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The Kaya Identity and the "Conservation Bomb"

onepercent.jpgNot a spy thriller, the Kaya Identity is the formula which projects the amount of atmospheric CO2 as a function of population, GDP per capita, watts per dollar, and CO2 per watt. It's pretty straightforward: our carbon output depends on how much power we use, how efficiently we use it, and how "dirty" the production is. Recall that current atmospheric carbon dioxide levels are just under 380 parts per million, and that the general consensus among climatologists is that (looking just at CO2), the climate is up for some serious problems once we hit the 440ppm level. With the Kaya Identity, we can calculate just what combination of factors would keep us below that level.

The math isn't hard -- it's just multiplication -- but charting it out over course of the next century can get a bit tedious. Fortunately, for a class in the Geosciences department at the University of Chicago, Professor David Archer put together a Kaya Calculator allowing you to plug in preferred figures for each element and see what results. For most factors, you don't have to give absolute numbers, just the amount of change every year. The calculator is set to show the results over the course of the 21st century, and displays a number of graphs detailing the figures. The most important of the resulting graphs is "Carbon-Free Energy Required for CO2 Stabilization" -- that is, how much of our overall energy production will have to be carbon-free in order to stabilize CO2 at a given portion by 2100.

With the default figures -- taken from the global trends of the last century -- we'd need over 17 terawatts of carbon-free power (out of the total produced) to stabilize at 450ppm in 2100. I've reproduced the graph showing these results above. Unfortunately, the chart doesn't indicate just what the total energy production would be; the Intergovernmental Panel on Climate Change (IPCC) can help here -- their average scenario for energy use in 2100 is roughly four times the present, or about 40-50 terawatts.

But that assumes we don't try to change things.

As this Real Climate article (from which I found the Kaya Identity calculator) suggests, getting to 17 terawatts of carbon-free power is staggeringly difficult. But that's with the default value of an 1% annual average improvement in efficiency; this improvement is largely a side-effect of overall changes to technology. If we give greater attention to increasing efficiency, we can have enormous payoffs down the road.

Efficiency is a funny thing; over time, small improvements can have dramatic effects. Globally, our overall rate of annual improvement in efficiency is about 1% for the last century; that is, each year we can produce about 1% more GDP per Watt consumed than the previous year. But (as we've noted before), that 1% figure doesn't tell the whole story. Improvements in efficiency have been much greater than that for some regions and for some periods of time. For example, between 1981 and 1986 (the early 80s oil shock), the United States managed annual efficiency improvements averaging 3.4%; over that same time period, California improved by 4.5% every year. Average annual improvements for both fell back to around 1% between 1986 and 1996, but jumped again in the late 1990s (2.7% for the US and 3.9% for California) -- probably reflecting the economic shift away from heavier industries and towards less energy-intensive businesses.

twopercent.jpgSo -- without changing any other values -- if we alter the Watt/$ reduction box in the Kaya Calculator from -1% to -2%, something very interesting happens. Instead of needing 17 terawatts of carbon-free power to stabilize at 450ppm in 2100, we'd need 4 TW. That's not 4 terawatts out of ~50, either; that's 4 TW out of about 18 TW, because the boosted efficiency has reduced the overall consumption.

And let's look at what happens when we go to -3% annual change, a figure still below what the US managed in the early 1980s, and well below California at that time. Stabilizing at 450ppm would require... no carbon-free energy. How's that possible? Because global energy consumption would have dropped to about 7 terawatts, or around half of current consumption.

threepercent.jpgOf course, peak oil and the need to move swiftly to reduce CO2 output won't let us forget carbon-free power. But look again at the 3% result: we could possibly stabilize at 350ppm -- a far safer CO2 load than 450ppm -- by adopting 4-6 terawatts of carbon-free energy along with the more aggressive efficiency (the 6 TW peak in 2050 reflects the more limited effect of efficiency at that point). Actually being able to reduce atmospheric carbon would undoubtedly mean increasing carbon sinks and relying on some forms of sequestration, but a dramatic reduction in the amount of CO2 put into the atmosphere helps enormously.

Art Rosenfeld and John Wilson of the California Energy Commission refer to this as the "Conservation Bomb;" the chart below comes from a presentation John Wilson provided to me. It's a graphic representation of what I've been talking about above: the difference in energy consumption under different efficiency improvement scenarios. Two elements stand out: the first, that a 4% improvement would bring us down to about 3 terawatts -- again, a rate of improvement not without precedent; the second, that the total energy demand is predicated not on the status quo of rich nations/poor nations, but on a global population of 10 billion all with EU-equivalent lifestyles.


