Kaya's Equation
Max Kummerow
Atmospheric CO2 concentration has risen, so far, from 280 ppm to over 400 ppm, due to humans
burning fossil fuels and clearing forests. Greenhouse gas (GHG) emissions grew about 2 per cent/year
over the past 40 years, accelerating to 3 per cent/year during 2000-2010 and accumulating to over 740
gigatons.1 Two percent growth doubles annual emissions every 35 years.
The IPCC’s Fifth Assessment Report issued in 2014 examined 900 scenarios to explore possible climate
futures. Results vary depending upon assumptions, but substantial reductions in GHG emissions, to 50
per cent or less of current levels by 2050 and continuing down towards zero emissions by 2100, would
almost certainly be wise. The consequences of not reducing emissions include hotter and colder
temperature extremes, rising sea levels, ocean acidification, species extinctions, storm damage and risks
to food crops and water supplies, flooded cities and a planet less hospitable to human life.
And, of course, fossil fuels will run out and become more expensive to extract, so the only question is
whether to transition to non-carbon fuels before or after burning the earth’s stocks of coal, oil and gas,
the legacy of hundreds of millions of years of solar energy captured by prehistoric plants. Like living on a
dwindling savings account, subsidizing the world economy with fossil fuels ends when the wells run dry.
Koichi Kaya's equation helps us understand options for reducing carbon emissions.2 Unfortunately, at
present, three out of four of the right hand side terms in the Kaya identity are increasing.
C = C/E * E/Y * Y/P * P
C = Carbon emissions (or more broadly, Greenhouse gas emissions, GHG)
E = Energy generated and consumed by humans
Y = Economic output (goods and services, GDP)
P = Population
1
2
IPCC 5th Assessment Report, 2014. Over 830 authors and thousands of reviewers worked on this U.N. report.
http://en.wikipedia.org/wiki/Kaya_identity
The C/E ratio is GHG emissions per unit of energy produced. 3 Over 33.6 gigatons of carbon are currently
released annually by humans in producing and consuming over 13,100 megatons oil equivalent of
energy. This ratio can be reduced by switching to non-carbon energy sources, such as wind and solar,
but has been increasing recently due to increasing use of dirtier energy sources, such as coal and tar
sands.
The E/Y ratio shows the efficiency of energy use in the economy. This ratio has been improving globally,
falling by about 1.4 per cent/year since 1990. Europe uses half as much energy/$GDP as the U.S.A so the
trend of increasing energy efficiency can continue as the world catches up to best practices. But
efficiency improvements face diminishing returns. Laws of physics, chemistry and biology impose lower
bounds on energy conservation. Producing fertilizer, growing crops, heating and cooling buildings,
storing food, transporting goods, forcing chemical reactions, etc. will always require energy inputs.
Per capita incomes, Y/P, meanwhile, have been growing, especially in Asia, in parallel with growing fossil
fuel consumption that provides an energy (work or labor) subsidy to output, with just a hiccup during
the 2007-209 financial crisis. World per capita income growth averaged about 2 per cent/year since
1970. Economic growth remains a central goal of governments, firms and individuals. Billions of people
live in poverty and need additional growth in output to meet basic needs.
Global fertility fell from over 5 children per woman to 2.5 children between 1970 and 2010, a major
cultural change in family size norms reflecting improved status for more than half of the world’s women.
But, meanwhile, population doubled from 3.5 to over 7 billion. So despite falling fertility rates, global
population still grows at over 1 per cent/year, adding about 80 million a year, a billion every 12 years.
Demographers project a 30 per cent increase to near 10 billion by 2050.
Eventually, the GHG problem can be solved by pushing the C/E ratio to zero by adopting renewable
energy sources. But, despite efforts to switch to non-carbon emitting, renewable energy sources, the
global C/E ratio has increased since the year 2000. A falling ratio of energy return on energy invested,
EROEI, has been increasing C/E as easy to access sources of fuels run out. Most of the world’s major oil
fields are “mature” or in declining production phases. Growing demand has been met by increasing coal
burning in China, mining of tar sands, deep water drilling and fracking, all “dirtier” sources of energy.
It will take massive investments in solar, wind, a better grid and other major investments in new
technology to shift to renewable energy. Gasoline, aviation fuels, and diesel fuels will be hard to replace
for transportation. It's still cheaper to run cars, ships, tractors, airplanes, trucks and railroads on dirtier
tar sands oil rather than renewable energy sources.
At present, the annual percentage changes in the Kaya equation are approximately:
C
= C/E
E/Y
+2 per cent = .3 per cent
Y/P
P
-1.4 per cent
+2 per cent
+1.1 per cent
Three of the four right hand side terms are still going in the wrong direction, so net growth in emissions
3
Numbers reported in this note come from World Bank “World Development Indicators” data. The World Bank
figures cite U.N. population projections and the International Energy Agency as primary sources of data.
continues. Converting a process currently growing emissions at 2 per cent per year, a rate that will
double GHG annual emissions by 2050, in a mere 35 years to a process generating half as much GHG
emissions poses a challenge. That would require almost a 2 per cent per year drop in emissions every
year to 2050, starting now. Emissions growth will almost certainly continue and take a decade or two at
best to turn around, even assuming enormous future political, economic and technological changes.
Getting emissions cut in half by 2050 seems a pipe dream, especially if the main focus is on reducing C/E,
a ratio with a strong possibility of trending upwards due to dirtier fuel sources.
Improving C/E by shifting to sustainable, non-carbon emitting energy and improving E/Y by efficiency
gains both rely mainly on better technology. Reducing Y/P and P, on the other hand, depend mainly on
changing human cultures and behaviors, such as family size, tax policies and consumption choices.
