Why Our Intuition About Sea-Level Rise Is Wrong(oceans.nautil.us)
oceans.nautil.us
Why Our Intuition About Sea-Level Rise Is Wrong
http://oceans.nautil.us/feature/564/why-our-intuition-about-sea-level-rise-is-wrong
135 comments
At a distance of 100 km, the gravitational acceleration caused by the greenland ice sheet is .019 m/s^2 or ~0.2% g. Doesn't sound like a lot but it's still 524 times higher than the effect of the moon's gravity which creates the tides. The ice sheet has the same gravitational effect as the moon at a distance of approximately 2300 km.
> Doesn't sound like a lot but it's still 524 times higher than the effect of the moon's gravity which creates the tides.
Contrary to common belief, tides are not caused by the direct influence of the moon's gravity (it's far too weak to have any effect)[1]. The tidal forces are caused by the gravitational gradient from the moon (and the "centrifugal" forces from our path around the earth-moon barycenter), and I don't believe you'd get the same effects from a gravity source on the surface of the earth.
Even a lot of very respectable scientists and textbooks get this wrong.
[1] See https://www.youtube.com/watch?v=pwChk4S99i4 for a pretty good explanation
Contrary to common belief, tides are not caused by the direct influence of the moon's gravity (it's far too weak to have any effect)[1]. The tidal forces are caused by the gravitational gradient from the moon (and the "centrifugal" forces from our path around the earth-moon barycenter), and I don't believe you'd get the same effects from a gravity source on the surface of the earth.
Even a lot of very respectable scientists and textbooks get this wrong.
[1] See https://www.youtube.com/watch?v=pwChk4S99i4 for a pretty good explanation
Just to add to this answer and perhaps save you the click, what he is referring to is that the force pulling the water upward at high tide is not the direct gravitational pull of the moon. It is that the gravitational force from the moon at the edge of the earth is greater than the force at the center (because it is closer to the moon). Similarly the force on the opposite side of the earth is less (because that side is further from the moon than the earth's center). So the water molecules are drawn away from the center of the earth (near side because they are being pulled slightly harder than the center of the earth, and far side because they are being pulled slightly less hard than the center of the earth). Hence the high tides on both sides of the earth, not just the side closer to moon.
If I correctly understood the video linked above, the primary cause is actually due to the tidal acceleration (e.g. moon's gravity) of objects on sides 1 and 3 (see diagram below), relative towards the earth's surface, being mostly radially inward [1]. The majority of the ocean water along the sides of Earth is being pulled in very slightly, and in aggregate across the massive surface of the ocean, this results in enough pressure to push up the water at sides 2 and 4. Tides are pushed up due to pressure, not pulled up.
The analogy they used is that tides are more like a pimple being squeezed than taffy being stretched.
[1] See timestamp 4:45 in the video: https://www.youtube.com/watch?v=pwChk4S99i4&feature=youtu.be...
---
Diagram:
M = Moon
Numbers = 4 "sides" of the Earth, relative to the Earth-Moon line
The analogy they used is that tides are more like a pimple being squeezed than taffy being stretched.
[1] See timestamp 4:45 in the video: https://www.youtube.com/watch?v=pwChk4S99i4&feature=youtu.be...
---
Diagram:
1
4 E 2 M
3
M = Moon
Numbers = 4 "sides" of the Earth, relative to the Earth-Moon line
Or, to put it another way, the surfaces of the Earth closest to and farthest away from the Moon are traveling at the same orbital velocity of the Earth. However, they should be in different orbits; the point closest to the Moon is too slow for the orbit it is in and the point farthest is too fast. The former wants to into a lower orbit while the latter wants to go into a higher orbit.
In a further translation from gibberish:
Or, to put it another way, the surfaces of the Earth closest to and farthest away from the Moon are traveling at the same orbital velocity around the center of the Earth/Moon system. However, they should be in different orbits; the point closest to the Moon is too slow for the orbit it is in and the point farthest away is too fast. The former wants to into a lower orbit while the latter wants to go into a higher orbit.
Or, to put it another way, the surfaces of the Earth closest to and farthest away from the Moon are traveling at the same orbital velocity around the center of the Earth/Moon system. However, they should be in different orbits; the point closest to the Moon is too slow for the orbit it is in and the point farthest away is too fast. The former wants to into a lower orbit while the latter wants to go into a higher orbit.
It seems this would made the effect from the icebergs bigger rather than smaller, because the gradient decays by r^3 instead of r^2, so the distance is more important?
Like, the gravitational acceleration is a = GM/r^2 while the gradient is da/dr = -2GM/r^3
So for moon vs glacier at 1000km you'd get
- 2 * (Gravitational constant) * (mass of moon) / (391184 km)^3 = - 1.638×10^-13 reciprocal seconds squared
vs
- 2 * (Gravitational constant) * (1e19 kg) / (1000 km)^3= -1.335×10^-9 reciprocal seconds squared
Like, the gravitational acceleration is a = GM/r^2 while the gradient is da/dr = -2GM/r^3
So for moon vs glacier at 1000km you'd get
- 2 * (Gravitational constant) * (mass of moon) / (391184 km)^3 = - 1.638×10^-13 reciprocal seconds squared
vs
- 2 * (Gravitational constant) * (1e19 kg) / (1000 km)^3= -1.335×10^-9 reciprocal seconds squared
It's the gradient applied over the whole ocean that causes the tides. In other words, the forces are not enough to create any kind of local change in the depth of the ocean. It's not a gravitational "pulling" as we're accustomed to think about, but more of a global squeezing of water from that gradient applied to the entire ocean. I'll have to give some more thought to the idea of a gravity source on the surface of the earth, but I doubt it would work the same way (we're comparing a relatively small mass in a concentrated location on the earth with that same mass distributed mostly evenly over the earth).
As you said, it's the gradient which matters. The gradient determines how much the sea level changes over a distance. But, the sea level change is distinct from the tides. The difference in water level between two connected locations at the same moment in time is the same for the ocean and the lake.
The video you linked to compares lakes and oceans because the lunar tides vary with time. The lake level difference between Cleveland and Buffalo at 6 will be the same as the sea level difference between New York and Providence at ~5:30. You need to compare your sea level to the sea level a quarter of the way around the world to understand why your local sea level changes from 6:00 to 12:00.
