Talk:Geoid

Earlier comments

Thanks for adding the link to Physical geodesy! Martin Vermeer— Preceding unsigned comment added by 130.233.136.69 (talk • contribs) 15:08, 31 January 2003 (UTC)

I had in fact for some time been missing some explanation of "Geoid". S.— Preceding unsigned comment added by 217.168.172.214 (talk • contribs) 15:50, 31 January 2003 (UTC)

Wrong character

Hi, I think there's an error in the formula: you write "φ and λ are geocentric latitude and longitude respectively", but nowhere in the formula can I see any φ ...

Laurence Vanhelsuwe — Preceding unsigned comment added by LaurenceV (talk • contribs) 08:45, 14 April 2005 (UTC)

The problem is that Wikipedia:TeX markup permits simple TeX characters to be displayed as HTML characters, thus in a different font, which here appears to change the character, even though both are phi. Thus I changed <math>\phi</math> $\phi$ to <math>\phi\ </math> $\phi \$ by adding the math text space '\ ' immediately after the math character, which forces it to be rendered as a PNG character, just like those in the formula. — Joe Kress 07:16, Apr 17, 2005 (UTC)

Gender specific pronouns

The earth has no gender, so is it necessary to call it a she ?

I'll change the article over to using gender-neutral terms?— Preceding unsigned comment added by Ahpook (talk • contribs) 14:03, 29 July 2005 (UTC)

Counting Coefficients

Greetings!

When you count the geopotential coefficients at the end, you get 130,317. You should probably mention what maximum degree (n) you used and why you chose that value. After all, in principle, n is infinite.

Oh, and if you're interested, here's a quick and visual definition from the project I work on (GRACE): http://www.csr.utexas.edu/grace/gravity/gravity_definition.html

Take care! Jennifer Bonin — Preceding unsigned comment added by Reythia (talk • contribs) 16:00, 4 April 2006 (UTC)

I'll try to clarify this. After all, there are new models in the works with degree=order=2160 (over 4 million coefficients), good to 1/6 degree. MFago 14:46, 5 April 2006 (UTC)

References and Intro

Was it a good idea to split the top into the short intro and a new "description" section? More closely follows other Wikipedia articles, so I made this change. Also, this article could really use more citations. Unfortunately, I haven't quite figured out the "cite" template... MFago 15:43, 5 April 2006 (UTC)

Centrifugal Force

Hi, I can't find the answer to this anywhere!

Does the geoid take into account centrifugal force from the Earth's rotation? If so, would it be incorrect to refer to it as a mathematical figure of the gravity field alone? And if not, would it be incorrect to say that the mean sea level assumes the shape of the geoid?

Or is all of this too miniscule to make any difference?— Preceding unsigned comment added by 198.99.123.63 (talk • contribs) 18:36, 18 April 2006 (UTC)

There is not actually "a" geoid, but rather many different variations depending on whether or not one accounts for tides, etc. I do believe that it usually does account for rotation. Note that the equation given in the article is not for the geoid itself, but for the (non-rotational part of the) potential. Computing the geoid is rather more involved. I'll see if I can relocate my reference on this (at NIMA or a related site), and perhaps add more detail to the article. Also see Physical geodesy and Geodesy. The reference text the end of Geodesy is excellent and covers most of the details. MFago 23:21, 1 June 2006 (UTC)

Link added to above reference: No such thing as "The" EGM96 geoid, and tried to clarify a bit. Really needs more detail -- it's a complex subject, and I'm not entirely fluent. MFago 23:33, 1 June 2006 (UTC)

I was just wondering about this myself. The reason being that International Atomic Time is based on the rate of ticking of a clock sitting on the geoid. This definition removes any ambiguity due to gravitational time dilation, but i can't work out if it accounts for the dilation due to greater speed of movement of points on the equator compared to those at high latitudes. If the geoid doesn't include a centrifugal term, then it definitely doesn't. If it does, and is thus about equipotential from the point of view of a co-moving observer (as a geoid based on actual local measurements would pretty much have to be), then possibly it does, what with the equivalence principle and all that. Although i'm not at all sure about that - is there any particular reason to think time moves at the same rate at all points on an equipotential surface? No, probably not. And i don't even know what kind of geoid IAT uses. Oh god, this is confusing. I should not have to do general relativity to work out what bloody time it is! —Preceding unsigned comment added by 62.56.106.202 (talk) 18:54, 3 November 2008 (UTC)