Attention to social justice issues—providing for the world’s poor, surely must also play a positive role in
reducing consumption while increasing human well-being.
It is hard to see how carbon emissions could come down substantially without all four factors going in
the right direction. Even if we could use technology to cut emissions per unit of output in half over the
next 25 years, allowing Y/P and P to continue growing at 3 per cent means demand and use of energy
will double in less than 25 years. So the net result of a huge effort to reduce emissions would be 1/2 x 2
= 1, no decrease in emissions. This is a “carbon trap” where technology improvements are offset by
growth. This resembles the “poverty traps” of countries where economic growth treads water due to
high birthrates and more mouths to feed. On the other hand, if both technology and behaviors changed,
so that demand fell while efficiency and renewables also improve, then emissions could fall dramatically,
1/2 x 1/2 = .25, a 75 per cent reduction in emissions.
So a steady state or shrinking economy and falling population plus both efficiency gains and switching to
renewables can, in combination and with synergies, get much more accomplished as the world gets
serious about reducing GHG emissions. Failure to reduce C/E so far, despite decades of talk about
sustainable energy sources, shows far more must be done, and that technology alone probably can't do
the job if demand growth continues.
As a “thought experiment” notice that 15 per cent of current world energy supply comes from noncarbon sources (hydropower, nuclear, wind, solar, geothermal, biofuels). Therefore, if world population
were 1 billion (15 per cent of current 7.2 billion), then C/E could be zero with 100 per cent of energy
needs supplied by non-carbon sources. Falling population as a carbon solution is not an unthinkable
possibility—several countries already have falling populations due to low birth rates. Demographic
transitions from high to low fertility, however, have been associated with fast economic growth (rising
Y/P, especially in Asia). So restraining Y/P growth (a steady state or shrinking economy) would also be
required for population growth to have a net positive effect on emissions.
Cultural changes as profound as adoption of the major world religions or the scientific revolution of the
Enlightenment will be needed to stop growth. We need a positive, compelling vision of a green,
sustainable planet with steady state economic throughput and a much smaller human population
sharing resources with a diverse community of interdependent species. Humanity has to accept
scientific truths that motivate learning to live within our means, within the ecological limits of earth's
capacity to maintain human life without degrading our habitat.
Instead of campaigns promising growth and jobs, leaders will have to promise wealth taxes, carbon
taxes, cuts to consumption, responsibility, social justice and sustainability. Instead of saying “population
growth means we need more jobs” politicians should say “too many jobs are wrecking the earth, we
need to cut the number of people.” We need to adopt a lifeboat ethic of sharing scarce resources fairly,
reviving social justice ethics. Human can thrive through caring for nature and caring for "the least of
these my brethren" including future generations.
Our goals should include warm human relationships, community, security and self-discipline, rather than
selfishness, bigger houses and new cars on a damaged planet. Big changes, but good changes. Luckily
research on the psychology of happiness teaches that people can live good lives with sufficiency rather
than more and more consumption. Adler mentions “life tasks” of community, work and intimacy. He
does not mention getting rich. If we do this right, the cultural and behavioral changes required to solve
CO2 emissions will leave us healthier, more connected to nature and each other, with more joyous and
secure lives.
The earth’s breathable atmosphere extends less than 5 miles above the earth’s surface, a thin film of air
consisting of a mix of elements (oxygen, carbon, nitrogen, water) that makes life possible and keeps
earth’s temperature regulated. We live on the Goldilocks planet—Mars is too cold, Venus too hot, Earth
has been just right for human life. Not surprising, since we evolved here.
Big carbon pools on earth that total over 35,000 gigatons exist sequestered in fossil fuels, biomass, soils
and dissolved in oceans. If an appreciable percentage of that carbon gets into the atmosphere, we are
cooked. In total these huge pools of carbon could contribute many times more GHG to the atmosphere
than the 740 gigatons there now, through self-reinforcing, unstoppable, accelerating non-linear
feedback loops of melting ice and burning forests. A runaway Greenhouse warming history sent Venus's
surface temperature to 450 C. Our human enzyme systems fail and we die if our body temperatures get
above 42 C. Crops also fail if climate changes too much. Extinctions would destabilize every ecosystem
on earth if climate changes too much. Earth's solar constant, the amount of energy per square metre
reaching us from the sun, provides heat inputs here about half those of Venus. Earth’s current surface
temperature averages about 16 degrees C. NASA scientist Jim Hansen has written that if we burn all of
the coal, oil, gas and tar sands, probability of a Venus Syndrome on earth rises to "a dead certainty."
Julian Simon called human intelligence "the ultimate resource." But Barbara Tuchman's book The March
of Folly covers historical cases where good advice was ignored with disastrous results. The future
depends on our ability to use the ultimate resource wisely, perhaps the most limited resource of all.
Jared Diamond says societies that fail to adapt to new conditions collapse. Switching to non-carbon fuels
poses quite a challenge of adapting to new conditions created by our own inventions on a global scale.
Don’t despair. It used to be impossible to abolish slavery or for women to vote or have less than six
children, but good people made those major cultural changes happen. Cultures do change. We have
powerful institutions including education, mass media, international cooperation, markets and carbon
taxes that could get a lot of carbon reduction accomplished and rein in growth with amazing speed.
Technologies exist to allow family planning and for making electricity from sun and wind and for running
cars on hydrogen. A combined strategy using all four terms in the Kaya Identity, motivated by a positive
vision of a green future earth and communities of responsible, happy, connected, empowered citizens,
could get it done.