Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: chris on 04/09/2020 09:12:49
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Great question from today's Ask! The Naked Scientists phone-in (https://https://www.thenakedscientists.com/ask) on 567 CapeTalk:
Jen asked, "if everyone on Earth waded into the ocean up to their shoulders at the same time, what would be the effect on sea level?"
I speculated that it would be tiny, compared with the huge effects of atmospheric pressure, temperature, tides, waves, winds and the vast size of the oceans compared with the people.
But am I right?
I have also offered to provide the calculations to work out the scale of the effect. This homework is due in on Friday morning next week. Who can help me?!
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According to this
https://www.scientificamerican.com/article/antarcticas-ice-shelves-have-lost-millions-of-metric-tons-of-ice/
"Antarctic ice shelves have lost nearly 4 trillion metric tons of ice since the mid-1990s,"
And that caused a sea level rise of the order of 20 cm.
People weigh about 50 Kg (most people are children) so there are about 20 people to the tonne.
And there are about 10 billion people so that's about 500 million tons of people.
People have roughly the same density as water- we more or less float- so we would add as much depth to the sea as half a billion tons of water.
That's about 8000 times less water than came from the antarctic (I'm ignoring the other ice sheets to make life simpler).
So the rise in sea level from a mass swim would be something like 2.5 micrometers.
If you got bored, you could find the area of the world's oceans- it's about 1/3 of the area of the Earth, and divide the volume of the people (about 500 million cubic metres) by that area and get a better estimate of the depth increase.
You could sharpen up the estimate of the volume of people too.
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the area of the world's oceans- it's about 1/3 of the area of the Earth
I thought the Earth's surface was about 70% water? (not 1/3 water...)
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A good thorough answer from B-C, despite the one error Evan points out.
I'd like to mention what it would take for all of humanity to get into the ocean "at the same time". What is the length of the combined shoreline available to humans? Some of the places it would take some time to get from the beach to a swimming depth.
A rough estimate of the shoreline is something like half a million km which yields a wall of people around 10 deep. So that's not unreasonable. It takes less time for 10 people to enter the water than it does for any one of them to get to a swimming depth, at least in some places. In other places, people 10-deep are jumping off cliffs like lemmings. Jumping off a boat doesn't count since anyone in a boat is already contributing to the sea level.
Also, the sea level will rise at the shores far more than those 2.5 micrometers since all the new volume is there and it would take time for that displaced water to reach the places in the ocean where people are not doing this.
Water evaporates from the ocean at a rate of about 16 billion kg per second if my sources are correct. All of humanity masses maybe 30 times that, so if they all manage to get their 10-deep line into deep water in under half a minute, they might actually out-pace the rate at which the ocean empties itself.
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the area of the world's oceans- it's about 1/3 of the area of the Earth
I thought the Earth's surface was about 70% water? (not 1/3 water...)
If it's any consolation, the original typo was "/3
Doh!
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Also, the sea level will rise at the shores far more than those 2.5 micrometers since all the new volume is there and it would take time for that displaced water to reach the places in the ocean where people are not doing this.
Very good point about the amount of available coastline!
But wouldn't the rate at which people were getting into the water be slower than the rate of water redistribution?
Also, presumably bringing all that mass close to the seashore would depress the land there a bit, so sea level would apparently rise (by a picometre or so?), and all the gravity associated with those people would pull up the water more, making a further apparent rise, surely?
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"Antarctic ice shelves have lost nearly 4 trillion metric tons of ice since the mid-1990s,"
And that caused a sea level rise of the order of 20 cm.
Also from Donald Trump's Big Book of Important Stuff:
"Archimedes died over 2000 years ago, so his Principle is out of date and the melting of floating ice caused an increase in sea level."
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Very good point about the amount of available coastline!
But wouldn't the rate at which people were getting into the water be slower than the rate of water redistribution?
Also, presumably bringing all that mass close to the seashore would depress the land there a bit, so sea level would apparently rise (by a picometre or so?), and all the gravity associated with those people would pull up the water more, making a further apparent rise, surely?
OK, let's iron out a few variables. Suppose the weather is nonexistent and the water is mirror calm all over the Earth. All the people are already at the shore but waiting, so their gravity isn't going to change much by a small amount of motion. We remove the moon so tides go away. Can't measure a micron of sea level if it's boinging up and down with the tides.
That said, we have two scenarios: Do it quick or do it slow and wait for a new equilibrium to form.
Quick method: A relatively small group of people jump into a tight bay and the water level rises there in accordance with the new volume displaced. That might be even a centimeter. The water eventually runs out of the bay, but this is the quick and dirty method here. We're not measuring the sea level with a stick in the middle of the ocean (which is unaffected for hours by this), but just a local measurement. What people are doing elsewhere in the world is immaterial for the quick method. You get a temporary local sea level rise due to the local group going in. The change causes a tsunami of sorts that takes time to get to places not near shorelines. Point is, with the quick method, it's the local group that matters, not the whole population of Earth getting in the water. It seems not in the spirit of the OP, so we instead go to:
Slow and permanent method: The entire population gets in the water and stays there until a new equilibrium forms, which might take days (or much more!). The sea level rises in accordance with a calculation similar to what BC did in the initial reply.
The surprising part of the answer for this is that it doesn't matter what water you get into. I have a small waterfall in my back yard with a pond that could hold probably a dozen people submerged. Suppose 12 people do that instead of wading into the ocean. Sea level rises just as much (after some time) due to that. They don't have to be in the ocean at all. The people displace their weight in water which exits the pond that much sooner and adds their mass to the ocean after a day (in my case). My brother can do the same thing where he lives and it would take decades for the sea level to rise from his action, but it would eventually. He lives near water that runs into Lake Superior, a lake that drains so slowly that any change to its level might linger for literally decades. But sea level would rise eventually due to my brother sitting in a nearby pond.
