2014 at 7:10 am
    F = P*g*e*f

    I’m not disputing that, but given that P and g in normal circumstances would be considered “exogenous”, all the “equation” says is that in order to reduce global anthropogenic CO2 emissions, all that energy and climate change policies can hope to achieve is 1) to lower energy intensity (which can never get below the limits set by thermodynamics); and 2) to lower carbon intensity of energy (which would simply be equivalent to decreasing the share of fossil fuels).

    Now, if a Senator or Congressman really is that stupid, you might just as well say: “Well, Sir/Madam, if we keep all other 60000 or so relevant variables constant, I am quite certain substituting a coal plant for a wind farm would lower CO2 emissions”. Whow !

  86. ferdberple says: July 19, 2014 at 7:28 am
    “The unstated premises of the Kaya Identity are:” –>Both conclusions are wrong

    The Kaya identity says nothing atmospheric CO2. It says nothing about atmospheric CO2 and temperature.

  87. At 31 minutes in, Dr Peilke shows a very interesting graph. CO2/GDP has been dropping almost linearly since 1980. In 1980 it was 0.9 and in 2006 it was 0.62. Based on a straight line projection, which is the type of projection climate science is best known for, we end up with a carbon free economy in 60 years.

    That is what we are seeing in the graph. If governments simply get out of the way and let people innovate, by 2040 CO2/GDP will be 0.30 and by 2070 CO2/GDP will be 0.0.

    The Kaya Identity tells us that human emissions of CO2 will be 0 if CO2/GDP = 0.0. Thus we can conclude that business as usual will result in world with largely carbon free energy by around 2070.

    So,what we really have is a bunch of governments running around spending money and creating panic, to solve a non problem. A problem that the market has been solving long before governments started meddling.

  88. OYG!

    A third post showcasing Willis Eschenbach’s mathematical errors and personality deficits? Does not the notion of quitting while one is really, really behind have any resonance here?

    Rule #1 of successful deep hole rescue – stop digging.

  89. IMHO the only real issue is the connection between CO2 and weather/climate/catastrophe/global warming. Even IPCC AR5 admits uncertainty about the magnitude of CO2 radiative forcing/feedback. The thirties were the hottest/extremest w/300 ppm (Goddard). Just focus on that, and all the semi-related issues becomes increasingly tiresome sideshows. Kick out one leg of three and the rest collapses.

  90. The Kaya identity says nothing atmospheric CO2
    ==========
    Not correct. In logic there is the “unstated premise”. It is part of the equation logically, it is simply not formally stated. To see if the conclusion is logically true, you need to add the unstated premise to the formal equation as part of your evaluation.

    If the CO2 emission in the Kaya Identity were not going into the atmosphere, then the Kaya Identity would not exist. If 100% of human emissions was being absorbed for example by increased plant growth this web site would not exist and we would not be talking about the Kaya Identity. The Kaya Identity exists based on the unstated premise that human emissions drive atmospheric CO2.

  91. A few posters are challenging the notion Kaya is an identity. I think Johan considers this an important distinction. I do not consider the distinction particularly relevant.

    All identities are equations. Maybe there are some equations that are not identities. Have not thought that notion through.

    Others have challenged Kaya because the terms are not exact for all countries and all circumstances. That complaint is a red herring. Kaya is good enough to guide policy response. Someone linked to this Ruth Dixon post above: http://mygardenpond.wordpress.com/2014/07/13/a-graphical-look-at-the-kaya-identity/#more-706
    Very valuable.

    Others complain about Kaya because they think it is a tool of alarmists. It is in fact the opposite – Kaya is a strong argument in favor of adaptation not mitigation because it drives out the true cost of mitigation.

    In particular, Kaya shows the devastating impact of mitigation policy that drives up energy cost on the poor countries.

  92. Now, if a Senator or Congressman really is that stupid…

    Never misunderestimate the ignorance of representative government. It is populated by giving an uninformed public promises of a chicken in every pot, pot in every brownie, and free health care, food, and shelter to foreigners willing to hike into the country illegally.

  93. ferdberple says: July 19, 2014 at 7:45 am
    “The Kaya Identity exists based on the unstated premise that human emissions drive atmospheric CO2.”

    More accurately, Kaya is relevant because of the assumption that human CO2 emission drives atmospheric CO2. No disagreement there. However, that assumption is not part of Kaya.

  94. RobertInAz says: July 19, 2014 at 7:47 am
    Maybe there are some equations that are not identities. Have not thought that notion through.

    Well yeah, maybe, who knows. y=x is an equation, and it is certainly true for y = 1 and x =1, and also true for y = 2 and x = 2, and actually, for an infinite number of cases. Now, I wonder, I really wonder, would it also be true if y = 1 and x = 2, or if y = 2 and x = 1, or …

    Now, of course, there is a proof that says 2 = 1
    a = b
    a^2 = ab
    a^2 – b^2 = ab-b^2
    (a-b)(a+b) = b(a-b)
    a+b = b
    b+b = b
    2b = b
    2 = 1

    With thanks to Dr. Math for this classic fallacy.

  95. Not sure what all the fuss is about.

    Is there anybody who is saying that CO2 emissions are not the product of energy use? And that the more energy we use the higher emissions will be? And that our production of wealth requires a certain expenditure of energy?

    That’s all this says – trivial yes, true yes.

  96. At 42 minutes in, Dr Pielke shows exactly how effective government policies are at de-carbonizing the economy. The UK was de-carbonizing at 3% per year prior to the Climate Change Act. After the Act was passed, the UK has been de-carbonizing at 1% per year. The UK spends billions to cut emissions, and as a result the problem gets worse. The effect of the UK government trying to pick winners and losers.

  97. Johan says: July 19, 2014 at 6:39 am “Now, I ask you, my engineering friends, is F = P*g*e*f an IDENTITY ????? Is it, if you know that in mathematics identity means an equation which is true regardless of what values are substituted for any variables? So, is this what engineers are saying: 20 = 2 * 5 *7 * 2.4; or maybe 34 = 9 * 2.7 * 30 * 0.1 ??? ”

    Not quite. Consider F=MA. Where F is expressed as KG * M/SEC**2, M is KG and A is expressed as M/SEC**2. I would consider this a physics identity. The dependent variable is on the left, the independent variables are on the right. Applying Johan’s approach of inserting random values on the left and and the right of course leads to ridiculous results. In Kaya, the value on the left is calculated from the values on the right. It holds for a broad range of real world examples. In F=MA, you can insert implausible values on the right. It does not impact the usefulness of Newton’s second law of motion.

  98. RobertInAz says: July 19, 2014 at 8:13 am
    Not quite. Consider F=MA. Where F is expressed as KG * M/SEC**2, M is KG and A is expressed as M/SEC**2. I would consider this a physics identity.

    Ah, we have a philosopher in the room! Before going over to the Dark Side (becoming an economist), i did obtain a bachelor’s degree (many moons ago) in physics. I have never known a physicist to call F = ma an identity. BTW, Newton defined F as F = (dp/dt), and Euler “popularized” it into F = ma, but not relevant.

    Now, in your defense, there is a mathematician turned philosopher named Whitehead who did claim that F = ma is an identity, but what he (probably) meant was that if we define F as ma, the problem is, the “fundamental” equation f = ma becomes ma = ma, which is trivial and meaningless.

    So yes, if we turn this whole matter over to philosophers, I’m sure we’ll have some kind of answer a few thousand year from now.

  99. For those who believe mandates work and spending more tax dollars to subsidize alternative energy should look at the experience with production of mandated cellulosic ethanol which has been a absolute failure (0.8 million gal versus 6 million mandated). At what point do we realize that attempts to build commercial cellulosic ethanol is not in the near future although the government “doubled down” on spending..
    “The US Environmental Protection Agency lowered the amount of cellulosic ethanol required in 2013 to the amount actually produced, relieving refiners and importers of the need to buy credits to cover shortfalls against the earlier mandate.
    The adjusted volume is 810,185 ethanol-equivalent gal. The earlier requirement, published on Aug. 15, 2013, was 6 million gal.
    EPA made the change in response to petitions for reconsideration from the American Petroleum Institute and American Fuel and Petrochemical Manufacturers.
    AFPM welcomed the move.
    “I expect EPA to use the same rational thinking to revise its proposed 2014 ethanol and biodiesel requirements, which are already long overdue,” said AFPM Pres. Charles T. Drevna.
    He said EPA has proposed a mandate of 17 million gal of cellulosic ethanol for 2014 and noted production of the material in the first quarter totaled less than 75,000 gal.”

    http://www.ogj.com/articles/2014/04/epa-cuts-2013-cellulosic-ethanol-mandate.html

    The US 2014 budget for climate change is $21.6 billion. Can anyone tell me what progress has been made with the hundreds of billion of dollars spent over the years, besides increasing our carbon footprint with all of academia and grant recipients traveling to conferences in posh places?

  100. Less GDP Good
    More GDP Bad
    Seams pretty clear what the Malthusian crowd gets out of balancing the Kaya identity, i.e., confirmation for their assumptions, shortsighted policies and alarmist ideals all wrapped in the illusion of mathematical certainty.

  101. Wrong/incomplete question. Are CO2 emissions only/totally/solely/alonenessly the result/consequence/product/result of mankind’s energy use? Well, no. And CO2 is not the only GHG. Now “they” are coming for methane! A psychopathic anti-coal agenda is driving all of this nonsense.

  102. Total CO2 Emissions = Sum of all CO2 Emissions

    The Kaya and Beer CO2 emissions are not exclusive, they are overlapping subsets of total CO2 emissions. The number of arbitrarilary definable subsets is is very large. The left side of the Kaya Identy represents total CO2 emissions related to population, per capita GDP, and energy per GDP. The product of these factors is only useful for describing changes in this subset of CO2 emissions as arbitrarily defined. Other factors could be included to describe a different subset.

    The arrangement of units in an equation to define an identity is called dimensional analysis.

  103. Tim Hammond says: July 19, 2014 at 8:11 am
    Not sure what all the fuss is about.

    It keeps us off the streets. Our wives like that.

  104. Johan says: July 19, 2014 at 8:29 am
    I have never known a physicist to call F = ma an identity.

    No argument. However, if it walks like a duck and quacks like a ……

    This semantic discussion does not impact the relevance of Kaya to real world policy making.

  105. Johan says: July 19, 2014 at 8:37 am It keeps us off the streets. Our wives like that.”
    +1

  106. Dr Pielke at 56 minutes in talks about average human lifespan. In 100 years we have substantially increased human lifespan, without any global treaty to increase lifespans.

    What would have happened if we placed a tax on death? What would have happened if we used cap and trade to reduce death? Would this have reduced death? According to economic theory, this should have the effect of reducing death.

    The problem not accounted for in economic theory is that there is no alternative to death. Price sensitivity, supply and demand simply do not apply when there is a monopoly. CO2 is a similar problem. CO2 has a de facto monopoly as far as energy production is concerned.

  107. I started this thread in 1989 when it was simple global warming. Premises: 1) earth is warming at an alarming rate (seems subjective and lately not so) 2) the sole cause is rising levels of atmospheric CO2 concentrations (Keeling) 3) mankind’s industrial activity is solely responsible for this increasing CO2 concentration (only because no one has bothered to locate other sources such as ocean floor volcanic vents. IPCC AR5 admits it has no knowledge of the bottom half of the oceans.) After twenty five years not one of these points has been conclusively demonstrated.

  108. Now, of course, there is a proof that says 2 = 1
    a = b
    a^2 = ab
    a^2 – b^2 = ab-b^2
    (a-b)(a+b) = b(a-b)
    a+b = b
    b+b = b
    2b = b
    2 = 1

    With thanks to Dr. Math for this classic fallacy.

    I don’t understand why this old divide by zero example is supposed to have anything to do with Dr. Roger Pielke Jr. and the matter in question today. Obviously if a = b then (a – b) = 0 and you can not divide both sides of the equation by zero. But so what? Why is that part of this Kaya Identity discussion?

    Someone enlighten me?

  109. The Kaya “identity” is too simplistic to be of any scientific use. It simply lends scientific credibility to the political opinion that we developed people are too destructive, and too numerous, to be allowed to continue our way of life.

  110. Michael 2 says:
    July 18, 2014 at 8:11 pm

    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, Ian is addressing the absorption spectrum of CO2, that is how that molecule absorbs selective wavelengths of infra red radiation, which does follow a logarithmic curve. You are referring to concentration which relates to the gas mixture. Ian is entirely correct that the atmosphere is already absorbing most of the IR it is sensitive to in the system so increasing CO2 will only have a diminishing effect on heat content. This is the great flaw of the alarmist community argument. They assume that the CO2 / heat relationship is linear. It is not.

  111. Mark Stoval (@MarkStoval) says: July 19, 2014 at 9:00 am
    Someone enlighten me?

    Hello? It was a joke, in response to RobertInAz who claimed that “Maybe there are some equations that are not identities. Have not thought that notion through.”
    If you can prove that y = x is true regardless of what values are substituted for y and x, than clearly y = x is an identity. If not, it’s an equation but not an identity.

  112. RobertInAz:

    At July 19, 2014 at 8:41 am you say

    This semantic discussion does not impact the relevance of Kaya to real world policy making.

    YES!
    As I have repeatedly said, the Kaya Identity is a useful propaganda tool but has no other use.

    Richard

  113. Mike Jonas says:
    July 18, 2014 at 10:39 pm
    RobertInAz – Willis got it right. The equations are circular logic.

    You make the case best. While the equation/identity is true, and appears useful, it only applies to statistical averages, and none of the terms on the right, other than population, can be determined directly.

    The equation does not sum over individual contributions. We are not calculation the GDP contributed by John Doe, only the average per person, which comes from the total GDP divided by the population. So the product “total GDP per person” x “population” is no more meaningful than just one term, “total GDP.” Likewise, CO2 per unit GDP is not a known quantity, nor is GDP per unit energy.

    The known quantities are Total CO2, Total GDP, Total energy, Total population. The ratios in Kaya are not known.

    To be useful, an equation/identity should be based on quantities that are directly measurable. When Total CO2 is needed to find one of the terms on the right hand side, the whole thing is trivial, as Willis has stated.

  114. It would’ve been real nice if Pielke Jr. had at least admitted that the equation is *not* an identity, and is not justified through algebraic construction.

    It would be even nicer if he and others would write the equation properly, with the required variables included, rather than using the exact same text to refer to both a variable *and* a unit.

    The confusion and controversy have, as their root cause, imprecision in expression.

  115. richardscourtney says: July 19, 2014 at 9:12 am “YES!
    As I have repeatedly said, the Kaya Identity is a useful propaganda tool but has no other use.”

    On the contrary, Kaya reflects real world data (see Ruth Dixon: http://mygardenpond.wordpress.com/2014/07/13/a-graphical-look-at-the-kaya-identity/#more-706 )

    It is relevant to policy making because it quantifies the economic and engineering impossibility of the mitigation approaches most loved by the alarmists.

  116. If you can prove that y = x is true regardless of what values are substituted for y and x, than clearly y = x is an identity. If not, it’s an equation but not an identity.

    I am still not getting the joke here. In the case of a function y = x we see that the value of y is dependent upon our choice of x. If I pick x = 1 then y = 1.

    Consider f(x) = 2x +2 when x = 4. We get 2(4) + 2 = 10 and that is it. So, f(4)=10 and nothing else. Y = 10. You don’t get to just pick both x and y independently of each other then claim it satisfies the given relationship for god’s sake. If that were true it sure would make grading math tests a whole lot easier! (no child left behind indeed!)

  117. Consider F=MA. Where F is expressed as KG * M/SEC**2, M is KG and A is expressed as M/SEC**2.

    Rewritten as the “Kaya Identity” is presented, with only units, we would teach our physicists:

    KG*M/SEC**2 = (KG)(M/SEC**2)

    The “Kaya Identity”, presented in the same way we present F = ma would read:

    F = P*g*e*f

    The people who write the “Kaya Identity” with units only, instead of including variables, are wrong.

  118. Mark Stoval (@MarkStoval) says: July 19, 2014 at 9:21 am
    I am still not getting the joke here

    My word! All I had to do to prove that y = x is not an identity, is to provide a counter-example. Which is exactly what I did. What if y = 2 and x = 1. Clearly, 2 does not equal 1, hence we conclude y = x cannot be an identity.
    (drum roll). Enters the joke. Oh, but wait, what if we can prove that 2 = 1 … !!!

    I cannot believe I even have to explain such a silly joke. This whole thread on KAYA is more absurd than any Monthy Python sketch I’ve ever seen.

  119. scarletmacaw says: July 19, 2014 at 9:13 am
    To be useful, an equation/identity should be based on quantities that are directly measurable. When Total CO2 is needed to find one of the terms on the right hand side, the whole thing is trivial, as Willis has stated.

    It would be nice. I would replace “To be useful” with “To be most useful.”

    Total CO2 is not needed to determine any of the terms on the right. I don’t know where that notion originates. In fact, total CO2 from energy production is probably derived from adding up all sources of energy and then calculating the CO2 emitted by each. We can eliminate the population and GDP terms of Kaya and just focus on energy terms to get total CO2.

    The point of the first two terms is to illustrate Pielke’s Iron Law: politicians are not going to reduce population and they are not going to reduce GDP. Therefore, they have to either increase the GDP efficiency of energy or decrease the CO2 emitted by energy. Kaya illustrates in a quantitative way the magnitude of GDP efficiency increases required or the magnitude of CO2 reductions required. The results of applying Kaya to the alarmist desired CO2 scenarios shows they are not obtainable.

  120. Johan says: July 19, 2014 at 9:29 am “My word! All I had to do to prove that y = x is not an identity, is to provide a counter-example. Which is exactly what I did. What if y = 2 and x = 1.”

    Oh my oh my. You have a physics degree and are currently an economist? I guess as an economist, you can provide counter-example to all of the trigonometric identities listed here. Mathematicians do use the term identity – a lot.

    http://en.wikipedia.org/wiki/Trigonometric_identity

    In fact, you can invalidate all of modern mathematics with similarly framed counter-examples. Start here:

    http://en.wikipedia.org/wiki/List_of_mathematical_identities

  121. I cannot believe I even have to explain such a silly joke.

    Sorry, but you can’t divide by zero, nor can you just pick any value you want for x and y if y is the dependent variable and x is the independent variable. I think they might have named the variables in that manner for that reason you see. What I really did not get is why the non-proof (error in logic) of 1=2 has anything at all to do with the topic under discussion.

    I first saw your “proof” in an undergrad number theory course in ’72 if memory serves me. It was presented to demonstrate that subtle errors in logic will creep into your work (divide by zero in this case) if you are not rigorous. I still find no reason to equate Dr. Pielke’s work with that “proof”.

