I suspect the most difficult bit of the problem is defining what we mean by “the length of Antartica’s shore”. Crinkles below a certain size are irrelevant because water can’t flow over them. So we mean the length of the shore as measured by a ruler whose length is the Capillary length of water in air, which is 2.7 mm. Of course no one has ever measured this, but perhaps we can estimate it by using coarser measurements and fitting a curve to them.
Yes, this is the trickiest part. According to some French jokes, Slovenia has 42 kilometers of coast. I agree. This is still not the funny part of those jokes, this is the factual part.
Several thousand kilometers, maybe 10 thousand kilometers of Antarctica’s coast by the same methodology.
According to this amazing paper, Antarctica has a coastline of 39849 km when measured at the 100 m scale, and 43449 km when measured at the 25 m scale. They say its fractal dimension is 1.096448. Fitting a curve of the form L = M*r^(1-1.096448) to those two points I get that for r = 2.7 mm we get L = 107349 km. This methodology is perhaps nonoptimal, but I think it’s the best we’ve got.
So for the purposes of this question I’ll take the perimeter of Antarctica to be 100 000 km. Wikipedia says the total area of the ocean is 360 000 000 km^2. So to rise 6 m needs a volume of 2.16 10^15 m^3. A century is 3.16 10^9 s, so we need 6.84 10^5 m^3s^-1. The Amazon averages 2.09 10^5 m^3s^-1, so we need about three of them. If the coast of the Antarctic is 10^8 m then we need 6.84 litres flowing over each meter every second.
You’re wrong here. See the coastline paradox. Lines can be as long as they want, just by being extremely crinkly. There’s no law that says a shorter curve cannot enclose a longer one.
I am right here. Those small bays are not important in this case when we want to calculate the amount of water pouring out to sea. The mouth of the river Amazone is 200 km wide. Not as wide as the sum of all underwater bays and peninsulas.
Okay. So when I was calculating how many Amazons were needed the perimeter didn’t matter, and the answer was just 3. But when you asked how many litres would be pouring over each meter of perimeter I did the calculation based on the idea that an equal amount of water was passing over each bit of the perimeter.
Otherwise the answer is of course that the water forms together into rivers so that most of the perimeter has no water passing over it but the mouths of the rivers have a great deal of water passing over them.
Three Amazons are the right answer. AFAIK, the biggest river there is approximately as large, as the biggest river on the island of Crete. Which may be beautiful, but quite lousy in cubic meters per second.
Where and how some people see three Amazons on Antarctica, is a mystery to me. The amount of ice falling directly into the sea, is quite pathetic, as well.
But mostly, I love how the arithmetic is reigning supreme above all the sciences.
Wikipedia is another nice source of info. It claims that, during the past 20,000 years, the fastest increase in sea level was around 5 meters per century.
(The page on sea level rise mentions 3 meltwater pulses; clicking through it looks like Meltwater Pulse 1A is the one that researchers are the most confident about.)
This increase has some geological traces in the state of Washington. That was the North American glacier melting, for the most part. We don’t see much of that kind of flooding on Greenland or Antarctica recently. This is a real thing.
I am certain, that if your arithmetic isn’t sound, then your science is most likely bogus, no matter how fancy it looks.
But mostly, I love how the arithmetic is reigning supreme above all the sciences.
This was a good puzzle, but I don’t see how it follows from the puzzle that arithmetic is “reigning supreme” above all the sciences. For one thing, I thought that most scientific estimates of sea level rise over the next 100 years were a lot lower than 6 meters. Do you have any links to projections of 6 meters?
Okay, well. The next time I’ll ask, how fast the world ocean is losing water. But that’s for the next time. We had to eliminate this fast-rising possibility first.
Where and how some people see three Amazons on Antarctica, is a mystery to me. The amount of ice falling directly into the sea, is quite pathetic, as well.
The amazon begins distributed across brazil, as the occasional drops of rain. Then it comes together because of the shape and material of the landscape, and flows into streams, which join into rivers, which feed one big river. If global warming is causing antarctica to lose mass, do you expect the same thing to happen in antarctica, with meltwater beginning distributed across the surface, and then collecting into rivers and streams?
How about glacial flow? Ice doesn’t move fast, but it does move. It can postpone melting until it’s in contact with seawater. What do you think the ratio of mass moved by rivers vs. glaciers is in Antarctica?
