I’ve written a post showing you how individual choices affect global warming. You should read that instead. This long, dry technical post explains my methods, and in particular how I go from annual emissions to warming estimates. It’s has lots of numbers in, so it’s really only for people who want to check my figures.

One key point up front. There will be nothing in here about who is to blame for climate change, or what you should or shouldn’t do about it.

Those aren’t scientific questions.

All that science can do is tell us the likely consequences of our actions. A good way of thinking of it is that all science can do is put carbon ‘price tags’ on different choices. As to what you choose to buy… in these posts I’m determined to summarise the science without politics or spin or my own preferences injected, and that means I can’t tell you anything about what choices you should make.

Two caveats before I dive in. First, none of the figures below are exact; estimating emissions is an inexact process. They’re still the best guide we have to the effect of our actions. Second, I will always use pre-COVID figures, as it’s far too early for anyone to understand the long-term effects of COVID-19.

Footprints are confusing.

Articles like this often talk about ‘carbon footprints’. I can see why, but I’m going to try to avoid that term because it’s misleading. Why? Well, different people’s ‘footprints’ overlap. Here’s an example…

If you have to fly for work, that creates emissions. Are you to blame, for choosing that job, or is it your boss’s fault for sending you abroad? Or maybe we should blame the owners of your company? Or perhaps the airlines’ shareholders? Actually, if you have a pension, you own a chunk of all the big companies out there, so we need to blame you again.

All of those people can act to reduce the emissions; their ‘footprints’ overlap. Journalists love the idea of a carbon footprint, because it lets them blame people for global warming, which sells copy. (On which more here; search for ‘Journalism’.) But it’s more confusing than helpful if we want to understand how much our choices can slow warming.

Measuring emissions from individual actions

There are three things that you need to do to measure emissions correctly:

  1. If you buy and use a computer, most of the emissions caused will come from the manufacturing process rather than from the electricity used when it’s on. If we don’t include these ‘embodied’ emissions in measurements, they’re meaningless. There are two ways of counting embodied emissions: life-cycle analysis (LCA) and the Leontief Input-Output method (IO). LCA underestimates emissions, perhaps by a factor of two. That is to say, life-cycle sucks. We want to use sources that use IO wherever possible.
  2. Not all emissions are from CO₂. It causes maybe 75% of warming, but other greenhouse gases matter. We want sources that include these. The right unit of emissions is tons of CO₂ equivalent (t CO₂e), which includes all gases, weighted according to how much warming they cause by 2100. I’ll generally refer to 8t CO₂e as 8 tons of emissions for readability. (See the start of this for what I mean by a ‘ton’.)
  3. Any national statistics you use need to be for consumption rather than production. That means that if a computer is built in China and exported to the UK, it counts in the UK emissions statistics, because it’s an individual in the UK who benefits from the computer.

How Bad are Bananas?

There’s an excellent book called How bad are bananas by Mike Berners-Lee, based on his own research, that gets all three of the points above right. (Second edition released Sep 2020 in the UK.) It estimates the emissions from all sorts of activities, from bananas to forest fires. I’m going to rely on this heavily wherever possible, because using one source makes the relative emissions of different individual actions more accurate, and those are what matter when choosing between actions. I’ll always sanity check the numbers against other sources, though.

How Bad are other Greenhouse Gases?

There’s one thing we’ll have to be careful of when using How bad are bananas. As best I can tell, he measures the relative effect of greenhouse gases using their ‘global warming potential’ 100 years after release. What we want is different in three ways:

  • We’re looking at 2100 rather than 2120.
  • We’re interested in a measure of the final temperature increase. Bizarrely, global warming potential doesn’t measure that! Instead it’s (roughly) a measure of the average temperature increase over, say, 100 years. What we’re after is the global temperature change potential.
  • For reasons I don’t understand, Berners-Lee doesn’t account for the CO₂ eventually formed from other greenhouse gases, called climate-carbon feedbacks.