  122. “I think that much of the dissent over it has to do with the difference in viewpoints between science and engineering.”

    The viewpoints of science and engineering? How about the viewpoint of Jr High Math.

    The Kaya Identity is a fancy pants version of The Multiplicative Identity Property:

    x = (1)x

    The Kaya Identity does not show the relationship between population, GDP, energy consuption and CO2. I think what would be needed would not be an identity but and equation along the lines of Ohm’s Law. A “Kaya equation” that shows the relationship of population, wealth (I would use income per capita not GDP) and CO2 emissions.

    How this formula is used politically becomes ugly very quickly. Poverty and population control = good…….wealth and babies = bad.

  123. I propose a procedure that would once and for all make our leaders aware of the cost and implications on life style and comfort of every law or regulation.
    The approach is that any new government proposal such as de-carbonization should first be implementation on the governing class first as a trial, in this case the Administration, all congressional representatives and their staff including all the cabinet members and their staff. Since their activities do not appear in any significant way contribute to the GDP, it would lower the emissions per GDP of the country without affecting the economy. More importantly it would make them fully aware of the consequences of their actions, since they appear to be oblivious to the effect of new laws/regulations. If there are no negative consequences after a 5 year trial, then the proposal could be gradually extended to other areas starting with cities. Does anyone think that if the “Affordable Care Act” was implemented under these rules there would have had so many problems and issues if it directly impacted them? Remember Congress sought and received an executive exemption, although they were supposed to also comply with the ACA.

    Think about it. Who has the largest footprint in the world? Surprising, it is those individuals who are concerned about your carbon footprint. How much would the US carbon footprint be reduce if the every government agency including the White House cut it’s carbon emissions 20% near term. Besides the cost of our energy use would fall and fossil imports would decline.

  124. Scott Wilmot Bennett says:
    July 19, 2014 at 4:17 am
    “You can put any values you like into any variables and “c” will equal the value you gave it.
    Just do the Math yourself, as Dr Rodger Pielke Jr recommended, over and over.”

    There’s nothing wrong with your math – it just describes an *unrealistic* situation. Neither you nor anyone can find a real world example that is consistent with your hypothetical.

  125. RobertInAz says: July 19, 2014 at 9:41 am
    Mathematicians do use the term identity – a lot.

    Where and when did I say there is no such thing as “identity” in mathematics? I even gave the formal definition of identity – so many times already I am getting tired of it.
    In fact, there IS a KAYA identity, namely CO2 = P * (GDP/P) * (E/GDP) * (CO2/E), where CO2, P, GDP and E are just numbers (not variables). It’s the kind of identity where one says 24 = 4*3*2*1 (because an identity does not need to contain variables).

    Now, before you continue insulting me, by asserting that “Maybe there are some equations that are not identities. Have not thought that notion through.”, you already made a laughing stock of yourself. But maybe you can show us some formal proof that ALL equations, without any exception, are identities. I am sure mathematicians would be very interested in that.

  126. RobertInAz:

    Your post at July 19, 2014 at 9:21 am says in total

    richardscourtney says: July 19, 2014 at 9:12 am

    YES!
    As I have repeatedly said, the Kaya Identity is a useful propaganda tool but has no other use.

    On the contrary, Kaya reflects real world data (see Ruth Dixon: http://mygardenpond.wordpress.com/2014/07/13/a-graphical-look-at-the-kaya-identity/#more-706 )

    It is relevant to policy making because it quantifies the economic and engineering impossibility of the mitigation approaches most loved by the alarmists.because it quantifies the economic and engineering impossibility of the mitigation approaches most loved by the alarmists.

    “Kaya reflects real world data …”. Reflects?
    “It is relevant to policy making …”?

    QED

    Richard

  127. Thank you Dr Pielke jr.

    I tend to share the characterization by Pielke jr on what is called the Kaya Identity.

    A thought: if the so-called Thermodynamic Identity*** is an identity in the same sense as the so-called Kaya Identity is an identity, then the Kaya Identity could be as potentially useful as the Thermodynamic Identity. I think there is little doubt about the usefulness of the Thermodynamic Identity.

    *** Thermodynamic Identity*** => google it for a definition of it; it is a well discussed / documented concept.

    John

  128. Mark Stoval (@MarkStoval) says: July 19, 2014 at 9:43 am
    “nor can you just pick any value you want for x and y if y is the dependent variable and x is the independent variable.”

    To begin with, I never mentioned functions, you did. Secondly, y = x is a function, but it is also an equation (or do you disagree with that?). And no, you cannot pick any value you want for y and x, because it’s an equation but not an identity (it’s completely irrelevant that y = x also happens to be a function). Now, this may surprise you, but x^2 + y^2 = r^2 is an equation, but it is NOT a function. Still, it is obviously not an identity either, unless 3^2 + 4^2 = (whatever)^2.

    You also say: “I still find no reason to equate Dr. Pielke’s work with that “proof”.”

    How many times do I have to tell you this, I was not attacking Pielke but ridiculing one of the commenters.
    And as for the relevance to Pielke. Pielke is using F = P*g*e*f, where F, P, g. e and f are variables. And for anyone who has more than 2 brain cells left, F = P*g*e*f is an equation, not an identity.

    And now I’m out of the loony bin. Enough is enough !

  129. RobertInAz:

    “…Kaya is relevant because of the assumption that human CO2 emission drives atmospheric CO2…that assumption is not part of Kaya.”

    Yes. If you argue CO2 emissions don’t matter then Kaya is irrelevant to your argument.

    “Kaya is a strong argument in favor of adaptation not mitigation because it drives out the true cost of mitigation.”

    Agree. The Kaya Identity helped Pielke memorably demonstrate that the UK cut their CO2 emissions primarily by making the nation poorer, not by filling the countryside with wind turbines.

    ferdberple:

    “If governments simply get out of the way and let people innovate…”

    Pielke seems to be saying “give up your Soviet-style xx-year emissions targets and concentrate on developing low-cost, low-impact, low-carbon energy.” I’m not sure he wants governments to get out of the way, but he’s doing a good job showing what should be obvious to everyone by now: current governments are not just dysfunctional, they’re misanthropic.

  130. Catcracking says: July 19, 2014 at 9:48 am

    “Think about it. Who has the largest footprint in the world? ”

    The answer could be Barak Obama. He has a large house, a huge jet (which he uses often) and a very large support staff.

  131. I have mixed feelings about Pielke Jr. Unlike his father, he is not a physical scientist but he seems to buy the AWG story lock-stock-and barrel. He appears to be genuine, but I instinctively find anyone to be naive who voted for Obama, not once, but twice, and is still proud of it.

  132. I see the former ardent defenders of the utility of this Kaya Identity, are finally acknowledging its actual usefulness, as a tool of committee.
    But hey, maybe we can go 500 comments on this too..
    The official orchestrated hysteria toward carbon dioxide emission from the activities of mankind, as demonstrated by the IPCC and endless national bureaucracies, arose due to pseudo science and pretentious claims of scientific evidence that CO2 causes Global Warming.
    The work of committees, created and controlled by the likes of Canada’s Liberals, so we should look for truth and actual science in the creation of people who openly stated ; “Who cares if its true.. it works for us..”Like our past Minister of the Environment?

  133. The trouble with at least the GDP/Population ratio is that it doesn’t work as a simple linear ratio for policy (or perhaps any other) purpose. If you increase population in a productive economy (Western-type) the GDP normally grows faster than the population. US per capita GDP in 1869 was $2,013 (in 2000 dollar value) and in 2005 it was $37,600.

    http://isites.harvard.edu/fs/docs/icb.topic448946.files/lecture_facts_growth.pdf

    The population increased from~ 38M to 310M in this period (about 8 times). The GDP on the other hand grew by 150,000 times from $76.5B to $11.7T. Now, I get it. The greens formula is for a dictatorship or commie economy.

  134. Johan said at 8:08 am: “Now, of course, there is a proof that says 2 = 1”. However I’m afraid all your example actually proved was that 2*0 = 1*0 (as does every integer multiplied by zero). It did not actually give any conclusion that was fallacious: the algebra was simply wrong.

    And I personally think that saying that A/B * B/C * C/A = 1 (which of course is trivially true so long as none of A, B or C are zero) can produce useful conclusions, so long as considered in proper context.

  135. “And now I’m out of the loony bin. Enough is enough !”
    We’re not in Kansas anymore, but how do we get back?

    All (almost) of the discussion of the mathematics of Kaya misses the most important point.
    The “Kaya Identity” is NOT mathematics, it is statistics. If you plug in the real world numbers you will see that it is not exact, it is an approximation, it has an implicit error term. The discussion should be about how well this equation fits reality or doesn’t.

    It can just as well be used to show that reducing CO2 is ~a sideshow; it’s the path to insanity~

  136. So that’s what the “thermodynamic identity” is? I’ve applied it for over thirty years in real power plant performance analysis, it describes what happens to the steam energy flowing through a real steam turbine’s bade path. I don’t think the Kanye equation has a similar, real, physical, application.

  137. Why bother with carbon dioxide levels if carbon dioxide does not warm the world? Have you guys forgotten that there is no greenhouse warming caused by carbon dioxide today and there has been none for the last 17 years? Are you aware that for 17 years the greenhouse theory of Arrhenius has been predicting warming but nothing has happened? If your theory predicts warming and nothing happens for 17 years you as a scientist have no choice but to dump it into the waste basket of history. There is a place waiting for it right next to phlogiston, another failed theory of heat. I cannot understand how anybody calling himself a scientist does not understand the basics of how laws of nature operate. Cessation of warming for 17 years is not a frivolous hiatus but tells us that laws of nature are at work. You cannot turn these laws on or off at will. If there has been no greenhouse warming for 17 years there has been no greenhouse warming at all, period. In case you are wondering what to do without the comfort of the Arrhenius theory, there is another greenhouse theory called the Miskolczi greenhouse theory or MGT that does explain what is happening. It predicts exactly what we see: no warming despite an abundance of increasing atmospheric carbon dioxide. To understand this requires knowledge of what the greenhouse gases are doing that prevents their absorption of IR from showing up as warming. What is happening is that there are several greenhouse gases in the air that simultaneously absorb in the infrared. Arrhenius theory can only handle one of them, carbon dioxide in this case. But carbon dioxide is not even the most important greenhouse gas, water vapor is, and their cooperation is what we need to understand. Arrhenius fails at this but MGT is cap[able of handling the more general case of several GHGs simultaneously absorbing in the IR. In such a case the gases involved create a joint optimum absorption window whose optical thickness they control. The gases that count in the earth atmosphere are water vapor and carbon dioxide. Their joint optimum absorption window has a fixed IR optical thickness of 1.87, determined by Miskolczi from first principles. If you now add carbon dioxide to the atmosphere it will start to absorb in the IR, just as the Arrhenius theory tells us. But as soon as this happens, water vapor present will begin to diminish, rain out, and the original optical thickness of their absorption window is thereby restored. Absorption by the introduced carbon dioxide is still active of course but its warming effect is just balanced by the reduction of atmospheric water vapor that is happening simultaneously. This has been going on for the last 17 years and explains the absence of warming today. If rising carbon dioxide did not cause any warming for 17 years laws of nature tell us that it never has caused any warming at all. Any alleged greenhouse warming that happened before this time is nothing more than natural warming, misidentified by ober-eager climate scientists anxious to prove that greenhouse effect is real. Clearly any claims that adding carbon dioxide to the atmosphere causes anthropogenic global warming or AGW have to be nullified. And with it, alarmist demands for mitigation and emission control become irrational irrelevances, wasting public resources, and must be stopped immediately to curtail any further waste.

  138. The Kayla identity obviously makes the assumption that CO2 production is directly proportional to GDP, so substituting a different factor like beer producion is an apples and oranges situation.

  139. I’m trying to reconcile these two comments:

    john robertson says: July 19, 2014 at 10:46 am
    “I see the former ardent defenders of the utility of this Kaya Identity, are finally acknowledging its actual usefulness, as a tool of committee.”

    nutso fasst says: July 19, 2014 at 10:36 am
    “Agree. The Kaya Identity helped Pielke memorably demonstrate that the UK cut their CO2 emissions primarily by making the nation poorer, not by filling the countryside with wind turbines.”

  140. i learn best by doing – second best by watching someone else do – i read Pielke’s paper mentioned above (http://iopscience.iop.org/1748-9326/4/2/024010) – and came away enlightened – and slightly embarrassed

    while i thought of Kaya as a engine to generate the lefthand side – Piekle used the equation to examine the righthand side factors – concluding that the GDP effect of the Climate Change Act was too precipitious – so in a limited fashion – Kaya does give us the cost of certain changes

    i had been bothered by the use of raw Population & GDP numbers – thinking that they might be refined – but their use is close enuf for government work – and government work is what Kaya is intended for – and greenie influenced policy makers are usually interested in not adversely affecting the population numbers or gdp – and much more interested in energy efficiency in terms of co2 emissions

    unfortunately – the numbers plugged into the factors are assumptions calculated outside the equation – and Kaya is not intended to evaluate those assumptions – and the technological factors are fronts in the great global warming war

    if an opponent were to bring up Kaya in a debate – saying it proves that we need a green technology to avoid global warming – after pointing out that he hasn’t proved co2 guilty – then point out the Kaya makes a case for nuclear energy too

  141. Thanks to Dr. Pielke for participating. Interesting but I want to see how this is applied to the real world and my concern is how this will be sliced/diced as a basis for world development. I guess I missed something.
    I lived in third world countries in the midst of tribal subsistence, agri-poverty, banana republic social dictatorships. Dr. Pielke makes a short mention of it, the number of people who die from cooking over dung.

    - 3 million people die every from indoor air poisoning because they do not have fuel or electric. (WHO org)
    - 3.4 million people die every year including 760 000 children…because they are not allowed to have electric to run drinking water and sanitary systems. http://water.org/water-crisis/water-facts/water/
    - 850,000 people die every year because refrigerated vaccines cannot be maintained…because some activist group determined that we could not bring in 5000 feet of electric line and that a solar panel powering a single light bulb will be enough to run a refrigerator…although the doc had to chose between surgery light and the refrigerator.

    Only the rich with disposable income are focused on environment issues. I find this ethnocentric since the solutions offered remove choices for the poor and limit their opportunities for developed: a two tier system: rich countries and all others.
    .It was ‘interesting’ standing by watching Indians starve because Honduras put a ban on cutting limbs from trees for firewood. Only wood that has landed on the ground could be used…there are ways around that.
    .
    When comparing GDP as a measure for carbon emissions, it ignores countries with low GDP who rely on slash/burn farming and other pollution based processes. Slash/burn is the method to fertilize the low quality land, otherwise more jungle will be needed to get the same crop.
    Countries with less income not going to spend millions for air scrubbers on electrical plants.

    So using the Kaya in the real world, 50,000 cars must be taken off the roads in Massachusetts so that a community in Mosquito can have a washing bin instead of using the river….and free up women to do other things.
    Because, the reality is, this admin will never pass any of the 13 nuclear power permits started up 8 years ago, my Enviro light bulbs are not enough, and sending cash to the rich in a Banana republic makes that person very rich.

  142. After some more research, I concede Johan’s point that the Kaya identity is not like a mathematical identity. My post at July 19, 2014 at 9:41 am is completely wrong. Mathematical identities have no dependent variables. I should have stuck with physics.

    That said, while making the analogy between Kaya and the laws of physics I stated that these laws are like an identity, They are not like a mathematical identity, A physical law has independent and dependent variables so it is incorrect to refer to them as an identity.

    So I have to agree that calling Kaya an identity is a misnomer and is clearly getting in the way of understanding its usefulness.

    Good on you Johan.

  143. Maybe I’m overlooking something, but I don’t see why there’s any controversy about this. It looks like a useful tool to describe your degrees of freedom in altering CO2 emissions. In that sense it’s similar to F=ma. If I want to increase or decrease force this equation tells me that I can either alter mass or acceleration or both. Or I can increase one and decrease the other. But is it really this easy? Nope, because if you exchange on of your masses with a different object with different materials then the “a” changes. The Kaya Identity seeks to find all of the subtle effects that change the outcome.

    In another sense it’s like the Drake Equation. Whether you use a top down or bottom up approach your final result is only going to be as good as your knowledge of each variable. That makes it useless for most purposes except as a “what if” exercise. As a propaganda tool I can’t see that it’s significantly more useful to either side.

  144. Plants and photosynthetic organisms are the dominant life form on Earth. The leaves of plants are home to microbes (Pseudomonas syringae) which are excellent ice nucleating particles. When these bacteria are wafted into the upper atmosphere they cause rain, which waters the plants. Plants breath CO2 and exhale oxygen. Humans breath oxygen, and eat plants, then the humans dig up fossil fuels and burn them, which feeds the plants.

  145. Stupid question: why isnt the “Kaya Identity” replaced with CO2= f (population, gdp, energy consumption, efficiency) . It seems to me that would eliminate the confusion.

  146. Not having read much of the other discussions about this I am probably repeating other’s comments.
    Anyone here who runs a business will know that numbers can be explained in more ways then one. Numbers are not absolute by any means, only when used in a certain way, but there are always more ways then one. And which is more valid depends on opinion. One can turn a profit into a loss and the other way around (within reason) and eventually you do run out of options.
    According to the link given by Dr Pielke, and the graph supplied therein, China has the highest rate of emissions per $1000 GDP but they also have the lowest rate per capita, although no mention of this in the article that I could find.
    This is not meant as trying to criticize the equation by the way, just a fact.
    If I were a Chinese official I would use the per capita figure to clobber the rest of the world for not doing enough, and you could not fault their side of the argument.
    The UK comes out quite well in the per $1000 graph, but all they have really done is exporting their most dirty industries to the likes of China, India and others.
    And the UK is not alone with that, it was all done to help developing nations or so we were told by policy makers and it is was a sign of the times according to them running those companies.
    The equation stacks up as far as a mathematical formula is concerned for the CO2 issue based on the given parameters, but it depends on how you wish to look at it where the problem lies.
    In the case of this report, as this was written for the Brits all I can conclude is that it makes the British Government look pretty good compared to some others and that was the intention of the Brits in the first place.
    They already knew the outcome of the findings before they asked, Dr Pielke in this case, to conclude it. I do not wish to criticize Dr Pielke’s good work but to me this is a bit like Cadbury getting research done to show the benefits of chocolate, pay for the research and set the parameters and presto there is the conclusion we were looking for. How about that.
    Or is that being too skeptical.