. Using an optimized flux gate, ice discharge from Antarctica is 1932 ± 38 Gigatons per year (Gt yr-1) in 2015, an increase of 35 ± 15 Gt yr-1 from the time of the radar mapping.
That’s about 0.4 Amazon.
The precipitations alone compensate most of this. Almost 3 Amazons still missing for the 6 meters sea rise in a century,
Besides …
Icebergs generally range from 1 to 75 metres (3.3 to 246.1 ft) above sea level and weigh 100,000 to 200,000 metric tons
10 million icebergs per year? Per a few summer months? Highly unrealistic.
If the glacier is flowing off of the continent into the sea, then sea ice is in an equilibrium between melting at the edges and bottom and being replenished at the middle.
demands huge melting we don’t see
“See” how? It seems to me that you don’t have an involved understanding of the melting of glaciers. If we could measure the mass of the Antarctic glacier straightforwardly, then I’m sure we’d agree on the meaning of changes in that mass. But if we don’t see the particular melting process you expect, perhaps you’re just expectung the wrong process, and haven’t uncovered a conspiracy among all the experts.
Much smaller numbers, popular now
In my experience, actually reading the ipcc review has never been popular and still isn’t. I’m sure you could still find someone in the press claiming larger sea level rise, if you tried. But why pick the easiest opponent?
Across the frozen sea around most of Antartica even in the summertime?
I’m not sure if you’re actually curious, or if you think this is a “gotcha” question.
Here’s a picture. As the glacier flows outward (here’s measured flow rates), it begins floating on the sea and becomes an ice shelf, which then loses mass to the ocean through melting and breaking up into pieces, which then melt. This ice shelf is thick (100m − 1 km scale), because it’s a really thick sheet of ice being pushed out into the water by gravity. It then encounters the sea ice, which is ~1-4 meters thick. The sea ice gets pushed out, or piled up, because there are no particular forces holding the sea ice in place.
At this point I’m tapping out of the conversation. Either you’re ignorant but curious and there’s no point to me typing up things you could look up, or you want to feel superior while remaining ignorant and there’s no point to me typing up things you don’t care about.
That picture is silly. The deep-cold freshwater continental ice flowing into the ocean and melting there in the icy waters, but the 1-4 meters thick salty ice survives the Antarctic summer?
Actually, there are a few places on Antarctica, where glaciers flow into the ocean, but not very fast at all. And where is the heat to melt −40 degrees cold ice, 2000 cubic kilometers per summer? It is not only the question of the heat but the question of the heat transfer.
I think, most people still believe that picture anyway. Most people here, I guess, too.
Much smaller numbers, popular now, still demands huge melting we don’t see really
Perhaps, but:
If the global temperature continues to rise over the next century, then the rate of melting will be higher at the end of the 100 year period than it is now
In addition to Antarctica, Greenland has a significant (~ 2,850,000 km3) ice sheet. Melting of the Greenland ice sheet will also contribute to sea level increases
If the global temperature continues to rise over the next century
If. Then we might see something spectacular. But we need A LOT of warming, to actually warm up and melt that ice.
In addition to Antarctica, Greenland has a significant (~ 2,850,000 km3) ice sheet.
Fine, you’d need one Amazon on Greenland and only two Amazons for Antarctica. Doesn’t compute as well.
Imagine a summertime Greenland Amazon! It should be 3 Amazons really in that 1⁄3 of the year. The melting season is short.
We most certainly DO NOT see anything like that. By far!
Physics (or arithmetic) is almost boring here. The mass psychology of “the 97% percent of the scientific community” and of a large part of the public is very interesting. They keep seeing sea rising. Magically, since there are no such rivers to provide all that water. The number of icebergs around Greenland is at least 100 times too small to substitute one Amazon during the whole year or 3 Amazons in the summertime.
Presumably there is some temperature that would cause that much sea level rise in that much time. In which case that water would leave Antarctica in one way or another.
Of course, high temperatures are possible. But then, you will actually see not only 3, but even more Amazon rivers there. I am sure, when and if the temperature down there will be high above zero, now they are low below zero, only then we will see some spectacular events.
I suspect the most difficult bit of the problem is defining what we mean by “the length of Antartica’s shore”. Crinkles below a certain size are irrelevant because water can’t flow over them. So we mean the length of the shore as measured by a ruler whose length is the Capillary length of water in air, which is 2.7 mm. Of course no one has ever measured this, but perhaps we can estimate it by using coarser measurements and fitting a curve to them.
