numbers, not adjectives — D. J. C. MacKay
16 Quantifying Emission Consequences: Degree Person Days
When tackling climate change, it is important to have good measures to quantify the link between behaviour and consequences.
It is standard practice to measure emissions in units of tons of CO2e (carbon dioxide equivalents), where greenhouse gases are converted to CO2 equivalents, based on opacity to infrared light and longevity in the atmosphere. Below is a picture of a ton of CO2:
However, a ton of CO2 is an unintuitive quantity for most people, and the measure fails to account for the effects of climate change on people.
16.1 Global vs personal scale
The consequences of my own behaviour on climate is small in a global context. But we should not let ourselves be fooled by this true statement. The problem is that we are many, each contributing in small ways. Adding many small contributions is a common challenge, there is even a branch of mathematics called calculus, which takes this to the extreme by adding infinitely many contributions all of size zero. Fortunately, if you don’t enjoy calculus, we don’t have to go to quite such lengths for climate change.
The problem with the leading sentence of the previous paragraph is that it causes confusion by mixing scales. It measures the actions on a personal scale and their consequences on a global scale. You have to be very careful with your reasoning in these circumstances. It is much easier not to be led astray if we always compare apples to apples. And because our intuition is much stronger on a personal than a global level, the personal scope may give us the best insights.
16.2 Personal scope consequences
It is relatively straight forward to relate personal behaviour to emissions. It’s slightly more complicated to evaluate warming on a personal level. But that’ll be necessary to compare behaviour and consequences both on personal levels.
Of course the real consequences of climate change depend on your circumstances. For example, whether you are threatened more by sea rise or by wild fires? But we can quantify the warming which causes these effects. Three fundamental properties together determine these: the temperature difference, the duration of the warming and the number of people experiencing it.
To capture these effects, I propose the “Degree Person Day” unit. A degree person day, is the effect on the climate corresponding to 1 person having to endure +1˚C of warming for 1 day. The unit captures the three desired properties: temperature, duration and number of people exposed. It embodies the ideas that twice the temperature increase and twice the duration and twice the population exposure all twice as bad. These all capture the notion of measuring the consequence of “twice as much warming”.
16.3 Conversion from CO2 emissions
We need to be able to connect our emissions to the degree person day consequences. The conversion between tons CO2e and degree person days is:
1 ton of CO2e = 500 degree person days.
So, adding 1 ton of CO2 to the atmosphere causes one person to have to endure +1°C hotter environment for 500 days. Not hotter than the pre-industrial average, but hotter than if we hadn’t emitted that ton. The degree person day specifically measures the consequences of releasing CO2 for a single person.
To derive this conversion factor, we need to take a few facts into account. Firstly, if you release 1 ton of CO2 into the atmosphere, then about 45% of it (called the airborne fraction) stays in the atmosphere for a longer time, whereas the rest quickly dissolves in surface waters (where it causes acidification). Next, one part per million [ppm] of atmospheric CO2 corresponds to 7800 million tons of CO2. Finally, 1 ppm of CO2 in the atmosphere causes a temperature rise of 0.01°C. We are 8000 million people on earth enjoying the climate, there are 365 days in a year and CO2 stays in the atmosphere for about 300 years. Therefore:
0.45 ton / 7800 million ton per ppm × 0.01 °C / ppm × 8000 million people × 365 days per year × 300 years = 500 degree person days.
16.4 Interpretation
You may be uncomfortable with this interpretation. You may think that the real consequence of releasing 1 ton of CO2e in isolation would be a tiny fraction of a degree, felt by 8000 million people. But this is not quite true, let me explain why. We desire to evaluate the marginal consequence of emitting one more ton of CO2e. In other words, we seek to isolate the effect of that one ton. But we need to be careful here; every ton is emitted in the context of all the other emissions. There is nothing special about one ton compared to any other, all emitted tons of CO2 and their environmental consequences are indistinguishable. The consequences of emitting one ton, can only be understood in the context of the others. It only makes sense to ask about the fraction of the effect of the total, it does not make sense (even in theory) to attempt to identify which fraction. That simply has no physical meaning. Only the aggregate emission has physical reality. In other words, any breakdown we perform is merely a figment of our imagination, a helpful mental construct which assists us in getting an intuitive understanding of the magnitudes involved. This means, that any breakdown of the effect is as valid as any other – none are any more real than any other. Therefore it is as legitimate to say that emitting one ton of CO2 causes +1˚C of warming for 1 person for 500 days, as for example, +1˚C of warming for 500 people for 1 day. (Of course, it is not equivalent to +500˚C of warming for one person for one day, but this extreme interpretation wouldn’t much help your intuition anyway, which is the reason for doing the exercise in the first place.)
An analogous familiar example comes from income tax. Taxes collectively fund many societal needs, but insisting that “my” contributions specifically fund selected items isn’t credible. Once in the chancellor’s chest all £s are identical. Only their collective effects are real.
The equivalence we’ve established above is the key property that allows the degree person day to express consequences for one person. And this in turn allows us to compare behaviour and consequences both within personal scope, without confusing different levels.
For example, using a tank (50 litres) of petrol produces about 114 kg of CO2 corresponding to 60 degree person days. Or one return seat on a London - San Francisco flight, around 2 tons of CO2 equal to 1000 degree person days.
We can straight forwardly use the degree person day to integrate our average behaviour to global consequences. Since every human currently on average emits ~6 tons of CO2e per year, every year we continue doing this will add 3000 days (or 8 years) of +1°C warmer climate for everyone. Since the Paris Agreement came into effect in 2016 we’ve added the about 80 years of +1°C warming for everyone.
16.5 Discussion
Of course, summary measures, like the degree person day, shouldn’t be taken overly literally. Instead it’s a measure that gives an intuitive notion of the climate consequences of releasing CO2. Just like eg. GDP (Gross Domestic Product) doesn’t quantify the income of a particular citizen, it still measures income in an aggregate way. Similarly, we won’t be able to identify a particular person, whose environment will heat up by +1°C for 500 days as a consequence of releasing a ton of CO2.
Similarly, degree person days don’t necessarily imply that the temperature rise will be +1°C. In fact, temperature rise isn’t uniformly distributed around the world. Our measure takes into account that higher temperature rise, for longer duration, and for more people are all relevant considerations. This is true on average, even if for a particular person the consequences of twice the temperature difference may not be equivalent to twice the duration, etc.
Degree person days are an relatable, useful way of quantifying the consequences of greenhouse gas emissions at a personal level.