  147. JohnH says:
    July 19, 2014 at 12:18 pm
    [it's] useless for most purposes except as a “what if” exercise.

    that’s it in a nutshell – well put

    JohnH says:
    As a propaganda tool I can’t see that it’s significantly more useful to either side.

    it’s use assumes CO2 to be dangerous – the overarching controversy – the question of the danger of increasing co2 – is not mentioned – unless someone brings it up

  148. I would point out that based on the “Kaya Identity”, doubling the population while keeping gdp, energy consumption, and efficiency equal results in zero increase in CO2 emmisions. I guess CO2 is independent of population.

  149. “I would point out that based on the “Kaya Identity”, doubling the population while keeping gdp, energy consumption, and efficiency equal results in zero increase in CO2 emmisions. I guess CO2 is independent of population.”

    Only if you use the incorrect understanding of Kaya. With the the correct understanding: 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: then doubling population while holding all other terms constant will double CO2.

  150. “In the case of this report, as this was written for the Brits all I can conclude is that it makes the British Government look pretty good compared to some others and that was the intention of the iBrits in the first place.”

    on the contrary
    nutso fasst says: July 19, 2014 at 10:36 am
    “Agree. The Kaya Identity helped Pielke memorably demonstrate that the UK cut their CO2 emissions primarily by making the nation poorer, not by filling the countryside with wind turbines.”

  151. “Only if you use the incorrect understanding of Kaya. With the the correct understanding: 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: then doubling population while holding all other terms constant will double CO2.”

    The “Kaya Identity” is misunderstood when it is poorly stated.

    1) it’s not an identity, it’s an equation;
    2) the equation is stated with units only, not variables.

    With the correct equation presented, it will be correctly understood. The proper way of writing out the Kaya Equation is:

    F = P*g*e*f

    It is left as an exercise for the reader to understand that because the Kaya Equation is *not* an identity, it cannot be constructed algebraically from CO2 = CO2.

    • Curious George says “krishel: Please correct in the Wikipedia.”

      You can do this yourself. *I* could do it. Anyone can do it but the warmists love it the way it is and the skeptics rather enjoy it too. I’ve got my screenshot and when it changes (if it changes), I’ll screenshot it again to show the workings of the Ministry of Truth.

  152. RobertInAz says:
    July 19, 2014 at 9:30 am

    Total CO2 is not needed to determine any of the terms on the right. I don’t know where that notion originates. In fact, total CO2 from energy production is probably derived from adding up all sources of energy and then calculating the CO2 emitted by each. We can eliminate the population and GDP terms of Kaya and just focus on energy terms to get total CO2.

    Total CO2 is what is used to find the CO2/energy term. That it comes from adding up a few sources does not change anything. Kaya does not separate the sources, it only uses the CO2 sum divided by the energy sum. In both cases those numbers are probably WAGs, but that’s another matter entirely. Even if they were dead-on accurate, Total CO2 is needed in the right hand side of the equation. So you have Total CO2 = f(Total CO2).

  153. Krishel says @July 19, 2014 at 1:40 pm:

    The “Kaya Identity” is misunderstood when it is poorly stated.

    And followed it with a self-fulfilling example.

  154. Total CO2 is what is used to find the CO2/energy term.
    Hmm. How is total CO2 determined/measured if not as I described?

  155. RobertInAz says: (July 18, 2014 at 11:48 pm) “In which case, every identity that forms the basis of modern physics is circular logic.“. Not at all. In a normal physics ‘identity’, each factor brings something new to the equation without taking anything away. In the Kaya formula, each term from the second onwards takes away a factor from the previous term, until there is nothing left but what it started with. As I explained, taking GDP per person for example, we don’t know GDP per person in its own right, if we did then this part of the equation would be valid; we only know it as total GDP divided by total population, and therefore the terms cancel out.

    You make the same error as Willis when you say: “So the exact same number that goes into the ‘top’ of one equation goes into the ‘bottom’ of the next equation.” The correct description is: “The units of the variable at the top of one term of the equation are the same as the units of the bottom of the next term of the equation. In physics, we confirm our equations are right when the units on the right cancel out to equal the units on the left.“. Of course the units have to be the same right and left. But that’s not the point. The point is that in the Kaya equation the quantities are necessarily exactly the same ‘top’ and ‘bottom’ and hence add nothing to the equation.

    What the Kaya equation seems to be trying to say is that CO2 emissions can be reduced by reducing total population or GDP per person or energy per dollar of GDP or CO2 per watt. That’s all true, but not very helpful. For example, CO2 emissions can be reduced by replacing old coal-fired power stations with new ones or with gas or nuclear, improving house insulation and using passive-solar design, sending freight by rail instead of road, repairing roads faster or making traffic lights more efficient – or even by improving girls’ education. Sure, each of these can be mapped post-facto to one or more of the terms in the Kaya equation, but the equation didn’t help and doesn’t help.

  156. I see a lot of ‘mathematicians’ apparently unable to figure out that Kaya is a simple tool that uses statistics to help people reason about policy implications. (Does anybody seriously believe that Pielke sees Kaya as akin to the laws of physics? Good lord.) It shows policy makers that they have a choice: if they want to reduce emissions, they can either bankrupt their countries, or they can focus on energy innovation.

    I also see a lot of people who are having allergic reactions to the idea of “government interference”. Right or wrong, the “do nothing” option is not on the table, nor will it ever be on the table. If governments are implementing policies to reduce CO2, I would much rather see them shift the bulk of their efforts towards energy innovation.

    • JamesNV says Right or wrong, the “do nothing” option is not on the table, nor will it ever be on the table.”

      Oh? How did you happen to become Keeper of the Table?

  157. So what’s the point of reducing CO2? Obama/EPA limited US power generation to 1,100 pounds CO2 per MWh which will make a 2.2% difference in global CO2. Big deal! Why are governments compelled to reduce CO2?

  158. If one were to express the Kaya Identity if text form it would be something like:
    Carbon dioxide emissions are directly related to energy use, GDP and population.

    And it would be undeniably true, as a rough rule of thumb.

    Instead it is expressed as a series of precise, directly proportional numeric relationships, intended to impress the innumerate with its precision and by extension accuracy.

    This is closely akin to the neophyte with a calculator who believes that because he saw 5 events in 7 seconds that they must occur every 0.71428571428571 seconds and that the last digit is significant despite the lack of precision of the input.

    It is also a generalization beyond what the evidence supports.

    Specifically, the claim that these factors are directly proportional is obviously false. They all require the stipulation that ‘all other things being equal’ which is never true. If for example, population increases, some things become more efficient (transportation) others might become less efficient (results of land use pressure).

    These factors make the Kaya Identity as valid and useful as the statement that 77 degrees Fahrenheit is 10% hotter than 70 degrees Fahrenheit. It is neither precise, accurate nor true, but perhaps 80% of the people will believe it because it looks mathematical.

    • “the Kaya Identity as valid and useful as the statement that 77 degrees Fahrenheit is 10% hotter than 70 degrees Fahrenheit.”

      Or that 1 degree F is infinitely hotter than 0 degrees F!

  159. RobertInAz says:
    July 18, 2014 at 11:59 pm
    “In defense of the report, the description immediately before the ambiguous equation was correct:
    “we simply refer to them as CO 2 emissions. 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: “”

    And now, let’s apply the “Tools in the toolbox”, as the warmist sociologists love to call them:
    a) Population. That’s easy: Smallpox and civil war should take care of that.
    b) GDP per capita: We know what to do about that: Abolish profits, equal pay for every job, killing every incentive to be productive. Cuba leads the way.
    c) Energy Use per GDP: EU just decreased that by adding blow and hookers to official GDP. Easy as cake!
    d) CO2 per energy: Ok, that’s complicated. One needs brains for that. No tool in the policy toolbox. a,b and c should suffice.

  160. John Brisbin says: July 19, 2014 at 4:02 pm “It is also a generalization beyond what the evidence supports.”
    On the contrary, Kaya reflects real world data (see Ruth Dixon: http://mygardenpond.wordpress.com/2014/07/13/a-graphical-look-at-the-kaya-identity/#more-706 )

    The key point is for a particular country, Kaya holds for the purpose of policy analysis. It is not a perfect tool. What tool would you suggest to help policy makers understand the cost of mitigation?

    • RobertInAz says “What tool would you suggest to help policy makers understand the cost of mitigation?”

      No tool exists. Mitigation of a naturally occurring substance, CO2, has never before been attempted on a large scale. Consequently you come up with an idea and let the idea reveal the costs.

      Kaya is useless. It is because the terms cancel that what you are left with is exactly one factor — the CO2 efficiency of energy. Until and unless you have “carbonless energy” all other approaches are doomed. You don’t need Kaya for this.

  161. Mitigation – of what? Why? CO2 does not equal warming does not equal apocalypse does not equal any needed policy “mitigation” solutions. First step in a solution is making certain you have the correct problem. What does the Kaya tell policy makers they need to do? Why do the “policy makers” need to do anything??!! Too much time on their hands? Trying to insure their “legacy?”

  162. Absolutely astonished that wuwt continues to even entertain this complete nonsense.
    Yes, Kaya is an identity, but it is also a tautology: it conveys no wisdom and has no utility at all, in stark contrast to Newtonian mechanics, Maxwell´s electro-magnetics, or Einstein´s mass-energy relationship, for example, which were also expressed as simple equations, but had insight and made us wiser and helped catapult us into modernity.
    Kaya is of the pure crap pseudo-science category that usually only finds an audience among scientifically/mathmatically illiterate enviro-fascist art-school student types and climate scientists.

  163. nickreality65, The reality is that policy makers believe it to be a problem. So they ARE going to do something about it. What would you rather them do? ‘Investing’ in energy innovation, research and development is not necessarily a bad idea regardless of CO2.

    • JamesNV says “Investing in energy innovation, research and development is not necessarily a bad idea regardless of CO2.”

      Quite right. Fossil fuel will run out. Substitute is needed. However, since the cart was hitched to a gimpy horse, now that the horse appears somewhat crippled it may be hard to move that car.

  164. Looking at the past decades of alternate energy “investing”, yeah, it can be a bad thing. A massive waste of resources. I remember the big solar boom of the seventies. How many of those systems have been abandoned? Such “investing” diverts resources from real problems. A natural museum recently opened nearby with a nice gift shop. I can think of no greater harm to the environment than the production of a lot of useless crap – and wind and photovoltaic and CFL “investments” fit that description.

  165. I’m enjoying the scientific “macho men”, strutting around showing off their “hard science” cred, aggressively dismissive of “fluffy” things like economics, art and psychology because it’s so “soft” (maybe a little too feminine?). Seems a bit neurotic. ;)

  166. megawati says: July 19, 2014 at 4:24 pm “Yes, Kaya is an identity, but it is also a tautology: it conveys no wisdom and has no utility at all,”

    Dr. Pielke has documented many cases where Kaya provides useful insight. Perhaps you could explain where he is wrong. Did you read them? Did you read my explanation on how many WUWT readers (starting with Willis) misunderstand Kaya? Which understanding of Kaya are yiou basing your assertion on?

    • RobertInAz says “Dr. Pielke has documented many cases where Kaya provides useful insight.”

      Has it convinced anyone not already convinced of the “A” in “GW”? I don’t know, seems iffy.

      “Perhaps you could explain where he is wrong.”

      He illustrates that the terms cancel right in his program leaving “C = C”. You can insert anything at all in the middel so long as it cancels. If the thing you inserted happens to be explanatory, that’s fine, but you don’t need this “device” or gimmick. Just explain what you intend to explain.

      “Did you read them?” yes.

      “Did you read my explanation on how many WUWT readers (starting with Willis) misunderstand Kaya?” Yes. You show algebra then explain that it isn’t algebra. Very clever!

      “Which understanding of Kaya are yiou basing your assertion on?”

      Mine (of course). The same is true of everyone commenting on it, each is commenting from his own understanding of it.

  167. This conversation began as a discussion of the Kaya identity and the scientific/mathematical/engineering merits of its application as a tool in guiding CO2 mitigation policies. (the 50 to 1 project explained it better and simpler) Not now nor never have there been solid scientific justifications for such CO2 mitigation so the merits of the Kaya equation are moot.

    James NV: And just where does all of that energy go? Into the atmospheric system. The US uses around 100 Quad Btu/y. Where does that go?

    100 Quad Btu/y * atmos lb / 0.24 Btu/lb F = F/y independent of CO2.

  168. Oops, launched too soon. 100 Quad Btu/y / (0.24 Btu/lb F * Atmos lb) = F/y Check it, like I have to ask.

  169. JamesNV says:
    July 19, 2014 at 4:29 pm

    “Investing’ in energy innovation, research and development is not necessarily a bad idea regardless of CO2.”

    Wind energy is 1000s years old and died out because it was so limited – innovation isn’t the right word here. Also, innovation is good but not holus bolus investment in the full scale real deal before you have done the research, knowing that at this stage the efficiency is 15%. We all know what the new replacement should be able to deliver to be a reasonable alternative and this is where the research should begin, but not on a country-wide scale.

    Also, few comment on the enormous waste of resource that we have in hundreds of thousands of climate scientists doing the same thing they have been doing since 1990 with no change in the theory or improvements. We should be disappointed if only ONE researcher did the same thing without variation for over 30 years despite the track record of forecasting from the theory being abysmal. It would be the same thing to keep looking for phlogiston long after the likelihood of its existence is near zero. I’m afraid there are no Einsteins, Newtons, Maxwells, Plancks, Bohrs…. in this pathetic ‘science’. A good example of what is exasperating to thinking, searching persons is the article on the Yamal, Russia pingo feature in which an ARCTIC RESEARCHER was totally unaware of such a landform and gave a fanciful theory for its formation connected to CAGW.

    http://wattsupwiththat.com/2014/07/18/new-pictures-of-the-hole-in-yamal-and-pingo-was-its-name-o/

    • Gary Pearse says “we have in hundreds of thousands of climate scientists doing the same thing”

      Successful “consensus” mythology. It is not known how many climatologists are doing the same thing, maybe a few dozen. Most here can probably name the principle players from memory.

      What you see in the mainstream media typically is based on the 12,000 *papers* reviewed by John Cook for his 97 percent consensus claim. Of that 12,000, 64 to 72 were really about AGW.

  170. RobertInAz says:
    July 19, 2014 at 4:07 pm
    John Brisbin says: July 19, 2014 at 4:02 pm “It is also a generalization beyond what the evidence supports.”
    On the contrary, Kaya reflects real world data (see Ruth Dixon: http://mygardenpond.wordpress.com/2014/07/13/a-graphical-look-at-the-kaya-identity/#more-706 )

    The key point is for a particular country, Kaya holds for the purpose of policy analysis. It is not a perfect tool. What tool would you suggest to help policy makers understand the cost of mitigation?

    end of quote from RobertInAz (sorry I seem to have no formatting controls)

    The population based graph you refer to is conveniently on log-log scales. What it seems to indicate is that the supposedly linear function is linear (within +- 1-2 orders of magnitude)

    I call that scientific sophistry. Close enough for climate science, though.

  171. I read the paper and listened to the lecture. It was a somewhat boring lecture that did make a few obvious points.

    I did notice that Pielke had one huge mistake in his thinking. The major mistake is that Pielke does not seem to understand the economic distortions that are caused by subsidies and indirect subsidies and costs that are added due to anti-CO2 legislation.

    For example – the government tells a utility that they must have 20% clean energy. The utility decides to put up windmills and add the infrastructure to handle the windmills. They need to shutdown some of the existing power plants and build new plants to provide “peak power” when the windmills are not generating enough power. The amount of infrastructure needed is enormous as are the costs for the windmills. The end result is that most of the components for the windmills, new plants and infrastructure are manufactured in places like China. To manufacture the new plant, the infrastructure and windmill components requires large amount of emissions as the steel, copper, carbon fiber, fiberglass, housings and etc. are all manufactured. The other cost is transporting all the components and the using large amounts of cement, the transport of workers and etc. etc. The end result is that some of the windmill projects may never generate the amount of power to pay the energy costs for building the infrastructure, installing the infrastructure transporting it, switching to new power plants and building the windmills. However, they have effectively shifted the CO2 emissions to China for the power that is generated. Going to 20% clean energy though does increase the cost massively for energy because essentially, the energy user is financing a huge amount of waste that only has the benefit of shifting CO2 generation to China and does not actually have any net CO2 reduction or if there is some it is very small.

  172. Step 1) Independently crowd source estimations for each factor on the rhs for some country. Do the same for the CO2 term on the lhs.
    Step 2) Determine the mean, median, or mode for each factor.
    Step 3) Divide the product of the rhs factors’ mean, median or mode into the respective mean, median, or mode for the lhs CO2.
    Step 4) Repeat from step 1 for all countries of the world.
    Step 5) Plot a frequency histogram of the results for step 4 using an appropriate bin size.
    Step 6) If the shape of the frequency histogram is more or less normal with a small standard deviation, then use its mean as a constant of proportionality after the equal sign. If the shape of the frequency histogram is otherwise, than scrap the Kaya Identity.

    There, fixed it!

  173. @Outtheback 12;37.
    You nail it.
    Its Bistro-maths.
    Or is it the joke about the 3 accounts seeking the same job.
    Final answer;”Whatever you want the numbers to be”
    Your hired.

  174. O/T Do you reckon any of these so called climate change bullshit artists, ever go out of the front door and look up at the sky? Is it cloudy, raining, snowing, sunny etc., check their barometers if they have one, or thermometers, well I do. Any amount of graphs and maths leave me cold. I am no good at math, one of the reasons I could not go for a Science degree, I couldn’t even work our the scientific calculator. But I do know history and archaeology. And I am skilled in horticulture and agriculture, even bonsai. And I know spring follows winter, then summer and autumn (fall) and in Australia we always needs a healthy dose of rain. If too heavy we flood. We have tropical, sub tropical and temperate, alpine, and up North has the big wet, (monsoon) . Luckily, I have my grandfathers notes on when he visited Australia in 1892 and 1894. He revealed that rough seas demolished the American fleet in a very bad cyclone. A coal tender turned turtle in Port Jackson,
    (that’s Sydney) after a strong Southerly buster hit it while being loaded. So what’s new, eh.

  175. Anthony wrote (main post):

    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.

    Anthony,

    The point of the Kaya Identity is simply to provide an analytical framework to account for the technical relationships that result in the flow rate of anthropogenic CO2. Yes, in math terms it’s ‘trivially true’. Also, it doesn’t (in itself) ‘fully represent’ a complex system, but it provides the framework for representing whatever degree of complexity might be desired — in examining how GDP affects energy use, how energy use affects CO2 emissions, and so forth. The Kaya Identity is worthy of respect as a useful truth.