The video you linked to compares lakes and oceans because the lunar tides vary with time. The lake level difference between Cleveland and Buffalo at 6 will be the same as the sea level difference between New York and Providence at ~5:30. You need to compare your sea level to the sea level a quarter of the way around the world to understand why your local sea level changes from 6:00 to 12:00.
Nothing of this disproves the effect of the polar ice. The forces still apply, they're just not shifting daily.
> The forces still apply, they're just not shifting daily.
No, the forces are completely different. If we have an object on the surface of the earth that has enough mass to roughly produce the same nearby gravitational acceleration as that felt by the moon (which is minuscule and undetectable by most instruments), that object would not produce changes in ocean levels as we see with the moon. Again, the oceans are not rising/falling due to the moon's gravity pulling on them. It only happens because the moon is far enough away that its tiny gravitational acceleration on the earth is (1) felt everywhere on earth, and (2) felt everywhere on earth in slightly different amounts.
For a smaller, closer object (even with similar nearby gravitational acceleration), the tidal forces will not be the same because that gravitational acceleration will fall off to near zero in a very short distance.
No, the forces are completely different. If we have an object on the surface of the earth that has enough mass to roughly produce the same nearby gravitational acceleration as that felt by the moon (which is minuscule and undetectable by most instruments), that object would not produce changes in ocean levels as we see with the moon. Again, the oceans are not rising/falling due to the moon's gravity pulling on them. It only happens because the moon is far enough away that its tiny gravitational acceleration on the earth is (1) felt everywhere on earth, and (2) felt everywhere on earth in slightly different amounts.
For a smaller, closer object (even with similar nearby gravitational acceleration), the tidal forces will not be the same because that gravitational acceleration will fall off to near zero in a very short distance.
You are mixing tidal forces with local attraction forces due to ice. Even though the forces due to ice are not felt everywhere in the planet, they do have an effect that can be calculated, and it is stronger in the body of water closer to the poles. The result of this force causes water attraction in the polar regions. So the effect that is felt in other parts of the planet is not due to the gravity force, but due to the displacement of water happening in polar regions - after all the water needs to go somewhere.
I was originally responding to the claim that "it's still 524 times higher than the effect of the moon's gravity which creates the tides" - that's why I mentioned tidal forces. If the ice creates that much direct, local gravitational attraction[1], then my point is we shouldn't be comparing it to the moon at all (because the forces involved are not the same as those involved with the moon and tides).
[1] Even the claim about the ice sheet (and its melting) contributing significantly (via gravity) to global sea level change seems dubious since, as noted elsewhere in this discussion, the Earth Gravitational Model appears to be affected much more by factors other than ice sheet thickness or surface features.
[1] Even the claim about the ice sheet (and its melting) contributing significantly (via gravity) to global sea level change seems dubious since, as noted elsewhere in this discussion, the Earth Gravitational Model appears to be affected much more by factors other than ice sheet thickness or surface features.
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Hmm, but a water molecule 100 km from an Arctic ice sheet is also experiencing the pull of an "equal" weight of water 100km the other direction, albeit ever so slightly offset angularly.
The lunar system is seemingly much less symmetrical but we still get some amphidromic points (points of zero tidal range) and neep tides (lowest "high" tide) can be very small.
The lunar system is seemingly much less symmetrical but we still get some amphidromic points (points of zero tidal range) and neep tides (lowest "high" tide) can be very small.
The interviewee is talking about ice on land (Greenland and Antarctica), not about ice in the ocean. If the ice on land melts, then those water molecules migrate away from Greenland because they drop to sea level. That loss of mass would happen regardless of the gravitational pull of water 200 km away and would change the gravitational gradient of the water 100 km away.
Another way to think of it: there's not an "equal" weight of water above Greenland because it's raised above sea level by the land. The weight of rock underneath the ice sheet needs to be included as well.
Another way to think of it: there's not an "equal" weight of water above Greenland because it's raised above sea level by the land. The weight of rock underneath the ice sheet needs to be included as well.
That pull would be there regardless though.
This is the answer which makes the most sense to me.
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1) the center of the ice sheet can be much closer to the water than the center of the earth. Some water around greenland is at 600 km from the center of the ice sheet, and 6000 km from the center of the earth. This factor 10 difference is squared because gravity's strength drops off with the square of distance.
2) Both forces are orthogonal, so you take the ratio to get an idea of how much the ice sheet attraction is slanting the water surface. This might be a very small angle, but if you have a small angle sustained over hundreds of kilometers then you can arrive at a height difference of meters. E.g. if the ratio is 10^5, then you have a 1 meter height difference at 100km distance (ignoring that the ratio actually changes over that distance to simplify).
2) Both forces are orthogonal, so you take the ratio to get an idea of how much the ice sheet attraction is slanting the water surface. This might be a very small angle, but if you have a small angle sustained over hundreds of kilometers then you can arrive at a height difference of meters. E.g. if the ratio is 10^5, then you have a 1 meter height difference at 100km distance (ignoring that the ratio actually changes over that distance to simplify).
So... why wouldn't this show up consistently in the EGM96 data?
EGM96 is a definition of Earth's equipotential height constructed by measuring it with satellites like GRACE. Its as close to a definition of true sea level as you're going to get. But it doesn't have this kind of consistent uplift near tall masses throughout the model. The Southern Ocean's height is sinusoidal about Antarctica. We do see an increase in equipotential height in the Andes, and in the eastern Pacific nearby. But near the Himalayas the equipotential height is lower.
https://en.wikipedia.org/wiki/File:Earth_Gravitational_Model...
EGM96 is a definition of Earth's equipotential height constructed by measuring it with satellites like GRACE. Its as close to a definition of true sea level as you're going to get. But it doesn't have this kind of consistent uplift near tall masses throughout the model. The Southern Ocean's height is sinusoidal about Antarctica. We do see an increase in equipotential height in the Andes, and in the eastern Pacific nearby. But near the Himalayas the equipotential height is lower.
https://en.wikipedia.org/wiki/File:Earth_Gravitational_Model...
I guess because plainly visible "tall masses" are not the only things contributing to the geoid? E.g. earth crust thickness might dominate.
