Sea Level Isn't...Level

Is this supposed to be a photo of saltwater oatmeal?

I think the picture is a tongue in cheek demonstration of the paradoxical, multiple meanings of the English language.

These organic grains are not suspended in water but they may or may not have been grown with the aid of natural (organic) fertilizers suspended in water.

Quite right!

No, they aren't due to the salinity, they are the principal causes of the increased salinity, which in turn increases the density, and causes the resulting flows.

Wow! That's an interesting map! I had no idea there was that much variation. Source?

I should have noted the source, and now I cannot find it. However, NOAA has similar map showing the same large difference in salinity.

https://sos.noaa.gov/datasets/sea-surface-salinity-monthly-real-time/

Well, both do have flow lines.

OK, so SE’s post #21 with the Greenland facts and the Gravity calculator motivated me to do some calculations. I couldn’t find an estimate of the mass of the Greenland Ice Sheet (GIS). The Area was given as 1,710,000 km² and the thickness was said to be 2,000 to 3,000 m. I used 2500 m for the thickness, giving the volume to be 4,257,000 km³. Using the density of ice of 919 kg/m³, the mass calculated to be 3.912 Giga-Ton or 3.912 * 10¹² kg from an online calculator (don’t know which one I used). The gravitational force calculator SE provided had a gazillion digits and overflowed the exponent, so it was unusable for this task. I used the one below:

https://www.omnicalculator.com/physics/gravitational-force

So this is a complicated problem, but if we model this having all the mass concentrated in the middle of Greenland and calculate the pull to an equivalent mass just off the shore of the closest point (550 km) we get 3,376 Newtons (N). If we move that equivalent mass 2,000 km away from shore we get 157 N. This is nearly a horizontal pull, and the sea level rise will depend on the slope of the sea floor around Greenland and the effect of the cohesion (surface tension) of the water for many miles. I don’t know how to calculate it, so I think the best approach is to compare these calculations to the pull of the moon at its closest (357,000 km) on the equivalent GIS mass (that comes out to be 150,468,511 N or ~150 MN). The ratio of this to GIS pull of the mass just offshore is 44,570 to 1, and the ratio to the mass 2000 km off shore is ~ 958,000 to 1. I would call each of those insignificant. I submit these values for peer review.

..."The Gravitational Force of the Moon on Objects on the Earth
Just as the Earth pulls on the Moon, the Moon pulls on the Earth and everything else in space. The strength of the Moon's gravitational force is given by Newton's Law of Universal Gravitation

F = G m M_Moon / r²_Moon

where G if Newton's gravitational constant, m is the mass of the object being pulled on by the Moon, M_Moon is the mass of the Moon, and r_Moon is the distance between the Moon and the object. A similar force acts between the Earth and various objects, except that we use the distance to the Earth, r_Earth, and the mass of the Earth, M_Earth, in place of the lunar values. Since the Earth's force on something is the object's weight, W, we can write

W = F = G m M_Earth / r²_Earth

M_Moon / M_Earth is about 1/80, and for an object at the surface of the Earth r_Earth is about 4000 miles, while r_Moon is about 240,000 miles, or 60 times greater; so at the surface of the Earth the pull of the Moon is 80 times smaller than the object's weight because of its lesser mass, and another 3600 (= 60 squared) times smaller because of its greater distance. Combining these two effects,

the Moon's pull on objects near the Earth is only 1/300,000th of their Earth weight. So if something weighs 150 pounds due to the pull of the Earth, the pull of the Moon on that object would be about 150/300000, or 1/2000th of a pound.

This is a very small force but it produces a number of interesting effects because it acts on every object near the Earth, including the Earth itself."...

You have to take into account the pull of the Earth's gravity....

https://cseligman.com/text/moons/earthmoontides.htm

"You have to take into account the pull of the Earth's gravity...."

It is taken into account when the tide is measured. The moon pulls vertical and horizontal (the entire ocean), and the GIS pulls mostly horizontal, but the fact remains that at a distance or 2000 km from the closest Greenland shore, the GIS has just a hair more than a millionth of the pull of the moon, so I must conclude that the tide (ocean level) is not significantly affected. Therefore I revise my "fluff-meter" for the article from 90% to 99.9%.

...but it's a lot easier to pull from the side than from the top....the difference between dragging a weight on a sled through the snow and lifting it up off the ground....

Except that there are masses pulling sideways in every direction. Those masses are not quite uniformly distributed around Greenland, so the net horizontal force isn't quite zero, but it can't be very large. The curvature of the Earth makes those sideways forces act at an angle below horizontal, so they have a horizontal and a vertical component. While the horizontal components act in all directions and thus their vector sum is close to zero, the vertical components all act downward, so their vector sum is clearly greater than zero and points downward.