    The Kaya Identity does not purport to be a ‘physical science tool’. Technological change, as Pielke notes, affects the values of two of the ratios that make up the identity, but that’s the extent to which physical science comes into it. The Identity adds nothing to our understanding of how any given flow rate of anthropogenic CO2 will affect climate. Pielke does not claim otherwise.

    The Kaya Identity is certainly a policy tool, if that is what you mean by ‘political tool’. In the text, Pielke uses the Kaya Identity to show how a particular policy would only be feasible given implausible assumptions about future changes in the ratios that make up the Identity. Isn’t that useful?

    I am disheartened at the number of comments that make empty arguments against the Kaya Identity without engaging with Pielke’s actual use of it. We have already had two long threads in which people made such arguments in a vacuum. Now that we have an actual text (and/or video), I would expect that people would respond to it.

    I’m also hugely disappointed that you, Anthony, refer to Willis and Roger as having two ‘viewpoints’ — presumably somehow of equal weight, despite the vast (!) difference in their expertise. You introduce Roger here as one of Willis’s ‘more strident critics’, when Roger is the expert on the matter, while Willis has not yet shown that he even understands just how the Kaya Identity is used. In scholarly discourse, the proper approach is for a well-developed analysis to be tested by criticism. It is Roger who has that analysis, not Willis. Furthermore, Roger has certainly not been ‘strident’, but low-key and very substantive. Willis, on the other hand, has taken drive-by pot-shots.

    I would have expected better of both of you.

  176. The Kaya Identity appears to me to be an abstract representation designed to display the relationship between Global CO2 emissions, Global Population, Global GDP, and Global energy consumption. As that, it can be used to simply explain a complex problem – BUT – using it to establish public policy is IMHO extremely dangerous.

    I say this because the purported goal is to reduce CO2 emissions to zero. Using the Kaya Identity it becomes obvious that the ways to achieve this goal are
    a) Reducing the World Population to zero – Complete genocide and self-annihilation
    b) Reducing the Global GDP to zero – I’m pretty sure this would lead to a complete collapse of civilization as we know it.
    c) Reducing the Global energy consumption to zero – everyone would starve to death or die from exposure, which would effectively achieve point a).
    d) Reducing Global CO2 emissions to zero – which can only be achieved by a), b), c), or converting all carbon based energy systems to non-carbon energy based systems.

    Obviously the only logical choice becomes converting all carbon based energy systems to non-carbon energy based systems, since the Kaya Identity shows that in order to achieve zero emissions, any combination of the other three choices means that we must reduce at least one of the other three variables to zero – which would result in the extinction of the human race.

    The worst thing about this is that nobody seems to realize that it is impossible to turn back the carbon emission clock. Even if we reduce our CO2 emissions to zero, the concentration of anthropogenic CO2 in the atmosphere will continue to rise simply because our population continues to grow. The present human population of the earth is at least 6 times what it was in 1850 – consequently the natural CO2 contribution of humans is also at least 6 times what it was in ‘pre-industrial’ times. Unless there has been a corresponding explosion in CO2 consuming lifeforms this means that ‘natural’ anthropogenic CO2 emissions will continue to contribute to the increase in CO2 concentrations in the atmosphere, albeit at a slower rate.

  177. Mike Tremblay says:
    July 19, 2014 at 11:26 pm

    The worst thing about this is that nobody seems to realize that it is impossible to turn back the carbon emission clock. Even if we reduce our CO2 emissions to zero, the concentration of anthropogenic CO2 in the atmosphere will continue to rise simply because our population continues to grow. The present human population of the earth is at least 6 times what it was in 1850 – consequently the natural CO2 contribution of humans is also at least 6 times what it was in ‘pre-industrial’ times. Unless there has been a corresponding explosion in CO2 consuming lifeforms this means that ‘natural’ anthropogenic CO2 emissions will continue to contribute to the increase in CO2 concentrations in the atmosphere, albeit at a slower rate.

    No, this is wrong because the CO2 we breathe do not come from fossil sources.

    All the CO2 we exhale come from the food we eat, and the carbon in that food has been captured from the air. These processes cancels out and is zero in sum.
    /Jan

  178. Krischel,
    You can’t compare the Kaya identity to F = ma because F = ma defines what we mean by ‘force’. It doesn’t follow from mere algebraic considerations regarding its units because before it is stated there is no notion of force in the theory. The Kaya identity on the other hand does follow from mere algebraic considerations.

    That the Kaya identity may be useful is beside the point, it is ridiculous to give an algebraic identity a grandiose name as if it captures some deeper truth.

  179. Jan Kjetil Andersen,
    All the CO2 we exhale come from the food we eat, and the carbon in that food has been captured from the air
    Carbon in food is often captured directly from hydrocarbons. Food from the Gulf of Mexico is a prime example: http://living-petrol.blogspot.com/
    Microbes consume more hydrocarbons than we do. If we don’t burn them, they will anyway. The carbon “budget” is not fixed in a zero-sum superficial surface cycle.

  180. Actually none of it matters because after several decades and scores of additional CO2 ppm the evidence is crystal clear that CO2′s influence over global warming and climate is inconsequential.

  181. gnomish [July 18, 2014 at 7:53 pm] says:

    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!

    Repeated for truth!

    To Josh, picture a kettle of slow cooking frogs leisurely wading around in their comfortable pool debating nonsense while the chef grins. Maybe you can somehow work in Angels and pinheads too.

  182. Khwarizmi says:
    July 20, 2014 at 3:11 am

    “All the CO2 we exhale come from the food we eat, and the carbon in that food has been captured from the air”
    Carbon in food is often captured directly from hydrocarbons. Food from the Gulf of Mexico is a prime example

    Thank you for an interesting link Khwarizmi, but I think that the share of non-photosynthesis based food must be negligible compared to what we get from photosynthesis-based products.

    / Jan

  183. Cynicism alert!

    My interpretation of the Kaya identity: if someone is truly worried about catastrophic AGW due to CO2-emissions, but refuses to accept an increase in realistic alternative energy sources to fully fill the production-gap that shutting down fossil fuels will leave, must be for population reduction and/or radically shrinking economies.

    Populations can be reduced in two ways. The short term solution is some kind of genocide, the long term is forced sterilizations or some other draconian measures to reduce birth rates. This long term solution is probably to slow given that we have to ACT NOW™!!

    Economies can be shrunk and people can be put in poverty and misery by many means, taxation and/or highly regulated plan based economies could be viable options. Unfortunately this will probably have an adverse effect on birth rates, so perhaps some kind of combo of population control and economy control needs to be put in place just for safety’s sake. The fear of you or your family being killed by something other than malnutrition or cold could at least add some kind of excitement into the extremely dull life you will be living.

    So, with rising populations and economies in developing nations, requiring somewhere around 3-4 times the current energy consumption and 2-3 billion more people in a few decades, we are left with a choice of three paths:

    1) Kill every 9 out of 10 humans give or take.

    2) Make sure that life is truly depressing for those 9 out of 10 humans by taking away any means to reach a reasonable standard of living.

    3) Build nuclear power plants like there’s no tomorrow. Take the alarmist word for it and accept that the climate science is settled and divert all those research funds into short and long term science projects with one aim, abundant energy for all. This has a side benefit that we need old school schooling focusing on the the sciences that don’t have science it their names: physics, mathematics etc. Who knows what we’ll find as a humanity if we would go in this direction. But since this path requires free thinking and motivated individuals I guess it is out of the question.

    F*ck it

  184. Michael 2 says: July 20, 2014 at 10:53 am Kaya is useless. It is because the terms cancel that what you are left with is exactly one factor — the CO2 efficiency of energy. Until and unless you have “carbonless energy” all other approaches are doomed. You don’t need Kaya for this.

    It is this persistent misunderstanding the prevents people to understand Kaya’s usefulness. For example, you can lower per capita GDP. This is the effect of some mitigation strategies. Kaya helps quantify the amount of lowered per capita GDP required to meet a CO2 target. Politicians can decide if they want to do that. They don’t, explicitly.

    Another example is increasing the energy efficiency of GDP. This is actually a potentially fertile area for innovation. This will be especially true when we stop focusing on the last term. An example of this is on recent contracts, we are bidding hotelling space only for the technical workforce. (This are call center size work spaces). The expectation is the majority of workforce will work remotely most of the time. Collaboration tools become paramount.

    • “Kaya helps quantify the amount of lowered per capita GDP required to meet a CO2 target.”

      I simply do not believe it or you. This Kaya thing, revised so it doesn’t self-cancel, is somewhat of a measure of past performance.

      If you start tinkering with society, you will also change the thing being measured. Suppose you knocked GDP per capita to ZERO, which is true or nearly true in some third world nations. Do they stop emitting carbon dioxide? No, very likely on a per-capita basis they emit MORE — they burn whatever is handy, wood usually, and the impact on the environment is much worse than a wee bit of global warming.

      Suppose you increased the carbon efficiency of energy — the one thing that would be “win win”. So what happens if the constraints are removed? Population would skyrocket most likely with sufficient energy — between people feeling like they can have more children and probably even a cessation or reduction of war (some people LIKE it so it will never completely go away).

      Suppose you could change the energy per unit of GDP? Well, when anyone here says how exactly that is to be done maybe we can explore it. Essentially that’s the opposite of the industrial age — going back to knitting at home. GDP without energy.

  185. This bears repeating. I’m frankly dumbfounded skeptics here do not realize Kaya is a skeptic’s tool. It is the warmists attacking Dr. Pielke on his blog on this subject.
    Dr. Doug says: July 19, 2014 at 8:59 pm
    The Kaya Identity is certainly a policy tool, if that is what you mean by ‘political tool’. In the text, Pielke uses the Kaya Identity to show how a particular policy would only be feasible given implausible assumptions about future changes in the ratios that make up the Identity. Isn’t that useful?

  186. Jan Kjetil Andersen says:
    July 20, 2014 at 12:42 am
    ————————————————————————————————————————-
    Actually, I am not wrong – the CO2 we exhale does come from the food we eat, that point is correct, but the oxygen that we inhale to produce the CO2 comes from the photosynthetic conversion of any CO2 (regardless of its source) that is present in the atmosphere. This is one of the canards foisted by the CAGW crowd – the CO2 that is being released from the burning of fossil fuels HAS to have been in the atmosphere at some point in the past, hence the higher concentrations of CO2 present in the atmosphere before the carboniferous era. If you reread what I posted, you will see that i wrote that ‘Unless there has been a corresponding explosion in CO2 consuming lifeforms this means that ‘natural’ anthropogenic CO2 emissions will continue to contribute to the increase in CO2 concentrations in the atmosphere’ – the explosion of carbon consuming lifeforms during the carboniferous is what resulted in the reduction of CO2 in the atmosphere at that time and also resulted in the creation of the fossil fuels that we are presently using.

  187. In a comment above I raised the point that determining what happens to carbon dioxide levels is is irrelevant because it is not the cause of global warming. And it is not, as I pointed out, because those proposing that it causes greenhouse warming simply cannot explain why there has been no warming for 17 years. They are so desperate to explain it away that they have started to look for that “missing heat” in the ocean bottom, of all places. This is just an example of how much they wish the stoppage of warming to go away. It has gone so far that they have persuaded their captive science journals to print articles on that stupidity and other unlikely hypotheses. Fact is that their greenhouse theory of Arrhenius is an abject failure and must be discarded. This leaves them with no rational explanation for the pause Somehow nobody on this blog even blinked an eyelash when I said that and most could not be pulled away from thinking that the Kaya identity means something. It does mean something. It means exactly as much as rearranging the furniture on the deck of the Titanic meant after it hit the iceberg. The iceberg for global warming fantasists is 17 years of no warming which their several dozen supercomputers simply cannot explain. Roger Pielke Jr. is a smart man but he has put a huge amount of effort into an aspect of global warming that has no chance of leading anywhere. Instead letting yourself be pulled into fighting side issues, why not concentrate on the main thing: the observed absence of greenhouse warming for the last 17 years? Without greenhouse warming there can be no global warming movement and getting rid of it should be our aim.The warmists are doing all they can to deny the absence of warming by claiming that it has merely slowed down, not stopped. They have minimized it both in AR5 and in NCA and Obama just ignores it. We must be ready to handle any future attempts to cover up or misinterpret what this lack of warming means for global warming, and be ready for novel attempts to deny it.

  188. In his lecture, Pielke rejects emission target mandates, perpetual subsidies, and cap and trade. He promotes expanding energy access to those who lack it, and rejects population control and restrictions on GDP growth. That leaves efficiency improvements and technological breakthroughs as “levers.”

    We don’t want the wealth being squandered on fear mongering propaganda and crony green energy schemes to be redirected to crony research institutions. So, is there any “investment” that might spur innovation?

    How about incentive prizes for a viable thorium reactor design and durable solar roofing that exceed a certain output/cost ratio?

  189. RobertInAz says:
    July 20, 2014 at 11:50 am

    This bears repeating. I’m frankly dumbfounded skeptics here do not realize Kaya is a skeptic’s tool.

    I just posted the same notion here: http://wattsupwiththat.com/2014/07/12/the-beer-identity/#comment-1690445

    Willis got me to thinking outside the box by abandoning Dr. Kaya’s purposes to ponder unintended uses of the identity. Just one example but because this is largely a policy/political tool there are surely other unintended abuses that can be discovered to exploit one’s agenda du jour.

  190. July 20, 2014 at 12:01 pm

    Jan Kjetil Andersen says:
    July 20, 2014 at 12:42 am

    Actually, I am not wrong

    Yes you are.

    Take an example; imagine that the World had had 1 Billion fewer people than today. Well there would be emitted less carbon from the breathing from 1 billion fewer people, but food for 1 billon people would not have been produced. That means that the farms of the world would not have captured the carbon for food for 1 billion people. The less carbon capture on the farmlands equals the less emissions by exhaling CO2. This means that it is a zero sum carbon budget.

    There would probably be more wilderness and less farmland, but the carbon captured in the wild plants is released when the plants rotten. That is also a zero sum budget.

    / Jan

  191. bushbunny says:

    July 19, 2014 at 8:43 pm

    “O/T Do you reckon any of these so called climate change bullshit artists,….”
    =============
    What do you have against artists ?

  192. Jan Kjetil Andersen says:
    July 20, 2014 at 1:55 pm
    Yes you are.
    —————————————————————————————————————————
    No, I am not wrong – but let’s not get in a trivial tit for tat contradictory argument.

    The carbon cycle is called a cycle for a reason – all the CO2 that gets consumed or sequestered will eventually return to gaseous CO2 it started at, it’s just a matter of how long that takes.

    In a simple breakdown of the level of concentration of CO2 in the atmosphere, it does not matter where it came from, what matters is whether the rate of emission of CO2 is greater than the rate of absorption. The sources of emission consist of natural (including ‘natural’ emissions from humans) or anthropogenic (from fossil fuels). Considering that the anthropogenic sources are exclusively from fossil fuels it can be conclusively demonstrated that the current level of CO2 in the atmosphere is most probably due to our consumption of fossil fuels and the resultant emission of CO2. I say ‘most probably’ because if you make an assumption that the natural processes are at equilibrium for emission and absorption of CO2 from the atmosphere then the only source of increase is from the burning of fossil fuels – the spigot in Pielke’s bathtub. Unfortunately, the assumption that natural sources are at equilibrium is false.

    Your example of a 1 billion person drop in the population resulting in a zero sum budget is also false. Disregarding the fact that most of the CO2 removed from the atmosphere is done by microscopic plankton, farms that do not grow food are still teeming with plant life so there is not a net reduction in the plant life capturing carbon. As far as wild plants releasing their carbon when they die and rot, i recommend you study how fossil fuels were formed.

  193. “..Considering that the anthropogenic sources (CO2) are exclusively (coal fired power plants!!!)from fossil fuels…” What about the other GHGs, methane, etc. What about contemporary HC fuels, ethanol, bio-gas methane, wood, bagasse,…..
    “…assumption that the natural processes are at equilibrium…” I do not consider this a valid assumption. There are plenty of good reasons to believe that for a dynamic earth equilibrium does not exist, does not last. CO2 could be ramping up because of gradual warming driven by solar cycles or ocean floor (nobody knows what’s going on down there.) volcanic vents independent from man’s activities (coal fired power plants). Just because we don’t know the answer doesn’t mean we can just fill in man, even though he is the divinely inspired, created, centerpiece of the cosmos. The earth will adjust and accommodate. If we don’t really know why a volcano erupts does tossing in virgins (coal fired power plants) help?

  194. Got carried away. Forgot to mention there is a significant agricultural component to CO2 emissions.

  195. Wow, what a bunch of fuss over something that is pretty simple. The Kaya identity is a way of demonstrating variances – the general, necessary impact of messing with one or more of its terms. For that, I think it’s pretty good. If you want to use it to calculate exactly how much of this or that you need… well… see the last paragraph below. Oh, and don’t get hung up on whether or not CO2 causes the earth to melt, or whatever – that isn’t the point of the KI.

    The Kaya identity is best understood if you *don’t* cancel out the various numerators and denominators. I think everyone is getting hung up on the obvious fact that if you cancel them all out, you get C = C. That is true, but it is a feature, not a bug. This is no different from a trigonometric identity, except that seeing the numerators and denominators side by side triggers old middle school algebra instincts to cancel. Don’t do that – it just confuses things.

    So let’s reformulate it:

    E = q*Ei*Ci

    q = quality of life – i.e. GDP/population is sort of a measure of this. For policy purposes, it’s a lot more interesting than GDP.

    Ei = Energy intensity – don’t worry about what it is made of, for now

    Ci = Carbon intensity – don’t worry about what it is made of, for now

    We can easily see that decreasing emissions requires (Ei and Ci held constant) a decrease in the quality of life – GDP/capita.

    So, if we don’t want to decrease the quality of life, just mess either Ei or Ci.

    And, we can do that.

    And that’s the point of the KI.

    Some have argued that it isn’t precise. In one sense, that’s false – it is, by definition, an identity. But in another sense, it’s true – you can’t really hold some variables constant in the real world. And, of course, there are non-linearities.

    However, this shouldn’t matter. It isn’t meant to be a precise way of tuning policy. In fact, if you are trying to precisely tune a policy, you are committing the fundamental error of progressivism – the idea that you can actually tune things exactly.

    So, this provides a way of *demonstrating* sensitivities, which is useful for explaining the most important policy conclusion: you cannot significantly reduce emissions without either hurting quality of life, or making dramatic *independent* improvements in Ei or Ci, and you need to thus look at the likelihoods of those improvements and their (invisible in this identity) impact on GDP/P.