The definitive reference for all this is this IPCC report (see section 8.7). As this table shows…

Calculations for methane are on the wonderfully named page 8SM-17 of this supplement.

… these factors don’t matter much for nitrous oxide (N₂O), but they do for methane (CH₄). (The other greenhouse gases don’t cause enough warming to worry about.) I think Berners-Lee uses the factor of 28 (top of GWP₁₀₀ column), whereas we want GTP₈₀ ‘with cc fb’. Unfortunately that’s not in the table, but it’s likely a little larger than GTP₁₀₀ with cc fb, which is 11.

So, should we correct for this? I’m reluctant to because I’m not completely sure what Berners-Lee is doing; his main comment on methane is that it ‘is 28 times more potent than carbon dioxide’, but his model is sophisticated and he may be using something more sophisticated internally. So I am not going to try to correct any numbers, but please bear in mind that the effect of methane may be smaller than he estimates. This mostly affects emissions from cattle.

Numbers

TCRE

From IPCC Mitigation Pathways Compatible with 1.5°C… (2018), p105

Have a look at the graph above, which plots warming against (cumulative) CO₂ emissions. Don’t worry about the red points, which are projections; just focus on the black ones. You can see that there’s a pretty good straight-line relationship between emissions and warming. That is, if you double CO₂ emissions, you double warming. The graph suggests each 1000 Gt of CO₂ is associated with something like 0.5°C of warming. One has to be a little careful here, because there are other greenhouse gases, meaning each 1000 Gt of CO₂ will cause a bit less than 0.5°C of warming. More on that in a second.

The key number here has the intimidating name of the transient climate response to cumulative CO₂ emissions, or TCRE. The paper cites various estimates from other research; it looks like TCRE is in the range 0.2–0.7 °C per 1000 Gt CO₂. This is wide enough that our estimates of warming will be significantly less exact than estimates of emissions.

The paper says

studies using observational constraints find best estimates of TCRE of 0.35°–0.41°C per 1000 GtCO₂

We’ll go with the midpoint of that range, TCRE = 0.38 °C per 1000 Gt CO₂.

I should say that at high levels of warming, the graph above may stop being a straight line as feedback effects kick in. This is a complex topic and I won’t broach it here as I can’t find a way to fit it into the main article without making that incomprehensible.

Greenhouse gases

From here.

Digging into the literature, it seems like for other greenhouse gases, you should convert to CO₂-equivalent (CO₂e) amounts and apply TCRE. So e.g. 1 ton of nitrous oxide has the same effect as 298 tons of CO₂, so that 1t N₂O = 298t CO₂e; that means 1000 Gt of nitrous oxide would cause 298 * 0.38 °C = 113°C of warming.

There’s a sanity check we can apply here… we don’t have good historical estimates of emissions of methane and N₂O, but we guess that the proportions of different gases have stayed roughly the same. The graph above shows that CO₂ accounts for about 75% of emissions: for every 3 tons of CO₂, there’s 1 ton CO₂e of other gases. That means that each 1000 Gt of CO₂ comes with about 333 Gt of other CO₂ equivalents, for a total of 1333 Gt of emissions. Multiplying by TCRE gives 1.333 * 0.38 = 0.51°C of total warming when 1000 Gt of CO₂ is emitted. That’s reassuring, because it’s consistent with the 0.5°C/1000 Gt slope we estimated from the graph at the start of this section.

The Little Planet

If you’ve read the main article, you’ll know we’re turning emissions figures into something more comprehensible by illustrating their effect on a Little Planet. The Little Planet is 7.8 billion times smaller and 7.8 billion times more sensitive to emissions than Earth. That means that one person driving a mile on the Little Planet has the same effect on its temperature as 7.8 billion Earthlings driving a mile each has on Earth’s temperature.

It’s pretty easy to adjust TCRE for the Little Planet; we just multiply by 7.8 billion to get:

Little Planet TCRE = 2.96 °C per 1000 tons of emissions.

