Why Our Intuition About Sea-Level Rise Is Wrong
oceans.nautil.us
oceans.nautil.us
Can you get really get 50m of local displacement from 10^-5 Earth masses?
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.
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.
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).
That said, I'm not a geophysicist.
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
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 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.
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.
from the wikipedia entry for tides.
>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.
Distance and mass seem to cancel out almost perfectly
Wonder which one I'd put money on.
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.
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.
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
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.
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...
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Diagram:
1
4 E 2 M
3
M = Moon
Numbers = 4 "sides" of the Earth, relative to the Earth-Moon line
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
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.
[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.
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 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.
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).
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...
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
> 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.
"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. "
[0] https://en.wikipedia.org/wiki/Simpson%27s_paradox#UC_Berkele...
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.
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.
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.
And I was the nerd in high school pointing out Rome is north of NYC.
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.
I haven't done the deep research to confirm that, so just take this a me spreading a rumor.
* The US state closest to Africa is Maine.
* New York City is south of Rome.
* Los Angeles, California is east of Reno, Nevada.
Another one (somewhat more obvious) is that the southernmost point in the USA is on the Big Island of Hawaii.
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.
"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 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.
I agree that the image is a bit confusing.
Is there a chance it is beneficial to keep the next ice age at bay?
Intuitively seems like it should... But then this is an article about how bad intuition is for complex problems.
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.
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 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?
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.
https://www.timeanddate.com/time/leap-seconds-background.htm....
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.
This article has many such gems. Fascinating and well-written.
(Note that it was originally published in 2016).
https://www.harvardmagazine.com/2016/08/what-roman-ruins-rev...
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?