The Science of the ‘Trillion Tonne’ Limit

By Luke Harrington

A recent post by Catherine Leining, ‘The trillion tonne challenge: Think cumulatively, act immediately on infrastructure’, explores the significance of limiting our cumulative carbon emissions to one trillion tonnes, and how keeping to such a target might be approached. But where has this number come from? How is it calculated? And why is it such a significant realisation when it comes to defining mitigation targets?

The idea that we can correlate a temperature threshold to a fixed number of cumulative carbon emissions was only first explored in a series of seminal papers in 2009. All of these research groups make use of simple climate-carbon cycle models* to calculate global-scale changes to greenhouse gas (GHG) concentrations and temperature as a function of corresponding emissions. I have worked personally with the model used by the Oxford group (see Allen et al. 2009), and can shed some light on the science of the link between cumulative emissions and global temperatures.

There have been many different attempts to relate a limit on global CO₂ levels to a corresponding upper limit on global temperature rises (normally selected as 2°C relative to pre-industrial levels). For a long time, the best approach was thought to be a fixed upper limit on CO₂ concentrations; the name of 350.org was fundamentally based around this … though the limit they chose was based on the conclusions from mainly James Hansen, rather than a consensus of scientific community. More recently, it was thought that a 450ppm upper limit would be appropriate to stay within a 2 degree threshold. Clearly there are limited policy applications with this ‘target’ being constantly re-adjusted.

The problem is that GHG concentrations, while being easy to measure, represent an intermediate variable that links what we put into the atmosphere (emissions) to the corresponding climate response (temperature change). But carbon cycle feedbacks make these relationships difficult to quantify in a warmer future. As seen below, if a direct relationship between emissions and temperature can be quantified, that takes away the uncertainty associated with steps A2 and A3.

Schematic overview showing the key steps relating emissions to global temperature changes for a simple model framework. Source: Meinshausen et al (2011).

The long lifetime of CO₂ means that on centennial timescales, the global temperature response is insensitive to the rate of emissions; the key issue is rather how much is emitted in total. The significance of emission rates can be considered more important for short-lived climate pollutants (such as methane), but the sheer size of global CO₂ emissions makes it the key determinant driving temperature increases (to be discussed further in an upcoming post). 20^th century temperature trends demonstrate there is a strong correlation between temperature increases and cumulative emissions of CO₂. In addition, this correlation is approximately linear whether you are looking at the present climate (well-constrained) or future climate projections (poorly-constrained), so we can be more confident when quantifying the cumulative limit on emissions for a future temperature target.

Mean global temperature increase (relative to 1765) as a function of cumulative CO2 emissions only (measured in GtC), for the latest RCP emission scenarios. Calculations made with the Oxford simple climate-carbon cycle model. Non-CO2 GHG emissions are not included. Source: Luke Harrington's BSc (Hons) dissertation, 2013.

As seen in the plot above, estimates for cumulative CO₂ emissions (excluding non-CO₂ GHGs) show an approximately linear temperature rise of between 1.7 and 1.9 degrees C towards the trillion tonne target, regardless of the scenario chosen (IPCC estimates including the other GHGs bring the estimates up to nearer two degrees). The versatility of this relationship means cumulative emission limits could be set for temperature targets both lower or higher than two degrees, if desired.

Identifying this direct relationship between cumulative emissions and global temperatures helps to dramatically reduce uncertainty when setting mitigation targets. It also simplifies the story of how much carbon we have left to burn, so we can push forward and work on how this might be rationed out over the next few decades.

*A simple coupled climate-carbon cycle essentially contains two parts: a radiative energy balance model with a carbon cycle box model component. Though these types of models are highly parametrised (the Oxford model actually only has five key equations to represent the entire global climate system response), they actually do a very good job of representing how first-order variables (like GHG concentrations and global temperatures) behave through time.