    • John Moore says “The Kaya identity is best understood if you *don’t* cancel out the various numerators and denominators. I think everyone is getting hung up on the obvious fact that if you cancel them all out, you get C = C. That is true, but it is a feature, not a bug.”

      Of course it is a feature. *I* wouldn’t use it, but what do I know about persuading billions of people that I am a brilliant scientist?

      It makes no difference if you cancel or don’t cancel

      Suppose 10 = 7 * (6/7) * (5/6) * (10/5) (the numerator in the fourth term on RHS must be the same as the LHS term). In fact, it doesn’t make the slightest difference what numbers you use along the way so long as you remember that the numerator of each term is the denominator of the next.

      Obviously, if you have actually *measured* something, then feel free to insert it, at which point it ceases to be the Kaya Identity.

  196. Dr. Roger Pielke Jr.
    Please answer me this question: What is the half life of CO2 in the atmosphere?

    I think I should also do a followup question: Do you believe that any CO2 released into the [atmosphere] remains in the atmosphere?

  197. Greg Cavanagh says: July 20, 2014 at 7:35 pm
    Dr. Roger Pielke Jr.
    Please answer me this question: What is the half life of CO2 in the atmosphere?

    Not relevant to the Kaya discussion, Outside his area of expertise.

    I think I should also do a followup question: Do you believe that any CO2 released into the [atmosphere] remains in the atmosphere?
    Hmm, the presence of CO2 in the atmosphere makes the answer to this trivial. Perhaps you want to rephrase.

    p.s. I’m not Dr. Pielke.

    • RobertInAz quoting a question from Greg: “Do you believe that any CO2 released into the [atmosphere] remains in the atmosphere?”

      Robert says “Hmm, the presence of CO2 in the atmosphere makes the answer to this trivial. Perhaps you want to rephrase.”

      Trivial and yet you choose not to declare your answer.

      “p.s. I’m not Dr. Pielke.”

      No doubt. I suspect he would say that any particular molecule of CO2 is eventually going to be taken up in some way — such as turned into a carbonate rock or into plant cellulose.

      • All this blah blah about how much CO2 is or remains in the atmosphere is orthogonal to the subject at hand.

      • John Moore — the subject at hand had changed. In a few minutes it may change again. Indeed, you have already changed it from a discussion of how LONG does CO2 remain in the atmosphere to how MUCH is or remains in the atmosphere.

      • @Willis “According to the Kaya Identity, what happens to the amount of CO2 emitted from doubling those variables?

        Well … nothing. No change in the slightest. The population and the GDP and the energy used all appear in both the numerator and the denominator, so they cancel each other out. ”

        Willis, you failed to note that total energy appears in two terms, not just one. That means that your numbers require the carbon intensity of energy production to be reduced by the increase in total energy.

        So, after you plug in the numbers, go back and look at the values of each of the four ratios and you will see this.

        The key to using this is to NOT cancel things out in the equation, and to look at the final values of the four ratios, not just the final value of each side, which will, of course, be equal to E.

        And that is why the identity is useful: Plugging in the numbers shows these interdependencies.

  198. And if CO2 has no meaningful impact on global warming or ice caps melting or sea levels rising or hurricanes blowing or people sweating it’s all a bunch of moot gum flapping.

    • “And if CO2 has no meaningful impact on global warming or ice caps melting or sea levels rising or hurricanes blowing or people sweating it’s all a bunch of moot gum flapping.”

      If everybody believed that, you would be right. They don’t.

  199. John Moore: You take the liberty of holding some ratios constant; I’ll take the liberty of holding some of Kaya numbers constant: If the GDP grows twice, everything else being constant, CO2 production does not. change. If the population doubles, everything else being constant, CO2 production does not change.

    Does it make sense? Of course not, even though it is mathematically true. The issue is that in the real world all parts of the identity influence each other – holding selected numbers or ratios constant does not make sense. If Kaya identity nudges you in that direction, better check twice.

    • The equation doesn’t address GDP – it addresses GDP per person. If you want to play with the GDP, note that the carbon emission only holds constant (for constant population) if you halve the energy usage per GDP. And if you do that, it does make sense.

      If you don’t do that, the equation shows that emissions go up. And that, also, makes sense.

      Put another way, the equation shows that to double the GDP while holding emissions constant, you have to halve the Energy/GDP. And that’s the whole reason that it’s valuable – it shows that the Energy/GDP is a big constraint on your ability to hold down emissions while increasing GDP.

      Note that for the above analysis, to make explanation simpler, I assumed that P is constant and Ci is constant. This sort of holding variables constant is normal in multivariate analysis. In the real world Ci and Ei are closely tied together, but my point holds.

  200. Oh, and don’t get hung up on whether or not CO2 causes the earth to melt, or whatever – that isn’t the point of the KI. – John Moore
    = = = = =
    The “identity” is built on the very premise that our CO2 emissions are warming the planet dangerously, and thus must be limited. The truth value of that premise does matter. 17+ years of accelerated emissions but no warming is not a problem for you? It is healthy and scientific to be “hung up” on falsification of the hypothesis by the real world, because a false hypothesis is not one you would want to cling to or agonize over for the rest of your life. What a tragic waste of time that would be.
    “If everybody believed that [CO2 did not have a meaningful impact], you would be right.” – John Moore
    = = = = =
    Wrong. Truth is not established by consensus: truth is established by the real world, not by its representations or representatives. The real world, despite popular beliefs, indicates “no meaningful impact” for CO2.

  201. Mike Tremblay says:
    July 20, 2014 at 4:10 pm

    Your example of a 1 billion person drop in the population resulting in a zero sum budget is also false. Disregarding the fact that most of the CO2 removed from the atmosphere is done by microscopic plankton, farms that do not grow food are still teeming with plant life so there is not a net reduction in the plant life capturing carbon. As far as wild plants releasing their carbon when they die and rot, i recommend you study how fossil fuels were formed.

    Thank you for the answer Mike, but I do not follow you in this.
    We all know how fossil fuels where formed, that is trivial. The thing is that only a tiny fraction of the plants and animals are sedimented and form fossil fuels. The overwhelmingly bigger part rot and release the carbon when the plants die.

    However, one part that do not rot and release carbon is the one that is used for making food. The Carbon in that part is released when we breathe, but it makes no difference in the carbon budget since microbes in the rotting process would have released if that food had not been made.
    /Jan

  202. Here’s my problem with the Kaya Identity. To refresh my tired memory, here is the identity again.

    CO2_{emissions} = Population * \frac{GDP}{Population} * \frac{Energy}{GDP} * \frac{CO2_{emissions}}{Energy}

    Suppose we put in the actual numbers of today for population, GDP, CO2 emitted, and the rest. This gives us the current amount of CO2 emitted today.

    Now, suppose that the population doubles and the GDP doubles and the energy used doubles. That seems like a very probable change, that in the future we’ll have more people using more energy and producing more stuff.

    According to the Kaya Identity, what happens to the amount of CO2 emitted from doubling those variables?

    Well … nothing. No change in the slightest. The population and the GDP and the energy used all appear in both the numerator and the denominator, so they cancel each other out. As a result, the conclusion has to be that a doubling of the population combined with a doubling of the GDP and a doubling of the energy used will have no effect on CO2 emissions.

    Does anyone believe that doubling the population and doubling the GDP and doubling the energy used will NOT change CO2 emissions? Yet that is exactly what the Kaya Identity says.

    What am I missing here? As an identity the Kaya Identity is assuredly true, but how is this useful in the real world?

    w.

  203. Jan Kjetil Andersen says:
    July 20, 2014 at 9:32 pm
    —————————————————————————————————————————
    Simply put Jan, the rotting process does not return all the carbon to the atmosphere in the same amount of time as consumption by people, and as such it acts as a carbon sink compared to human consumption. To give an example, somewhere in the past I remember someone saying that it takes 1 acre of farmland to feed 1 person for 1 year. Now, given that nearly 100% of CO2 absorbed from the atmosphere by that acre will be returned to the atmosphere by the consumption of the food produced from that acre within the same year, there will be a zero net change in the atmospheric CO2 concentration over the course of one year for that acre.

    Now, the fact is that in order to create one acre of farmland, one acre of undeveloped land must be converted to farmland, and since the undeveloped acre is not used to produce food, and because the process of decay is much slower, the time to return 100% of the CO2 sequestered by that same acre is on the order of tens of years for grasslands, hundreds of years, in the case of forests, or millions of years, in the case of swamps and jungles. All of this means that any undeveloped land, when developed into farmland, is removed from the negative CO2 balance into the zero CO2 balance and effectively becomes a net CO2 increase – in other words, before the land is developed it is removing CO2 from the atmosphere, and after it is developed it is not , even though it is not emitting CO2, so effectively all the CO2 produced by the human dependent upon that acre of farmland is being added to the balance of CO2 in the atmosphere.

    If we expand this to the whole biologically related balance of CO2 production and consumption, and make another false assumption that the non-biological/non-anthropogenic CO2 balance is in equilibrium, (ie. CO2 emission from volcanic sources is in equilibrium with CO2 absorption by metallic ions), you can see that any increase in the CO2 producing (animal) populations has to be matched by an increase in the CO2 consuming (plant) populations in order to maintain zero increase in the CO2 concentrations in the atmosphere. In fact, in real terms this population matching is rarely achieved, with constant ‘boom and bust’ cycles in the living populations of both plants and animals. Thus, we see in the geological record, and in the present Keeling curve, natural cycling of the CO2 concentration curves – and this provides a possible explanation of the increases and decreases in CO2 concentrations in the past that cannot be provided by man’s consumption of fossil fuels.

  204. Wow, scary stuff in print.
    The excuse a politician needs to implement population reduction strategies under the guise of building a better world.

    Where have we heard that before?

    And the excuse? “It’s mathematical. To save the planet, we must take active measures to reduce the population.” All the factors in the equation have the same end. Reduce population, reduce GDP (standard of living), reduce energy consumption. Fact is, energy consumption has been an integral factor in current longevity. (Think refrigeration to keep food cold to keep bacteria from growing.)

    For those thinking we aren’t already taking active measures, look at Obamacare;
    Driving up the cost of healthcare makes it less available.
    Open border without sending ill people to quarantine?
    Escalation of costs in food and energy?

    I never thought I would see such things in my day.

  205. Willis Eschenbach says:
    July 20, 2014 at 9:48 pm
    What am I missing here? As an identity the Kaya Identity is assuredly true, but how is this useful in the real world?
    ————————————————————————————————————————-

    As I understand how Dr. Pielke presented it, it is useful if you want to establish an emission goal and want to know what the consequences will be for the GDP, Population growth, and energy consumption. To me, it obviously fails if you want to establish zero emissions – which is the purported goal – unless you commit to the absolute conversion of all energy sources from carbon based to non-carbon based energy sources.

    IMHO, since it was created by an economist, it is very similar to the obsession that economists had with reducing the deficit (carbon emissions) while ignoring the fact that as long as there was a deficit the national debt (CO2 concentrations in the atmosphere) was increasing. You can’t stop the national debt from increasing until you reduce the deficit to zero, and you can’t reduce the national debt until put the deficit into a surplus – something that in terms of CO2 concentrations, will never be achieved in our lifetimes, the lifetimes of our children, nor the lifetimes of our grandchildren.

  206. My take is the Kaya Identity is correct and useless. Here is my Pop Identity:
    Population = Males + Females

    It is correct and useless for forecasting purposes because it does not tell me how many males and females in any given year in the future. But it is accurate in any given year in the past.

  207. I see that this blog fudges the difference between an equation and an identity.

    The difference is simple at first sight: the sign for an equation is “=” but for an identity is 3 horizontal bars.

    You prove an identity to be true using mathematics. In mathematics identities can be solved or not. If solved they are true. If not solved they may be true or not. Maybe somebody else can solve and identity I cannot solve. If an identity is true it is true because of the tautological nature of mathematics.

    You don’t prove an equation by mathematics. In fact, if an equations sets out a law of nature or your theory how nature works, you can never prove it to be true. You may or may not be able to show that it is false. If the relationship is not capable of being proven false, then it is not science.

    The method of showing a relationship to be false is: the hypothesized relationship becomes unsatisfactory for explaining the observations of interest. You need a new theory.

    So Newton’s laws of motion were not false for Civil War artillery 150 years or so ago . But the same physics do not explain many phenomenon related to GPS satellites and their receivers which use the theory of special relativity developed by Einstein a little over 100 years ago..

    The Kaya Equation describes a theory about the behavior of nature. Whether or not it will be falsified depends on whether or not it explains observations better than some other theory. If the Kaya Equation is not satisfactory for the purpose it was put forward we will say that it has been falsified.

  208. The question was asked, Why all the fuss about the difference between emissions from fossil fuels and other fuels? Or, why did Dr Murray Salby lose his job?

    Murray Salby is a leading climatologist, author of a leading university textbook in atmospheric physics a new edition of which is on my bookshelf. Dr Salby was fired from Macquarie University. reason. We do know that he had given a lecture in which he claimed that most of the CO2 in the atmosphere was not generated from fossil fuels but from other sources.

    We have a new paper by multiple authors that you can read for yourself on this subject because it is open source (free).

    Simulating the integrated summertime ?14CO2 signature from anthropogenic emissions over Western Europe, D. Bozhinova, M. K. van der Molen, I. R. van der Velde, M. C. Krol1,, S. van der Laan, H. A. J. Meijer, and W. Peters. Atmos. Chem. Phys., 14, 7273-7290, 2014, URL: http://www.atmos-chem-phys.net/14/7273/2014/

    Abstract: “We find that the average gradients of fossil fuel CO2 in the lower 1200m of the atmosphere are close to 15 ppm at a 12 km×12 km horizontal resolution.”

    My comment: The significance of this is that total CO2 in the atmosphere is usually taken as about 400 ppm now and 280 ppm before the onset of the industrial age.

    Main text:

    “Radio carbon dioxide (14CO2) can be used to determine the fossil fuel CO2
    addition to the atmosphere, since fossil fuel CO2 no longer contains any 14C.”

    Figure 4(B) on page 7281 shows the maximum observed fossil fuel CO2 (ffCO2) as 50 ppm.

    My comments:

    For densely-populated Western Europe the study recorded only 3.75% as the average fossil fuel CO2 in the lower 1200 meters (4,000 ft) of the atmosphere and only about 12.5% as the maximum before diffusion.

    Vertical diffusion of CO2 above 1200 meters has the effect of reducing the average percentage of fossil fuel CO2 percentage because only 15% of the mass of the atmosphere is below 1200 meters, while about 60% of its mass is between 1200 meters and top of the troposphere (about 10,000 meters). In addition, lateral diffusion takes place west to east and north to south.

    The average percentage of fossil fuel CO2 in the atmosphere must half or less the average below 1200 meters in Europe and even lower for the whole globe.,

  209. Willis Eschenbach says:

    “Suppose we put in the actual numbers of today for population, GDP, CO2 emitted, and the rest. This gives us the current amount of CO2 emitted today.

    Now, suppose that the population doubles and the GDP doubles and the energy used doubles. That seems like a very probable change, that in the future we’ll have more people using more energy and producing more stuff.

    According to the Kaya Identity, what happens to the amount of CO2 emitted from doubling those variables?

    Well … nothing. No change in the slightest. The population and the GDP and the energy used all appear in both the numerator and the denominator, so they cancel each other out. As a result, the conclusion has to be that a doubling of the population combined with a doubling of the GDP and a doubling of the energy used will have no effect on CO2 emissions.”

    CO2emissions = pop*GDPpc*EnergyIntensity*CO2Intensity

    If both population and GDP double, that means GDP per capita is unchanged. If both GDP and energy use double, that means energy use per unit of GDP (energy intensity) is unchanged. Assuming the same CO2 emission intensity (CO2 emissions per unit of energy unchanged), CO2 emissions will exactly double in your scenario.

    • Edim says “Assuming the same CO2 emission intensity (CO2 emissions per unit of energy unchanged), CO2 emissions will exactly double in your scenario.”

      How about just assuming that the Kaya Identity is useless? You cannot just “assume” the fourth term is unchanged and still call it mathematics.

      If you double energy in the third term (2E/GDP), you must also double it in the fourth term (CO2/2E) and the net effect is that the doubling of the numerator, divided by a doubling of the denominator, is “1″ or unchanged.

      You are quite right, as is everyone else here that refuses to process an algebraic equation as an algebraic equation but do please understand all the people that DO process algebra using the rules of algebra. What is this world coming to when sometimes an equation isn’t an equation?

  210. After a all of this commentary, Willis still declines to read and understand the text accompanying the ambiguous formula.

    Willis continues to repeat his initial misunderstanding.

    Sad.

    • RobertInAz says “Willis continues to repeat his initial misunderstanding. Sad.”

      And you continue to repeat yours (and I, mine, etc). Not sad! I haven’t had this much engagement in quite a while. I had no idea how few people can work ordinary algebra, or lay something out that deliberately looks like algebra but we are assured that it isn’t (you could, of course, lay it out differently so that it means what you seem to think it means).

  211. Willis Eschenbach says: July 20, 2014 at 9:48 pm
    Now, suppose that the population doubles and the GDP doubles and the energy used doubles. That seems like a very probable change, that in the future we’ll have more people using more energy and producing more stuff.

    According to the Kaya Identity, what happens to the amount of CO2 emitted from doubling those variables?
    For this toi play, the CO2 efficiency of energy production doubles. So if today, a KW of energy production emits 100 KG of CO2 – in the doubled population/GDP/Energy scenario, it will emit 50 KG of CO2. Kaya tells us this type of progress is implausible.

    In Willis’s thought problem, Population doubles, GDP per person stays the same, Energy per dollar GDP stays the same, so the CO2 efficiency of energy production must double to keep total CO2 constant.

  212. Willis, if you cancel everything out, of course you get CO2emissions = CO2emissions, but that’s not the Kaya Identity anymore. Furthermore, it doesn’t mean “no change in the slightest”, it means:

    CO2emissions(after your doublings) = CO2emissions(after your doublings)

    It may be undetermined, but it’s correct.

    However, if you use the Kaya Identity and its factors, then you can calculate the emissions if you know the factors (pop, GDPpc, EnergyIntensity, CO2Intensity).

  213. No, Willis is wrong, maybe not even wrong. If population doubles and the rest (GDPpc, energy intensity, emission intensity) stays the same, emission doubles, by definition.

    • Edim says: “No, Willis is wrong. If population doubles and the rest (GDPpc, energy intensity, emission intensity) stays the same, emission doubles, by definition.”

      No, you are wrong.

