Yes there is indeed climate change. There is no doubt that we (humans) have put a whole bunch of carbon dioxide into the atmosphere and that carbon dioxide is changing the climate. And things are pretty bad. Maybe seriously bad. So what if the global temperature rises enough to melt the Antarctic ice sheet? How much water is there and how much would the sea level rise? What about the Arctic polar cap? Why don’t we hear about the problems caused by the ice melting at the North Pole? (Because more ice melts every summer.)

Antarctic ice cap

Let me start with the ice at the South Pole. Normally I would do a traditional “back of the envelope“estimate and just get rough values ​​for things. However, in this case, I really don’t have a clue of the size of the Antarctic ice sheet. I’m not sure about the area or the depth ice cream. Honestly it’s not my fault. It’s because I grew up with it Mercator projection map. This type of map makes Antarctica incredibly huge.

To get a rough estimate of the size of Antarctica, we think of it as a circle with a diameter equal to the width of the USA. See, now we’ve made a connection between something that you don’t really want to feel and something that you might know. So how far is it from the United States? Let’s say it’s about 3,000 miles (4,800 km) wide. So if we estimate this as the diameter of a circular Antarctica, the area would be:

Illustration: Rhett Allain

Forgive me, but I’ll cheat a bit. Since I really don’t know if this value is legit or crazy, I’ll take a pic on the Antarctic Wikipedia page. Oh great, I’m pretty close. I feel better now. But wait! There is another thing difficult to estimate: the average depth of the ice cap at the South Pole. Well. I have already looked at the page and see that the average thickness of the ice is 1.9 km. All is for the best. There’s no way I would have guessed it’s so thick. That’s an insane amount of ice cream.

So now we can visualize this ice cap as a giant cylinder – perhaps more like a cylinder shaped like a hockey puck. I can calculate the volume as the area of ​​the base (a circle) times the height. I will keep the measurements in units of meters just to make things easier in the future.

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