Visualizing CO₂
The blanket of gas warming the Earth is, literally, about as much material as a blanket
Pick any article about climate change; it will be awash in statistics. Gigatons of CO₂, dollars per megawatt-hour, market share of EVs. It’s easy to get lost in the numbers and lose any sense of perspective.
For today’s topic, I thought I’d look for ways to actually visualize one of the most basic facts about climate change. This carbon dioxide that’s causing so much trouble: how much of it is there, exactly?
(I'm going disregard other greenhouse gases, such as methane and nitrous oxide. They have an important impact on climate, but exist in the atmosphere in quantities much smaller than CO₂.)
In total, the amount of extra CO₂ in the atmosphere, compared to the start of the Industrial Revolution, is about 1100 billion metric tons1. If we were to spread that evenly across the Earth’s surface – which, in fact, is exactly what we have done – how thick a layer would it form?
It’s difficult to visualize a gas. So let’s imagine we were to freeze the carbon dioxide into solid form. You’ve probably seen frozen CO₂ before: that’s what “dry ice” is. Distributed across the Earth’s surface, the extra CO₂ would form a layer of dry ice about 1.35 millimeters thick, or just under one twentieth of an inch2.
One twentieth of an inch doesn’t seem like much, but that’s actually about the thickness of a blanket, if you squeeze it flat. (I tried to Google “how thick is a blanket”, and got nowhere. So I went into the living room, grabbed my favorite fleece from the couch, and folded it over four times to make 16 layers. If I squeeze the resulting sexdecablanket3 down, it’s a bit less than an inch thick. So 1/20th of an inch is in the ballpark for one layer.)
Doesn’t it seem a bit odd that just one blanket-thickness of CO₂, almost literally a “blanket of CO₂”, can cause so much trouble? But we know that wrapping a blanket around something warms it up4. That applies to large objects as much as small ones5. Fortunately, all that CO₂ isn’t a very good blanket, as it’s only warming the planet by a degree or two. If we’d spent the last few centuries spewing fleece into the air, we’d really be in trouble.
Now Let’s Do Per-Person
Suppose we divide the extra CO₂ in the atmosphere by the population of the Earth. We just passed the 8-billion-person milestone. 1100 Gt / 8 billion people = 137.5 metric tons of CO₂ per person. How can we visualize 137.5 metric tons?
That seems like it might be in the right range for your bigger sort of tree. Let’s see if we can figure out how big a tree would need to be to contain that much carbon. It’s an obscure sort of question, but Eliana managed to dig up a worksheet on the NOAA website that relates a tree’s diameter to the amount of carbon it contains. For a red oak, it works out that if the tree’s trunk is 292 inches in circumference, then the above-ground portion of the tree contains about 137.5 metric tons of CO₂6.
The largest red oak on record appears to have a 405 inch circumference, so 292 inches is entirely feasible. I tried to find a picture of a tree that size; the best I could come up with, courtesy of The Gladwin County Record & Beaverton Clarion, is this photo of a 218-incher:
Our 292 inch tree would be substantially larger than this, but you get the general idea. (For scale, note the red building in the lower-left corner, which appears to be slightly behind the tree and hence looks a bit smaller than it should.)
(If we could somehow plant just one red oak tree per person, give them all the space, water, and other resources they need to grow, and wait until they achieve this size, that would make a huge dent in global warming – assuming we’d managed to do all that without disturbing land that already contains significant amounts of carbon. Unfortunately, as we saw last time, that’s difficult.)
Emissions vs. Atmospheric CO₂
So far, we’ve been talking about 1100 Gt of CO₂: the amount by which atmospheric levels have increased in the last few hundred years. However, our total historical emissions are much larger, around 2000 Gt or so (sources seem to disagree). Quite a bit of CO₂ emissions are absorbed by the ocean (causing acidification and other problems) or, in various ways, on land.
If we plug 2000 Gt into the formula, we get a red oak tree with a circumference of 374 inches. I am very disappointed in the Internet for not providing me with a photo of a red oak tree this size, but they do exist.
Ongoing CO₂ emissions run at about 37 Gt per year, or 4.63 metric tons per person per year. That corresponds to a red oak with a circumference of just 72 inches; you might just be able to wrap your arms around it, if you’re tall and your bones are made of rubber. Using the park bench for scale, this one seems like it might be a big large but in the right ballpark:
Twinkies
Any fan of Ghostbusters is familiar with another yardstick for measuring alarming situations: the Twinkie. If a Twinkie had the same carbon content as one person’s share of excess atmospheric CO₂, how large would it be?
Based on the nutrition facts (hah) for a Twinkie, a pair weighs 77g: 43g carbohydrate, 8g fat, and 26g unaccounted for. Using a mathematical simplification technique known as “who cares, it’s a damn Twinkie”, I estimate that this includes 29.7g of carbon7, or 14.85g per Twinkie.