      1. Nothing else “stays the same” if population doubles (duh).
      2. The Kaya Identity DOES NOT ALLOW you to double population without changing anything else.

      C = P * (G/P) * (E/G) * (C/E).

      Double P

      C = 2P * (G/2p) * (E/G) * (C/E).

      No change in “C”. The 2 in the numerator divided by 2 in the denominator leaves 1, the multiplication identity.

      And that is exactly correct! If you were to “suddenly” double the population, they would share the same productivity, or in other words, GDP divided among twice the people!

      Incredibly, the Identity does actually work — it shows that tinkering with “just” population isn’t going to work, neither changing “just” GDP.

      The only independent variable is “C” so if you want less “C” well then just make less of it.

  214. Curious George says: July 21, 2014 at 7:27 am
    “Edim dear, Robert dear, put numbers directly in Kaya. Willis is right.”

    Before:
    Total CO2 = 100
    Total population = 10
    GDP/Person = 10
    Energy/GDP = 1
    CO2/Energy = 1
    100 = 10 * 10 * 1 * 1.

    Total population = 20
    GDP/Person = 10 (unchanged – GDP doubles)
    Energy/GDP = 1 (unchanged – Energy use doubles)
    CO2/Energy = 1 (unchanged – energy efficiency remains constant)

    200 = 20 * 10 * 1 * 1.

    In order to get this wrong, you have to very carefully ignore the text that accompanies the ambiguous formula and you have to studiously ignore the many explanations in this thread about what Kaya means.

    So yes. If you continue to insist on ignoring reality – then Willis is right.

    • RobertInAz says “In order to get this wrong, you have to very carefully ignore the text”

      Actuallly, you have to ignore the formula/identity or whatever one wants to call it.

      Using your example, but the Kaya Identity, you start with

      Before:
      Total CO2 = 100 (C)
      Total population = 10 (P)
      GDP/Person = ? Cannot be determined but lets say GDP is 100 so 100/10 = 10 (G/P)
      Energy/GDP = ? Cannot be determined but lets say Energy (E) is 100 so 100/100 =1 (E/G)
      CO2/Energy = ? This can be measured but is specified as C/E or 100/100 = 1.
      100 = 10 * 10 * 1 * 1.

      Total population = 20

      Total CO2 = 100 (C)
      Total population = 20 (P)
      GDP/Person = ? Cannot be determined but lets say GDP is 100 so 100/20 = 5 (G/P)
      Energy/GDP = ? Cannot be determined but lets say Energy (E) is 100 so 100/100 =1 (E/G)
      CO2/Energy = ? This can be measured but is specified as C/E or 100/100 = 1.
      100 = 20 * 5 * 1 * 1.

      As you can see, the Kaya Identity moves some factors around but the result is unchanged. More pop, less GDP per person, all the same!

      Ah, but you said not to change any other term — the Kaya Identity does not allow that. If you change population in the first term, why do you not change it in the second term? If you change GDP in the second term, why do you not change it in the third term?

      Obviously if “G is not G” and “P is not P” and so on, then you can do anything you like and it will have all the respect it deserves (not much, in other words).

      Plainly you are *working* from something that is not the Kaya Identity. Why do you defend the indefensible? Acknowledge that the “identity” is mathematically useless and not even a very good persuader. You and others argue “what if we double population but don’t change anything else”. Well how likely is THAT?

  215. Willis, if you were to pay attention to the conversation you started OR to the actual way that the Kaya Identity is used (see Pielke!), you would know that this is nonsense:

    Willis (yesterday, 9:48 pm):

    Now, suppose that the population doubles and the GDP doubles and the energy used doubles. … According to the Kaya Identity, what happens to the amount of CO2 emitted from doubling those variables? Well … nothing. No change in the slightest. The population and the GDP and the energy used all appear in both the numerator and the denominator, so they cancel each other out. As a result, the conclusion has to be that a doubling of the population combined with a doubling of the GDP and a doubling of the energy used will have no effect on CO2 emissions.

    The Kaya Identity starts with the working assumption that each of the ratios remains constant. If CO2 emissions per unit of energy remains constant, then emissions in your scenario would double, of course.

    To be sure, as Pielke discusses, the ratios in the Kaya Identity do not remain constant over time. Energy/GDP tends to fall due to both technological change and (what I prefer to call) structural change in the economy. CO2/energy may fall due to both technological change and structural change in energy sources. The Kaya Identity, as competently used, accounts for all this and puts it into a framework that (i) aids our understanding and (ii) helps to identify what might (or might not) feasibly be done to change outcomes. Pielke uses the Identity to show how Britain’s official energy policy cannot plausibly achieve its goals.

    Willis, you waste people’s time and show great disrespect when you take uninformed and misguided pot shots at others’ analysis. Please, inform yourself now about how the Kaya Identity is actually used — and put into practice the first rule of holes.

  216. Willis said at 9:48 pm “Here’s my problem with the Kaya Identity …. what happens to the amount of CO2 emitted from doubling [all] those variables? Well … nothing“.

    If you take my earlier simplified formula up-thread A/B * B/C * C/A = 1 (which is equivalent Kaya-style to C = B * A/B * C/A) and assume both A and B double in unit time dt, then differentiating by time produces: dC/dt = dB/dt * A/B * C/A + B * d(A/B)/dt * C/A + B * A/B * d(C/A)/dt
    where dB/dt = B (it doubles in unit time); d(A/B)/dt (change in A/B in unit time) = 0 (A/B remains the same) and d(C/A)/dt = (dC/dt A – dA/dt C) /A*A where dA/dt = A (again it doublea in unit time), so d(C/A)/dt = (dC /dt – C) / A.

    Thus dC/dt = B * A/B * C/A + 0 + B * A/B * (dC /dt – C) / A, giving dC/dt = dC /dt.

    So (extrapolating no more than a little to the full “formula”) Kaya actually predicts that the amount of CO2 emitted from doubling all the variables is (drumroll please …) whatever the increase in CO2 happens to be.

    I don’t believe this greatly assists either side of the debate …

  217. Willis Eschenbach says:
    July 20, 2014 at 9:48 pm
    “Now, suppose that the population doubles and the GDP doubles and the energy used doubles. That seems like a very probable change, that in the future we’ll have more people using more energy and producing more stuff.

    According to the Kaya Identity, what happens to the amount of CO2 emitted from doubling those variables?

    Well … nothing. No change in the slightest. The population and the GDP and the energy used all appear in both the numerator and the denominator, so they cancel each other out. As a result, the conclusion has to be that a doubling of the population combined with a doubling of the GDP and a doubling of the energy used will have no effect on CO2 emissions.”

    Heh. Can we really be ~1000 posts in on something that is a simple math mistake?

    Let’s take a look at the math:

    CO2(1)=2P*(2GDP/2P)*(2E/2GDP)*(2E/2CO2) equation 1
    CO2(2)=P*(GDP/P)*(E/GDP)*(E/CO2) equation 2

    Divide equation 1 by equation 2 to get the ratio of CO2(1) to CO2(2)

    Gives you a ratio of 2:1 (we have one more 2 in equation 1 than gets cancelled out by the ratios).

    Cheers, :)

  218. D’oh. I flipped the last term in my equations 1 & 2 – should read 2CO2/2E and CO2/E respectively. The rest of my post is still good though.

    Cheers, :)

  219. Oops – I marked the change in the wrong variable. It is the energy usage per GDP which must magically be cut in half. The principle remains…

    I’ll add in numbers to show what I mean (when energy usage and GDP double).

    Let’s pick arbitrary values to start with:

    GDP = 1000
    P = 100
    TE = 50
    C = 20

    So C = 100 * 1000/100 * 50/1000 * 20/50 = 20
    Double GDP and P

    C = 200 * 2000/200 * 50/2000 * 20/50 = 20

    BUT: notice that the third term went from 50/1000 to 50/2000 – the Energy per GDP must be cut in half to hold carbon emissions constant. And that is the whole point of the equation.

  220. “For this toi play, the CO2 efficiency of energy production doubles. So if today, a KW of energy production emits 100 KG of CO2 – in the doubled population/GDP/Energy scenario, it will emit 50 KG of CO2. Kaya tells us this type of progress is implausible.”

    The recent EPA regulation limits US power generation to 1,100 pounds of CO2 per MWh, goal is 30% CO2 reduction, 2.2% of global total. Oh, boy!!

    My back of the envelope has coal/steam at about 2,200 lb/MWh, NG/steam at about 1,100 lb/MWh, simple CT at around 1,100 lb/MWh, NG combined cycle at around 600 lb/MWh. It’s all about efficiency, aka heat rate. A major shift away from coal to NG and CC is not only plausible, it’s a happenin’ raht now!

    NG produces about half the CO2 per Btu as coal, bur twice the water vapor!
    Observed a fracing operation in 1967 as an summer engineer & it wasn’t news then.

  221. Mike Tremblay says:
    July 20, 2014 at 11:25 pm

    Simply put Jan, the rotting process does not return all the carbon to the atmosphere in the same amount of time as consumption by people, and as such it acts as a carbon sink compared to human consumption.

    Firstly I see that we agree on a lot.
    1. We agree that some of the plant material which would grow in the wild if we produced less food would rot and release the carbon back to the atmosphere.
    2. We agree that it takes some time from the carbon capture in the photosynthesis to the rotting and that this time is highly dependent on the type of vegetation.
    3. We agree that some fraction of the plant material will not rot; it will sink in anaerobe sediments and eventually grow new fossil carbon.

    What we may disagree on is the amounts and the times. I think the fraction in 3 is so small that we can count it out of the equation. I don’t have the numbers for that, but it would surprise me if it is more than 1 percent.

    So let us count out 3 and concentrate on 1 and 2.

    , the time to return 100% of the CO2 sequestered by that same acre is on the order of tens of years for grasslands, hundreds of years, in the case of forests, or millions of years, in the case of swamps and jungles.

    You claim that the rotting process takes from decades to millions of years to bring back the CO2 to the atmosphere. I do not think so because you would then have seen all the carbon stored on those places. If it had taken two decades for grasslands to rot the grass, you would have found the two decades of dead grass in the soil. Likewise if it has taken a million year to bring the carbon captured in the jungle back to the atmosphere, you would have found a layer of one million year of plant growth in the jungle soil. You will not find that.
    The time from plant growth to plant rotting has to be much shorter than that.

    If the time for plants to rot in the wild equals the time from food production to food consumption then there would be a 100% zero sum budget as I described. However, you are probably right that the plant rotting in the wild on average takes a little longer than the time from food production to consumption. I would guess between five and ten years, but that only means that we have a delay in the emissions. I consider a delay in the emissions of less than a decade as quite negligible.
    /Jan

  222. The term Kaya Identity should have quotes around “Identity”, as it isn’t actually an identity. It’s simply a definition of a hypothesized functional relation amongst several variables, i.e., it defines what one could call the Kaya Function or Relation. Or one could call it the Kaya Hypothesis. To do otherwise is sloppy jargon.

  223. Michael 2 says:
    July 21, 2014 at 2:35 pm
    “And that is exactly correct! If you were to “suddenly” double the population, they would share the same productivity, or in other words, GDP divided among twice the people!”

    This is only true for “sudden” changes. Real life changes will happen gradually. Doubling the population will create *over time* twice as much demand for stuff, which will require twice as much supply for stuff.

    Cheers, :)

    • Shawnhet says “Doubling the population will create *over time* twice as much demand for stuff, which will require twice as much supply for stuff.”

      MAYBE. It depends upon the price elasticity of demand as well as simple demand. It could simply lead to scarcity and higher prices (ie, DeBeers diamonds) or *substitution*. DeBeers is a good example since not so long ago demand didn’t exist and has been made to exist solely through advertising.

      Eventually you hit Malthusian limits on any commodity where doubling the population simply does not and cannot double the supply. I suspect that to a certain extent all nations on earth are already pushing against this limit. I doubt a nation exists anywhere that can just double its supply of anything to meet the demand of a doubled population.

      Conversely, cutting a population in half is not necessarily going to cut demand (and carbon dioxide) in half. The remaining half will simply be more affluent and in fact this is seen in all modern nations with low birthrates.

      Already I sense in the United States a lessening of the work ethic, GDP could go down and perhaps already is, simply because today’s youth (certainly my offspring) generally don’t want to work as was done in the 1950′s when post-war industrial capacity was high and depreciation low.

  224. My experience is that when you think it is hard to understand a formula or identity, it helps to put in some figures.

    Kaya: C= P*(GDP/P) * (TE/GDP) * (C/TE)
    The figures for the world in 2007 are:

    Population: 6. 665 billion
    CO2 emission per Year: 29.7 billion ton
    Energy use: 494 Quadrillion BTU (or 145 000 TWH)
    GDP: 63 Trillion USD

    This means that the average GDP/Capita was 9550 USD /year
    And the average Energy efficiency (TE/GDP) was 2.3 KWH per dollar
    And the average carbon intensity of energy was 0.205 Kg CO2 per KWH.

    Then we have a framework for estimating how much we must improve energy efficiency or reduce carbon intensity of energy production if we shall reach a given goal for reduction of the CO2 emissions.

    If the population doubles and all other factors are kept constant the emissions will of cause also double.

    Source: http://books.google.no/books?id=vebDRK0a6OAC&pg=PA130&lpg=PA130&dq=kaya+energy+per+gdp&source=bl&ots=rA6RHsvdRQ&sig=kEx99Im6kmlQBqKVGHVxU32AEoI&hl=no&sa=X&ei=o5bNU4-SOcX-ygP1_YLQAw&ved=0CEMQ6AEwBQ#v=onepage&q&f=false

    /Jan

    • Jan Kjetil

      Kaya: C= P*(GDP/P) * (TE/GDP) * (C/TE)
      The figures for the world in 2007 are:

      Population: 6. 665 billion
      CO2 emission per Year: 29.7 billion ton
      Energy use: 494 Quadrillion BTU (or 145 000 TWH)
      GDP: 63 Trillion USD

      And you get C = C.

      It’s a good thing you already knew “C” — 29.7 billion tons!

      Let’s cut population in half. It’s in the numerator and denominator — no change!

      Lets cut GDP in half. It’s in the numerator and denominator — no change!

      Cut C02 in half — success!

      “If the population doubles and all other factors are kept constant the emissions will of cause also double.”

      No. But let’s try it, simplifying the numbers a bit, using “terms” instead of “factors”. Up until now, chaging a FACTOR, such as population, is instantly and immediately canceled in the next TERM.

      So — doubling P, but keeping the next TERM at the same RATIO, requires to double GDP (not that you or I can actually do that, this is a theoretical exercise).

      And if you double GDP, and you want the third term to maintain ratio, you must double TE. Good luck with THAT.

      And if you want the fourth term to remain the same, you must double CO2.

      And because it is a tautology or identity, you double what you started with. Thus, it doesn’t matter what it is, you must double it — but only in the scenario that you really think you can double GDP and Total Energy.

      In practice doubling population will approximately halve the per-capital energy (and DP) depending on where you live.

      In practice you have really just doubled energy production with its attending carbon dioxide. The other terms are irrelevant.

  225. Michael 2 says: July 21, 2014 at 2:39 pm
    “I had no idea how few people can work ordinary algebra, or lay something out that deliberately looks like algebra but we are assured that it isn’t (you could, of course, lay it out differently so that it means what you seem to think it means).”

    Michael,
    You and illis and a few others continue to interpret the formula on page 12 of the report in a way that is different from the immediately preceding text. To repeat that text one more time (it is on page 12). CO 2 emissions. 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:
    .
    The following formula does not reflect this text:
    CO 2 emissions = Population x (GDP/Population) x (Energy/GDP) x (CO 2 /Energy)
    It should read
    Total CO2 emissions from energy production =
    Total population * (GDP/Person) * (Energy / GDP Unit) * (CO2 Units / Energy Unit)

    That is what the text says. These two formulas are different. Willis keeps pulling up the ambiguously framed formula and does not understand or fails to acknowledge the difference between the formula and the text.

    That said, the correct formula can be re-framed less usefully as:
    b> Total CO2 emissions from energy production =
    Total population * (Total GDP/Total population) * (Total Energy / Total GDP) * (CO2 Units / Energy Unit) and you can cancel to get

    b> Total CO2 emissions from energy production = (Total Energy ) * (CO2 Units / Energy Unit)

    But you cannot cancel out total energy against the Energy Units variable in the CO2 efficiency of energy production term. Energy Unit is simply a unit of measure.

    The proper Kaya formulation is more useful because focusing solely on the CO2 efficiency of energy production term has unfortunate side effects such as also decreasing GDP.

    • Robert says: “To repeat that text one more time (it is on page 12).”

      You can re-read mine a few times too.

      “continue to interpret the formula on page 12 of the report in a way that is different from the immediately preceding text.”

      Well there you go. You ignore the obviously flawed formula that doesn’t capture the meaning of the text. But it *is* that formula that is on display for a bit of ridicule. Laugh at it with the rest of us. It’s amusing and it draws a lot of attention to the “text”. There’s no such thing as bad press.

      As to the problems in the text, others have discussed them at length according to how important each term is to them personally. Yours (and mine) is on the energy term — the only thing directly amenable to change, and also the only thing that can be accurately measured. It should not be calculated, it should be MEASURED and suddenly the tautology vanishes (so do the other terms but they were never there).

  226. Michael 2 says:

    1. Nothing else “stays the same” if population doubles (duh).
    2. The Kaya Identity DOES NOT ALLOW you to double population without changing anything else.

    Michael, these are Willis’ conditions:

    P(2) = 2P(1), G(2) = 2G(1), E(2) =2E(1)), C(2) unknown.

    C(2) = 2P * (2G/2P) * (2E/2G) * (C(2)/2E) and canceling out:

    C(2) = C(2).

    This is undetermined and it cannot be said what happens to CO2 emissions – we don’t know what happens with the emission intensity (C/E). However, assuming the same emission intensity (the same fuel mix or the same carbon content of the average fuel mix), the emission doubles. If the emission intensity is 50% lower, then nothing happens to CO2 emissions (2*0.5 = 1), in spite of the doubling of population, GDP and energy used (Willis’ conditions). In fact, in this case, the doubling of energy used is enough information – population and GDP is irrelevant if we already know the energy used (E) and its CO2 emission intensity (C/E).

    This is exactly why the Kaya Identity is useful – you can analyze the factors that influence the change in emissions (emission intensity, energy intensity, GDP per capita and population).

  227. Michael 2 says:
    Oh? How did you happen to become Keeper of the Table?

    Just an informed opinion. We *are* talking about government here. They have to be seen to do *something*. One thing to consider is how all these people are going to save face when it finally becomes apparent to everybody that CO2 wasn’t such a big issue after all.

