numbers, not adjectives — D. J. C. MacKay

Quantifying climate change: Degree Person Days

by Carl Edward Rasmussen, 2024-06-28

When tackling climate change, it is important to have good measures to quantify emissions and their 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. Here I propose an alternative measure: the Degree Person Day. 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 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 now. The degree person day specifically measures the consequences of releasing CO₂ for one other 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.

We can express the consequences of activities using degree person days. 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. Since every human currently on average emits 5 tons of CO₂ per year, every year we continue doing this will add 2500 days (or 7 years) of 1°C warmer climate for everyone. Since the Paris Agreement came into effect in 2016 we've added the about 50 years of 1°C warming for everyone.

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. The actual literal incremental consequence would be more like an almost imperceptible temperature rise, experienced by 8000 million people and lasting for hundreds of years. But the point is, that this is very difficult to imagine. In the context of large global emissions, it is equally valid to slice it differently, by focussing on the consequence of emissions for a single person, making the measure more intuitive. We only experience the cumulative effect, which is the same either way of looking at it, one decomposition isn't any more real than another.

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.

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