In the context of this discussion, we're not so much interested in the absolute shape of the geoid, as in how much it might change because of melting ice sheets
In the context of this discussion, we're not so much interested in the absolute shape of the geoid, as in how much it might change because of melting ice sheets
You’re missing one of the effects gravity and ice have. From the article:
> The second thing that happens is that this gravitational attraction that the ice sheet exerts on the surrounding water diminishes. As a consequence, water migrates away from the ice sheet. The third thing is, as the ice sheet melts, the land underneath the ice sheet pops up; it rebounds.
The land underneath the glacier or ice sheet (and it has to be on land, because ice displaces it’s melted volume when floating) pops up and increases in altitude (from the centre of earth) due to the drop in weight.
This popping up effect will of course affect surround land not under the ice because rock isn’t that flexible.
> The second thing that happens is that this gravitational attraction that the ice sheet exerts on the surrounding water diminishes. As a consequence, water migrates away from the ice sheet. The third thing is, as the ice sheet melts, the land underneath the ice sheet pops up; it rebounds.
The land underneath the glacier or ice sheet (and it has to be on land, because ice displaces it’s melted volume when floating) pops up and increases in altitude (from the centre of earth) due to the drop in weight.
This popping up effect will of course affect surround land not under the ice because rock isn’t that flexible.
I'm not a physicist. I did get curious and went to Wikipedia. You're mostly spot on:
>It covers an area of almost 14 million square kilometres (5.4 million square miles) and contains 26.5 million cubic kilometres (6,400,000 cubic miles) of ice.[2] A cubic kilometer of ice weighs approximately one metric gigaton, meaning that the ice sheet weighs 26,500,000 gigatons.
26,500,000 gigatons is 2.65e+18 kg in scientific notation.
I compared this to the moon, which is 7.35 x 10^22 kg, or about 30,000 times as heavy. The moon does create quite some tidal effects, while at 384,400 km distance.
Since gravity is inversely proportional to the square of the distance Both the 50m of local displacement as well as the 2000km distance until it sufficiently cancelled out sound believable to me.
>It covers an area of almost 14 million square kilometres (5.4 million square miles) and contains 26.5 million cubic kilometres (6,400,000 cubic miles) of ice.[2] A cubic kilometer of ice weighs approximately one metric gigaton, meaning that the ice sheet weighs 26,500,000 gigatons.
26,500,000 gigatons is 2.65e+18 kg in scientific notation.
I compared this to the moon, which is 7.35 x 10^22 kg, or about 30,000 times as heavy. The moon does create quite some tidal effects, while at 384,400 km distance.
Since gravity is inversely proportional to the square of the distance Both the 50m of local displacement as well as the 2000km distance until it sufficiently cancelled out sound believable to me.
the mass of the iceshield / mass of the moon = 5 10^-4. But at a distance of 2000km compared to 4 10^5 km for the moon, the iceshield should have similar gravitational pull. the inverse square of 2000km / the inverse square of 4 10^5 km = 4 10^4. (4e4=(1/2000000^2)/(1/(4e8)^2))
Distance and mass seem to cancel out almost perfectly
Distance and mass seem to cancel out almost perfectly
I think you are off by an order of magnitude, it should be 2.65 10^19 kg. one gigaton is 10^12 kg , 26,500,000=2.65*10^7
You're right, thanks!
I found this Minute Physics video about "sea level" very enlightening [1], and I think it can help here (just replace mountains by "huge masses of ice").
[1] https://www.youtube.com/watch?v=q65O3qA0-n4
[1] https://www.youtube.com/watch?v=q65O3qA0-n4
If the Earth were perfectly round the center of mass would be in the exact center, but if it had lopsided bulge on one side the center of gravity would shift in that direction. The water, being liquid, will want to form a sphere around that new center of mass. That deviation from center means a corresponding increase in water around the surface in that direction. So intuitively, if you think about it this way, 30 something meters deviation from center doesn’t seem too counterintuitive.
Is an effect like this similar to the difference between the water level of the Atlantic and Pacific? It never made intuitive sense to me that the Panama Canal for example had to deal with a significant water level difference between the two sides, as the two bodies of water are contiguous at other points on the Earth’s surface.
The Panama Canal has locks mainly to raise (by 26m) the water-level over the land. It's less work to flood the area than to dig a giant channel between the oceans.
https://armyengineer.com/history/panama/engineers/How_Canal_...
The average sea level difference on each side is minor in comparison (20cm). Plus, the average sea level isn't constant through the whole ocean. It's variable depending on location due to different salt concentrations (salty water is less dense).
https://oceanservice.noaa.gov/facts/globalsl.html
https://armyengineer.com/history/panama/engineers/How_Canal_...
The average sea level difference on each side is minor in comparison (20cm). Plus, the average sea level isn't constant through the whole ocean. It's variable depending on location due to different salt concentrations (salty water is less dense).
https://oceanservice.noaa.gov/facts/globalsl.html
Oh man, thanks for this! I did not realize that it was essentially to hoist the boats over uneven terrain, always assumed the canal was a straight dug channel. Never enough to go search out the answer, but it always tickled the back of my mind when it came up. Thank you!
Hard to imagine a floating ice cube having an effect on a sphere with mountains, though.
It floats, so it bulges out from the earth, shifting that mass away from perfect center. Given that it’s not liquid, it bulges out non uniformly in one direction and biases center of mass in one specific direction. It also doesn’t matter too much that it’s not particularly high, as it it covers a large area in the general direction. Anything on the northern hemisphere would bias center of mass in that direction.
EDIT: I’m not totally sure about the bulging out part of the floating ice is true, but there are also glaciers on land such as over Greenland that would shift the center of mass.
The force vector from a polar ice sheet doesn't get cancelled out by the rest of the earth though (because they aren't pointing in opposite directions). Plus, you have to account for the force of the ice sheet, plus the water it attracts, plus the water that those combined attract, etc.
I'm no good with calculus so can't run that back-of-the-envelope for you, but it doesn't seem all that surprising to me.
I'm no good with calculus so can't run that back-of-the-envelope for you, but it doesn't seem all that surprising to me.
Even if we ignore all that, and treat everything as a point mass, it's still believable, I think.