Yes, this is the trickiest part. According to some French jokes, Slovenia has 42 kilometers of coast. I agree. This is still not the funny part of those jokes, this is the factual part.
Several thousand kilometers, maybe 10 thousand kilometers of Antarctica’s coast by the same methodology.
According to this amazing paper, Antarctica has a coastline of 39849 km when measured at the 100 m scale, and 43449 km when measured at the 25 m scale. They say its fractal dimension is 1.096448. Fitting a curve of the form L = M*r^(1-1.096448) to those two points I get that for r = 2.7 mm we get L = 107349 km. This methodology is perhaps nonoptimal, but I think it’s the best we’ve got.
So for the purposes of this question I’ll take the perimeter of Antarctica to be 100 000 km. Wikipedia says the total area of the ocean is 360 000 000 km^2. So to rise 6 m needs a volume of 2.16 10^15 m^3. A century is 3.16 10^9 s, so we need 6.84 10^5 m^3s^-1. The Amazon averages 2.09 10^5 m^3s^-1, so we need about three of them. If the coast of the Antarctic is 10^8 m then we need 6.84 litres flowing over each meter every second.
The equator is 40 000 km long. Antarctica can’t be 2.5 times longer. The Polar circle is what—about 8000 km long.
The beaches of Antarctica must be shorter than that.
EDIT: Or at most twice as long.
You’re wrong here. See the coastline paradox. Lines can be as long as they want, just by being extremely crinkly. There’s no law that says a shorter curve cannot enclose a longer one.
I am right here. Those small bays are not important in this case when we want to calculate the amount of water pouring out to sea. The mouth of the river Amazone is 200 km wide. Not as wide as the sum of all underwater bays and peninsulas.
Okay. So when I was calculating how many Amazons were needed the perimeter didn’t matter, and the answer was just 3. But when you asked how many litres would be pouring over each meter of perimeter I did the calculation based on the idea that an equal amount of water was passing over each bit of the perimeter.
Otherwise the answer is of course that the water forms together into rivers so that most of the perimeter has no water passing over it but the mouths of the rivers have a great deal of water passing over them.
Three Amazons are the right answer. AFAIK, the biggest river there is approximately as large, as the biggest river on the island of Crete. Which may be beautiful, but quite lousy in cubic meters per second.
Where and how some people see three Amazons on Antarctica, is a mystery to me. The amount of ice falling directly into the sea, is quite pathetic, as well.
But mostly, I love how the arithmetic is reigning supreme above all the sciences.
Wikipedia is another nice source of info. It claims that, during the past 20,000 years, the fastest increase in sea level was around 5 meters per century.
(The page on sea level rise mentions 3 meltwater pulses; clicking through it looks like Meltwater Pulse 1A is the one that researchers are the most confident about.)
This increase has some geological traces in the state of Washington. That was the North American glacier melting, for the most part. We don’t see much of that kind of flooding on Greenland or Antarctica recently. This is a real thing.
I am certain, that if your arithmetic isn’t sound, then your science is most likely bogus, no matter how fancy it looks.
This was a good puzzle, but I don’t see how it follows from the puzzle that arithmetic is “reigning supreme” above all the sciences. For one thing, I thought that most scientific estimates of sea level rise over the next 100 years were a lot lower than 6 meters. Do you have any links to projections of 6 meters?
Sure, Inconvenient Truth of Al Gore. He hasn’t returned his Nobel prize, so this still stands.
OK, noted, and thanks. I haven’t actually read An Inconvenient Truth.
But, I think most current scientific estimates are lower, so “reigning supreme above all the sciences” still seems a bit hyperbolic.
Okay, well. The next time I’ll ask, how fast the world ocean is losing water. But that’s for the next time. We had to eliminate this fast-rising possibility first.
Everyone knows Peace prizes don’t count.
Everyone knows Academy Awards do count. He has an Oscar, too.
The amazon begins distributed across brazil, as the occasional drops of rain. Then it comes together because of the shape and material of the landscape, and flows into streams, which join into rivers, which feed one big river. If global warming is causing antarctica to lose mass, do you expect the same thing to happen in antarctica, with meltwater beginning distributed across the surface, and then collecting into rivers and streams?
Yes. How else could it be?