The article's first sentence now clarifies that the geoid indeed incorporates the Earth's rotation. —173.56.111.206 (talk) 08:54, 14 April 2024 (UTC)

Broken Links

I just saw that all of the NGA links are broken. I cannot locate any of this data on the new "enhanced" site -- it appears to be unavailable? MFago 23:52, 1 June 2006 (UTC)

Fixed. They simply changed all *.htm to *.html, and their search engine was of no help. MFago 00:04, 2 June 2006 (UTC)

Geoid Picture

Unfortunately the picture of the Geoid (actually the geoid undulation) that used to be on this page was evidently taken from the GRACE website without proper permission. Anyone have access to another similar graphic that would be useable here? The raw data for the EGM96 geoid (less detailed than GRACE, but still illustrative) is available at: NGA EGM96 data (labeled as "Geoid Height File"). Matlab can easily make a similar plot from this data, but I do not have access to this software. Anyone able to help, or have another idea?MFago 14:36, 2 June 2006 (UTC)

Nowadays, the key data from GRACE can be found on US government websites (NASA.gov, NGA.mil, etc), which are public domain. —173.56.111.206 (talk) 08:54, 14 April 2024 (UTC)

Possible image error

Shouldn't the local plumb lines in the image in the Description section be orthogonal to the geoid? Shinobu (talk) 12:42, 1 February 2008 (UTC)

Yes, belated thanks. The image was corrected in 2009. —173.56.111.206 (talk) 08:54, 14 April 2024 (UTC)

Sea floor

The geoid seems also to be used, along with satellite data, for estimating the topography of the sea floor; see Exploring the Ocean Basins with Satellite Altimeter Data, especially under "3. Explanation of the Gravity Anomaly". There may be a better home for this, but even if the main information goes elsewhere a 'see also' might be appropriate. (The gravitational anomoly is mentioned technically in Physical geodesy, but without discussion of use.) Mark— Preceding unsigned comment added by 98.210.255.2 (talk • contribs) 06:52, 27 November 2008 (UTC)

The second diagram shows the geoid as being above the ellipsoid where there is land but below it where there is an ocean. The first picture doesn't show this picture at all. Why this difference?194.241.59.190 (talk) 16:04, 20 February 2010 (UTC)

The schematic picture now is in the section labeled "Simplified example", which explains that the reality is more complex because of variations in the Earth's density. —173.56.111.206 (talk) 08:54, 14 April 2024 (UTC)

Unclear grammar

In the first paragraph, 2nd sentence "Although the former " it's unclear what it refers to. --maye (talk) 15:35, 6 May 2009 (UTC)

Current version: "Although the 'ground' of the Earth..." —173.56.111.206 (talk) 08:54, 14 April 2024 (UTC)

Erm... help for beginners :)

"If that perfect sphere were then covered in water, the water would not be the same height everywhere. Instead, the water level would be higher or lower depending on the particular strength of gravity in that location." - so does that mean that more gravity pulls the water-level down or does it mean that more gravity collects more water above it pushing the water level up? It may seem obvious to you, but it's not to some of us here :) Clarification would be appreciated :) Malick78 (talk) 21:37, 28 June 2010 (UTC)

I agree with Malick. Could someone who understands this properly state something like "A greater height on the geoid corresponds to a stronger local gravitational field" or vice versa? I've seen online discussions about the map from Goce in which lay-people interpret the map both ways, even after reading this Wikipedia article. BruceMcAdam (talk) 12:27, 29 June 2010 (UTC)

Seems no one understands this page... ;) Malick78 (talk) 23:43, 1 July 2010 (UTC)

