From Meteorology to Mitigation: Understanding Global Warming

The "Kaya Identity"


We can actually play around with greenhouse gas emissions scenarios ourselves. To do so, we will take advantage of something known as the Kaya Identity. Technically, the identity is just a definition, relating the quantity of annual carbon emissions to a factor of terms that reflect (1) population, (2) relative (i.e., per capita) economic production, measured by annual GDP in dollars/person, (3) energy intensity, measured in terawatts of energy consumed per dollar added to GDP, and (4) carbon efficiency, measured in gigatons of carbon emitted per terawatt of energy used. Multiply these out, and you get gigatons of carbon emitted. If the other quantities are expressed as a percentage change per year, then the carbon emissions, too, are expressed as a percentage change per year, which, in turn, defines a future trajectory of carbon emissions and CO 2 concentrations.

Mathematically, the Kaya identity is expressed in the form:

F=P*( G/P )*( E/G )*( F/E )


F is global CO 2 emissions from human sources
P is global population
G is world GDP
E is global energy consumption

By projecting the future changes in population (P), economic production ( G/P ) , energy intensity ( E/G ) , and carbon efficiency ( F/E ) , it is possible to make an informed projection of future carbon emissions ( F ) . Obviously, population is important as, in the absence of anything else, more people means more energy use. Moreover, economic production measured by GDP per capita plays an important role, as a bigger economy means greater use of energy. The energy intensity term is where technology comes in. As we develop new energy technologies or improve the efficiency of existing energy technology, we expect that it will take less energy to increase our GDP by and additional dollar, i.e., we should see a decline in energy intensity. Last, but certainly not least, is the carbon efficiency. As we develop and increasingly switch over to renewable energy sources and non-fossil fuel-based energy alternatives and improve the carbon efficiency of existing fossil fuel sources (e.g., by finding a way to extract and sequester CO 2 ), we can expect a decline in this quantity as well, i.e., less carbon emitted per unit of energy production.

Fortunately, we do not have to start from scratch. There is a convenient online calculator (Kaya Identity Scenario Prognosticator), provided courtesy of David Archer of the University of Chicago (and a RealClimate blogger ). Below, a brief demonstration of how the tool can be used. After you watch the demonstration, use the link provided above to play around with the calculator yourself.


The online calculator (Kaya Identity Scenario Prognosticator) has been updated and does not look exactly like the Kaya tool shown in the following videos. The format of the new tool is slightly different from the videos below, but all of the functionality is still available, you will have to use the pull down menus to select which chart you want to view, and you are limited to viewing just two graphs at a time. You will also have to enter the initial values referred to in the video. The initial values are: Population Plateau=11 billion, GDP/Person=1.6, Watts/$=-1.0, and Carbon Released/Watt=-0.3.

Video: Kaya Demo - Part 1 (4:59)

Kaya Demo (part 1)
Click here for transcript of Kaya Demo (part 1).

PRESENTER: OK, we're now going to play around with this online calculator that uses that Kaya identity to project future CO2 emissions. And this identity, as we now know, uses the fact that CO2 emissions are going to be a product of various terms that contribute to emissions growth, population, GDP per person, relative economic growth, energy intensity, the amount of energy we can get for a dollar-- a given amount of money, and carbon efficiency, how efficient we are at producing energy in a non-carbon intensive manner.

So the idea is that population, we can use demographic projections that, for example, have global population leveling out somewhere around 11 billion later this century. Projections of relative-- that is per capita economic growth, that as the world becomes more industrialized as developing nations develop more industrial economies, that we're likely to see an increase in relative economic expansion per person. Energy intensity, in principle, should decrease over time. As we develop more efficient means of obtaining energy, we will decrease the cost in dollars for a given watt of power.

And finally, carbon efficiency. As we switch over to less carbon intensive sources of energy, we will decrease over time, the amount of carbon that we emit for each unit of power, say, a terawatt of power. So we can calculate CO2 emissions trajectories as a product of these various terms. Now, let's use the default values that are set in the calculator and do the calculation.