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The earth has a total surface area of approximately 5.1x1014 sq. meters. 70% of this is ocean, say 3.6 x 1014 m2.
Average human volume is about 50 liters, 5 x 10-2 m3. So 7.8 x 109 people displace about 3.9 x 108m3
therefore sea level rise = (3.9/3.6) x 10-6 m, say 1.1 micron.
But that assumes Archimedes is still alive - see above. As Donald Trump famously said of Stephen Hawking "If he were British, he'd be dead".
If they all swim the number will be a bit less because their heads won't be immersed.
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I am currently above sea level so I must drag the nearby bits of the sea up slightly by some sort of tidal pull.
I'm quite a long way from the coast so that effect is small.
If I went to the seaside, I'd be much nearer the sea so my gravitational forces on it would be bigger and it would rise more.
If we all waded into the sea we would warm it up slightly and it would expand.
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If they all swim the number will be a bit less because their heads won't be immersed.
There are two ways you can get part of your body out of the water (eg your head):
- Swim quickly, so the "angle of attack" of your body pushes the water down, and pushes your body up. This is as you suggest.
- The other method, for people who (like me) aren't fast swimmers is to inflate your lungs more, to make you more buoyant. As Archimedes pointed out, your mass hasn't changed, so the volume of displaced water is the same, whether your head is completely out of the water, or or body is just touching the surface.
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If they all swim the number will be a bit less because their heads won't be immersed.
There are two ways you can get part of your body out of the water (eg your head):
- Swim quickly, so the "angle of attack" of your body pushes the water down, and pushes your body up. This is as you suggest.
- The other method, for people who (like me) aren't fast swimmers is to inflate your lungs more, to make you more buoyant. As Archimedes pointed out, your mass hasn't changed, so the volume of displaced water is the same, whether your head is completely out of the water, or or body is just touching the surface.
In the OP they waded out. They are standing on the seabed, not swimming.
The deeper the water you are standing in, the more of it you displace.
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Deduct 2.5 liters per capita for head-up. This reduces the sea level rise to about 1.05 micron.
Human buoyancy is remarkably variable. Most people just float in sea water, but I met some very muscular guys on a diving course who didn't need auxiliary weights to sink without their kit.
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Beautifully done BC :)
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Even though his calculation is based on an obvious untruth!
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Thank you @Bored chemist
Your answer was gratefully cited and recited on CapeTalk last Friday to answer this question.
https://www.thenakedscientists.com/podcasts/ask-naked-scientists/covid-19-has-world-over-reacted
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Even though his calculation is based on an obvious untruth!
Is that based on your "hollow Earth" beliefs?
https://www.thenakedscientists.com/forum/index.php?topic=80501.msg613549#msg613549
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No, Archimedes' Principle.
The Antarctic Ice Shelf is floating, so it cannot increase the level of the liquid it is floating in if it melts.
But see Reply #6 above if you are a Republican voter.
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So, you didn't read the article then?
OK, here's a clip.
"As ice shelves melt, they become thinner, weaker and more likely to break. When this happens, they can unleash streams of ice from the glaciers behind them, raising global sea levels."
I presume you are sticking with your support for the hollow Earth and the non conservation of angular momentum.
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Antarctic ice shelves have lost nearly 4 trillion metric tons of ice since the mid-1990s, scientists say.
No figures quoted for additional glacier calving, nor, as far as I can see, for the consequent sea level rise. Nor, in fact, any suggestion that glacier calving has actually increased.
Reported global sea level has apparently risen by about 8 cm since 1990, when it was in fact at a local minimum. The published graphs that go back to 1880 suggest a fairly linear rise of 20 cm since 1900 but the meaning of "global sea level" is a bit obscure before 1992 when satellite altimetry became available, and has been pretty consistent at 3.18 mm/year with the postglacial rise over the last 8000 years.
"People kind of talk about how increased ice shelf melt can lead to more discharge of grounded ice and sea-level rise," Adusumilli said. "But then the immediate influence of ice shelves on the ocean is also very important."
Worthy of the Little Dictator himself.
The good news is that my calculation in reply #8 above, based only on facts, concurs pretty well with whatever wild guesses you made!
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No figures quoted for additional glacier calving, nor, as far as I can see, for the consequent sea level rise. Nor, in fact, any suggestion that glacier calving has actually increased.
Feel free to find data that you are happy with.
The answer is still going to be of the order of a micron.
Fundamentally it doesn't matter.
If I had cited some mad denialist site that said sea levels had fallen by x cm because there were now y more cubic metres of ice, it wouldn't have made any difference.
The ratio (give or take some scrabbling with units) is the area of the seas.
And if you divide the volume of the people by the area of the seas, you get the increase in depth. It doesn't matter what calculation someone else's web page had made with that area. I'm just lazy enough to let them do most of the work.
Now, given that my calculation was based on the area of the sea (and some conversions of units), and that I got more or less the right answer, what "obvious untruth!" was my reply based on?
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"Antarctic ice shelves have lost nearly 4 trillion metric tons of ice since the mid-1990s,"
And that caused a sea level rise of the order of 20 cm.
As for the assertion that plus or minus makes no difference, I'm reminded of a Fred Hoyle story from the 1960s.
In the course of a chalk and talk lecture, a student pointed out a missing factor of 1014 between two equations. Long pause, then Fred said "it's not significant".