Another way of putting that is that if each person on earth were to emit 1000 tons of CO₂ right now, global temperature would quickly jump up by about 3 °C.

The Future

In the main article, I look at the impact of your choices assuming that you’ll be on the planet for another 50 years. To compute those, we’ll need to adjust for decreases in embedded emissions as electric cars, better batteries, heat pumps and other green technologies come into play. For example, a kilogram of beef in 2060 will have less embedded carbon than a kilogram of beef in 2020, and we need to take that into account when finding the impact of going vegetarian.

Modelling all this in the most rigorous way possible is hard. First we’d need to model emissions decrease rates in transport, agriculture, and all the other sectors of the economy. Then we’d need to figure out how each sector depended on each other sector; after all, part of the emissions embedded in your food come from their transport. Putting all that into a mathematical model would give you annual emissions decrease rates for everything you consume, plus a scientific publication or two.

The future is another country. They emit things differently there.

Rather than trying that complex modelling process, I’m going to use a simplifying assumption, namely that emissions embedded in all the different things you consume decrease by the same percentage each year. So driving a mile, a kilogram of lamb, etc., all reduce their emissions by the same percentage each year.

Figuring out that actual percentage became such a big task that I wrote a whole other (long) article on on it. The tl;dr for it was:

In developed countries, the average annual per-capita emissions reductions to 2100 will be between 1% and 2%.

We’ll use the range from that article, 1–2%, to estimate the decrease in emissions from each of your actions (eating meat, etc.) for each year during your life.

Computing Lifetime Emissions

If there’s a 1% reduction each year, that means your 2021 emissions from an action are 99% of those in 2020, your 2022 emissions are 99% of those in 2021, and so on. So, for example, the food eaten by an average person in the UK contains 3.2 tons of embedded emissions as I write in 2020. With a 1% annual reduction, I’d assume 0.99 * 3.2 = 3.168 tons in 2021, 0.99 * 3.168 = 3.136 tons in 2022, and so on.

If you add those numbers up over the next 50 years, you find UK average lifetime emissions from food will be 126.4 tons, which is 39.5 * 3.2 tons. (By comparison, if we weren’t accounting for technological progress at all, we’d have got 50 * 3.2 tons or 160 tons.) So for a 1% reduction rate we can go from annual emissions (3.2 tons) to lifetime emissions (126.4 tons) by multiplying by 39.5.

Of course, the exact multiplier depends on the actual reduction rate we pick:

  • 1% annual reduction: lifetime emissions are 39.5x those in 2020.
  • 1.5% annual reduction: lifetime emissions are 35.4x those in 2020.
  • 2% annual reduction: lifetime emissions are 31.8x those in 2020.

I’ll use the 1.5% reduction rate and 35.4x multiplier for the main article, but it’s good to see that if we had gone with 1% or 2%, it would only change our final figures by 10% or so. (31.8x is 90% of 35.4x.) In particular, that reassures me that using the same reduction rate for every sector is a decent approximation.

Yearly Rule

We found this rule above:

Little Planet TCRE = 2.96 °C per 1000 tons of emissions.

We can combine that with our 35.4x multiplier to get a more convenient rule. Suppose I make a choice that reduces my emissions, such as going vegetarian, and that it saves 1 ton of emissions this year (2020). The impact of that change will reduce each year, just as described above; I’ll only save 0.99 tons in 2021, and so on. Over my life I’ll save 35.4 tons. That will reduce the Little Planet’s 2100 temperature by 35.4 * 2.96 / 1000 = 0.105 °C. I’ll use that exact number for calculations, but it’s useful to remember this rule of thumb:

Little Planet Rule: A lifestyle change which reduces emissions by 1 ton / year in 2020 makes the Little Planet 0.1 °C cooler in 2100.

Well, I thought it was meant to be a planet. Credit: NASA

Key science, with sources. Minus bad statistics. Minus shaky methodology. Minus politicisation, left or right.