The earths radius is very approximately 6.4km. So 1km out from the ice sheet, we have 1(1/6.4^2) (earth) vs 10^-5(1/1^2) (ice), which is very roughly 1/2500th of the effect of earths gravity. But the earths gravity is strong! The forces it exerts on the ocean are titanic - it doesn't seem outside the realms of belief that even this small percentage of the force could produce an observable effect, when the forces are so huge, and the differences are only measured in meters.
I think part of the reason we find this difficult to grasp intuitively is we don't really have a good mental model of just how titanic many of these forces are - huge numbers are just not something we, as a species, are good at understanding.
The earths radius is very approximately 6.4km. So 1km out from the ice sheet, we have 1(1/6.4^2) (earth) vs 10^-5(1/1^2) (ice), which is very roughly 1/2500th of the effect of earths gravity. But the earths gravity is strong! The forces it exerts on the ocean are titanic - it doesn't seem outside the realms of belief that even this small percentage of the force could produce an observable effect, when the forces are so huge, and the differences are only measured in meters.
I think part of the reason we find this difficult to grasp intuitively is we don't really have a good mental model of just how titanic many of these forces are - huge numbers are just not something we, as a species, are good at understanding.
Earth’s radius is 6371 km, not ~6 km.
Radius of 6 km is comparable to the size of Halley's comet :-)
Let's see,.. Mitrovica's robust computer modelling vs. your back of the envelope calculations...
Wonder which one I'd put money on.
Wonder which one I'd put money on.
If your fancy computer model doesn’t approximately equal your back of the envelope calculation, that’s generally a knock against the computer model rather than the napkin math. Exceptions exist, but for a system as linear as this you should be able to separate out gravity and look at it on its own no problem.
Do you have a link to a paper, I couldn't find one on google
The one linked in the article? https://advances.sciencemag.org/content/1/11/e1500679
Check out the Canvendish experiment! Watch gravity work in a classroom.
https://youtu.be/MbucRPiL92Q
https://youtu.be/MbucRPiL92Q
G is 6.67e-11, so for 1kg of matter 1000km away from a center of that mass the force is (e-11 x e19 / e(6x2)), around e-4 newtons or e-5 kg of weight equivalent. Idk what’s that worth ocean-wise.
This isn't intuitive to me either, given that the ice sheet is less dense than the surrounding water. I mean, it floats. Never mind the effect of the surrounding landmass, which is WAY more dense. I'm not ready to call his theory "fact" like Nautilus is.
That said, I'm not a geophysicist.
That said, I'm not a geophysicist.
The arctic ice sheet floats. Greenland is an island and Antarctica a continent, both of them surrounded by a little floating ice.
Melting that ice shifts a km-deep layer of ice from a fixed position above nearby sea level to being part of the liquid ocean. This means that it doesn't exert any gravitational pull on the ocean nearby, so the water-covered part of the globe becomes a little bit more spherical. Not much more spherical: The article says 30-50m on the coast of Greenland, which is a very small fraction of the earth's radius.
The 30-50m column of water is distributed elsewhere.
Melting that ice shifts a km-deep layer of ice from a fixed position above nearby sea level to being part of the liquid ocean. This means that it doesn't exert any gravitational pull on the ocean nearby, so the water-covered part of the globe becomes a little bit more spherical. Not much more spherical: The article says 30-50m on the coast of Greenland, which is a very small fraction of the earth's radius.
The 30-50m column of water is distributed elsewhere.
Replying to myself, this implies that near Greenland, the gravitational effect of the ice cap should be ~30 times as big as the moon's (which causes a tide of a little over a meter). Which doesn't seem horribly implausible.
The moon causes a rise of about 54cm, and the sun around 28cm.
from the wikipedia entry for tides.
https://en.wikipedia.org/wiki/Tide#Amplitude_and_cycle_time
from the wikipedia entry for tides.
https://en.wikipedia.org/wiki/Tide#Amplitude_and_cycle_time
An amplitude of 54cm is about a meter peak-to-peak.
Parent is writing about Antarctica, the ice sheet is not floating but would be replaced by air which is a lot less dense.
And the land rising effect is certainly there, its well known from our norther hemisphere where satellite measurements have tracked for quite a while now how i.e northern Europe still rises in comparison to the southern parts due to the not being covered by the ice age glaciers anymore.
And the land rising effect is certainly there, its well known from our norther hemisphere where satellite measurements have tracked for quite a while now how i.e northern Europe still rises in comparison to the southern parts due to the not being covered by the ice age glaciers anymore.
I don't think the comparison with the surrounding land mass is relevant here. The landmass might have a much larger effect than the ice, but the landmass will not melt. While my mental image considers the water to envelop the world as a sphere, I actually have no idea how large the differences in the distance from the core to the water surface is in different parts of the world.
> I actually have no idea how large the differences in the distance from the core to the water surface is in different parts of the world
Taking the core to be a point, the distance to the sea's surface would depend on factors such as
* The earth’s variation from a pure sphere (6,378.137 km (3,963.191 mi) at the Equator and 6,356.752 km (3,949.903 mi) at the poles) [0, 1]
* The local depth of the sea (up to 10,984 metres for the Mariana Trench [2])
* Tidal effects [3]
[0] https://en.wikipedia.org/wiki/Spheroid
[1] https://en.wikipedia.org/wiki/Figure_of_the_Earth
[2] https://en.wikipedia.org/wiki/Mariana_Trench
[3] https://en.wikipedia.org/wiki/Tide
Taking the core to be a point, the distance to the sea's surface would depend on factors such as
* The earth’s variation from a pure sphere (6,378.137 km (3,963.191 mi) at the Equator and 6,356.752 km (3,949.903 mi) at the poles) [0, 1]
* The local depth of the sea (up to 10,984 metres for the Mariana Trench [2])
* Tidal effects [3]
[0] https://en.wikipedia.org/wiki/Spheroid
[1] https://en.wikipedia.org/wiki/Figure_of_the_Earth
[2] https://en.wikipedia.org/wiki/Mariana_Trench
[3] https://en.wikipedia.org/wiki/Tide
And, I suppose, the centripetal force caused by the rotation. But maybe that is the whole reason for earth being a spheroid?
And correct me if I'm wrong, but the local depth of the sea should not matter, as water would fill the depth before the levels stabilized. But perhaps the local volume of the water affects the size of the effects of tidal forces and local land mass.