"...giving the volume to be 4,257,000 km³. Using the density of ice of 919 kg/m³, the mass calculated to be 3.912 Giga-Ton or 3.912 * 10¹² kg ...."

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The effect is bound to be low when your calculation is low by 6 orders of magnitude. _{(There aren't just a thousand cubic meters in a cubic kilometer, but instead, a billion.)}

Volume is area times thickness. What math do you think I got wrong? Show us your math for the same. Others feel free to jump in here.

4,257,000 km³ × 1,000,000,000 m³ /km³ × 919 kg/m³

=3.91 × 10¹⁸ kg

That is completely improper. The following calculators give the same value:

https://www.easycalculation.com/physics/classical-physics/mass-calculator.php

https://goodcalculators.com/mass-density-volume-calculator/

Using the density of ice of 919 kg/m³ and the volume from Rixter's post (290,000,000 km³) they give the mass of 265,510,000,000 kg (~265 E+9 kg).

When you use those calculators, or any calculator for that matter, you must make sure all entries are in appropriate units. If your volume is in cubic kilometers, then your density must be in kg/cubic kilometer. As at least two prior posts have indicated using other notations, there are 10^9 cubic meters in a cubic kilometer, so the density of ice is 919 * 10^9 or 9.19 * 10^11 kg/km^3. (assuming the 919 kg/m^3 you provided is correct. It sounds reasonable, but I didn't check it.)

Of course the actual density varies considerably, depending on the amount of trapped air and other impurities, the pressure, and the actual crystal structure(s).

I didn't see your post until today. I had no problem about there being 10^9 cubic meters in a cubic km. He didn't state the problem in a manner to show what I had done wrong. The online calculators wanted the density in kg/m³ which is what I had. The volume took the units multiple ways. I must have used m³ because km³ was not one of the choices. So using the volume given by Rixter of 2,900,000 km³ and the density of 919 kg/m³ = 919 E+9 kg/km³ that gives a mass of 2.67 E+18 kg. Thanks for your input. This is why we do peer review.

This new value for the mass of the Greenland Ice sheet (GIS) gives some surprising results. The ratio of the mass of the moon to the GIS is 28,651 to 1. Does that seem reasonable to you? The battleship USS Missouri weighs 58,000 tons loaded. The GIS if concentrated in the middle of Greenland would have a gravitational pull of 34,167 N or 7,681 lbs on the ship if it was sailing by the shore (550 km away). That would seem to be enough to tip it over. Of course the mass is not all concentrated, and as dkwarner pointed out, the curvature of the earth might change that. Would the earth in between block the attraction of the ice on the other side or just change the angle a little? This is all based on Newtons theory of gravity. Does Einsteins theory change anything here?

Using the mass of the Moon that i found on a quick search (7.35E22 kg) [the actual value provided had 9 significant digits; does someone actually know the value with that kind of precision? I suspect that it is a conversion from some value in the metric system, with no regard to precision.], I get a ratio of 27,500 to 1. That's definitely in the same ballpark, so yes, it's reasonable.

It's VERY tricky to calculate gravitational attractions using the imperial measurement system, and it's late in my day, so I won't attempt to verify the attraction between the GIS and the ship today. Maybe tomorrow morning...

On the other hand, whatever attraction exists, acts on the CG of the ship, so should not tend to tip it over.

I saw on the internet the mass of the moon to be 1.619 E+23 lbs and 7.65 E+22 kg. These disagree by about 4%, but I wasn't asking if the mass of the moon was reasonable, but the ratio of the GIS to the moon (to ascertain if the GIS mass is reasonable.)

Two things:

First, any pull on the ship is also a pull on the sea, so what is level changes and the ship won't tip over.

Second, point mass approximation is only helpful when the dimensions of the bodies are small compared to the separation. For an illustration of things gone awry with a point mass approximation think about the gravitational attraction at the surface of cube at the center of one face as compared to at that same center of a face with the closest quarter of the cube remaining, but the rear three quarters sliced away. With a point mass approximation, (since the proportions are related to mass divided by the distance to mass squared, with 1/4 the mass as 1/4 the distance) the quarter block would have 4 times the gravitational pull than the full block...which is obviously wrong.

"First, any pull on the ship is also a pull on the sea, so what is level changes and the ship won't tip over."