An aggressive focus on improvements to efficiency amounting to an average of 3-4% annually over the century could mean a world where everyone can live well without risk to the climate. To say that the effect of improving the efficiency of use is dramatic is perhaps an understatement. Without it, avoiding disastrous greenhouse effects will be nearly impossible; with it, avoiding the worst-case scenarios is almost over-determined.

Efficiency is quite literally world-changing.

Comments (23)

Ah, but two points:

(1) Money spent on efficiency improvements (R&D needed to make them happen, tax incentives, etc. etc.) is money NOT spent on carbon-free energy sources. And vice versa. The real question is which solution is most cost-effective to reduce the CO2 impact. Not addressed in the calculator (which is otherwise very nice).

(2) The de-industrialization shift in the US makes it easy for us to improve energy intensity: we've just shipped half our manufacturing to China. But that means China's energy intensity gets worse. De-industrialization is a whack-a-mole solution that doesn't really help (and the numbers that come from it, 3% or more decline per year, are therefore highly unrealistic applied on a world-wide scale).

The real solution is to raise taxes, use the taxes to fund R&D in all the solutions, and let the higher energy costs force people to choose good solutions through market choices. Efficiency actually works against market improvement (it makes each unit of energy worth more, and therefore if energy costs are fixed, people use more, not less).

Jamais, thank you very much for posting this. It succinctly demonstrates what some of us have been saying for about 20 years - efficiency improvements are the engine driving progress toward sustainability. Efficiency dwarfs renewables (but no one ever invites me over for a beer and to check out the spiffy insulation).

There's a real difficulty: the energy prices fluctuates quickly, but efficiency improvements or backsliding happen slowly. Oil prices respond to current demand, but it takes about 10 years to turn over a vehicle fleet. Producers also respond on a long time lag - it takes time to explore, drill, transport and refine.

Price shocks in the 1970's led to conservation and increased exploration. Then in the 1980's, oil prices collapsed. By the 1990's, millions or people were driving bronto-mobiles and building starter castles. Now those folks will be caught with their pants down, and it will take at least a decade to turn things around. Energy prices move too quickly to give us guidance about how to proceed. Perhaps the price of oil, coal and gas should be tied to the PPM of CO2 in the atmosphere, i.e., a carbon tax.

There's happy news if you're an American: we Americans use roughly 25% of the world's fossil fuels. If we lived more like Europeans, and did the kind of R&D we used to, we could cut that in half or more, freeing roughly 12.5% of the world's fossil fuels - energy now essentially wasted while providing no meaningful benefit. Our household uses energy at roughly middle-class European levels, and we live damned well. I don't think we're exceptional; I honestly think that most Americans could do what we've done. Americans have more power to do more good with less sacrifice than anyone else on Earth.

For what it's worth, Arthur, China's rate of efficienty improvement is faster than that of the US and EU, even with the shift of some industrial production there. In addition, it turns out that there's a lot of room for improvement in industrial process efficiency (I wrote about improvements in water use efficiency a couple of weeks, ago, and power efficiency is similar).

A global efficiency improvement rate of 3% is entirely reasonable.

As for calculations of whether carbon-free energy or efficiency improvements are the most cost-effective, that remains to be seen -- but it's strongly suggestive, given that focusing on carbon-free energy without efficiency improvements (at least not above the baseline ~1%) means needing to be generating at least 17TW of carbon-free out of ~50TW total by 2100, versus only having to do 5TW of carbon-free out of 7TW total if you're pushing efficiency.

It's physically impossible for many process to sustain efficiency improvements indefinitely; once you are converting 100% of your electricity to light, there is no room for improvement.  The efficiencies of all such devices will be subject to the law of diminishing returns, and efficiency will asymptotically approach a limit.

The point about efficiency of consumption, or carbon efficiency of production, is a good one; the USA could boost electric production per ton of coal by at least 20% using IGCC, and then cut emissions in half again by sequestering the CO2 produced in the gasifier; not allowing for growth, that would suffice for 21 years of 4%/year reductions.

If we really want to do something about atmospheric carbon, the way is with a uniform carbon tax (level set by treaty and probably adjusted with respect to a market basket of currencies).  This handles the question of efficiency vs. carbon-free production without having to think about it:  set the tax at the level which cuts CO2 emissions to the required value and the most economical solution to emissions reduction automatically becomes the cheapest.

That's assuming that you can catch all the tax cheats who dig their own fuel....

E-P, it's certainly true that once you get to 100% efficiency, there's nowhere to go but indistinguishable from magic -- but we have a long way to go before that.

As for catching the carbon criminal tax cheats, that's when Greenpeace becomes an armed vigilante group...

