I'm confused about the effect of gravity anomalies on sea height

In summary, differences in gravity affect the local height of the sea due to the formation of an equipotential surface. Water will flow to regions of lower gravitational potential, which are often created by positive gravity anomalies. The Earth's rotation also affects gravitational potential, with water tending to flow towards the poles to create an oblate shape. This can be seen in gravity maps, where regions with stronger gravity have higher sea levels. However, this can be confusing as it may seem that water should flow towards the equator, but this is not the case when considering the entire gravitational potential. Ultimately, the Earth's rotation and local gravity anomalies must be factored in when trying to map local gravity effects on sea level.
  • #1
Jaams
8
0
TL;DR Summary
Lower than average weight at the equator causes the earth to be wider, yet positive gravity anomalies are claimed to cause an increase in sea height.
Summary: Lower than average weight at the equator causes the Earth to be wider, yet positive gravity anomalies are claimed to cause an increase in sea height.

Summary: Lower than average weight at the equator causes the Earth to be wider, yet positive gravity anomalies are claimed to cause an increase in sea height.

I'm trying to understand how differences in gravity would in practice end up affecting the local height of the sea. We know that at the equator, everything weighs less, and the sea-level is also higher up than average, seeing as the Earth's wider at the equator. But then if you look at a gravity map, you can see that they say that places with stronger gravity will have a sea-level that's higher up. That's in my opinion a contradiction, and I'm having trouble figuring out what I'm missing.

I'll attach the gravity maps made based on sea-level height, then mGal, and then a picture of the Earth's oblate shape caused by Earth's rotation:

goce.gif


g001_eigen-grace01_deg70.jpg


The images above are sadly oriented differently, but the blue and red areas correspond with each other, showing that increased gravity = increased sea-level.

014shape_SouthAmerica_small-e1463945439504-580x468.jpg


Here you can see the diameter of the Earth and how it increases as you get closer to the equator.

I'm hoping that someone can explain to me how this works. If anyone knows of any website or earlier thread that goes over this, then that's good too. I wasn't able to find one.
 
Physics news on Phys.org
  • #2
Notice the scale of these plots. The first one is in meters and over the Pacific Ocean it ranges from about -50 m to about +10 m with little or no prolateness in evidence. The globe is in km and ranges from about 6361 km to about 6373 km over the Pacific Ocean with strong prolateness.

Basically, the first plot has subtracted off the prolateness of the second so that you can see the small little deviations that you cannot see on the larger scale.
 
  • Informative
Likes anorlunda
  • #3
The seas will tend to form in such a way to create an equipotential surface. In other words, where the gravitational potential is lower, water will necessarily flow in so that the water across the sea surface has equal potential energy. Where there is more local gravity, the seas will have lower potential energy at the same surface height. So water from surrounding areas will flow so increase the sea surface height to that the gravitational potential of water at the surface is equal across the entire surface. This only works with a fluid such as water.

Centrifugal effects due to the Earth's rotation also affects gravitational potential. This effectively lowers the rate of gravitational free-fall at a given distance from the Earth centre at the equator compared to locations at higher northern or southern latitudes. So water at the surface will tend to flow away (slightly) from the equator toward the poles to create an equipotential surface. This has to be factored in when trying to map local gravity effects due to mass variations under the seas.

AM
 
Last edited:
  • Like
Likes Dale
  • #4
Dale, you're right, but my confusion lies with a different issue and I'll explain it below:

Andrew Mason, to summarize (based on my interpretation), you're saying that the positive gravity anomalies draw more water in and the sea level rises there, and that water is drawn to the poles from the equator for the same reason.

I'm confused by that, because water would in my opinion need to be drawn to the equator for the Earth to be oblate, and for there to be any water at the taller equator in the first place.

I hope this response makes my source of confusion more apparent.
 
  • #5
Jaams said:
I hope this response makes my source of confusion more apparent.
Use vectors instead trying to relate local gravity to water level.
 
  • #6
A.T. said:
Use vectors instead trying to relate local gravity to water level.
I don't know how you want me to actually use vectors and approach this, but I'll try.

I'm aware of how gravity and the centrifugal force add up to an oblate shape, and I get that if there were spots of high local gravity added into that calculation, at those locations level would be more towards the center than in surrounding ones, suggesting that a high gravity spot will decrease sea height.

But that doesn't really take into account much at all (I only took direction into account), so I have no confidence in that.
 
