Yes, there is indeed climate change. There’s no question that we (the humans) have been putting a whole bunch of carbon dioxide into the atmosphere, and this carbon dioxide is changing the climate. And things are looking pretty bad. Maybe seriously bad. So what would happen if the global temperature increased enough to melt the ice cap in Antarctica? 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 that melts at the North Pole? (Because more ice melts each summer.)

Antarctic Ice Cap

Let me start with the ice at the South Pole. Normally, I would do a traditional “back of the envelope” estimation and just get approximate values for stuff. However, in this case, I really don’t have a feeling for the size of the Antarctic ice cap. I’m not sure about the area or the depth of ice. Honestly, it’s not my fault. It’s because I grew up with this Mercator projection map. This kind of map makes Antarctica impossibly huge.

To get a rough estimation of the size of Antarctica, we think of it as a circle with a diameter equal to the width of the United States. See—now we’ve made a connection between something you don’t really have a feeling for to something you might be familiar with. So, how far is it across the US? Let’s say it has a width of width of around 3,000 miles (4,800 km). So, if we approximate this as the diameter of a circular Antarctica, the surface area would be:

A equals 1.8 times 10 to the 13th power times by m sqaured
Illustration: Rhett Allain

Forgive me, but I’m going to cheat a little bit. Since I really don’t know if this value is legit or crazy, I’m going to take a peek at the Wikipedia Antarctica page. Oh great—I’m reasonably close. I feel better now. But wait! There’s one other tough thing to estimate—the average depth of the ice sheet at the South Pole. Well, heck. I already looked at the page and I see that the average ice thickness is 1.9 km. It’s all for the best. There’s no way I would have guessed it’s that thick. That’s a crazy amount of ice.

So now we can visualize this ice sheet as a giant cylinder—maybe more like a hockey-puck-shaped cylinder. I can calculate the volume as the area of the base (a circle) multiplied by the height. I’m going to keep the measurements in units of meters just to make things easier going forward.