(*yawn*... clearly, I need more sleep)

China may be improving, but only because it's way off scale - from Smil's "Energy at the Crossroads", China used some 33 MJ/$ of GDP (exchange rate valued), 3 times the energy intensity of the US (about 11 MJ/$) in 2001. So there would seem to be a lot of improvement available there - but it could be quite illusory. Let's look at some sample numbers here:

Year 1: $10 of GDP in US, using 110 MJ
$1 of GDP in China, using 33 MJ
total: $11 gross product, 143 MJ

Year 2: $9 of GDP in US, using 96 MJ (3% improvement)
$2 of GDP in China, using 64 MJ (3% improvement)
total: $11 gross product, 160 MJ

I.e. BOTH countries improved their energy intensity numbers by 3%, but the transfer of production from US to China resulted in an INCREASE in world energy use, not a decrease. World energy intensity actually went up, even though the energy intensity in both countries went down.

The energy intensity business is very complex, and full of subtleties not evident at first. The purchasing-power-parity issue is another one: if you measure China's GDP by PPP numbers rather than exchange-rates, it's actually very close to the US number of 11 MJ/$. But it's not improving much either by that measure.

One of the oddest things about energy intensities, despite definite significant improvements in efficiency of all sorts in the western world in the 20th century, is that the global ratio of world production to world energy use remained roughly constant throughout the 20th century - at about that 11 MJ/$ level.

I.e. the global energy intensity number that goes into the Kaya identity is not perhaps what you first think it is because of the GDP dependences. And improving at a much faster rate than the 1% or so typical of recent decades is going to be very, very, very hard.

The other big problem is the interdependence between efficiency and growth. Historically we've seen GDP growth rates of about 1.6%/year. China has had dependable growth rates in the 6-10% range or more for a long time; energy efficiency improvements around the world may spur even faster growth rates - and then we're right back at the same problem.

Much better to ensure we have the major carbon-free energy sources we will need under 99% of the realistic scenarios here.

On the limits to efficiency improvements - Engineer-Poet makes a good point. The efficiency of conversion of chemical (and nuclear) energy to electricity was pretty much stuck through most of the 20th century at about 35%, the Carnot (thermodynamic) efficiency limit for a steam turbine. A couple of things have allowed us to surpass that in recent years, through methods that convert the energy more directly rather than just burning to make heat: gas turbines (which use the mechanical energy of the burning gas much as an airplane jet engine does) and fuel cells.

For gas turbines we can use natural gas directly; this is already quite widespread, and efficiencies of well over 50% are typical. Theoretically this could go as high as 85%. We can also turn coal into gas as suggested; similarly we can turn natural gas or coal into hydrogen through chemical processes that lose some of the original energy; these are naturally less efficient overall, but still can be an improvement over burning coal directly.

Fuel cells also produce heat through their internal resistance - when run at the high power levels you'd need in a real power plant, efficiencies of 50-60% are typical, even though theoretically fuel cells can reach 90% or better.

In any case, we can certainly improve the 35% typical of the 20th century to 50% or more, and possibly as high as 85 or 90% efficiency in conversion of chemcial energy to electricity. So, in one of the heaviest uses of primary energy we have today, there's room for a factor of 1.5 to 2.5 improvement.

Now, suppose we have energy efficiency improvements (not the same as energy intensity, as explained earlier, but never mind that for now) of 3% per year. Compounding annually, we've hit the maximum 2.5 limit in just 30 years. How can we possibly expect to sustain that for a full century???

Even 1% continual improvements may be very hard to sustain for another century: 100 years at 1%/year is a factor of 2.7, more than is even theoretically available in chemical to electric conversion.

Efficiency improvements obviously have limits, but they're vital and necessary. They aren't sufficient. Jamais' post also mentions a population stabilized at 10 billion. Absolutely vital, although with dedication and resources, it could be stabilized below that.

Our blind spot is to see the necessity of stabilizing physical throughput - the quantity of physical material and energy flowing through the human political economy. We don't distinguish "growth" from "development." The former has real limits; the latter is only as limited as human knowledge, ingenuity and curiosity.

Stabilized population. Stabilized throughput. Ultra-high efficiency. Ecological restoration. Each strategy necessary. Each has limits, but offers potential synergies with the others.

I appreciate Arthur's and E-P's sober reminder that efficiency isn't a magic bullet. But it is one of the most important tools in the toolkit for the foreseeable future. Let's get to work.

The real point is that we need to structure incentives such that people don't invest in carbon-free production when efficiency yields more bang for the buck, and vice versa.  This is one of many essentials and cost must be minimized so that other priorities aren't shortchanged.

David, E-P -- I agree.