How about glacial flow? Ice doesn’t move fast, but it does move. It can postpone melting until it’s in contact with seawater. What do you think the ratio of mass moved by rivers vs. glaciers is in Antarctica?
A solid state river, promptly melting in the icy, ice covered ocean, is even less plausible than a large watery river. Don’t you think so?
That’s about 0.4 Amazon.
The precipitations alone compensate most of this. Almost 3 Amazons still missing for the 6 meters sea rise in a century,
Besides …
10 million icebergs per year? Per a few summer months? Highly unrealistic.
Neat!
Glaciers don’t have to form icebergs in order to melt. It can just melt where it meets the sea.
You know, now that you mention it, 6 meters sure is a lot. Where did you get that number from? See p. 1181 for IPCC projections.
How many liters per meter per second in icy waters? After the sea ice has already melted away? Which never does in most places?
Told you, The Inconvenient Truth by Al Gore.
Much smaller numbers, popular now, still demands huge melting we don’t see really.
If the glacier is flowing off of the continent into the sea, then sea ice is in an equilibrium between melting at the edges and bottom and being replenished at the middle.
“See” how? It seems to me that you don’t have an involved understanding of the melting of glaciers. If we could measure the mass of the Antarctic glacier straightforwardly, then I’m sure we’d agree on the meaning of changes in that mass. But if we don’t see the particular melting process you expect, perhaps you’re just expectung the wrong process, and haven’t uncovered a conspiracy among all the experts.
In my experience, actually reading the ipcc review has never been popular and still isn’t. I’m sure you could still find someone in the press claiming larger sea level rise, if you tried. But why pick the easiest opponent?
Across the frozen sea around most of Antartica even in the summertime?
No conspiracy, I agree. Some lack of basic arithmetic skills only.
I’m not sure if you’re actually curious, or if you think this is a “gotcha” question.
Here’s a picture. As the glacier flows outward (here’s measured flow rates), it begins floating on the sea and becomes an ice shelf, which then loses mass to the ocean through melting and breaking up into pieces, which then melt. This ice shelf is thick (100m − 1 km scale), because it’s a really thick sheet of ice being pushed out into the water by gravity. It then encounters the sea ice, which is ~1-4 meters thick. The sea ice gets pushed out, or piled up, because there are no particular forces holding the sea ice in place.
At this point I’m tapping out of the conversation. Either you’re ignorant but curious and there’s no point to me typing up things you could look up, or you want to feel superior while remaining ignorant and there’s no point to me typing up things you don’t care about.
That picture is silly. The deep-cold freshwater continental ice flowing into the ocean and melting there in the icy waters, but the 1-4 meters thick salty ice survives the Antarctic summer?
Actually, there are a few places on Antarctica, where glaciers flow into the ocean, but not very fast at all. And where is the heat to melt −40 degrees cold ice, 2000 cubic kilometers per summer? It is not only the question of the heat but the question of the heat transfer.
I think, most people still believe that picture anyway. Most people here, I guess, too.
Perhaps, but:
If the global temperature continues to rise over the next century, then the rate of melting will be higher at the end of the 100 year period than it is now
In addition to Antarctica, Greenland has a significant (~ 2,850,000 km3) ice sheet. Melting of the Greenland ice sheet will also contribute to sea level increases
If. Then we might see something spectacular. But we need A LOT of warming, to actually warm up and melt that ice.
Fine, you’d need one Amazon on Greenland and only two Amazons for Antarctica. Doesn’t compute as well.
Imagine a summertime Greenland Amazon! It should be 3 Amazons really in that 1⁄3 of the year. The melting season is short.
We most certainly DO NOT see anything like that. By far!
Physics (or arithmetic) is almost boring here. The mass psychology of “the 97% percent of the scientific community” and of a large part of the public is very interesting. They keep seeing sea rising. Magically, since there are no such rivers to provide all that water. The number of icebergs around Greenland is at least 100 times too small to substitute one Amazon during the whole year or 3 Amazons in the summertime.
I am sorry, the arithmetic is just crucial.
Presumably there is some temperature that would cause that much sea level rise in that much time. In which case that water would leave Antarctica in one way or another.
Of course, high temperatures are possible. But then, you will actually see not only 3, but even more Amazon rivers there. I am sure, when and if the temperature down there will be high above zero, now they are low below zero, only then we will see some spectacular events.
Now, we don’t.