I'm not an expert on this, but my guess is that the level of the water joins all points of equal gravitational potential. Thus in areas where gravity is stronger, you have to go up to a greater height to achieve the same gravitational potential as a point where the gravity is weaker. Thus the water would be higher there. Muraho (talk) 10:59, 18 August 2010 (UTC)

I've removed that whole section. There is no direct relationship between the water level and the local strength of gravity. When traveling in a geodesic along the surface, the rate of change in the direction of the force of gravity determines whether the water surface locally follows a concave or convex curvature. When a heavy lump is ahead, the gravity vector moves a bit forward (compared to pointing to the centre of the Earth) and the water surface will curve up. Past the heavy lump, the vector will point a bit backward, and the water surface curves down.  --Lambiam 09:08, 2 November 2010 (UTC)

So isn't this sentence wrong? The surface of the geoid is farther away from the center of the Earth where the gravity is weaker, and nearer where it is stronger. It contradicts both my intuition and the illustration. —Tamfang (talk) 07:27, 29 August 2013 (UTC)

Good catch. The article now says, more correctly and more intuitively: "Generally the geoid rises where the Earth's material is locally more dense, exerts greater gravitational force, and pulls more water from the surrounding area." I tried to make the lead section clearer, too. —173.56.111.206 (talk) 08:54, 14 April 2024 (UTC)

Pronunciation

How is this word pronounced? I always assumed (without really thinking about it) that it is pronounced "gee-oh-id". However, on reflection is seems more likely that it is "gee-oyd". To match ellipsoid. Is this correct? Muraho (talk) 11:00, 18 August 2010 (UTC)

According to dictionaries it is /ˈdʒiɔɪd/.  --Lambiam 08:42, 2 November 2010 (UTC)

The article's first sentence now says "geoid (/ˈdʒiː.ɔɪd/ JEE-oyd)". —173.56.111.206 (talk) 08:54, 14 April 2024 (UTC)

Mathematical formulas

Does the inclusion of mathematical formulas in the section Spherical harmonics representation serve a purpose? Without giving the numerical values of the coefficients, they do not supply any actually useful information. Even if this could somehow be argued to serve some purpose, the right place for such detail would be the EGM96 article.  --Lambiam 09:29, 2 November 2010 (UTC)

It's somewhat helpful for technical readers, by conveying the complexity and the resolution of modern geoid calculations. —173.56.111.206 (talk) 08:54, 14 April 2024 (UTC)

New data from Goce satellite

Scientists use a geoid model to illustrate the force of gravity on Earth from data from the Goce satellite. (BBC). Can a knowledgeable editor update this article? Dr.enh (talk) 02:41, 2 April 2011 (UTC)

Belated thanks. The article's GOCE info was updated the day after you posted this. —173.56.111.206 (talk) 08:54, 14 April 2024 (UTC)

Rotation of the Earth

As I understand it from [this source] the geoid is an equipotential surface based in the sum if the non-rotating gravitational potential and the centrifugal potential. This is confirmed by this sentence in the lead, '...the geoid is the equipotential surface that would coincide with the mean ocean surface of the Earth if the oceans and atmosphere were in equilibrium, at rest relative to the rotating Earth'. However, we also have this sentence, 'In that idealized situation, other influences such the rotation of the earth, winds due to solar heating, and so on have no effect'. This may suggest to some that the rotation of the Earth is not taken into account in the calculation of the geoid. I suggest that the words, 'such the rotation of the earth', are removed. Martin Hogbin (talk) 21:29, 1 April 2013 (UTC)

I have been bold and made the change. The academic source that I added seem clear enough. Martin Hogbin (talk) 10:57, 2 April 2013 (UTC)

More Rotation of the Earth

A related observation: the first paragraph states: "The geoid, simply stated, is the shape that the surface of the oceans would take under the influence of gravity alone."

Such a surface would be very nearly a sphere. The reason that the geoid is nearly an ellipsoid is that its shape is due to gravity plus the effect of the rotating earth. The geoid entry in Encyclopedia Britanica includes the statement "This potential function describes the combined effects of the gravitational attraction of the Earth’s mass and the centrifugal repulsion caused by the rotation of the Earth about its axis."

