The Unbearable Logic of the Kaya Identity

The ‘trillionth tonne’ of carbon is a  powerful risk indicator (I previously blogged about it here). As the Oxford University hosted web site shows, we have used up around 567 billion tonne of our one trillion tonne carbon budget: jpg

So that leaves 433 billion tonnes. If we go over the budget, we likely commit the planet to 2 degrees Celsius of warming above pre-industrial revolution levels. That level of warming is viewed as commensurate with dangerous climate change since it will produce a range of impacts extremely negative for mankind. How quickly we will grind through that 433 billion tonnes is the topic of this post.

The U.S. government agency the Carbon Dioxide Information Analysis Center (CDIAC) publishes a time series of emissions from fossil-fuel burning, cement manufacture and gas flaring going back to 1751 here and for land-use change emissions here. This is the benchmark record of human-induced emissions for most academic studies.

The recent estimate for fossil-fuel and cement related emissions for the year 2011 is 9.5 billion tonnes and can be found on the CDIAC site here. Land-use change emissions are updated less frequently but have been running at around 1.0 billion tonnes per annum (also available on the CDIAC site).

For 2012, the Global Carbon Project, a collaboration between various universities and scientific institutions  from around the world, estimates that fossil fuel emissions (including those associated with cement production) rose by 2.7% in 2012 to reach 9.7 billion tonnes. Put those two numbers together, and we are placing around 10.7 billions tonnes of carbon into the atmosphere. So if we then divide our remaining 433 billion budget by 10.7 billion tonnes of yearly output, we have 40 years before we likely commit ourselves to a world of dangerous climate change.

That is the good news (sort of) since 40 years is quite a long time. The bad news is that carbon emissions are not static, but are expanding every year. Further, that increase is a product of some  very powerful forces that are captured in an identity created by Japanese energy economist Yoichi Kaya. The identity breaks down the rise in global carbon emissions into four major components as can be seen below:

Kaya Identity jpg

If you want to get a sense of population growth, look at the real time world statistics site Worldometers. For our Kaya indicator, however, we require percentage growth rates; the United Nations provides a low, medium and high estimate here. For reference, I have put the United Nations medium growth rate estimate (for 5 year periods through to 2100) into a chart (click for larger image).

UN Population Growth Rate Forecast jpg

This medium estimate sees population reaching 8.9 billion in 2050 and only a little higher at 9.1 billion in 2100 (for long-term UN estimates out to 2300 see here). Nonetheless, population growth alone will be a significant driver of emissions for the next few decades: growth will average a little less than 1% per annum in near decades before trailing off down to zero by around 2100. In short, more people means more carbon emissions.

Next down the Kaya identify is GDP growth per head; that is, the rise in world living standards. The OECD recently came out with a paper entitled “Looking to 2060: A Global Vision of Long-Term Growth“, which forecasts that global GDP per head will rise at an average of 2.6% per annum through to 2060 (see page 11 in the hyperlinked report).

My personal view is that such rates could possibly be sustained for a decade or two, but before long the terrible twins of resource depletion and climate change will batter growth rates down. Unfortunately, we will likely lock in the trillion tonnes of carbon before we do the battering—but I digress. Regardless, we can use the OECD’s 2.6% GDP growth rate as a ranging shot: a pessimist may expect a lower figure, and an optimist a higher figure.

Next up is energy per unit of GDP. This is predominantly a function of how much the tertiary industries (services) contribute to GDP as opposed to the primary (agriculture and resource extraction) and secondary (manufacturing). The final part of the identity is how much CO2 is released per unit of energy produced. This is a function of the energy mix: fossils fuels release lots of carbon when burnt (with the worst being coal) to produce energy, nuclear and renewables, like solar and wind, less so.

But at this stage I am going to take a short cut for the sake of simplicity. Energy per unit of GDP combined with CO2 per unit of energy can be called the carbon intensity ratio (the amount of CO2, or carbon, required by unit of GDP). According to PricewaterhouseCoopers (PWC), carbon intensity declined (that means we are releasing less CO2 per unit of energy produced) at a rate of 0.8% per annum between 2000 and 2011 (see here).

From the above, I hope you can see we have a problem. Population will grow at a little less than 1% over the next decade or so, and carbon intensity has also been falling  by a little less than 1% for the last couple of decades. If the carbon intensity improvement stays on trend, it will roughly offset population growth. Unfortunately, we still have to take account of growth in GDP per person in the Kaya identity. Thus, overall carbon emissions will likely increase by about 2% or so per annum absent a collapse in GDP growth or a major push in renewables and/or nuclear (far beyond what is currently planned).

If you want to get a sense of how emissions will evolve, then I recommend you play around with a simple model of the Kaya identity hosted by the University of Chicago. Enter you own numbers and then press “Do the math”. This model was built for Professor David Archer‘s climate change course at the University of Chicago.

Do the math jpg

As a result, a series of graphs will be generated like this:

UC Emissions jpg

Through generating such charts, you can see how difficult it is to flatten the carbon emission curve. Accordingly, bar some policy revolution that dramatically improved the carbon intensity ratio, we will see our carbon budget exhausted  far before 40 years has passed. So it’s simple: we need a policy revolution.

One response to “The Unbearable Logic of the Kaya Identity

  1. Indeed, according to the Kaya Identity, the only lever we have is carbon intensity. Policies can address the carbon per unit energy or the energy per unit GDP. I used the Kaya Identity in a number of analyses that led me to conclude we’re almost certainly going to emit that trillionth tonne and head well past 2C. So we have to figure out when that will happen and how we’ll respond while simultaneously developing and implementing, as you put it, revolutionary energy policies. A one-time R&D expenditure or slightly higher fuel efficiency standards, while nice, won’t be nearly enough.

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