Sometimes the Internet really comes through: of course there’s a web page checking Egon’s math on the size of the Ghostbusters Twinkie. It states, and I am inclined to accept, that modern Twinkies are 9.9cm long.
So: there’s currently 137.5 metric tons per person of excess CO₂ in the atmosphere, or 37.5 metric tons of carbon, equivalent to the carbon content of 2,525,253 International Standard Twinkies. A single Twinkie containing that much carbon would be 136.2 times larger in each dimension, or just under 13.5 meters (44 feet) long. In Ghostbusters, Egon says “According to this morning's sample, it would be a Twinkie 35 feet long, weighing approximately 600 pounds.” Our Twinkie is only moderately longer than that; though Egon was way off on the weight.
Wait, Did I Have a Point Here?
Surprisingly, yes.
We tend to talk about climate change in terms that are too large or abstract to grasp intuitively. By translating CO₂ emissions into a tangible object, we can get some grasp of the scale of the problem. We saw that the amount of carbon we emit per person, per year, is equivalent to a medium-sized tree. That’s not small; you’re not going to dent it by purchasing a reusable drinking straw. But it’s not astronomical either. It’s within the scale of things that we can reasonably influence, especially at the scale of industrial policy. This shouldn’t really be surprising, as it was mostly industrial activity that created the problem in the first place. But it’s nice to confirm it.
Per NOAA, atmospheric CO₂ levels are currently about 421 parts per million, vs. 280 prior to the Industrial Revolution: an increase of 141 ppm. A FAQ on the Lawrence Berkeley National Laboratory website tells us that 1 ppm is 2.13 Gt of carbon, or 7.81 Gt of CO₂. Multiplying by 141 ppm gives 1101 Gt CO₂.
The Earth has a surface area of about 510 trillion square meters, or 5.1 * 10^18 square centimeters. 1100 Gt is 1.1 * 10^18 grams. So there are 1.1 / 5.1 = .216 grams of CO₂ per square centimeter.
Dry ice has a density of about 1.6 grams per cubic centimeter, meaning the layer of dry ice would be 0.216 / 1.6 = 0.135 centimeters thick.
That’s the Greek prefix for “16”, but honestly “sexdecablanket” sounds like a cutesy name for something very, very different. I’m not sure what, exactly. But probably something I wouldn’t want to discuss in a family-friendly blog.
For the nitpickers out there: I know, I know, blankets don’t actually warm things up. Otherwise, your linen closet would turn into an oven. What a blanket actually does is prevent heat from traveling through it. So if you wrap a blanket around something that is warmer than its surroundings – such as, for instance, your body, or the Earth – the blanket will reduce the rate at which heat escapes, leaving more heat inside.
Yes, more room for nitpicking here, but it basically works if we’re focused on surfaces and don’t have to take the increased thermal mass of the larger object into account, e.g. because the object is made of a material that conducts heat poorly. Dirt, for instance.
A 292 inch circumference yields a diameter of 292 * 2.54 / 3.14 = 236 cm. For red oaks, with a trunk diameter of D centimeters, the formula is 0.13 * D^2.42 * 0.521 kg of aboveground carbon. Then we multiply by 11/3 to get kg of CO₂, and divide by 1000 to get metric tons. Putting it all together: 0.13 * (292 * 2.54 / 3.14) ^ 2.42 * 0.521 * 11/3 / 1000 = 137.5.
The elemental breakdown of sucrose (a basic sugar) is C12 H22 O11. Waving my hands so vigorously that you can’t see what I’m writing on the chalkboard, I’ll pretend that this same ratio applies to all carbohydrates in the Twinkie, and that the unaccounted-for material has half the carbon content of sucrose (on the theory that some of it will be materials containing no carbon at all, such as water and salt, but some will be at least vaguely organic – or at least, as organic as anything else in the Twinkie).
In C12 H22 O11, the carbon has molecular weight 144, and the total molecular weight is 342, so carbon is 42% of the total. (A calculation this ridiculous had to have a 42 in it somewhere.)
As for fat: the fat in Twinkies is mostly from tallow (yum!). According to Wikipedia, tallow is made up of lots of fatty acids but the highest proportion is oleic acid. Oleic acid is 76.96% carbon by weight. So we could say one gram of fat contains 769.6 mg of carbon.
So, of the 77g Twinkie pair, we’re modeling (43 + 26/2) * 0.42 + 8 * 0.77 = 29.7g of carbon.
Dissatisfied with these slapdash approximations? I suppose you think you could do better? …If you can do better, I’d, um, appreciate a copy of your results.
This is great. Might even make it part of our pitch!