Change of sea level in relation to sea ground

My physics teacher said that if the sea ground is higher, then, because of the stronger gravitational force, the sea level is lower. I am not sure if this is true and he didn't give a very strong proof. I thought sea level equalizes all over the earth. Of course I am taking the sea level in relation to the earth's center of mass.

Note: I am not taking ebb and flow into account as it does not interfere with the question I am dealing with.

Any help will be welcome.

I have to say that impressive as it is, Borek's reference seems overkill for what looks to me to be a high school question.

I would appreciate someone explaining the term 'sea ground' as neither I nor Google can locate it.

Evo
Mentor
I have to say that impressive as it is, Borek's reference seems overkill for what looks to me to be a high school question.

I would appreciate someone explaining the term 'sea ground' as neither I nor Google can locate it.
I couldn't figure this one out either. I was thinking maybe he meant seabed, but that makes no sense either.

Borek
Mentor
From what I understand question is about the thickness of the water layer above seabed. OP thought that it depends only on some idealized water level that is identical everywhere (equidistant from the Earth center, or perhaps lying on ellipsoid that takes into account flattening of the Earth) and position of the bottom. That's not true, water level is not "constant", geoid (which is more or less defined as the surface of water would it cover all Earth) differs from ellipsoid in many places. In many places the difference is proportional to the water depth, as lack of rock mass beneath means less water is attracted to these places.

That's my understanding, I don't pretend to know for sure.

The thickness of the water, or any fluid layer, varies with latitude on a spinning object like the earth.

Try this

The OP is probably about the effect of local gravity anomalies on sea level. For instance the mass of mountains/glaciers attract the water a little bit, rising the local sea level, according to Niels Axel Morner.

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This is tricky.

At the first sight, water is definitely less dense than rock (1 g/cm3 vs. 2.7-3 g/cm3), and you would expect the gravity above deep water to be lower, and the sea level would be lower too (in other words, sea surface would be closer to the center of the planet). Note that this is the exact opposite of what the physics teacher said.

However, there is a second effect. The Earth is in a state of what's known as isostatic equilibrium. We can roughly think of the crust as a layer of rock with varying thickness floating on top of semi-liquid mantle. The mantle is heavier than the crust (3.3 g/cm3 and up), and oceans are formed in places where the crust is thinnest. (Why? Imagine two icebergs of different sizes floating in the ocean. The larger iceberg will protrude further away from the surface in both directions.) Therefore, areas with lower density near the surface, like oceans, have higher density further down.

The two effects very nearly cancel each other. For example, just the direct effect of having 5 km of water instead of rock would change local gravity enough to drop the sea level on the order of kilometers. But the isostatic correction cancels almost all of this, and the real sea level is only lowered by 10 m or so. On average. Since the world we live in is annoyingly random and irregular, and the two factors are so close to each other, we can't really say which way they will add in any particular point.

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Borek
Mentor
and the real sea level is only lowered by 10 m or so

Depending on the point o view 10 m is either nothing or a lot.

I don't really have anything interesting to add: Andre and Borek have got this one nailed.

(The physics teacher was wrong. It is true that a higher sea bottom will cause stronger gravity. S/he was (probably) thinking that sea level behaved a bit like a rubber sheet, in that it would be pulled down where gravity was strongest. In fact the ocean is not at all like that, in that it is free to move sideways -- where gravity is strongest the water is pulled in sideways and piles up (in fact there is even a second order effect whereby the piling up water causes a second order increase in the local gravity field which attracts yet more water) this naturally causes the sea level to rise.)

We can roughly think of the crust as a layer of rock with varying thickness floating on top of semi-liquid mantle. The mantle is heavier than the crust (3.3 g/cm3 and up), and oceans are formed in places where the crust is thinnest. (Why? Imagine two icebergs of different sizes floating in the ocean. The larger iceberg will protrude further away from the surface in both directions.)

This is true, but dangerously oversimplistic, you have ignored the definite distinction between oceanic and continental crust, which is actually very important in understanding pretty much the whole subject of geology.

From the information I can find the correlation between gravity and terrain as either land or sea seems pretty poor.

http://www.jpl.nasa.gov/news/features.cfm?feature=11

Quote from NASA

There's big gravity low off the coast of India, where there are thought to be the remains of some old mantle features associated with the plate tectonics of India that led it to collide with the Himalayas. There's a big high in the South Pacific, also thought to be due to mantle structures

Well, that's gravity both abnormally high and abnormally low at the bottom of the sea?