And correct me if I'm wrong, but the local depth of the sea should not matter, as water would fill the depth before the levels stabilized. But perhaps the local volume of the water affects the size of the effects of tidal forces and local land mass.
Mostly related to your line of inquiry, the point on land that is furthest from the center of the Earth is Mount Chimborazo in Ecuador.[1] It is located one degree south of the equator and is very tall to begin with.
[1] https://oceanservice.noaa.gov/facts/highestpoint.html
[1] https://oceanservice.noaa.gov/facts/highestpoint.html
Not only that, but I think the whole idea here is just plain wrong. From the article:
> this gravitational attraction that the ice sheet exerts on the surrounding water diminishes. As a consequence, water migrates away from the ice sheet.
When an ice sheet melts, it doesn't create a void in its place. What was once ice becomes liquid water. That liquid water actually has a slightly higher density than it had when in ice form, but it will occupy slightly less volume in the ocean. Mass is conserved, and the net effect in terms of gravity is essentially zero.
If anything, you'd have slightly higher local gravity in that part of the ocean (due to a higher concentration of liquid water vs ice), but again, zero net change looking at the entire ocean.
> this gravitational attraction that the ice sheet exerts on the surrounding water diminishes. As a consequence, water migrates away from the ice sheet.
When an ice sheet melts, it doesn't create a void in its place. What was once ice becomes liquid water. That liquid water actually has a slightly higher density than it had when in ice form, but it will occupy slightly less volume in the ocean. Mass is conserved, and the net effect in terms of gravity is essentially zero.
If anything, you'd have slightly higher local gravity in that part of the ocean (due to a higher concentration of liquid water vs ice), but again, zero net change looking at the entire ocean.
If the ice was above sea level to start, then it does create a void (OK, a space filled with air). The mountain of ice turns into liquid water and flows all over the earth.
Gotcha. I thought the article was referring to polar ice in general, not just specifically ice sheets (over land areas). Still, the gravity produced by that mass doesn't seem to be enough to make a real difference (see my other comment questioning the comparison with the moon/tides).
I love counter-intuitive facts. They are a helpful reminder that things are more complicated than I think they are, and I don't understand the world as well I think I do.
"Gravity has a very strong effect. So what happens when an ice sheet melts is sea level falls in the vicinity of the melting ice sheet. That is counterintuitive. The question is, how far from the ice sheet do you have to go before the effects of diminished gravity and uplifting crust are small enough that you start to raise sea level? That’s also counterintuitive. It’s 2,000 kilometers away from the ice sheet. "
"Gravity has a very strong effect. So what happens when an ice sheet melts is sea level falls in the vicinity of the melting ice sheet. That is counterintuitive. The question is, how far from the ice sheet do you have to go before the effects of diminished gravity and uplifting crust are small enough that you start to raise sea level? That’s also counterintuitive. It’s 2,000 kilometers away from the ice sheet. "
Also Simpson's paradox is so counterintutive. [0]
[0] https://en.wikipedia.org/wiki/Simpson%27s_paradox#UC_Berkele...
[0] https://en.wikipedia.org/wiki/Simpson%27s_paradox#UC_Berkele...
Yes, it sure is, took me a while to get it.
I don't have any paradoxes but here are my two favourite surprising facts.
1: NY city on the East coast of N. America lies further west than Santiago the capital of Chile on the West coast of S. America
2: The Atlantic opening of the Panama canal lies further west than the Pacific opening.
1: NY city on the East coast of N. America lies further west than Santiago the capital of Chile on the West coast of S. America
2: The Atlantic opening of the Panama canal lies further west than the Pacific opening.
One that always surprises me, Edmonton (Canada's most northern city) is about the same latitude as Manchester in the UK.
Here's another one: the majority of Canada's population actually lives south of the 49 parallel, which for the most part is the US border.
The reason is most of the population is in Ontario and Quebec, and the majority of that population is south of the 49th. The southernmost part of Canada at Niagara falls is actually at the same latitude as northern California. Which is why it is a big wine growing region.
The reason is most of the population is in Ontario and Quebec, and the majority of that population is south of the 49th. The southernmost part of Canada at Niagara falls is actually at the same latitude as northern California. Which is why it is a big wine growing region.
Your recollection is not quite correct here. The border between California and Oregon is at the 42nd parallel, while Niagara falls is at the 43rd. The southernmost part of Canada is Essex County, near Detroit, which does cross the 42nd parallel. The Niagara region is a big wine growing region primarily because of the moderating effect of the Great Lakes on the climate and the shelter provided by the Niagara escarpment.
As a native to the US west coast, I was very surprised to realize that Toronto, Ontario is further south than Portland, Oregon.
Wow so I looked at a map: Portland, Oregon is north of Portland, Maine? Maine?! That is surprising.
And I was the nerd in high school pointing out Rome is north of NYC.
And I was the nerd in high school pointing out Rome is north of NYC.
I always refer to my Toronto colleagues ( I am in Seattle ) as Southerners...
Some of these mysteries clear up when you understand inland climate vs coastal climate.
The ocean changes temperature very slowly. In summer it's colder than land, and in winter it's warmer. This acts to keep land temperature semi stable over the seasons.
Inland there are no such dampeners. Summers get real hot and winters are very cold.
Which is why Edmonton probably (I haven't checked) has much colder winters than northern Norway.
The ocean changes temperature very slowly. In summer it's colder than land, and in winter it's warmer. This acts to keep land temperature semi stable over the seasons.
Inland there are no such dampeners. Summers get real hot and winters are very cold.
Which is why Edmonton probably (I haven't checked) has much colder winters than northern Norway.
Also very importantly Europe gets the Gulf stream to keep it mild
I have heard that's a myth, and it's really just that the North Atlantic is big and the prevailing winds go east.
I haven't done the deep research to confirm that, so just take this a me spreading a rumor.
I haven't done the deep research to confirm that, so just take this a me spreading a rumor.
Well that would be a turn up for the books because one of the often mentioned bad consequences of global warming is a loss of the North Atlantic Drift (gulf stream) from Europe and us ending up with a climate similar to what the same latitude of Canada has.
Where I grew up in Southern Scotland (some years get no snow) is at the same latitude as places Polar Bears live in Canada.
Or that the most northerly French-speaking town in the world is Dunkirk in France and not somewhere in Quebec.