I disagree with your thinking. Most of the mass in the GIS is above sea level. Also the sea would resist the part of the ship underwater from moving, so there would be a tendency to tip over. The sea level closer to shore is higher, so that exaggerates the effect, not nullifying it. The higher sea level close to shore is the main point in the article from the OP.

i respectfully disagree.

The combination of gravitational attraction from various masses that comprise the Earth including the GIS are going to sum to vectors with very nearly the same direction for a ship and the water near a ship. The Ship, top or bottom, will not be drawn towards the GIS more favorably than the water.

Horizontal will be perpendicular to the direction of the attraction vector. The ships stability will still be related to its center of mass and center of buoyancy. The water will still settle to horizontal being perpendicular to the attraction vector, no different than on any other sea on Earth.

I'm definitely NOT a seaman, so anyone who knows more than I do on the matter is welcome to chime in!

Narrow ships normally (always?) carry ballast, engines, and other heavy objects as low as possible in the ship, to prevent it from tipping over. Unless the ship is wider than it is tall, the center of gravity MUST be below the waterline. By definition, gravity effectively acts on the c.g., so should not tip the ship.

In your post #94, you say: "...7,681 lbs on the ship if it was sailing by the shore (550 km away). That would seem to be enough to tip it over."

That's roughly the weight of a small forklift. Does driving a forklift from one side of a battleship to the other side cause it to tip over?

Probably not. I might have exaggerated just a little. Some ships have overturned, but I don't know the circumstances:

Actually, the center of mass is typically above the center of buoyancy in almost all ships except submarines and certain sailboats with massive weighted deep keels.

I'm certainly not in a position to dispute your statement, and have often marveled at the height of cruise ships above the water. I do understand that if one side of the ship starts to move downward, the buoyant force on that side will increase, moving the center of buoyancy off center and tending to right the ship. Yet having the net supporting force act on a point lower than the center of mass is an inherently unstable arrangement.

"... Yet having the net supporting force act on a point lower than the center of mass is an inherently unstable arrangement ..."

This can be true for certain hull shapes and for completely submerged objects, but this isn't typical. Consider that for hulls that float, the.center of buoyancy can change dramatically depending on the alignment of the hull with the water surface.. Just to illustrate a point, consider a hollow water-tight shell in the shape of an chicken egg. If to scale with a normal chicken egg and the shell if of similar density, the egg shell will float on water and all positions will have center of mass above center of buoyancy (as just a small portion of the shell will be displacing water on the bottom side). Yet, the shell will exhibit a preferred orientation which can be noted as a type of stability.

Most water vessels, with the exceptions of submarines and possibly monohull sailboats with deep massive keels and perhaps a few other odd standouts, have center of mass above center of buoyancy and maintain stability with hull shape that leverages changes in contact surface to provide stability.

The reason for sticking to what seems like an inherently unstable design is that the benefits are worth it. Shallow draft allows more maneuverability and greater efficiency especially as speeds increase.

Thanks. I like your egg shape analogy. Now, will that stable position be with the sharper curvature up or down? When on its side, the pointy half will have its center of mass farther from the full center of mass, and thus have greater downward torque, so I believe tht stable position would be pointy end down.

I think it depends on the proportions.

I suspect most commonly it would be stable on its side, i.e. with the axis between the blunt and pointy end almost horizonal with the pointy end down slightly.

If the egg shell shape is not very elongated but rather squat, then I suspect the center of mass will be lowest when the blunt end is down.

In either of these cases, even small torque perturbations would result in significant and long lasting rocking as there would be little difference in height of the center of mass at the various positions, and nothing on such a hull that might slow such movements.

"....He didn't state the problem in a manner to show what I had done wrong..."

If by 'He' you are referring to me, I would draw your attention to comment 71

It explains that you messed up the units and details which units you missed. It further suggests you forgo the calculators and do this simple operation yourself.

What manner of stating the problem would have shown you more clearly what you had done wrong?

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Your original reply to my suggested correction was something along the lines of claiming my suggestion was completely inappropriate. Are you still of that mindset?

In your original calculation you arrived at a figure of 3cm fall due yo change in gravity from removal of ice sheet mass. Have you recalculated with the new mass removal figure that is larger by some 6 orders of magnitude? I bet it doesn't seem insignificant any more.

Your original response was rather condescending. Your second one showed a multiplier that I thought I had used, and I didn't know which one you wanted it to be applied to. Had you used one of the calculators I supplied you might have seen the problem.

"Your original reply to my suggested correction was something along the lines of claiming my suggestion was completely inappropriate. Are you still of that mindset?"

No, as you can see by my new calculation. My apologies.

