# RE: What is sea level?

In http://www.straightdope.com/classics/a1_160.html Cecil states that the shape of the earth is an ellipsoid. Not to get too picky or anything, but isn’t an ellipsoid a 2-dimensional object? The description for the geometrical shape in 3-dimensions I had understood to be an oblate spheroid.

PLEASE tell me that this is just an honest mistake and Cecil is not a closet flat-earther…

• LB

I’ve always heard “ellipsoid” and “oblate (or prolate) spheroid” used interchangeably, and I think that ellipsoid is actually the more correct of the two. An ellipse is a figure in two dimensions, and an ellipsoid is a surface of revolution of an ellipse. For the terminology to be consistent, a spheroid should be a surface of revolution of a sphere, which would end up being a higher-dimensional object. By analogy, a surface of revolution of a parabola is always called a paraboloid, and one for a hyperbola is a hyperboloid.

By the way, welcome, and please stick around!

Chronos -
I think I need to read my Websters more thoroughly next time because they agree with you on the ellipsoid…

Interesting idea about spheroid being a, well 4-dimensional sphere… I guess the terminology isn’t consistent there because they (Webster’s) say “a figure resembling a sphere; also : an object of approximately spherical shape”. I guess it’s just another example of inconsistency in language.

-LB

So, a humanoid would be a three-dimensional rotation of a two-dimensional human?

And a schizoid would be… um, nemmine, I’ve taken this as far as I want to.

For that matter, I suppose that the pseudo-English “factoid” would be another example of the opposite, being a 3-dimensional piece of information compressed into a McNugget of no intellectually nutritional value…

…but maybe this is going too far…

Actually, I’ve always understood there to be a finer distinction, which MathWorld confirms. An ellipsoid is a three-dimensional analogue of an ellipse. Imagine if you were to put a sphere into a cube, and then you stretched that cube into a rectangular prism, so that the three side lengths are not necessarily equal, and the sphere stretched with it. That’s an ellipsoid. Spheroids are ellipsoids in which two of the side lengths are equal, so they can be thought of as spheres which are stretched (prolate) or squashed (oblate) along one axis. They can also be thought of as surfaces of revolution of ellipses, which ellipsoids in general cannot.

So, the Earth is both an oblate spheroid and an ellipsoid, but oblate spheroid is more specific.

Well, strictly speaking the shape of the Earth is best described as a geoid, but it can be approximated as an ellipsoid.

“Sea Level” at the southern tip of India, for instance, is up to ~160 m closer to the center of the Earth than “Sea Level” off the coast of Peru. (Well, according to the geoid model sitting on my lap right now.)

Geoid maps:

http://www.usna.edu/Users/oceano/pguth/website/so432web/GeoidMap.htm

I remember reading in high school that one of the reasons the Panama Canal uses locks (besides the big mountain) is because sea level on one side of Panama is about 79 feet higher than on the other side. This always bugged me because I know that water tends to level out at the same height.

Nope. Since humans are already three-dimensional a humanoid would be a four dimensional rotation of a human. Or, you can use the far cooler sounding synonymn, hyperhuman.

Always be skeptical of what you learn in High School.

There is some daily difference in the height of the water on the Pacific and Atlantic sides of the Panama Canal, but it’s relatively small (10 feet or so), and is due to the tides and not to a difference in the average height of “sea level”.

As proof, look at the changes in elevation a ship goes through as it goes through the canal. Starting on the Pacific side, a ship starts at sea level and then is raised approximately 54 feet at the Miraflores locks (actually 2 raises of about 27 feet each). Then it proceeds through a man-made lake to the Pedro Miguel locks where it is raised another 31 feet or so. This puts it at about 85 feet above sea level. Going through some man-made cuts and channels, it comes to Gatun Lake, which is also about 85 feet sea level. After crossing the lake, it comes to the Gatun Locks, where it is lowered (in three steps) approximately 85 feet back down to sea level.

The locks exist because it was cheaper and easier (or at least the people building it thought it was, I’m certainly no expert) to boost the ships up and take advantage of the existing lake and some waterways (which were about 85 feet above sea level) instead of digging a simple canal all the way across.

Ugly

Shouldn’t that be the other way around? That a geoid is described as the shape of the Earth? “Describing” the Earth as a geoid is a bit circular: You’re essentially saying that the Earth is Earth-shaped.

And yes, I know that the geoid doesn’t exactly correspond to the shape of the Earth, either, but to the equipotential surface which is the best fit to the surface.

So what’s the reason for the 160m depression in the Indian Ocean? Is there some very dense mass just underneath that causes higher gravity there? Do we know? Is there the remnant of a large iron asteroid implanted into the earth? 160m just sounds like a lot.

It’s actually only ~107 m below average; ~160 m is the difference between the lowest part of the geoid and one of the highest.

Here:

http://einstein.gge.unb.ca/tutorial/tutorial.htm

you will find more than you ever wanted to know about geodesy and the geoid. A discussion of a geoid model (GEOID96) for the United States (which you’ll probably find more usefull and interesting) is here:

http://www.ngs.noaa.gov/PUBS_LIB/GEOID96_PAPER/geoid96_paper.html

In a (grossly simplified) nutshell, at any given place on the Earth, the geoid is defined as a plane that lies normal to the pull of gravity, taken as the direction a plumb bob points (which is taken as towards the center of the Earth’s mass) at that point. So, it is related to gravity anomalies within the Earth–but that’s about as much as I feel confident trying to explain!

After much pondering, I agree with you. However, I’d still argue that it’s better to say that the shape of the Earth “can be closely approximated as an ellipsoid”, rather than “is an ellipsoid.”

I also agree that that is incredibly anal and nit-picky, but I can’t help myself.

It depends on how precise you want to be. Personally, I would not call a person wrong who said “The Earth is a sphere”. But you’re right, of course, that there isn’t any word (other than maybe the useless “Earth-shaped”) which non-approximately describes the shape of the Earth. I guess physicists like myself just take it for granted that everything’s an approximation.

True. My position is that–as an Earth Scientist and an Educator–I prefer to make sure that people understand that we are looking at “models” rather than “objective reality”, because they usually don’t. For a scientist, this is intuitive; for a non-scientist, it very often isn’t.

That’s why people think of science as more flawed and faulty than it is-- a good scientist never says “I’m absolutely sure that this is what’s happening”. In court cases, a lawyer will ask an expert-witness scientist “Is this test 100% reliable?” and the scientist will squirm and say “Of course not”. Nothing is 100% reliable, but the test may be reliable a very significant part of the time. Of course, the lawyer (and the listening public) says “So you admit that the test results could be wrong!”, exaggerating the probability of failure to a large degree.