This is not true. The town of Radisson was built in the 70s during work on the James Bay Project and is still mainly francophone. It's about 2° north of Dunkirk.
https://en.wikipedia.org/wiki/Radisson,_Quebec
https://en.wikipedia.org/wiki/Radisson,_Quebec
Interesting but I'm not sure I'm buying it ;-)
Radisson is a small unconstituted locality so whether it qualifies as a town is questionable.
It also has a population small enough to fit in two or three buses.
How about Fermont in Quebec, then? http://www.toponymie.gouv.qc.ca/ct/ToposWeb/fiche.aspx?no_se...
It is predominantly French speaking, is 1° further north than Dunkirk, is incorporated as Ville de Fermont, has a population of about 2400.
It also has a Wikipedia page that claims "Fermont is arguably the world's northernmost Francophone settlement of any considerable size": https://en.wikipedia.org/wiki/Fermont.
It is predominantly French speaking, is 1° further north than Dunkirk, is incorporated as Ville de Fermont, has a population of about 2400.
It also has a Wikipedia page that claims "Fermont is arguably the world's northernmost Francophone settlement of any considerable size": https://en.wikipedia.org/wiki/Fermont.
It's much cooler that Dunkirk should hold this distinction, isn't it, so can we agree please that these rather undistinguished places in Canada don't count? Anyway Dunkirk is a proper town/city (91K people, interesting history) not like this awful sounding place where everyone lives in a single building because it's like the moon there or something.
I did wonder about Belgium but it looks like most of Belgium (and all of the French speaking parts) are further south than Dunkirk.
In general latitude comparisons between Europe and the USA are always surprising to me because of the very different climates. New York is to the south of Marseille for instance. Florida lines up with the southern (disputed) regions of Morocco.
There's also the odd fact that the lands to the east and the west of Greenland aren't ice covered while Greenland is (Google maps satellite view).
We should rename North-America to North-West-America and South-America to South-East-America.
I opened google maps to check #2 and stared for a while trying to understand what you meant... Then I zoomed out!
A few more:
* The US state closest to Africa is Maine.
* New York City is south of Rome.
* Los Angeles, California is east of Reno, Nevada.
* The US state closest to Africa is Maine.
* New York City is south of Rome.
* Los Angeles, California is east of Reno, Nevada.
Whoa! That’s cool.
Another one (somewhat more obvious) is that the southernmost point in the USA is on the Big Island of Hawaii.
Another one (somewhat more obvious) is that the southernmost point in the USA is on the Big Island of Hawaii.
My favorite example of Simpson's paradox: On average, in the United States, houses without central AC cost more than houses with central AC.
When you break it down by state it turns out this is almost entirely due to lots of expensive houses without central AC in California. In every single state houses with central AC are more expensive than houses without, but California with its high real estate prices and temperate climate skews the national averages.
When you break it down by state it turns out this is almost entirely due to lots of expensive houses without central AC in California. In every single state houses with central AC are more expensive than houses without, but California with its high real estate prices and temperate climate skews the national averages.
"What do Roman fish tanks tell us about sea levels?
"Wealthy Romans at the time of Augustus were building fish holding tanks. The fishermen would come in with the fish, they’d put them there so that the fish were fresh when they ate them—they wanted to keep them alive for a few days or weeks or whatever. The Romans were engineers, so they built these fish tanks at very precise levels relative to sea level at the time. You didn’t want the walls to be too low because at high tide the fish would swim out; you didn’t want it to be too high because you wanted tides to refresh the water within the tanks.
"Kurt Lambeck, a professor at the Australian National University, recognized that by looking at the present day elevation of those fish tanks, we could say something about how sea level had changed over the 2,500 years since then. If sea level over the last 2,500 years was going up at the rate that it went up in the 20th century, those fish tanks would be under 4 meters of water—12 feet of water—and I can assure you they’re not. You can see them. You can walk along the coast, they’re visible. What that tells you is that it is impossible that sea level went up by the rates that we saw in the 20th century for any extended period of time earlier than that. Sea level has not gone up over the last 2,500 years like it has in the 20th century."
Italy is tectonically active. The level of 2000 year old Roman constructions versus the sea may well have more to do with local ground rise or fall. This assertion needs significant supporting data.
"Wealthy Romans at the time of Augustus were building fish holding tanks. The fishermen would come in with the fish, they’d put them there so that the fish were fresh when they ate them—they wanted to keep them alive for a few days or weeks or whatever. The Romans were engineers, so they built these fish tanks at very precise levels relative to sea level at the time. You didn’t want the walls to be too low because at high tide the fish would swim out; you didn’t want it to be too high because you wanted tides to refresh the water within the tanks.
"Kurt Lambeck, a professor at the Australian National University, recognized that by looking at the present day elevation of those fish tanks, we could say something about how sea level had changed over the 2,500 years since then. If sea level over the last 2,500 years was going up at the rate that it went up in the 20th century, those fish tanks would be under 4 meters of water—12 feet of water—and I can assure you they’re not. You can see them. You can walk along the coast, they’re visible. What that tells you is that it is impossible that sea level went up by the rates that we saw in the 20th century for any extended period of time earlier than that. Sea level has not gone up over the last 2,500 years like it has in the 20th century."
Italy is tectonically active. The level of 2000 year old Roman constructions versus the sea may well have more to do with local ground rise or fall. This assertion needs significant supporting data.
The illustration seems misleading—showing increase in sea level starting right outside of a glacier. As discussed in the article, the area of diminishing sea level spans thousands of kilometers far from where a glacier used to be, depending on its mass.
The person interviewed claims that people usually don’t appreciate his points since they’re so counter-intuitive, well right there we have Nautilus not helping that at all.
The person interviewed claims that people usually don’t appreciate his points since they’re so counter-intuitive, well right there we have Nautilus not helping that at all.
Mitrovica has some videos on YT that probably do a better job of explaining.
As I understand it is gravity's inverse square law that makes the effect strongest closet to the glacier and tapering off over a couple thousand kilometers.
My understanding as well. The image, though, doesn't convey sea level dipping for many kilometers around former glacier edge and rising only further away (possibly in another hemisphere entirely)—instead it shows sea level rising immediately at the edge, which doesn't seem to track.