  228. In case that isn’t clear to Jan Kjetil and others –

    The proposal is to *constrain the ratios* so that if you double any of them you must double all of them and

    C = C

    becomes

    2C = 2C.

    There’s nothing in the formula that suggests anything is constrained, and there’s nothing in real life to suggest you CAN constrain any of the ratios.

  229. Michael 2 says:
    July 21, 2014 at 6:02 pm
    “MAYBE. It depends upon the price elasticity of demand as well as simple demand. It could simply lead to scarcity and higher prices (ie, DeBeers diamonds) or *substitution*. DeBeers is a good example since not so long ago demand didn’t exist and has been made to exist solely through advertising.”

    I don’t really disagree with you here but remember the context of your original point – that raising the population would somehow be constrained to keep the GDP the same. Your argument would only work if the price elasticity was non-existent (ie the demand can’t change). IOW, your assumption is highly unrealistic.

    “Eventually you hit Malthusian limits on any commodity where doubling the population simply does not and cannot double the supply. I suspect that to a certain extent all nations on earth are already pushing against this limit. I doubt a nation exists anywhere that can just double its supply of anything to meet the demand of a doubled population.”

    The fact that GDP is growing globally argues pretty strongly against Malthusian limits having any practical limiting factors on the economy. Furthermore, the constant dollar cost of almost all commodities is falling even while GDP and population are both rising. Fact is, commodities are becoming less and less important to GDP.

    Cheers, :)

    • Shawnhet says “The fact that GDP is growing globally argues pretty strongly against Malthusian limits having any practical limiting factors on the economy. Furthermore, the constant dollar cost of almost all commodities is falling even while GDP and population are both rising. Fact is, commodities are becoming less and less important to GDP.”

      Thank you for an intelligent conversation that could actually go somewhere.

      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.

      I suggest it is also important to not compare a regional process and a global process although I’ll admit to sometimes doing just that to provoke a discussion. In this case, “population rising” is a global phenomenon but not particularly a regional phenomenon, not in the places where GDP is rising (IMO – more specificity would help). China, having both a rise in GDP *and* Population, achieves this as partly a rebound from the Cultural Revolution and also a massive application of the energy subsidy of coal. The United States seems to have had a substantial decline in GDP a couple of times in the past decade while its population (excluding recent immigrants) is somewhat steady.

      Stated another way, a hyperinflated nation will have soaring GDP on the books, and obviously the per-capita GDP will also soar — but what is actually changing? That nation is sinking! But if we stipulate that all GDP will be in Standard Dollars then it would be more useful.

      Consider Norway — abundant hydropower. That entire nation is practically disconnected from the Kaya Identity. Population? Irrelevant. GDP? Irrelevant. CO2 production per Kilowatt? Nil.

      At the other extreme is a poor African nation — Population high, GDP extremely low, CO2 production per kilowatt? Hard to say when there’s no kilowatts — but they make plenty of CO2 from burning charcoal, wood, and dung.

      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.

      So what can each nation decide to do?

      Pol Pot succeeded nicely with population reduction, so did Lenin and Josef Stalin. Reduce GDP? Many nations can do that simply by meddling in the market or inserting a “deadweight loss of taxation”. How about simply mandating how much CO2 can be emitted? Obama’s EPA is going down that road and we will see how it goes if and when New England is cold and dark in the winter and Democrats have to choose between light and heat and party purity.

  230. I originally agreed with Willis that it seemed a trivial identity, but then I went and read how Dr. Pielke was using it here. I see it now as an heuristic formula to put the scope of lowering emissions to the degree advocated into perspective. It looks useful for that purpose.

  231. Michael 2 says:

    July 21, 2014 at 5:48 pm

    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

    Do you really think scientists are that foolish?
    /Jan

    • Jan Kjetil Andersen “Michael 2, the Kaya identity does not work that way.”

      I sit corrected. Who in their right mind would assume that just because it looks like algebra and is being used in science, that it is indeed algebra being used in science?

      “Do you really think scientists are that foolish?”

      I’m starting to arrive at that conclusion. The foolishness is persisting in defending a thing that any 8th grader on the math track can see is absurd.

      I use Ohm’s Law: E = I * R. This can be restated such that I = E/R, and R = E/I.
      Thus: E = (E/R) * (E/I).

      At least it doesn’t cancel out (E stays in the numerator all the way across).

      But you have the problem of the unknown quantity appearing on both the left hand side and the right hand side.

      The Kaya Identity is sold to the public as a way to calculate total CO2 emissions. Obviously it does no such thing. It is also sold to the public as a way to express the various factors that contribute to CO2 emissions. Because of the self-canceling nature of the formula it doesn’t even do that, and there’s no limit to the number of terms (and their irrelevancy) and arrive at the same conclusion.

      Still, I can see where the Kaya Identity should inform policy in the sense that ACTUAL changes in population probably will actually cancel out — double the population and each person is going to get half the resources with negligible impact on CO2 emissions.

      But scientists, or at least the people HERE advocating for it, say that I must double the population — then double the GDP to keep the ratio the same — then double the energy to keep the next ratio the same — then finally double the CO2 to keep the fourth ratio the same.

      So what actually is the GOAL? The goal is to keep the ratios the same. It seems to have very little to do with reality.

  232. Michael 2 says: July 21, 2014 at 5:48 pm
    Kaya: C= P*(GDP/P) * (TE/GDP) * (C/TE)

    Yet again. . This is not Kaya. This is yours and Willis’s misunderstanding. Again, the full context from the article Willis quotes.
    The simplest way to describe the deep decarbonization of energy systems is by the principal drivers of energy-related CO 2 emissions—for convenience, since the focus of this chapter is on energy systems, we simply refer to them as CO 2 emissions. 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:

    CO 2 emissions = Population x (GDP/Population) x (Energy/GDP) x (CO 2 /Energy)

    The words are correct. The formula which you and Willis constantly reproduce, is wrong.

    PLEASE READ THE WORDS

  233. Michael 2 says: July 21, 2014 at 5:48 pm
    Kaya: C= P*(GDP/P) * (TE/GDP) * (C/TE)

    And for the readers who have not been following this thread, the critical error is bolded above. You can apply the incorrect interpretation to the other terms and get correct answers. Interpreting the last energy term as total energy is what leads to all of the confusion.

    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.

    • RobertInAz says “Interpreting the last energy term as total energy is what leads to all of the confusion.”

      It requires no interpretation. If the denominator of the last term is the same as the numerator of any other term then it makes no difference if you have E/E or TE/TE.

      “The last term is CO2 per unit of energy. It is the CO2 efficiency of energy production. ”

      Indeed it is. I get that and I suspect so do most people here. That’s not what is *written* however and it is the written formula that provides sport. It’s about time the “deniers” get to have a little sport!

  234. Michael 2 says: July 22, 2014 at 8:22 am Indeed it is. I get that and I suspect so do most people here. That’s not what is *written* however and it is the written formula that provides sport. It’s about time the “deniers” get to have a little sport!

    The “sport” thread is here: http://wattsupwiththat.com/2014/07/12/the-beer-identity/
    This is where you, Willis and others can wax lyrical about the not-Kaya formula.

    This thread is supposed to be about Kaya. You are hijacking it because the beer identity thread is an exercise in naval gazing.

    [Rather "Navel gazing", right? 8<) .mod]

    • RobertInAz says “This thread is supposed to be about Kaya.”

      And so it is — all 299 comments!

  235. If you are attempting to apply the Kaya Identity to real world data and keep coming up wth CO2 = CO2 then take that as evidence you are doing it wrong and need remedial help to understand exactly what is implied by a mathematical identity and how they are used. Accept this as fact: Willis got it wrong. Don’t emulate his example. Pielke Jr got it right – give that a try.

    • dp says “keep coming up wth CO2 = CO2 then take that as evidence you are doing it wrong”

      I think I am glad you were not my algebra teacher in middle school, for that is exactly what I get every time I work it.

      “Accept this as fact: Willis got it wrong. Don’t emulate his example. ”

      I do not accept words on my computer screen as fact. I accept them as hints, more or less, which if I find interesting I can study primary resources where that is possible.

      An “identity” doesn’t have constraints. But many here insist that the Kaya Identity DOES have constraints, you cannot change any of the ratios BUT you can still change population. That’s not math. It’s a mind game following your rules and arriving at a conclusion that the rules guarantee. That’s not my game. It’s yours.

  236. RobertInAz says:
    July 22, 2014 at 4:18 am
    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:

    CO 2 emissions = Population x (GDP/Population) x (Energy/GDP) x (CO 2 /Energy)
    —-

    RobertInAz -

    what am i getting wrong

    it seems to me that GDP in (GDP/Population) is not the same as GDP in (Energy/GDP) since the latter is “unit of GDP”

    thanks

    –john eyon

  237. RobertInAz

    nevermind – i figured it out – the equation is simple stuff – the method is bafflingly new to me

    –john eyon

  238. “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.

  239. “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, :)

  240. Michael 2 says:
    July 22, 2014 at 9:24 am

    I use Ohm’s Law: E = I * R. This can be restated such that I = E/R, and R = E/I.
    Thus: E = (E/R) * (E/I).
    At least it doesn’t cancel out (E stays in the numerator all the way across).

    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

    The Kaya Identity is sold to the public as a way to calculate total CO2 emissions.

    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

  241. 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

  242. 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, :)

  243. 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.

  244. 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, :)

  245. 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.

  246. 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, :)

  247. RobertInAz says:
    July 22, 2014 at 12:47 pm

    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.

    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:

    CO2_{emissions} = Population * \frac{GDP}{Population} * \frac{Energy}{GDP} * \frac{CO2_{emissions}}{Energy}

    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:

    CO2_{emissions} = 2*Population * \frac{2*GDP}{2*Population} * \frac{2*Energy}{2*GDP} * \frac{CO2_{emissions}}{2*Energy}

    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:

    - Total Population
    - Per person GDP
    - Energy efficiency of GDP
    - CO2 efficiency of energy production.

    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.

  248. 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.

  249. 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.

  250. 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.

  251. John Moore says:
    July 22, 2014 at 4:14 pm

    “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.

    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:

        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.

        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

        CO2 emissions = population * co2-per-person.

        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).

  252. 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.

  253. RobertInAz says:
    July 22, 2014 at 4:54 pm (Edit)
    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.

    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.

  254. Bart says:
    July 22, 2014 at 4:56 pm

    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 the way to interpret it.

    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?

  255. 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

  256. 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.

  257. 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.”

  258. 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.

  259. 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.

  260. 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.

  261. 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:

  262. Willis Eschenbach says:
    July 22, 2014 at 5:13 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.”

    Reality check here: let’s assume that we double P, GDP and E but keep the CO2/E ratio constant – what happens to CO2 emitted? What happens to CO2 if we reduce the CO2/E by 10%? What happens if instead of assuming a value for the CO2/E ratio, we *measure* it instead?

    • Shawnhet: “What happens if instead of assuming a value for the CO2/E ratio, we *measure* it instead?”

      Then the tautology disappears and the formula can actually be calculated.

    • Shawnhet says: “let’s assume that we double P, GDP and E but keep the CO2/E ratio constant”

      You don’t actually get to do that. Ratios have no physical existence. It is a word that describes an abstraction that exists only in your mind.

      Does the apple know it is being compared to an orange? Probably not.

      You decide what actual physical parameters you CAN change and the ratio might change, might not, depending on how clever or forceful you are.

      I can hardly believe we are all still here arguing about it as if you or anyone else can just change, or not change “ratios”.

      What is changeable are physical things. The ratios of physical things will change as soon as you put your mind to observing the ratio. Until then its like Schroedinger’s Cat, maybe it is a ratio and maybe it isn’t.

  263. Willis, you are clearly misinterpreting the formula. As others have patiently pointed out, the authors include a definition for their formula. Why do you continue to ignore the definition they give? They are practically in the same sentence:

    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:
    CO 2 emissions = Population x (GDP/Population) x (Energy/GDP) x (CO 2 /Energy)

    Your entire argument amounts to “the formula as written is misleading”. Well, sure. If you ignore the definition they give you right above it, when they introduce it to you. And if you ignore how they actually use the formula in the study. So yeah, if you take the formula completely out of context, and make up your own interpretation, then I guess you can argue that.

    How about:

    CO 2 emissions = Population x (GDP/Person) x (Energy/GDP-unit) x (CO 2 /E-unit)

    Does that help? Or are you going to continue to argue that your misinterpretation is the REAL Kaya identity, and keep beating up on that straw man?

    • JamesNV says “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: CO 2 emissions = Population x (GDP/Population) x (Energy/GDP) x (CO 2 /Energy). Your entire argument amounts to ‘the formula as written is misleading’.”

      Or you could just read any of half a dozen of my comments where I write that very thing. It makes no difference how many times you re-write the exact same formula — population still cancels, GDP still cancels, energy still cancels and you must enter in the fourth term the thing you are trying to calculate.

      But it is still wrong. CO2 emissions come only from CO2 emitters.

    • JamesNV “As others have patiently pointed out, the authors include a definition for their formula. Why do you continue to ignore the definition they give?”

      How about because formulas are not supposed to need “explaining”?

      If I wrote

      2 = 3

      and then explained it by saying “2 * infinity = infinity, but 3 * infinity is also infinity, and since infinity equals infinity (by inspection), therefore, 2 = 3″.

      So in the WORDS I explain it, but you don’t NEED the explanation. The math is trivial and as a statement it is “false.”

      So long as you follow the ordinary rules of algebra, the Kaya Identity is “CO2 = CO2″ and it really doesn’t matter what values you choose for P, G, or E because each of them is both numerator and denominator.

      If you are NOT going to follow the rules of algebra, for heaven’s sake don’t make it LOOK like algebra!

  264. Willis Eschenbach says:
    July 22, 2014 at 5:01 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

    Hi Willis
    As I read how the Kaya is defined you are wrong there.

    It says in AR4 WG3 chapter 1.3.1.2 “The Kaya identity (Kaya 1990) is a decomposition that expresses the level of energy related CO2 emissions as the product of four indicators: (1) carbon intensity (CO2 emissions per unit of total primary energy supply (TPES)), (2) energy intensity (TPES per unit per unit of GDP), (3) gross domestic product per capita (GDP/cap) and (4) population”

    http://books.google.no/books?id=U_4ltxID60UC&pg=PA107&lpg=PA107&dq=kaya+(1990)+identity&source=bl&ots=AMAzYpI0X4&sig=ZSnfi-sQF9gIccmDgU5zNrC-cp8&hl=no&sa=X&ei=5EjPU-DnNofg4QT6-IH4Dg&ved=0CHAQ6AEwCQ#v=onepage&q=kaya%20(1990)%20identity&f=false

    Those four factors are the free variables. It is therefore wrong to say that if you cut the population in half and keep all other factors unchanged the result will be unchanged. The result will be 50% reduction because the “GDP per capita” is the free variable, not the GDP.

    /Jan

    • Jan says: “The result will be 50% reduction because the “GDP per capita” is the free variable, not the GDP. ”

      That’s TWO variables, a ratio. GDP is a quantity, Population is a quantitty, GDP per capita is a fraction, a ratio of these two variables.

      “It is therefore wrong to say that if you cut the population in half and keep all other factors unchanged the result will be unchanged”

      What any person means by “factor” seems somewhat unpredictable and perhaps the term should be avoided or at least explained each time.

      Anyway, many or most here see the variables as being the independent variables, such as P, G, E. If you change “P” you have NOT changed “G” or “E”. Since “P” is both numerator and denominator, CO2 is NOT CHANGED just because you changed “P”. Something changes — just not CO2, the thing being calculated. Instead, the ratio changes in the second term – G/2P is half of G/P.

      So the correct interpretation of the FORMULA is that doubling P halves (G/P) making it (G/2P).

      As a policy consideration that is exactly correct — doubling population without changing the other factors (G, E) will cut everyone’s everything in half.

      The implication is clear — reducing population, especially if you reduce the non-productive parts, increases “G” for the remainder. China is pursuing that goal, Pol Pot did so rather abruptly although I doubt it was for the reason of increasing GDP per capita.

  265. Greg Cavanagh says: July 22, 2014 at 8:21 pm
    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.
    Hi Greg,
    You and I (and I suspect Dr. Pielke) agree here. The short half life of CO2 in the atmosphere makes the alarmist case even more hysterical. Consider the argument:
    - CO2 increase leads to changes in the planetary energy budget over the course of a few years
    - This energy budget changes will be long lasting irrespective of future CO2 emissions.
    - Therefore we must implement the alarmist agenda now!
    But since CO2 has a short half life, when we eventually do run out of fossil fuels or invent zero point modules (these being required for deep decarbonization), the energy budget should rapidly return to pre-industrial levels.

  266. 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. (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.

    In relation to the Kaya, I find Dr Pielke’s logic and that of the paper he links to, torturously circular. The assumptions are simplistic and unproven. No attempt is made to demonstrate the validity of the relationships, or the choice of “factors” and his appeals to the authority of this tautological Identity completes the fallaciousness of its citation.

    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.

    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

  267. Scott Wilmot Bennett (4:31 am):

    As far as I have seen, no one denies that the values of the ratios in the Kaya Identity may differ for different countries. It is not meant to be ‘universally applied’ in the sense that bothers you. It is not a scientific law with universal constants — and no one claims that it is. Rather, it is a tool to analyze how and why the values of the ratios (including, ultimately, CO2 emissions per unit of GDP or per head of population) vary across time and place, and how these values can be changed.

    I’m sure that land area indeed makes a difference, but not only land area. The difference between Australia and Singapore is largely in their economic structures — how they produce their GDP, and thus how energy-intensive their economies are. Also relevant are their sources of energy, which differ in CO2 intensity. These differences are accounted for in different values of the ratios in the Kaya Identity.

  268. Willis:

    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

    Willis, perhaps you could help us by practicing what you quite rightly preach: Please quote the exact words from some user or proponent of the Kaya Identity where they say that GDP, energy, or CO2 emissions are independent of other variables. Only when you have done so do you have a case. Otherwise you are arguing simply with your own mental construct, not with anyone who applies the Kaya Identity.

    No, the consistent practice, as far as I have seen, is to say that GDP depends on population, energy use depends on GDP, and CO2 emissions depend on energy use. The ratios in the Kaya Identity express those realistic relationships.

    I suppose that your real difficulty is that you can’t escape your mental construct about what the identity “ought” to mean, as opposed to how its practitioners apply it. At some point you’ll just have to acknowledge that the Kaya Identity (i) has proven useful and (ii) works as an equation. What more should one expect?

