Even though none of you (except Brett) bothered to do the math exercise, I still provide you with the answer to my question. How much will ocean levels rise if 33x10^6 km^3 of ice melts?
My off the top of my head guesses came up with a solution of 76m. The "official" answer, as told me by a co-worker, is 68m. With that one number as a starting point, I was able to come within about 20 feet of the correct value. Not bad, eh? And now, because I can't resist, a brief walk-through of the calculation:
First, we need to know how big the surface of the Earth is. The surface area of a sphere (always assume spherical, though strictly speaking the Earth is not) is A = 4*Pi*r^2. So what is the radius of the Earth? This can be hard, but let's think . . . From LA to NY is what, about 3000 miles? And that covers 3 time zones. So 24 time zones (Earth has to be 24 times zones, otherwise it wouldn't make sense) would be 24,000 miles. So that's the circumference. Assuming Pi=3, the diameter then is 8000 miles, and the radius is 4000 miles. (Quick check, the real answer is 3,963 miles. Not bad!) So the surface area is about 520,743,000 km^2. (Used calculator, I never said those aren't allowed, and changed to metric.)
So, if we spread 33x10^6 km^3 over 5.21x10^8 km^2, that would give us 63m over the entire Earth. But, then I estimated that only 75% of the Earth is ocean (real answer: 71%), which is where all that rise would be. So that gives 63m/.75 = 84m of rise.
Except we forgot that if water expands when it freezes, then it must shrink when it melts. How much? I guessed 10% (actual answer: about 8%) So only the actual volume of water to spread over the oceans is only 90% of what we were given, so the actual rise should be 84m * 0.9 = 76m. Tada!
Though Brett didn't comment on the previous post, he did complete the assignment (as I indicated he would . . . or maybe because I indicated he would). He came up with a number somewhat higher than mine, a bit over 100m, because he used different guesses. But the point remains, whether you trust the fancy scientific calculations, my quick guesses or Brett's quick guesses, the oceans would rise a few hundred feet if all that ice melted. So if you live on the coastline now, you won't need to invest in a snorkel that is any longer than about 300 feet.
(Of course, your lungs would never be able to work a snorkel that long, but that's topic for another day.)
12 comments:
There's actually 4 time zones between New York and LA. Pacific, Mountain, Central, Eastern. Did they realign those?
But they are three time zones apart. NY is three hours ahead of LA.
did you take into consideration loss of displacement from the ice?
You seem to be assuming that the water will only rise where you estimated the oceans were (i.e. 75% of the earth) - when in reality the more the water rises, the larger the surface area of water on the earth becomes. I would guess this is where the bulk of the 8m difference comes from.
Here's another 'large' calculation that I was asked to estimate recently: What percentage of power is lost between the power plant and the end user? Hint: The only important assumption is that most transformers are 98-99% efficient - with this info you can get pretty close...
Brett, Melissa's basic point is correct. Assuming LA and NYC are roughly in the middle of their respective time zones, three complete time zones would be traversed going from one to the other.
Ben, the ice we are considering here is the land based ice, which would be principally in the antarctic and Greenland sheets. Because the ice is on land, it truly does make the ocean levels rise when it melts. Floating ice (arctic) does not make the oceans rise, just as melting ice cubes do not make your Kool-Aid over flow.
Tyler, you make a valid point. The percentage of Earth covered by water will certainly increase as the water rises, thus making subsequent rises more difficult to affect. I am certainly unqualified to estimate how that increase would run, as it would require detailed analysis of the topography of the coastlines of the world. However, I would venture to guess that with 200ft of ocean rise, the 70.8% wouldn't increase beyond the 75% that I assumed, so I actually overcompensated for that. (Going from 71% to 75% would mean the land mass goes from 29% to 25%. That's a 14% reduction in land on Earth, which would seem a lot for 200 feet of water.)
I would guess that the largest source of error in the calculations comes from the initial estimate of the total ice volume, which I pulled off some website somewhere.
Finally, another interesting detail is that Antarctica and Greenland would both rise significantly with trillions of tons of ice no longer pushing them down. How far, I really have no idea, but those land masses could actually grow if the ice all melts.
I'm guessing that last comment is actually Clark, pretending to be Shanny.
And that comment by Melissa was actually by Adam. All these husbands hiding behind their wifeys!
But neither LA or New York are in the middle of their time zones, in fact you should know since part of main is actually in a different time zone than New York, that NYC is on the eastern edge of the time zone. However, I had made the assumption that LA was closer to the western edge of the time zone than it is. It's surprising how much California goes in.
Yea, go me, I put Maine as main. Maybe I'll go get some sleep now.
We're getting pretty picky here for a calculation that was supposed to be all about reasonable guesses!
This map and this map both show LA and NYC a bit on the eastern side of the middle in their respective time zones.
Wikipedia puts LA at W118°15' and NYC at W74°00', which would make them 44°15' apart. Time zones ideally would all be exactly 15° wide, but aren't always, for political/practical purposes. So, getting right down to it, LA and NYC are the equivalent of 2.95 time zones apart. Just a shade under 3, as it turns out.
Also, in my comment where I accidentally pretended to be Shannon, I mentioned the rise in continents due to decreased ice load. This is known as isostatic rebound, and would take thousands of years to occur. (Of course, melting all that ice would likely take thousands of years, too.)
Of course, there is an actual flaw in my logic for determining the circumference of the Earth that none of us have picked up on yet (including myself).
Actually, there are two flaws, both relating not to the "3 time zone" estimate, but the "3,000 miles" estimate.
First off, it's not 3,000 miles. Google maps says we can drive it in 2,777 miles, and certainly a straight line would be shorter still. But that's not a flaw in logic, just an estimate that was 10% off.
The first flaw is that LA and NYC are clearly not on the same longitude. LA and Caracas might be 3 time zones apart (though they're probably not) and are probably 7,000 miles apart. Only the longitudinal distance between the cities should count.
The second flaw is that neither of the cities are on the equator. Two cities in very northern Canada could be three time zones apart while being only 1,000 miles apart.
Lucky for me, these two flaws help to counteract each other. The north-south displacement relative to each other increases the final earth diameter estimate, while the cities positions off the equator decreases the estimate. This is one of the beauties of estimates. Often, the little details that you forget to account for wind up taking care of each other.
Your larger point about the usefulness of estimates is right on.
Just being able to come up with the idea to estimate the circumference of the earth using miles per time zone--regardless of how accurate your figures turn out to be--is a skill that is sorely lacking these days.
Of course, once everyone has wikipedia on their cell phones, no one will be able to do it anymore. We'll all be like the cashiers who can't mentally calculate change.
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