From the information I can find the correlation between gravity and terrain as either land or sea seems pretty poor.

http://www.jpl.nasa.gov/news/features.cfm?feature=11

Quote from NASA

Well, that's gravity both abnormally high and abnormally low at the bottom of the sea?

The terrain will be imprinted on the gravitational field. But of course that's not the whole story! Gravity also changes as a function of other things, the density of the rocks below happens to be signifacnt and usually the thing that geophysicists are most interested in. If there is low gravity somewhere, that suggests that there is something of low density below, a rising plume for example....

The terrain will be imprinted on the gravitational field

I've just posted to show that this is not so. Tha NASA gravity map looks nothing at all like a physical map of the earth.

I've just posted to show that this is not so. Tha NASA gravity map looks nothing at all like a physical map of the earth.

That's because the terrain is not the whole story. There are other factors, like density, which are influencing the gravitational field.

Gravity is simply a function of mass and distance.

Terrain influences the gravitational field because it brings dense rock closer to the satellite which is measuring gravity. (Also, when interpreting gravitational maps you sometimes have to be very careful, often they are deliberately processed to remove obvious components of the gravitational field such as topography to enable interpretation of otherwise hidden anomalous features.)

Following up on the gravity low in the Indian ocean, recent work suggests that this low is caused by low density regions in the mantle. Interestingly, this research goes further and associates the formation of these low density upwelling regions with the process of subducted tectonic plates impinging the core mantle boundary.

The global geoid is characterized by a semi-continuous belt of lows that surround the Pacific Ocean, including isolated minima in the Indian Ocean, Ross Sea and northeast Pacific and west Atlantic oceans. These geoid lows have been attributed to Mesozoic subduction1,2. Geodynamic models that include slab graveyards in the lower mantle as inferred from seismic topography or from plate reconstructions correctly predict the general trend of geoid minima3,4. However, these models fail to accurately reproduce localized geoid lows in the Indian Ocean, Ross Sea and northeast Pacific Ocean. Here we show that the geoid lows are correlated with high-velocity anomalies near the base of the mantle and low-velocity anomalies in the mid-to-upper mantle. Our mantle flow models reproduce the geoid minima if the mid-to-upper mantle upwellings are positioned above the inferred locations of ancient subducted slabs. We find that the long-wavelength trough in the geoid is linked to high-density slab graveyards in the lower mantle, whereas upwelling regions in the mantle above 1,000 km depth cause discrete lows within the larger trough. We suggest that this mode of upwelling in the mid-to-upper mantle is caused by buoyant hydrated mantle that was created by processes around and above subducted slabs.

http://www.nature.com/ngeo/journal/v3/n6/full/ngeo855.html

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My physics teacher said that if the sea ground is higher, then, because of the stronger gravitational force, the sea level is lower. I am not sure if this is true and he didn't give a very strong proof.

This is the original question.

How does recent discussion relate to sea level and what is sea ground?

D H
Staff Emeritus
How does recent discussion relate to sea level and what is sea ground?
The original question was ill-posed. What, exactly, is sea ground, and what exactly did the teacher mean?

So, let's try to answer the question in a simple way. How could we make the sea ground higher? A massive earthmoving effort is obviously needed, scraping the entire exposed land area of the earth into the oceans. With the mean elevation of the land being 840 meters and the mean depth of the oceans being 3865 meters (e.g., http://www.kinderscience.com/mean_elevation_of_land_and_sea.htm [Broken]) and the oceans covering 70.8% of the planet, this means we would have a world-spanning ocean with an average depth of 2491 meters. That compares well with the figure of 2440 meters given at http://hypertextbook.com/facts/2006/HelenLi.shtml.

So is this the sense that the teacher meant, that the average depth of the oceans would be less if the earth didn't have those lumps of land popping out of the ocean? That's a trivial kind of result. Playing with the math just a bit more, the surface of this world-spanning ocean would be about 245 meters higher than the current sea level. (One easy way to arrive at this figure: 0.292*840 meters = 245 meters. There are other ways, some rather convoluted, of arriving at the same result.

Since we now have a sea level that is higher than the current sea level, I don't know what the teacher was trying to demonstrate. Dragging in the geoid doesn't help a bit. What the teacher was thinking, who knows? The teacher was wrong.

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How does recent discussion relate to sea level and what is sea ground?

