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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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.
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.
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.
The Wizard of OZ is on TV tonight in Aus! I wonder how many know it was original written as an allegory of Economics with weather and climate as major themes.
Ruth Dixon sheds light, as usual, on how Kaya can have some skill, if both inputs and outputs are provided and interpreted without bias
See My Garden Pond – Kaya
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.
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.
Looks to me like the sort of “equation” that only an ologist would find indicative of anything at all.
Talk about oversimplification…
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.
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.
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.
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
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.
nickreality65 says:
July 19, 2014 at 4:20 am
yep.
Scott Wilmot Bennett says:
July 19, 2014 at 4:00 am
The Wizard of OZ is on TV tonight in Aus!
Check out the colloquial meaning of snow and poppies in the US. This may help:
http://turnmeondeadman.com/trippy-films-the-wizard-of-oz-1939/
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”.
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
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?
Joel O’Bryan says:
July 19, 2014 at 1:14 am
The KID will sort the sheep from the goats, I kid you not!
The KID, I love it! 😉
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
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? 🙂
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.
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?
And, once more, what is the connection between CO2 and climate/weather especially the catastrophic kind?
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.