I think the image is trying to convey that there's a rising immediately near the glacier due to the tectonic plate lifting up. Then there's a falling due to reduced gravitation. What's not shown would be (much further away) a rising due to increased water volume.
I agree that the image is a bit confusing.
I agree that the image is a bit confusing.
I think the green line is the sea level after the melting, since it is labeled Final Sea Level. It does not show a fall, only a rise, next to the glacier.
>If humans weren’t warming the climate, Earth might be poised to enter into another Ice Age in the future.
Is there a chance it is beneficial to keep the next ice age at bay?
Is there a chance it is beneficial to keep the next ice age at bay?
The agricultural regions of Europe and North America not being covered with sheets of ice may be a positive. Especially if you like having food.
Historically ice ages have not been very good for humanity.
Good article. I was hoping that he would talk about the effect on tectonic plate stability with these massive bodies of weight shifting around a spinning sphere.
This is actually very concerning. We have significant evidence now to suggest that asteroids in the past have caused large earthquakes. Sometimes on the other side of the impact zone (the antipode).
More scary though is what comets can do. They have a highly elliptical orbit, so they are much harder to spot than asteroids as they come out of nowhere. The elliptical orbit gives them much greater speed to. Comets tends to generate enormous levels of heat too, they explode shorty before impact as one did in Tunguska in Russia in 1908. Anyway it now seems that these "bursts" have happened during ice ages, vaporizing massive ice sheets. We are talking perhaps the entire northern hemisphere in some cases like the Younger Dryas Impact Hypothesis.
The crust floats like water and is as gooey as pudding when suddenly trillions of tons of weight just "disappears" above it. We have no idea how this unfolds currently except to say it is destructive and chaotic at the least.
More scary though is what comets can do. They have a highly elliptical orbit, so they are much harder to spot than asteroids as they come out of nowhere. The elliptical orbit gives them much greater speed to. Comets tends to generate enormous levels of heat too, they explode shorty before impact as one did in Tunguska in Russia in 1908. Anyway it now seems that these "bursts" have happened during ice ages, vaporizing massive ice sheets. We are talking perhaps the entire northern hemisphere in some cases like the Younger Dryas Impact Hypothesis.
The crust floats like water and is as gooey as pudding when suddenly trillions of tons of weight just "disappears" above it. We have no idea how this unfolds currently except to say it is destructive and chaotic at the least.
We do have some idea what happens - post-glacial rebound is very noticeable in some parts of the world that were heavily glaciated in the last ice age:
https://en.wikipedia.org/wiki/Post-glacial_rebound
https://en.wikipedia.org/wiki/Post-glacial_rebound
Just saw this. Fascinating.
Does the North America plate losing Greenland's ice increase earthquake risk on the west coast then?
Intuitively seems like it should... But then this is an article about how bad intuition is for complex problems.
Intuitively seems like it should... But then this is an article about how bad intuition is for complex problems.
The interview is nicely done. The followup questions were exactly what I would have asked, probably to explain the theory to someone who doesn't know much about geology
I recall Augustus reigned on the order of 2000 years ago, not 2500? Normally this would be a trivial detail, but the calculations under discussion would seem to require exacting precision.
I suspect this is an error on the reporter's part, so it's good that Nautilus is online and can update its articles.
I suspect this is an error on the reporter's part, so it's good that Nautilus is online and can update its articles.
I wouldn't call it trivial at all; 500 years is the difference between the Renaissance and present day. 2500 years ago, Rome had just become a republic, while 2000 years ago (during Augustus' time) it became an empire and would soon reach its territorial peak.
The idea is interesting and I'm glad to know about it, but there is a glaring flaw in his reasoning which nobody else here has commented on so I'll do it:
"I was in Holland a few summers ago and was trying to convince the Dutch that if the Greenland ice sheet melts, they have less to worry about than the Antarctic ice sheet melting. But it doesn’t register."
because, is there a polar melting hypothesis that melts the Arctic without melting the Antarctic? It could be that his idea is that both poles have water stacked up from ice sheet gravity more than it would be than melted, but the reasoning in that quote doesn't make that point, it makes a different point that is not useful, and he is I guess saying that there would just be more flooding than expected near the equator?
"I was in Holland a few summers ago and was trying to convince the Dutch that if the Greenland ice sheet melts, they have less to worry about than the Antarctic ice sheet melting. But it doesn’t register."
because, is there a polar melting hypothesis that melts the Arctic without melting the Antarctic? It could be that his idea is that both poles have water stacked up from ice sheet gravity more than it would be than melted, but the reasoning in that quote doesn't make that point, it makes a different point that is not useful, and he is I guess saying that there would just be more flooding than expected near the equator?
If you want to get a better feel for this NASA has made a great visualization tool https://vesl.jpl.nasa.gov/sea-level/slr-gfm/
this article doesnt do much to dispel the counterintuitive nature of the subject.
1) the mass of glacier sheets have gravity, so sea level is higher near glaciers
2) the weight of the glacier on the land its sitting on pushes the land into the water and raises sea level
3) when glaciers melt, they add water to the sea. however, the melting glacier removes gravitational mass and removes weight that was forcing the land it was sitting on into the water. the combination of these 3 effects is lowering the nearby sea level and raising the faraway sea level
4) the distance that makes a given spot nearby or faraway is dependent on the glacier sheet itself - how massive it is, its geometry, etc. the all-in, 3 dimensional accounting of where on the globe sea levels change for a given glacier melting is called its fingerprint.
the article claims that the major glacier fingerprints are unique such that global sea level data points can identify, simultaneously, what percentage of all glaciers are melting.
on a side note: the provided infographic is wrong - the yellow and green lines are touching at the edge of the glacier. its attempting to model pretty pictures in 3d with 2d lines, and its just not accurate. it sort of conveys the point, i guess, if you just squint and dont think about it.
1) the mass of glacier sheets have gravity, so sea level is higher near glaciers
2) the weight of the glacier on the land its sitting on pushes the land into the water and raises sea level
3) when glaciers melt, they add water to the sea. however, the melting glacier removes gravitational mass and removes weight that was forcing the land it was sitting on into the water. the combination of these 3 effects is lowering the nearby sea level and raising the faraway sea level
4) the distance that makes a given spot nearby or faraway is dependent on the glacier sheet itself - how massive it is, its geometry, etc. the all-in, 3 dimensional accounting of where on the globe sea levels change for a given glacier melting is called its fingerprint.
the article claims that the major glacier fingerprints are unique such that global sea level data points can identify, simultaneously, what percentage of all glaciers are melting.
on a side note: the provided infographic is wrong - the yellow and green lines are touching at the edge of the glacier. its attempting to model pretty pictures in 3d with 2d lines, and its just not accurate. it sort of conveys the point, i guess, if you just squint and dont think about it.