And here we go. This red curve is the projected future carbon emissions, given the values that we've chosen for the various terms. And the blue pluses here show historical values of carbon emissions. And so we can sort of see how our projection ties into the past historical trends. We can use a carbon cycle model that involves some assumptions about both the oceans and the terrestrial biosphere that calculates the changes in CO2 concentrations over time, given this carbon emission scenario.

And the red curve is what we're projecting for future CO2. By 2100, we reach about 700 parts per million. And you can compare that trajectory to various stabilization scenarios. The green curve shows what the CO2 concentrations would be if we were to stabilize CO2 concentrations at 350 parts per million. The blue is 450 parts per million and so on. The yellow is 750 parts per million. Eventually, CO2 concentration stabilizes at 750 parts per million in that stabilization scenario.

So we can see how our projected emissions are comparing with various stabilization scenarios. And if we take this as sort of business as usual, these various assumptions about population, GDP, energy intensity, and carbon efficiency, then we see that, in fact, we'll be well over the 750 stabilization scenario. We'll already be at 700 parts per million at 2,100 with CO2 continuing to rise.

We can calculate accordingly the amount of carbon free energy we would need, given the assumptions of population, energy intensity. We can calculate how much carbon free energy we would need to produce to meet our energy demands if we are to keep CO2 to the specified level. And so we see the amount of carbon free energy that would be required in the various CO2 stabilization scenarios. And the red curve is the amount of carbon free energy that we would need to--

Credit: Dutton

Video: Kaya Demo - Part 2 (3:55)

Kaya Demo (part 2)
Click here for transcript of Kaya Demo (part 2).

PRESENTER: OK. So we were just looking at the carbon-free energy requirements. And the red curve tells us how much carbon-free energy we would need to produce, given the assumptions that we've made here and given the scenarios shown for both carbon emissions and CO2 concentrations.

We can also see how our assumptions regarding each of these terms compare to historical numbers, population growth in the past versus our projected population growth under this assumption that we've made of stabilizing global population at 11 billion later this century or early next century, the assumption of a GDP per person relative economic expansion of 1.6% per year-- these are the historical values, the pluses. And the curve shows what we're projecting for the future.

Energy intensity-- our curve sort of follows the past couple decades of data, as far as energy intensity is concerned. And so we might imagine that there have been some developments in technology that have led to a trend in recent decades that may be more representative of the trend we would expect in the future than, say, the numbers from the early 20th century. So our projected energy intensity over time sort of matches the past few decades of energy intensity information.

And finally, carbon efficiency-- this is the decline we're projecting as we become more carbon efficient in our energy usage, fewer gigatons of carbon produced per terawatt. We are extrapolating the past trend. And we project increasing carbon efficiency, increasingly less reliance on carbon-based energy as time goes on.

So these are the underlying assumptions in our default projection here. And as we've seen, in that default projection, which corresponds to business as usual, we're going to be upwards of 700 parts per million by the end of the century.

If we're looking to stabilize CO2 concentrations at, say, 550 parts per million-- down in here, the purple curve-- then clearly, we are going to need to change our behavior. We're going to need to change these various terms, some combination of these terms, in such a way that we lower CO2 increase.

And accordingly, as the purple curve shows, we would need to produce less carbon-free energy in that stabilization scenario, in the 550 parts per million stabilization scenario.

So we can play around with these numbers and try to figure out how we would actually go about achieving a particular stabilization, what terms we might be able to change through technology and through future policy changes, and how those changes would translate to a CO2 emission scenario and our ability to stabilize CO2 concentrations at some particular level.

So the next thing we'll do is to play around a little bit with these numbers and see if we might be able to lower our projected CO2 increase from the current trajectory, the business-as-usual trajectory that has us at 700 parts per million, well over twice pre-Industrial by the end of the century.

Credit: Dutton

Video: Kaya Demo - Part 3 (4:59)

Kaya Demo (part 3)
Click here for transcript of Kaya Demo (part 3).

PRESENTER: OK. So first of all, imagine that we found a way to stabilize a population at a significantly lower level. Through appropriate governmental policies, we found a way to limit global population to 10 billion, rather than 11 billion. Well, how does that change things?