The first paragraph of the current wiki article is therefore misleading and confusing because (1) there is no explanation of why the earth would be an ellipsoid under the influence of gravity alone, and (2) a plumb line is always under the influence of the rotating earth and would therefore not be normal to the geoid if the geoid were due to the influence of gravity alone. I would suggest that this paragraph be changed to be more accurate. "The geoid, simply stated, is the shape that the surface of the oceans would take under the combined influence of gravity and the earth's rotational velocity." Rocket Laser Man (talk) 20:21, 14 June 2013 (UTC)

Yes, I noticed this but decided that gravity could be interpreted to include the contribution of centrifugal force. How about we have, "The geoid, simply stated, is the shape that the surface of the oceans would take under the combined influence of gravity and centrifugal force due the earth's rotation."? Martin Hogbin (talk) 00:35, 15 June 2013 (UTC)

References

Contradiction at Latitude

At Talk:Latitude#Contradiction with Geoid I have noted a contradiction with this article. I suggest that any discussion is carried out on that talk page. JonH (talk) 11:03, 25 May 2013 (UTC)

Good catch. I clarified this article to say that plumb lines are perpendicular to the geoid "at sea level". —173.56.111.206 (talk) 08:54, 14 April 2024 (UTC)

@Strebe: You rightly pointed out that my "sea level" edits weren't clear enough. Nevertheless, the "parallel" & "perpendicular" claims aren't generally accurate, as described at Latitude#Astronomical latitude. Can you think of a better way to clarify the text here at Geoid? —173.56.111.206 (talk) 02:03, 18 April 2024 (UTC)

Isn’t the deviation of a plumb-bob’s vertical from normal to the geoid due to the fact that the plumb-bob isn’t normally on the geoid, but (typically) somewhere above it? Because this article’s description is always about conditions on the geoid, I’m not sure there needs to be any more complication to the text. It is not my understanding that the parallel and perpendicular comments are incorrect, albeit, in general, they are hypothetical rather than practical. But I’m at the limits of my knowledge here. Strebe (talk) 06:53, 18 April 2024 (UTC)

Even at sea level, tides are also a source of deviation from those theoretical geoid properties. See if my 2nd attempt to clarify the text is better? —173.56.111.206 (talk) 23:25, 18 April 2024 (UTC)

Are the tidal deviations non-negligible? My understanding is that they are not normally accounted for in surveying, the variation being inconsequential to to most activities. For example, they are not considered when measuring plumb-line deflection, which is purely the the difference between astronomical and geodetic measurements without averaging over time. I think your edits are fine. Strebe (talk) 00:40, 19 April 2024 (UTC)

Thanks. Plumb deviations caused by mountains & tides could be noticeable on land & sea, respectively. The latter shouldn't matter for surveying, but to be safe I added it to the paragraphs about ship travel. When the tide pours in & out of the Bay of Fundy, for example, I suspect there's a measurable tilt of the horizon. —173.56.111.206 (talk) 02:12, 19 April 2024 (UTC)

The work of Vaníček

I notice that a 'partisan' tag has been added to the section on the work of Vaníček. Vaníček's work is reported in what, by most standards, would be considered reliable sources and thus should be included here.

Is there some controversy about his work? Martin Hogbin (talk) 08:24, 18 June 2014 (UTC)

This article is supposed to be about the geoid, ideally with no undue focus on any particular author who has published research about it. I suggest removing that section if it cannot be enlarged to encompass a worldwide view. Fgnievinski (talk) 22:08, 18 June 2014 (UTC)

Criticism of Article.