The problem I have with this stuff is that I just can't imagine how bad it could possibly be if sea levels rose even three meters over the next hundred years.
Significant fractions of many coastal cities are under 3m above sea level. Even if they could put up walls, many seaside communities are also under 3m.
[deleted]
All the discussion about gravity is good, but I was equally interested in the slowing of the earth's rotation. 1.8ms per day? It seems like that's large enough to be noticed with modern clocks/astronomy outside of eclipse records. Is this confirmed outside of eclipse records?
Yes. That's why we have leap seconds.
I thought that was just to correct for the initial definition of a second which was inaccurate. But, it looks like it is the reason for leap seconds:
https://www.timeanddate.com/time/leap-seconds-background.htm....
https://www.timeanddate.com/time/leap-seconds-background.htm....
Leap seconds can be affected by things like big volcanic eruptions and earthquakes. That's why they are defined "as needed" instead of at regular intervals, and why they are applied somewhat irregularly.
This struck me, too. So days were 4 hours shorter 2500 years ago? The evidence our ancestors worked fewer hours a day just keeps piling up [0]!
[0] https://news.ycombinator.com/item?id=16656903
[0] https://news.ycombinator.com/item?id=16656903
> So days were 4 hours shorter 2500 years ago?
No. The cumulative clock difference between two clocks, one of which is adding leap seconds due to the slowing of Earth's rotation, the other of which is not, is not the same as the rate of slowing of the Earth's rotation.
The current rate of slowing is about 1.4 milliseconds per 100 years. That means that, 100 years ago, the length of 1 day was 1.4 milliseconds shorter than it is today. So let's suppose that 100 years ago, the day was exactly 86,400,000.0 milliseconds long. Then today would be 86,400,001.4 milliseconds long.
Now add up all those days over the last 100 years, i.e., 36,525 of them, and suppose the rate of increase in the day is linear. Then the average extra milliseconds per day is half of 1.4, or 0.7 milliseconds, and the total number of milliseconds in those 36,525 days is
3,155,760,025,567.5
instead of the
3,155,760,000,000.0
that it would have been if the length of the day had been constant. That's an extra 25,567.5 millliseconds over 100 years, which is a lot bigger than 1.4. That's the difference between the cumulative clock difference and the rate of slowing.
No. The cumulative clock difference between two clocks, one of which is adding leap seconds due to the slowing of Earth's rotation, the other of which is not, is not the same as the rate of slowing of the Earth's rotation.
The current rate of slowing is about 1.4 milliseconds per 100 years. That means that, 100 years ago, the length of 1 day was 1.4 milliseconds shorter than it is today. So let's suppose that 100 years ago, the day was exactly 86,400,000.0 milliseconds long. Then today would be 86,400,001.4 milliseconds long.
Now add up all those days over the last 100 years, i.e., 36,525 of them, and suppose the rate of increase in the day is linear. Then the average extra milliseconds per day is half of 1.4, or 0.7 milliseconds, and the total number of milliseconds in those 36,525 days is
3,155,760,025,567.5
instead of the
3,155,760,000,000.0
that it would have been if the length of the day had been constant. That's an extra 25,567.5 millliseconds over 100 years, which is a lot bigger than 1.4. That's the difference between the cumulative clock difference and the rate of slowing.
Perhaps I'm missing some sarcasm, but the article states that two clocks, one synchronized to the earth's rotation, and the other keeping atomic time, they would drift by a total of 4 hours over 2500 years, not drift by 4 hours per day. Those are completely different things.
I thought the main contributor to the rise was the thermal expansion of water as it heats up. I don't see a single mention of this in the article ?
> What do Roman fish tanks tell us about sea levels?
This article has many such gems. Fascinating and well-written.
(Note that it was originally published in 2016).
This article has many such gems. Fascinating and well-written.
(Note that it was originally published in 2016).
More on Roman fish tanks if anyone wants to read about this topic. I thought this was very insightful:
https://www.harvardmagazine.com/2016/08/what-roman-ruins-rev...
https://www.harvardmagazine.com/2016/08/what-roman-ruins-rev...
Ice is less dense than water. Why would ice's gravity be more influential than the waters?
Because when the ice melts, the water does not remain where the ice was, but rather enters the ocean. Water entering the ocean anywhere in the world will tend to raise the height of the ocean worldwide.
Gravity pulls on both objects. The water (along with the rest of the planet) pulls the ice down, the ice pulls the water up.
I’m trying to get as many people out to see Florida one last time before it’s underwater.
This article is bizarre.
Some quotes that strikes me as just really really odd:
"Jerry Mitrovica has been overturning accepted wisdom for decades" - no one is this good.
"What he calls postmodern geology" - this is very concerning. Postmodernism is like Foucault and Derrida and about power and society. Foucault is actually the most cited academic of all time statistically, so for a Professor to knowingly use this word to describe the science of geology is just strange.
"Though a practiced public speaker" - what is this? should he be ashamed?
"These are known as sea-level fingerprints, because each ice sheet has its own geometry. Greenland produces one geometry of sea level change and the Antarctic has its own. Mountain glaciers have their own fingerprint." - what?
Some quotes that strikes me as just really really odd:
"Jerry Mitrovica has been overturning accepted wisdom for decades" - no one is this good.
"What he calls postmodern geology" - this is very concerning. Postmodernism is like Foucault and Derrida and about power and society. Foucault is actually the most cited academic of all time statistically, so for a Professor to knowingly use this word to describe the science of geology is just strange.
"Though a practiced public speaker" - what is this? should he be ashamed?
"These are known as sea-level fingerprints, because each ice sheet has its own geometry. Greenland produces one geometry of sea level change and the Antarctic has its own. Mountain glaciers have their own fingerprint." - what?
Can you get really get 50m of local displacement from 10^-5 Earth masses?