    • Dr. Doug says “you are attacking a straw man.”

      Of course, and so are the warmists. Consider Lewandowsky’s “Fury” paper — exactly how many skeptics believe the earth is flat? We have no idea — the online survey says 11 respondents claiming to be skeptics also claim the earth is flat (which it is in most of Kansas and Nebraska).

      And yet the the implication or claim is that these 11 people are representative of skeptics and/or deniers, and on that basis, the warmists attack those 11 people as if representative, when in fact warmists are at least as conspiratorial believing the Koch brothers are behind all “denial”.

      But you can see right here today that some skeptics are educated, write well, think clearly and still do not subscribe to the whole kit and caboodle of anthropogenic global warming. It seems reasonable to me to want math formulas to actually *work* like math formulas.

  269. Dr. Doug says:
    July 23, 2014 at 7:57 am

    Willis:

    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

    Willis, perhaps you could help us by practicing what you quite rightly preach: Please quote the exact words from some user or proponent of the Kaya Identity where they say that GDP, energy, or CO2 emissions are independent of other variables. Only when you have done so do you have a case. Otherwise you are arguing simply with your own mental construct, not with anyone who applies the Kaya Identity.

    I have already done so when I quoted and used the equation from the original paper. Look at the equation. It contains the following variables:

    Population
    GDP
    Energy Uses
    CO2 emissions

    If you cannot see that those are independent variables, I fear I cannot help you.

    However, the ratios (per capita GDP, energy intensity of economy, carbon intensity of energy consumption) are clearly NOT independent, as the independent variables appear in more than one of them.

    w.

  270. John Moore says:
    July 22, 2014 at 6:37 pm

    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.

    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).

    Thanks for that, John. I see nothing in there that I’d disagree with.

    My difficulty with the Kaya Identity is that we don’t learn anything from it. It can’t prove or establish anything about the real world, because you can replace any given value (say GDP) with another given value (say Gross National Product or Total Goods Produced) and it is still an identity.

    In general, IF we imagine that CO2 is a problem (which I don’t), there is only one ratio of interest. This is how much carbon we produce for every unit of GDP. We’re not gonna cut the population in half. Nor do we want to cut the GDP in half. That leaves only the question of how much CO2 we produce for each unit of GDP … and for that we don’t need the Kaya Identity.

    All the best,

    w.

    • Willis:

      My difficulty with the Kaya Identity is that we don’t learn anything from it. It can’t prove or establish anything about the real world, because you can replace any given value (say GDP) with another given value (say Gross National Product or Total Goods Produced) and it is still an identity.

      In general, IF we imagine that CO2 is a problem (which I don’t), there is only one ratio of interest. This is how much carbon we produce for every unit of GDP.

      Those of us, like yourself, who are paying intention indeed do not learn anything from it. But some subset of the population can learn something useful from this, and I think that’s its real use.

      The CO2/gdp-unit is an interesting ratio. But by decomposing it we get other interesting ratios: energy use / unit of GDP and carbon emitted / unit of energy.

      Those are useful things to consider. For example, there has been a lot of public discourse about each of those two ratios. “Green energy” usually means less carbon emitted / unit of energy. “Energy conservation” is about reducing energy use / unit of GDP.

      Hence the ratios in the KI have been and continue to be in common usage in policy discussions and thus putting them into the KI is useful.

      I submit that this rather loose, limited use of KI is what counts. Expecting precision from it doesn’t work. Teaching those who have been paying numerate attention is redundant.

  271. John Moore says:
    July 22, 2014 at 6:37 pm

    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).

    This I do disagree with. For example, the most common trig identity is that

    Tangent = Sine / Cosine

    Since the sine of a right triangle is the length of the opposite side over the hypotenuse (O / H), and the cosine of the right triangle is the length of the adjacent side over the hypotenuse (A / H), this means that the tangent = O / A, the opposite side over the adjacent side.

    This is useful because it gives us a way to calculate the tangent of an angle. But it doesn’t reduce to CO2 = CO2, as the Kaya Identity does, giving us no way to calculate the CO2 emissions.

    w.

  272. Willis, to clarify my last point:

    You seem hung up on what you think the Kaya Identity “ought” to mean — specifically, that GDP, energy, and CO2 ought to be treated as independent variables.

    Practitioners of the Identity instead treat the ratios as independent variables. Do you see that yet? (If not, then you need to do your homework.)

    If you see this, then can you give a cogent reason why their usage is invalid? You yourself have amply demonstrated that the equation works out fine. There is nothing wrong with the algebra.

    Here’s a challenge: Show that Pielke’s actual use of the Kaya Identity gives wrong or misleading results. If not, then what’s your point?

  273. Willis, I see our posts crossed.

    As I said, you need to do your homework. You are not addressing how the Kaya Identity is actually used, and you are attacking a straw man.

  274. Willis Eschenbach says:
    July 23, 2014 at 8:31 am

    I have already done so when I quoted and used the equation from the original paper. Look at the equation. It contains the following variables:
    Population
    GDP
    Energy Uses
    CO2 emissions

    And what is your “original paper”?

    I have not found Yoichi Kaya’s original paper from 1990 online anywhere, but anyway, the identity was known to a wider public through the usage in the IPCC reports.

    The IPCC 2007 report says that: “The Kaya identity (Kaya 1990) is a decomposition that expresses the level of energy related CO2 emissions as the product of four indicators: (1) carbon intensity (CO2 emissions per unit of total primary energy supply (TPES)), (2) energy intensity (TPES per unit per unit of GDP), (3) gross domestic product per capita (GDP/cap) and (4) population”

    http://books.google.no/books?id=U_4ltxID60UC&pg=PA107&lpg=PA107&dq=kaya+(1990)+identity&source=bl&ots=AMAzYpI0X4&sig=ZSnfi-sQF9gIccmDgU5zNrC-cp8&hl=no&sa=X&ei=5EjPU-DnNofg4QT6-IH4Dg&ved=0CHAQ6AEwCQ#v=onepage&q=kaya%20(1990)%20identity&f=false

    /Jan

  275. The perseveration of Willis’ silly error is oddly placed in a technical blog. The old saw that insanity is defined as repeating the same thing and expecting a different response comes to mind. It suggests ignorance of some basic mathematical constructions is far more extant than one might have thought. It is damaging to reputations when a person who regularly critiques the math and science of others persists in defending such an obvious error. Given the number of valid proper examples of the Kaya Identity at work, and the presence of interactive tools that clearly identify correct usage, the continued debate has become an embarrassment for the host site.

  276. Michael 2 says:
    July 23, 2014 at 7:36 am
    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.”

    No, you are making the same mistake Willis is. Look at it this way: this problem as phrased is a way of relating the CO2 in the non-doubled situation to the CO2 in the doubled situation.

    As such, CO2(2)=XCO2(1) and you are trying to solve for X.

    Using Kaya to expand the CO2 terms we get the following:

    2P1*(2GDP1/2P1)*(2E1/2GDP1)*(CO2(2)/2E1)=X*P1*(GDP1/P1)*(E1/GDP1)*(CO2(1)/E1)

    which reduces back to
    CO2(2)=XCO2(1)

    In other words, **without assuming something*,Kaya doesn’t tell us anything about how much CO2 is going to increase when energy, population and GDP double – the question is *what assumptions* make the most sense for the real world.

    Willis assumes that X is 1 – that it is impossible for CO2 to vary under any circumstances, ever which is pretty unrealistic in my opinion. Another more plausible assumption is the CO2/E stays constant(and this pretty closely matches our observations of countries over time). I must admit that this is a tricky notion – I missed the fact that I was making an assumption (that CO2/E stays constant) in my first response to Willis in this question.

    No one has to make the assumption that CO2/E stays constant necessarily but the one that Willis and you are making is not at all realistic. No matter how many times you do Kaya, you will never be able to prove that X=1 (or any other number). If you think you’ve proven that, respectfully, that’s just because you’ve done the math wrong ;)

    Cheers, :)

  277. Michael 2 says:
    July 23, 2014 at 9:32 am

    Jan says: “The result will be 50% reduction because the “GDP per capita” is the free variable, not the GDP. ”
    That’s TWO variables, a ratio. GDP is a quantity, Population is a quantitty, GDP per capita is a fraction, a ratio of these two variables.

    Michael 2, see the definition quoted from IPCC in my post 9:11 am

    The ratios are the free variables, not GDP. And for clarity, there shall be “per capita” in the denominator, not population

    By your logic one cannot consider the speed of a car in miles per hour as one free variable chosen by the driver. It is two variables; the miles and the hours. Try that to the police if you get a speed ticket.

    /Jan

    • Jan says “By your logic one cannot consider the speed of a car in miles per hour as one free variable chosen by the driver. It is two variables; the miles and the hours. Try that to the police if you get a speed ticket.”

      You have it exactly backwards. By my logic the speed of a car IS a specific independent variable. At any moment it has the single quantity “speed” and it can be measured and you don’t actually need time. Limit t ->0 for ds/dt.

      It can be *expressed* as distance-traveled over time to establish the meaning of the measure but the “meaning of the measure” is NOT THE MEASURE.

      A speedometer is measuring the magnetic force caused by a spinning magnet inducing electrical current in a spring loaded rotating metal plate. This force is more or less continuous and works against the spring moving the needle.

      It doesn’t need to wait an hour to see how far you went.

      So it is with Kaya Identity. You are substituting the “meaning of the measure” instead of providing the measures.

    • Jan “The ratios are the free variables, not GDP. And for clarity, there shall be ‘per capita’ in the denominator, not population”

      I don’t accept that. The fraction “GDP/Population” results in a single value whose unit is “GDP per Capita”. But you could arrive at that value other ways, including by fiat or specification. (After all, GDP is already a specification).

      The second term OUGHT to be a single variable “GDP per capita” independently measured or calculated or even assumed. Then its factors won’t cancel. None of the terms should be expressed as fractions because it means you don’t know what they are independantly of the other terms.

      Is anything measured? Population is measured. The rest of Kaya is a daisy chain of fractions, extremely elegant in its cleverness — no need to measure anything, everything is stated in terms of something else.

  278. That was strange. I posted a URL to YouTube and it actually embedded it. I had no idea WordPress worked this way! I’m not sure that’s useful.

  279. Willis Eschenbach says July 22, 2014 at 3:18 pm

    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.

    i would say that if it is “instructive to look…at the individual factors” then it is adding to someone’s knowledge of what is going on – altho that target audience will typically not include those of us who are challenging the co2 paradigm

    while it’s initially baffling that all quantities reduce to CO2 = CO2 – Kaya isn’t meant to be used in that way – it is meant to be used unfolded where the factors can be seen – and interestingly – that’s when the correct co2(n) value can be seen – Kaya can be said to exist in a subset of math – to call it invalid because it doesn’t follow tradition and show us CO2(n) when reduced might be analogous to calling Finite Mathematics invalid cuz it doesn’t use all the numbers

    Kaya works cuz the variables aren’t independent of each other – earlier i had called them “cherry picked” – but that isn’t correct – they were chosen because of their real-world relationship in the production of man-made CO2 emissions – sure they’re crude choices – i doubt changes in population or gdp will produce the precise changes in CO2 that Kaya says – and other factors might be defined to make a better Kaya (see Scott Bennett’s July 23 post) – hopefully the people using Kaya are aware of that

    Kaya may not be the best way to accomplish what the users want – but to find one requires fresh ideas – not just criticism

    i’m not here to convert Willis – he’s intelligent and will see the light in time – or i may see the light and recant – but right now – i’m (somewhat) confident in my perception of the Kaya Identity – and that clarification is all i wanted out of this

    –john eyon

  280. Michael 2 says:
    July 23, 2014 at 10:03 am
    Shawnhet says: “let’s assume that we double P, GDP and E but keep the CO2/E ratio constant”

    “You don’t actually get to do that. Ratios have no physical existence. It is a word that describes an abstraction that exists only in your mind.”

    Oh, come on. This is a perfectly reasonable assumption that reflects a physical reality (that we are only imperfectly good at getting energy using minimal carbon). OTOH, your assumption is that someone who buys their first car (and increases GDP doing so) can’t possibly increase CO2 emissions by driving it.

  281. Michael 2 says:
    July 23, 2014 at 10:21 am
    “Well then just make it a constant and all this hullabaloo goes away. :-)”

    This makes no sense.

    Did you read my 9:42 am post?

    I showed using *math* how you have to assume (or measure) *something* to calculate the change in CO2 per Kaya. I *assume* that CO2/E is constant because I think that this is a reasonable assumption. Whether it turns out to be a reasonable assumption will depend on later testing. You think it is more reasonable to “make” CO2 itself constant than the ratio of CO2/E but it quite plainly isn’t for any real world situation you would claim to name.

  282. dp says:July 23, 2014 at 9:13 am the continued debate has become an embarrassment for the host site.
    I’m not sure where Willis’s head is. Michael2 has admitted in a couple of comments he understands this is a straw man. I think it is just those two who insist on talking about the beer identity and not Kaya. I wish the host would close this thread. I keep tracking it because I am embarrassed for WUWT.

  283. Michael 2 says:
    July 23, 2014 at 10:45 am

    By my logic the speed of a car IS a specific independent variable. At any moment it has the single quantity “speed” and it can be measured and you don’t actually need time. Limit t ->0 for ds/dt

    The fact that you can make a mechanical device to show the speed does not change the principles. The speed is the ratio of distance divided on time. Instantaneous speed is the derivative of position with respect to time. Average speed is the distance covered divided on time used over a time period.

    Similar to that can any of the ratios in the Kaya be defined for both instantaneous and average values. You can for example define instantaneous energy efficiency as the partial derivative of energy used with respect to GDP, and average energy intensity as average energy use divided on a chosen amount of GDP. We have of cause no mechanical tool that show instantaneous energy efficiency, but that does not change the principle.

    Why can’t you just see how the IPPC, as I quoted above, explain which the free variables are? That is how the Kaya is used in the scientific community. You are insisting that the Kaya identity is something other than the creator has defined it to be.

    /Jan

    • Jan Kjetil Andersen: “The fact that you can make a mechanical device to show the speed does not change the principles.”

      Actually it does. The mechanical device has no concept of either time or distance, only rotational velocity which maps to speed a whole lot better than your odometer and stopwatch.

      Your definition cannot follow the limit of t down to zero but speed does not cease to exist at dt = 0.

      Consider a cartesian graph with a simple line Y = X. The slope is usually defined as dy/dx but what happens when dx =0? Algebra fails at this point. Calculus steps in and the differential is simply “1″. It can handle dt=0 just fine and you can calculate the slope of a POINT on that line! You cannot do that in algebra, but you CAN in calculus, because the line doesn’t lose slope just because dt = 0.

      So it is with speed. Speed is simply the slope of that line at some point on X. It requires no dt, but it does require knowing the function by which it came to exist.

    • Jan says: “You are insisting that the Kaya identity is something other than the creator has defined it to be.”

      There is no insistence. You are free to think of it as anything you wish. I am as free to do likewise. It looks like algebra therefore it is. The attention this is getting puts before thousands, maybe millions of people a thing that looks like algebra and a few dozen people say “No, it’s not algebra” but won’t change it. That’s pride. Take a duck, call it a swan, and insist the whole world calls it a swan. Who is really doing the “insisting” here?

      This should have been written as a *function* (IMO).

  284. Sigh. Wish I had an edit function. “Paying attention” of course, “not paying intention.”

  285. Willis to me (8:31):

    Look at the equation. It contains the following variables:
    Population
    GDP
    Energy Uses [sic]
    CO2 emissions
    If you cannot see that those are independent variables, I fear I cannot help you.

    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.

  286. Willis (8:32 am):

    My difficulty with the Kaya Identity is that we don’t learn anything from it. It can’t prove or establish anything about the real world, because … it is still an identity.
    … there is only one ratio of interest. This is how much carbon we produce for every unit of GDP. We’re not gonna cut the population in half. Nor do we want to cut the GDP in half. That leaves only the question of how much CO2 we produce for each unit of GDP … and for that we don’t need the Kaya Identity.

    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.

  287. Michael2 wrote:
    “How about because formulas are not supposed to need “explaining”?”

    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:

    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.

    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.

  288. RobertInAz says:
    July 23, 2014 at 11:59 am

    dp says:July 23, 2014 at 9:13 am the continued debate has become an embarrassment for the host site.
    I’m not sure where Willis’s head is. Michael2 has admitted in a couple of comments he understands this is a straw man. I think it is just those two who insist on talking about the beer identity and not Kaya. I wish the host would close this thread. I keep tracking it because I am embarrassed for WUWT.

    It does look like more people are starting to get it. Willis is a victim of his education system – self taught.

  289. John Moore says:
    July 23, 2014 at 12:17 pm

    Willis:

    My difficulty with the Kaya Identity is that we don’t learn anything from it. It can’t prove or establish anything about the real world, because you can replace any given value (say GDP) with another given value (say Gross National Product or Total Goods Produced) and it is still an identity.

    In general, IF we imagine that CO2 is a problem (which I don’t), there is only one ratio of interest. This is how much carbon we produce for every unit of GDP.

    Those of us, like yourself, who are paying intention indeed do not learn anything from it. But some subset of the population can learn something useful from this, and I think that’s its real use.

    The CO2/gdp-unit is an interesting ratio. But by decomposing it we get other interesting ratios: energy use / unit of GDP and carbon emitted / unit of energy.

    Those are useful things to consider. For example, there has been a lot of public discourse about each of those two ratios. “Green energy” usually means less carbon emitted / unit of energy. “Energy conservation” is about reducing energy use / unit of GDP.

    Hence the ratios in the KI have been and continue to be in common usage in policy discussions and thus putting them into the KI is useful.

    I submit that this rather loose, limited use of KI is what counts. Expecting precision from it doesn’t work. Teaching those who have been paying numerate attention is redundant.

    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.

  290. John Moore says:
    July 23, 2014 at 3:54 pm

    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.

    And you’ve cleared it up very well, in my case at least.

    Thanks,

    w.

  291. 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, :)

  292. 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, :)

  293. Michael 2 says:
    July 23, 2014 at 9:31 pm

    Jan Kjetil Andersen: “The fact that you can make a mechanical device to show the speed does not change the principles.”
    Actually it does. The mechanical device has no concept of either time or distance, only rotational velocity which maps to speed a whole lot better than your odometer and stopwatch.

    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).

  294. Shawnhet said:
    July 23, 2014 at 9:59 pm

    ” 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. ”

    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?

  295. Scott Wilmot Bennett says:
    July 24, 2014 at 2:30 am

    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

    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

  296. 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”.

  297. 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.

  298. “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.”

  299. 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, :)

  300. 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.

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