Well, we can see we've lowered our carbon emissions, our projected carbon emissions. The CO2 concentration at 2,100 is now a little bit above 650 parts per million. So we've knocked off about 50 parts per million of our projected CO2 increase by 2,100.

It would be very difficult to decrease the projected global population much more than that. But let's say we go for 9 billion. Then we've now lowered the 2,100 CO2 concentration to below 650 parts per million. So we're slowly working our way towards a 550 stabilization.

Let's imagine that we were able to increase energy efficiency more than is currently projected, through new technologies that have not yet been incorporated or implemented, perhaps large-scale use of fusion energy. So let's imagine that the energy intensity, that we can get a better improvement in energy intensity, something closer to 1.5% decline, versus a 1% decline in the amount of energy that we need per unit dollar.

Well, now we have lowered CO2 concentrations even more. We're a little bit above 550 parts per million. Now, of course, if we were to establish policies that favored non-carbon-based forms of energy, renewable energy, technology, then we can, of course, further improve our carbon efficiency.

And so we might imagine changing this number from minus 0.3% to maybe minus 0.6% or so through the introduction of appropriate policies. And now we have come very close to 550 PPM stabilization.

So we would have to go in and look in more detail at the assumptions that go into assuming that we can change our carbon efficiency by the amount that we've changed it or that we can change energy intensity by the amount we've changed it. If we, for example, look at how we now are comparing with the historical trajectories, we can see that our energy intensity curve is far more optimistic than would be suggested by even the past two decades, which we originally used to extrapolate the future trend somewhat optimistically.

If we look at carbon efficiency, then to decrease our reliance on our carbon-based energy by the amount assumed in the carbon efficiency number we've used, again, we would need to start doing significantly better in terms of that decline in use of carbon-based energy than we have done in even the past decade or two.

So clearly, changes in policy, changes in behavior-- somewhat dramatic changes in policy and behavior-- would be necessary to put us on the trajectories that are, in essence, dependent on these optimistic numbers we've now used to replace the so-called "business as usual" settings in our attempt to lower future CO2 emissions and future CO2 concentrations.

We can see, for example, that to follow this 550 PPM, we've come pretty close now to 550 PPM stabilization. We're a little bit above the 550 PPM stabilization, but not too far above--

Credit: Dutton

Video: Kaya Demo - Part 4 (2:57)

Kaya Demo (part 4)
Click here for transcript of Kaya Demo (part 4).

PRESENTER: OK. So continuing where I left off, so with these settings, with these assumptions, we've come pretty close to 550 PPM stabilization. If we look at the carbon emissions, we can see that, in fact, to achieve that CO2 trajectory, that roughly 550 PPM CO2 stabilization trajectory, we would need to bring emissions to a peak of less than eight gigatons per year by the next decade or so. And we would need to begin bringing them down.

And in fact, if we had sought to stabilize CO2 concentrations at an even lower level, say, 450 parts per million-- now, that's the blue curve here, which we're well above-- to stabilize CO2 concentrations at 450 parts per million, we would need to bring emissions to a peak even sooner. And we would need to start bringing them down far more quickly in future decades.

And so for your first course project described later on in this lesson, you are going to be playing around with the settings, the various assumptions for per capita economic growth, energy intensity, and carbon efficiency projections for the future and perhaps population assumptions about population growth and population stabilization and see if you can come up with a realistic scenario, a justifiable scenario, of assumptions for these various terms that allow us to stabilize CO2 concentrations at a level that would minimize the risk of exceeding what we might define as dangerous human interference with our climate.

So your first project will involve integrating what we've learned about climate models, using simple climate models to look at projected temperature increases, and then looking at the distribution, the probability of future temperature increases, and what changes we could make in policy and behavior that would allow us to stabilize CO2 concentrations at a level that gives us a fairly high probability of avoiding breaching some temperature, some warming limit, that we might define as dangerous interference with the climate.

So you'll have lots of time to play around with this and get used to using this tool yourself and combining it with projections that we make from our simple energy balance model to address these issues in your first project.

Credit: Dutton