  • #7
Jaams said:
... suggesting that high gravity spot will decrease sea height...
As I said, don't try to relate the local strength of gravity to the water level. You have to look at the effective potential instead. The water will form an equipotential surface.
 
  • #8
Jaams said:
I'm confused by that, because water would in my opinion need to be drawn to the equator for the Earth to be oblate, and for there to be any water at the taller equator in the first place.

I hope this response makes my source of confusion more apparent.
We think of water flowing downhill, but that is because "downhill" is toward a region of lower potential. Where it gets a bit complicated is with the effect of the Earth rotation.

It seems a bit counter-intuitive but being closer to a large mass reduces gravitational potential. That is because potential at a particular position is the energy that must be added to a unit mass at that position in order for it to escape the gravitational field entirely. It is always a negative quantity:

##U(r) = - G\int \frac{dM}{r_i}## where ##r_i## is the distance from the position of the unit mass (at radial distance r to the centre of mass of M) to the gravitating mass element dM .

So water at the same distance from the Earth centre but not near a large positive gravity anomaly will tend to flow toward that anomally which will build up a higher sea level there.

Factoring in the effect of the Earth's rotation is a bit trickier. I stand to be corrected, but here is my take on it:

The Earth crust (water excluded) is rigidly held together - it can't flow. It is kept together with gravity. Pressure from the weight of the Earth "above" the centre of mass (crust, mantle, iron core etc.) bears on the centre of mass and keeps everything compacted together. If the weight of the Earth was completely uniform in all directions there would be uniform pressure down to the core and the Earth shape would approach a perfect sphere. But the weight is not uniform because the Earth is rotating. The centrifugal effect (perceived as a force in the rotating reference frame of the earth) reduces that weight, having maximum effect at the equator and decreasing to zero at the poles. This pressure difference causes the Earth to bulge slightly at the equator. The reduced weight of a unit mass at the equator a distance r from the Earth centre of mass means it has a higher gravitational potential compared to an identical unit mass at the pole but at the same distance from the centre of mass of the Earth (ie. the rotation reduces slightly the energy required for the unit mass to escape the earth).

Since water, as a fluid, will seek a region of lower potential, sea height would tend to be lower near the equator, everything else being equal. Otherwise there would be a higher gravitational potential at the surface of the ocean at the equator than at the surface a distance away from the equator, in which case water would flow away from the equator to the lower potential surface.

AM
 
Last edited:

What are gravity anomalies?

Gravity anomalies are variations in the Earth's gravitational field caused by differences in the density of the underlying materials. These anomalies can be positive (higher gravity) or negative (lower gravity) compared to the expected value.

How do gravity anomalies affect sea height?

Gravity anomalies can affect sea height by causing the ocean surface to bulge or dip in certain areas. This is because the Earth's gravitational force is not evenly distributed, and areas with higher gravity will have a greater pull on the ocean, resulting in a higher sea level. Conversely, areas with lower gravity will have a weaker pull on the ocean, resulting in a lower sea level.

What is the relationship between gravity anomalies and ocean currents?

Gravity anomalies can influence ocean currents by affecting the distribution of water masses. Areas with higher gravity will have a greater mass of water, which can create a downward flow and contribute to the formation of ocean currents. Similarly, areas with lower gravity will have a lower mass of water, which can result in an upward flow and contribute to the formation of ocean currents.

Can gravity anomalies be used to predict sea level changes?

Yes, gravity anomalies can be used to predict sea level changes in certain areas. By mapping gravity anomalies, scientists can identify areas where the ocean surface may be higher or lower than expected, and this can help predict potential changes in sea level. However, other factors such as tides, winds, and ocean currents also play a role in sea level changes, so gravity anomalies alone cannot accurately predict sea level changes.

How do scientists measure gravity anomalies?

Scientists measure gravity anomalies using specialized instruments called gravimeters. These instruments measure the strength of the Earth's gravitational field at different locations, and the data is then used to create maps of gravity anomalies. Satellite-based gravimeters are also used to map gravity anomalies on a global scale.

Similar threads

  • Classical Physics
Replies
5
Views
835
Replies
2
Views
1K
Replies
20
Views
450
Replies
1
Views
525
  • Classical Physics
Replies
30
Views
3K
  • Sci-Fi Writing and World Building
Replies
0
Views
626
Replies
2
Views
952
  • Earth Sciences
Replies
20
Views
6K
  • Classical Physics
Replies
5
Views
777
Replies
1
Views
1K
Back
Top