My overall impression is that this is a very weak article that requires a lot of revision. For example, in the 'Description' section it states-- If the ocean surface were isopycnic (of constant density). --It is an elementary mistake to describe a two-dimensional surface as having a density. Gravity measurements are affected by the totality of rock and water densities encountered by extrapolating a plumb line from the point of measurement. Sea-water density differences are relatively trivial compared with lateral differences in rock density, which vary rapidly on a scale much smaller than the thickness of the Earth's crust. It is quite ludicrous to even mention the possibility of the geoid occupying hypothetical narrow canals cross-cutting the continents, as gravity is affected by the totality of vectors of mass both above and below the point of measurement. As the centre of gravity of the Earth - Moon system lies some distance below the surface of the Earth, satellite gravity measurements have to be constantly updated to take account of the phases of the moon and its distance from the Earth, precession etc. It is also very unlikely that the isostatic compensation depth is much more than 20 - 30 km deep. None of these caveats is addressed in the article. The entire article should be withdrawn until someone can contribute a closer description of reality. Meanwhile it would be best to describe the geoid as a surface that is defined by gravity departure from a defined ellipsoid that has an average Earth gravity field throughout and forget about the ups and downs of the oceanic surfaces until some contributor has a basic understanding of what's going on. Geologician (talk) 21:19, 25 December 2014 (UTC)

I want to add another couple of criticisms: this article usefully discusses what a real observer will experience but then totally IGNORES tidal influences! It should be obvious that you can't conflate an ideal (hypothetical) with a real (measurable) observer. It does this in a number of places. It is, in my view, a fundamental blunder to assume as the starting point for discussions that the Earth is some nebulous undefined ideal mass. I also don't think the editors of this section have put enough thought into what they are saying. An example is the following:"...the geoid is the equipotential surface that would coincide with the mean ocean surface of Earth if the oceans and atmosphere were in equilibrium, at rest relative to the rotating Earth..." As I already pointed out, this ignores the tides from the Sun and Moon (and Venus and...). But more to the point, it assumes the false idea that the Earth's rotation is that of a rigid sphere. It is not. The term "equilibrium" is also a problem here. I don't know what it means - it certainly doesn't mean thermal equilibrium - gasses (or more broadly compressible fluids) can't be both in a gravitational gradient and at thermal equilibrium.174.130.19.69 (talk) 16:26, 19 July 2016 (UTC)

I don't find these critiques useful. Using much hyperbole, Geologician pontificates about things "he" could have simply added to or subtracted from the article himself, if they were actually problems, and then finishes by ludicrously declaring the entire article should be withdrawn. Not helpful, particularly to people looking for basic information about the geoid, of which much is to be found in the article. As for both Geologician's and 174.130.19.69's dismissals on the grounds that other bodies' gravity also affects the geoid, the article already disclaims other influences explicitly. Hence the criticism is worse than a red herring; it is just wrong, and negligently so. Also wrong is the sneering lambasting of the article's use of 'isopycnic'. Contrary to Geologician's claim, the term isopycnic refers specifically to surfaces. True, a mathematical surface has no density. False, real surfaces have a density, when properly defined to. Nor is there any assumption that the earth's rotation is that of a rigid sphere. And so on. If these editors would like to start over, discussing one complaint at a time, we might be able to make some progress if there are really any problems to address. Strebe (talk) 20:45, 19 July 2016 (UTC)

The word "isopycnic" wasn't necessary or helpful, so I removed it from the article – and I described the continental canals as an approximation. The remaining criticisms don't seem relevant to the current version of the article. —173.56.111.206 (talk) 08:54, 14 April 2024 (UTC)

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spirit leveling from a tidal measurement station

The article says "Conversely, height determined by spirit leveling from a tidal measurement station, as in traditional land surveying, is always geoidal height". Is this accurate?

You'd get height based on local mean sea level at the measurement station, but: (1) it doesn't adjust for local mean sea level differences from the geoid and (2) as you get farther from that measuring point you're getting less accurate as the density of the earth changes. I think the sentence is trying to contrast with ellipsoid references, but it's confusing when trying to understand what the geoid is and how it's measured. In fact, this whole paragraph about ships observing sea level is unclear IMHO.

This article could also benefit from a discussion of gravity surveys and how the geoid is measured.

— Preceding unsigned comment added by 157.127.124.152 (talk) 20:17, 10 August 2020 (UTC)

Belated thanks. The GPS paragraph now refers to "orthometric height" instead of "geoidal height". —173.56.111.206 (talk) 08:54, 14 April 2024 (UTC)