One last note on efficiency (before I head off for a family visit this weekend): I'm not just referring to production efficiency, but also to use efficiency, broadly conceived -- from low-energy buildings to low-loss wall warts to redesigned urban communities. All of these are subject to physical limits, as well, of course, but the sheer number, diversity and base inefficiency of many of these processes and systems gives us far more room to improve than a focus on production efficiency might suggest.

Oh, and Arthur, despite the intentionally provocative language of the post, I completely agree that we need a lot more carbon-free energy generation.

Jamais - you're right about there being some room for improvement in use as well as production, but (focusing on electricity just now) most things that use electricity are already quite efficient. There is one very bad case though: lighting. Switching from incandescent to compact fluorescent lighting decreases power use roughly a factor of four; going to LED's would be at least another factor of two. So we could improve lighting efficiency a factor of 10 with very near-future technologies. This would have two effects:

(1) People would naturally install more lighting (I know my house is quite a bit darker than I'd like, at night.)
(2) It would reduce the 25% of household energy consumption that goes to lighting to perhaps 3-4%. Average household energy use would then drop from 100% of current to maybe 79% - i.e. A 10-fold improvement in lighting efficiency leads to only a 21% decrease in household energy use, because lighting isn't everything we do.

The biggest areas of household energy consumption are heating and cooling. Can we cut energy use there significantly more than we already have, with modern air conditioners etc? In ways that don't involve demolishing and rebuilding $30 trillion worth of houses?

But it does sound like we're all agreeing on a few things here :-)

On population: 8.5 billion vs. 11 billion is a 23% difference. That's 7 years of "3%" efficiency improvements; whether the population is 8.5 or 11 is irrelevant on the 100-year timescale.

Arthur Smith asks:

Can we cut energy use there significantly more than we already have, with modern air conditioners etc? In ways that don't involve demolishing and rebuilding $30 trillion worth of houses?
Led me to a fine result:
Yes, of course you can.

One century past
Men cut ice for summer's use
"Icehouses" stored it.

Now we can do more
Winter's ice for summer cool
Is downright simple.

Zeroing carbon
Is not so hard as some think
It can be easy.

(Popping in from the hotel)

Arthur, there's a *lot* that can be done to increase building efficiency. For cold-weather areas, retrofitting with the "R-2000" standard insulation would be very helpful (it's increasingly common in Canada), for example; an even more dramatic result could come from wallboard replacement with the BASF phase-change wax boards (although that would be a more expensive proposition). For warm areas, replacing the roof with white shingles can cause a significant reduction in the amount of cooling required.

E-P -- nice to see the poet side come out, too.

Robert Sczech:

Energy efficiencies of 100% are of course impossible, but nevertheless the potential for energy savings is tremendous. We do not even need much R&D - the principal facts and technologies are known. The main obstacle is ignorance and unwillingness on the part of the political and technical elites. Much business and therefore political interest is focussed on the idea of growth in sales of energy (oil + electricity). Every few weeks I receive in the mail an invitation by my local utility to install various lights on my property. They argue with safety but of course their motivation is to increase sales of electricity.

The greatest potential for energy savings is in cooling and heating residential buildings. Houses can be build at a small incremental cost which need a neglible amount of energy for heating. They are called low or zero energy houses (popular in Europe and Canada). It is in some sense a great crime to continue to build new houses which still require conventional heating systems. It is also possible to improve the insulation of the existing stock of older buildings. The main cost is labor cost since insulation materials are inexpensive. When I open the yellow pages in my phone book, I can find tons of heating oil dealers, but not a single company offering insulation services. Oil companies have no interest in improving insulation as this would cut into their earnings.

It is no exagaration to say that our building technology judged by energy efficiency is still at prehistoric levels. The main reason for this tragic state of affairs is that housing is build locally by poorly trained craftsman who continue to insist on their nail and hammer methods. If houses were build in factories, we would spend much less energy on heating and cooling.

In transportation, tremendous gains of energy efficiencies could be achieved by a few radical steps:

- shift traffic from roads to rail roads.

Trains require roughly 10% of the energy needed by cars to transport a given number of people. Same applies to truck loads.

- Reduce the top speed of cars to 45mph.

This would allow the car engineers to reduce the weight of the car by 60% or more. Using a much smaller engine, the mileage of the car could be lifted to 100mph with present day technologies. No new reserch would be required. Such cars could be build today.

Overall, I think we could save 50% of our energy consumption with little effort and without sacrificing life quality. Further improvements are possible but they will be harder.

To get really serious about energy conservation, we need to increase the cost of energy. Imposing a 100% tax on energy consumption would be a good start. As long as energy is cheap, there are no economic incentives to invest into energy consevation.

