## The Kaya Identity Crisis

July 24th, 2014 by Roy W. Spencer, Ph. D.

There have been several posts over at WUWT regarding whether the Kaya Identity equation is useful, or mathematically trivial, or just a tautology.

The Kaya Identity is a specific application of the more general “IPAT” (I=PAT) equation which estimates the global environmental impact “I” based upon what are believed to be the main drivers of I, usually put in terms that economists find useful and can estimate…population, per capita GDP, etc. You can read more about it here.

To get total global CO2 emissions with the Kaya Identity, you multiply together (1) population , (2) GDP per person (affluence term), (3) energy used per GDP (energy intensity) and (4) the amount of CO2 released per energy used. Again, the terms used are ones economists work with, and so it is more useful in economics and policymaking circles than in, say, climate science.

As Willis Eschenbach pointed out, simply as an algebraic equation, you can cancel out terms in the Kaya equation and get the trivial result that CO2 = CO2. This is what seems to have generated much of the hoopla over at WUWT.

But the same as true of just about any equation where the physical units must balance on both sides: say, the equation to estimate the miles driven if you know the average speed and the total time driving:

Miles = [hours]x[miles/hour]

You can cancel out the “hour” terms in the above equation, and get the seemingly trivial result that “miles=miles”… but the equation is still useful.

The same is true of the Kaya Identity. It is a useful tool, to the extent that the individual terms on the right hand side really are the main economic-related drivers of the quantity on the left hand side…and the units match.

Also, as Willis points out, you can put all kinds of silly terms in an equation with the units on both sides simplifying to the same thing. But the unit matching is only a necessary – but not a sufficient – condition for an equation to be physically meaningful.

The bottom line is that I don’t see anything wrong with the Kaya Equation.