Monday, March 26, 2007

Global Warming and the Numbers

Gadabout is curious about effects of global warming as related to a rise in sea water levels. After reading a few articles about climate change and the projected rise in sea water levels, estimated to be between 7 inches and 2 feet over the upcoming fifty years, I decided to do some math to associate a degree of magnitude in my mind that made sense. A rise of two feet seemed like a lot to me, so I looked up a few facts and broke out my trusty TI-30X IIS scientific calculator and ran the numbers.


The earth is 7,926 statute miles in diameter (Radius = 3,963)
The earth’s surface is about two-thirds water
The volume of water in the liquid state is equal to its frozen volume

Math Formula:

Volume of a sphere is derived: V = 4/3 Pi (R)^3


I ran two equations for volume, one for a 3,963 (20,924,640 ft)mile radius, and another for a 3,963 miles and 2 foot radius (20,924,642 ft...remember the 2 foot rise in sea levels). I subtracted the smaller from the larger and multiplied by 2/3 to account for land mass.

The result is 22183 cubic miles of water. In other words, it is a cube 28.09 miles on each side. So, the earth will need to melt an ice cube 28 miles high to result in a 2 foot rise in water levels. Now remember, this is water that melted above sea level. It does not take into account ice below sea level that need not be accounted for since it already displaces sea water.

We are talking about a 28 square mile ice cube. Wow! Now, I have no idea as to the height of the polar icecap. It could be 1,000 feet high or maybe 10,000 feet high, but for the sake of discussion, let’s assume a 5,280 (1 mile) foot elevation since it makes the math easier.

It would take 798.55 square miles of 1 mile thick ice to melt to produce an affect of a 2 foot rise in sea water. Okay, my math and assumptions are a bit simplified, but I am guessing this estimate is within +/- 20 percent, and errors on the conservative side.

Other facts for the record:

Cubic feet = 11,004,134,523,828,749

Ice cube in feet = 148,358 feet on each side

For the reader, I adjusted these numbers slightly from my original post to reflect a more accurate measurement in Earth's diameter.


Anonymous said...

Isn't the volume of water in the solid state greater than in the liquid state?

Gadabout Jack said...

Yes, you are correct. The density of ice is less than the density of liquid water, which is why ice floats to the top of a glass. Since ice is less dense, then it can be inferred under equal pressures that the volume per equal unit of mass of ice is greater than water. In fact, it is about 9% greater (I looked it up). I did not want to complicate the discussion with such conversions, so we have two choices. The first is to simply multiply the 28 mile square cube by 1.09 to visualize a larger ice cube. The second is to simply accept the visualization in the liquid state. Either way, I am tired of the math!

Anonymous said...

If the polar ice cap is actually floating on top of the arctic ocean, wouldn't most all of it be displacing the water underneath? How much is on top of dry land? Why does the ocean have to rise with warming--could the ocean level possibly go down based on a 9% loss in volume of the ice that is currently displacing water?

Gadabout Jack said...

Well, yes and no. You are right about submerged ice from floating icebergs, but most of the ice we are talking about is from above the surface, positioned firmly on tera ferma. Interesting point though, and is certainly germane to the general argument.

Bobo said...

My personal view is that though there is an amount of increased temperature over the past decade, it is not to a significant degree to create such alarm thoroughout the globe. In the next 50 years, I suspect that the trend will be something else and a whole new generation will a have a new subject for the world to end.

Gadabout Jack said...

Now we are talking! The end of the world!