The only person who knows 100% what they meant when they said "sea ground" was the original poster.

As far as I can see his question was answered to a sufficiently high standard earlier in the post (by Borek and Andre). Recent discussion moved on from that by looking at anomalies, e.g. the anomaly off the coast of India that you, Studiot, raised yourself.

The original question was ill-posed. What, exactly, is sea ground, and what exactly did the teacher mean?

So is this the sense that the teacher meant, that the average depth of the oceans would be less if the earth didn't have those lumps of land popping out of the ocean? ....

Dragging in the geoid doesn't help a bit. What the teacher was thinking, who knows? The teacher was wrong.

I agree the initial question was fuzzy but I think we can make a decent guess as to what was most likely meant.

I don't like your interpretation of the meaning, I don't see how the original poster could have meant smoothing the earth's surface when he said raising sea ground.

"Dragging in the geoid" helps, if you interpret the meaning of raising the sea ground as increasing the height of sea floor topography (which I think is the >90% most likely meaning).

D H
Staff Emeritus
How, exactly, does dragging in the geoid help though?

Suppose we got rid of the density variations but did so in a manner that kept the volume of the Earth constant. The Earth would eventually settle into isostatic equilibrium with the sea floor forming a geopotential surface whose distance from the center of the Earth is a simple function of latitude only. The sea level would form another geopotential surface about 2500 meters or so above the sea floor geopotential surface. The end result would be exactly the same as my Earth-moving mind experiment.

How, exactly, does dragging in the geoid help though?

The original question IS essentially about the geoid. It is asking about the relation between the shape of the geoid (which is, by definition, equal to the sea level minus the effects of tides, currents, and weather), and the shape of the underwater topography.

Without the isostatic correction, there would be a strong relationship between the two. In reality, as you can see here http://en.wikipedia.org/wiki/File:Geoid_height_red_blue.png, there relationship is very weak.

Thank you for your contribution, Hmaster. Have you ever heard the term 'sea ground' ?

If so perhaps you could define it for us.

Like DH I remain sceptical about the importance of the geoid in this question. I also note the continued omission of the effect of the earth's rotation on the shape of attached fluid bodies.

Sea ground is synonymous with sea floor. E.g.

http://www.dailyreckoning.co.uk/emerging-market-investment/deep-sea-diving-for-oil.html [Broken] "The drilling site is approx. 250 miles south west of New Orleans at a depth of 8 kilometres below the sea ground level (26,600 feet) - given the depth of the sea at this spot of 5860 feet, the full drilling depth is an astonishing 32,500 feet. "

How can the geoid be unimportant when the question is about the shape of the geoid?

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Evo
Mentor
Sea ground is synonymous with sea floor. E.g.

http://www.dailyreckoning.co.uk/emerging-market-investment/deep-sea-diving-for-oil.html [Broken] "The drilling site is approx. 250 miles south west of New Orleans at a depth of 8 kilometres below the sea ground level (26,600 feet) - given the depth of the sea at this spot of 5860 feet, the full drilling depth is an astonishing 32,500 feet. "

How can the geoid be unimportant when the question is about the shape of the geoid?
Hamster, congratulations on finding the only reference to sea ground on the internet. :tongue2: It's apparently a misuse of the words, it seems to mean sea bed or sea floor.

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D H
Staff Emeritus
The original question IS essentially about the geoid. It is asking about the relation between the shape of the geoid (which is, by definition, equal to the sea level minus the effects of tides, currents, and weather), and the shape of the underwater topography.
In an ill-stated manner, maybe.

Without the isostatic correction, there would be a strong relationship between the two. In reality, as you can see here http://en.wikipedia.org/wiki/File:Geoid_height_red_blue.png, there relationship is very weak.
For one thing that is an incredibly awful image. What can I say? It's wikipedia. That sharp color change at zero is worse than meaningless. It borders on intended misinformation.

Here are a couple better renditions of the EGM96 tide-free geoid: http://www.esri.com/news/arcuser/0703/graphics/geoid3_lg.jpg
http://earth-info.nga.mil/GandG/images/ww15mgh2.gif

You are assuming that the geoid should show the difference between continental and oceanic crust. It shouldn't, and it doesn't.

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You are assuming that the geoid should show the difference between continental and oceanic crust. It shouldn't, and it doesn't.

Huh? I am most certainly not assuming that. It should show the distance between the center of the earth and the sea surface. Continental vs. oceanic crust does not enter into it, not even indirectly.