"In your original calculation you arrived at a figure of 3cm fall due yo change in gravity from removal of ice sheet mass."

No, that was not my calculation. In fact I gave no figure for it. You can see from my later posts that I think it is significant now.

I That wasn't a friendly tone I used. My apologies. .

No problem. We all need to be nicer here, me included.

".... Using the density of ice of 919 kg/m³ and the volume from Rixter's post (290,000,000 km³) they give the mass of 265,510,000,000 kg (~265 E+9 kg). ...."

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I'm trying to get you to understand you have completely hosed up the units. You will have to drop the calculators for this simple math to see it easily.

Remember there are a billion cubic meters in one cubic kilometer.

....and make sure you are copying the numbers corrects.

Others feel free to jump in here.

"The total volume of Greenland’s ice sheet is about 2,900,000 km³"

https://web.viu.ca/earle/geol305/The%20Greenland%20Ice%20Sheet.pdf

See #44.

Yes but is that winter or summer, minimum or maximum? ...or is it midpoint est? ....and if there is such a huge meltoff of ice from the arctic and Greenland every year why isn't it more noticeable as to the sea level...? Millions of square miles of ice come and go every year...

Beach Report....no change

I have lived near Atlantic beaches for most of my life.

A lot of work goes into keeping the beach waterline usable from season to season. I find your image to be specious evidence of a constant sea level.

...as I said before, the amount of sand on the beach does not effect the sea level....and the picture is more tongue in cheek than scientific evidence....but the relationship of the shoreline to established landmarks cannot be denied, and that is the underlying basis of the beach report...

It's a hard job, but somebody has to do it...

1 Cubic Kilometer:1 Cubic kilometer is equal to a volume with sides 1000 x 1000 x 1000 meters. 1 km³ = 1 000 000 000 m³.

Whoever gave you an OT for that doesn't understand the metric system and/or simple math! There is no error in your post, and it is definitely on topic, in support of a previous post. Here's a GA to counter that OT.

Another problem is that point mass simplification falls apart when the dimensions of the masses are significant wrt the distance between the masses.

If in doubt, consider the following:

Gravitation on the surface at the center of a face of a massive homogenous cube 4 units on a side should be the same as on the outer surface at the center of a face of an outer block of four homogenous blocks of 1 by 1 by 4 units of the same density stacked to the same dimensions as the cube.

Yet using the point mass simplification the other three blocks are not needed. Just using one block a quarter of the mass would have greater influence than the cube since its center is 1/4 of the distance of the cube center and the proportion is mass over radius squared.

Of course this cannot be correct, and it shows the breakdown at close distances for the point mass simplification.

Here is a more recent (2018) peer reviewed article by the same author.

https://journals.ametsoc.org/doi/full/10.1175/JCLI-D-17-0465.1

Quantifying the Sensitivity of Sea Level Change in Coastal Localities to the Geometry of Polar Ice Mass Flux

The relevant equations are shown. Results are interesting!

Of course <...Sea Level Isn't...Level...>. It covers an oblate spheroid that has a an accompanying satellite; the two rotate about their centre of mass, causing tides.

"Level" is a concept that is usually only considered over a very limited distance, and is then considered to be a perfectly flat plane.

On a larger scale, if you consider a level surface one on which you could lay a "Level" and the bubble would remain centered or on which you could place a marble and it wouldn't roll downhill, then I submit that a geoid surface (a surface which is perpendicular to the gravitational force, or equal gravitational potential) should be considered "level". The sea surface ideally (without waves, etc.) is such a surface. If it weren't at equal gravitational potential, then water would flow until it was.

A geoid surface would be sculpted by gravity and centrifugal forces, and if you ignore solar and lunar tides, which are periodic and cancel out over the long run, then the ocean surface is "level" by definition.

So we seem to have a myriad of variables involved here, and a lot of uncertainty about the accuracy of measurements, not to mention even in a worst case scenario no notable sea level change would take place even within our grandchildren's lifetime....There is no compelling evidence that this would even be a bad thing, it might be a good thing, or just another thing....In any case it seems over hyped just like everything else about global warming...

"...There is no compelling evidence that this would even be a bad thing ..."

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The people of Venice might not agree

..."Exceptionally high tides in Venice occurs once every four years, on average. However minor flooding in the city happens around four times a year and usually within the winter months."...Nov 1, 2018

Now all the sudden it's global warming....well what was it in the past then...?

..."According to LiveScience, the rise in sea-level isn't the only thing that has Venice's famous canals rising every year because the city is subsiding.

Previous studies had suggested the city's subsidence had stabilised but it has been claimed that the city is tilting to the east.