Robert Sczech:

The greatest individual consumer of electricity in private households is not lighting - it is the refridgerator. The electricity consumption of all refridgerators and all AC equipment in the US is mindbogling! Any improvement in this area would have a dramatic impact on national power consumption.

I agree that improving efficiency for heating is, in principle, easy - though heating isn't just for maintaining a steady temperature: we still have ovens and microwaves and toasters and hot water heaters for a reason.

Rails can't substitute for roads in modern suburbia and exurbia; you can argue what that means exactly, but for instance the charitable work I was involved in today would have been extremely frustrating and time-consuming if I was restricted to railroad schedules or a car (I drive a Prius by the way) that can only travel under 45 mph; you can't be in three random places thirty miles apart from one another in a single day without an automobile to get you door to door.

But cooling is the bigger problem; the technology I like best for residential heating and cooling is ground-source geothermal: in principle you can install it anywhere; with heat pumps it cools and heats about as efficiently as theoretically possible, using steady underground temperatures. But are there factors of 10, or even 2 or 3, available through such techniques?

The key problem here is what the 3% a year (or even 4%!) Jamais proposes really means. After 100 years, improvement at 3% a year means we must be 20 times as efficient as we are now. Improvement at 4% a year means we need a factor of 50 in efficiency. And to keep improving at those rates beyond the end of the century would mean that much more. It seems rather unlikely we have factors of 50 or even 20 left across the whole spectrum of energy use. Factors of 10 I can see in a few places; factors of 2-3 are pretty widespread. But factors of 20-50 just seem beyond belief at this point.


In the end you cant count on too much greater efficiencies to be the end all be all of energy at some point and we already past this point you need more power.

As we transition to hydrogen and direct electric use for more and more things we will need the power to run all that stuff we currently run via methane and gasoline.

Yes biofuels will take up SOME of the slack but in the end some portion of fuel and such will be hydrogen.

We realy arnt that far away from fusion power maybe 20-60 years prolly depending on a few key tech advances and then power will truely be ours in vast amounts. How many of us are there when it happens tho is ... unknowable.

Robert Sczech:

Regarding efficiency gains or alternative energy, the key issue is the following: whatever we do, it will cost energy. The question is therefore, which of the competing proposals to solve our energy problems is least expensive in terms of the energy to be invested in order to secure or even improve our standard of life. A careful analysis will reveal that the cheapest solution long term is efficiency gains. Building a house which does not require energy for heating and cooling (and we know how to do that) - a house which will last 100 years with proper maintance - will be far more economical than the typical houses build today which rely on cheap fuel in order to be viable.

Those who have reservations about investing into efficiency should answer the basic question: Where is the surplus energy for waste to come from in the future? Fusion and hydrogen are presently dreams at best. Since hydrogen needs to be produced before it can be burned, hydrogem is not an energy source. In fact, it takes more energy to produce hydrogen than energy can be gained by burning it later. Many of the proposals for alternative energies are either dreams (fusion + hydrogen) or to small in size in order to make any difference (solar or hydro). The only viable option is efficiency gains. Efficiency gains include the redesign of our cities. Driving huge distances from suburb to suburb in order to accomplish trivial tasks is a very wasteful activity. Think abnout the millions of years it took nature to produce the oil which you waste by driving a prius for purposes which could be accomplished at a fraction of the cost if our cities were not designed for waste. Clearly, our future is bleak unless we start to think radically and question all the standard assumptions. One thing is sure. Fossil fuels will not last forever. In less than one century the game is over.

The only reason renewables (specifically solar and wind) are relatively small so far is that they're too expensive. That's partly a technical problem (some technologies are intrinsically more expensive than others), and partly an economics problem - economies of scale can provide a good part of the cost improvements needed, if we could just scale up a few orders of magnitude, and there's no fundamental physical reason we can't do it.

Robert Sczech:

You are right Arthur. Especially windmills look very attractive as they recover the energy invested into their production in less than 5 years. Despite the many advantages wind generators offer, there is still a stubborn resistance against them. Opponents object mainly against the large size of the windmills which affects the natural beauty of landscapes. It is a tragedy that these people see the windmills but can not see the pollution coming out of coal based power plants. Huge arrays of solar panels would be my preference. Unfortunately, the low density of sun energy makes it necessary to cover really huge areas with solar panels in order to make a difference in our energy needs. Maintaining such an installation would create new problems!

People do see the pollution coming out of coal plants; they just don't recognize the haze in the skies as related to the A/C running all the time.

We already have huge areas covered with roofing; if that roofing generated electricity we'd generate most of the energy we need.


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