Scientists tracked the elevation of Venice and its surrounding lagoons over a ten year period and have said that on average, the city is sinking up to two millimetres every year.

It's thought the subsidence is due to plate tectonics as the Adriatic plate, on which Venice sits, is subducting beneath the Apennines Mountains and causing the city and its environs to drop slightly in elevation."...

..."Residents and businesses typically reinforce their doors with metal or wooden panels to prevent water from entering the bottom floors, but photos on social media showed shop owners using water pumps this time to try to protect their goods."...

Yeah it happens all the time.....

https://www.thesun.co.uk/news/7620018/venice-sink-flood/

So you don't think residents of Venice would perceive an increasie in sea level as a bad thing?

That ship sailed a long time ago...

..."Yet even the quickest visit reveals that Venice is no longer a living city, with scores more tourists than actual Venetians crowding its lagoon, bridges and walkways. ... Once the Mediterranean's paramount city state, Venice today seems powerless to arrest the trend of ever more tourists and ever fewer residents."..Jun 29, 2019

..." the population living in Venice is just under 53.000 inhabitants as of January 2019."...

https://www.bloomberg.com/news/features/2019-06-30/venice-is-dying-a-long-slow-death

If Venice was a city in the US, it would rate in the 700 range of largest cities...small towns you probably never heard of unless you lived there...

http://rochester.nydatabases.com/database/population-us-cities

If they have a good imagination they will.

If they have a good memory they will know its been there all the time.

https://en.wikipedia.org/wiki/1966_Venice_flood

At the moment nothing new.

"... At the moment nothing new. ..."

This wasn't a comment about flooding in Venice being a new thing. Just the idea that this is the worst flooding ok n 50 years suggests it hasn't been getting worse and worse every year.

The comment was about SE claiming that there is no compelling evidence that sea level rise might be a bad thing (because the sea also increased rapidly several thousand year ago and people did not go extinct then, seems to be the argument).

I thought the argument was about sea level rise

So if there was a similar flooding 50 odd years ago and it has not gotten worse, then were is the sea level rise?

At least for Venice it seems other factors make flooding worse of which Wind and the city subsiding, whether its from weight alone or together with plate movement are the two major ones.

SE has brought forward good arguments to show that sea level rise is not as bad, but I would put your wording " not a bad thing" under personal opinion, which he is free to have but should not have an impact on the scientific question or your answers.

"...So if there was a similar flooding 50 odd years ago and it has not gotten worse, then were is the sea level rise?

...."

Yeah, I agree with this (and said as much in the post to which you replied). Having bad flooding that did not reach the record set 50 years ago certainly doesn't sound like sea level rise.

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Like I also said in the previous comment, my comment at the root of this thread was about whether sea level rise would be bad, which is the question raised by SE in the comment to which I was responding.

I believe many Venetians would view sea level rise as a 'bad thing' since the city is at or slightly under sea level currently

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Also, please note 'a bad thing' which you attributed to me is not wording I initially raised in this discussion. I was merely responding appropriately to SE mixed scientific/sociology claim:

"...There is no compelling evidence that this would even be a bad thing ..."

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Given the nebulous, nonfalsifiable nature of this statement, I felt (apparently mistakenly) the absurdity could be made obvious by asking for specific clarification in those same terms.

Absurdity be rampant here, no notice taken, no quarter given...

No, this doesn't happen all the time. That is why it makes the news. The sun rises in the east. This happens all the time and this daily feat doesn't make the news.

It only made the news because the mayor blamed it on global warming...and anything that is blamed on global warming makes the news....

No, this made the news because it is the second-highest flood ever recorded in Venice. The highest flood was in 1966.

The MOSE project was supposed to protect Venice from even a repeat of the 1966 flood levels. Last year's flood pointed out that this project is still not complete. I don't know how much if any of the incomplete MOSE systems were properly activated nor how effective those parts were. I do find it suspicious that no reports (at least no reports bombarding my eyes and ears) are forthcoming on the effectiveness of MOSE.

From your link: "it is now expected to be fully completed in 2022."

It can provide no protection until all major components are complete.

Well it's my understanding that the MOSE project is not finished or even helpful at this point, seems to be accusations of corruption still flying about....

This video from 2013....

I have been thinking about this and the video that SE posted here about the ice age scare in 1978.

This is 12 years after that major flood in Venice.

I wonder if 12 years from now where we are on the scare scales.

Simple mind would deduct a cold scare upcoming. Old mind says who (s)cares.

So no it does not happen all the time, but if there is any validity in the statement that history repeats itself, flooding always does!