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Local gravity effect on MSL and geoid

  1. Oct 25, 2014 #1
    I saw a video recently by a Professor Jerry Mitrovica in which he claimed that the gravitational effect of the Greenland and Antarctic ice sheets is so substantial as to 'raise' local sea levels. He suggests this is in the order of 100 meters for Greenland.

    See this video - around the 14 minute mark he claims that if the Greenland ice sheet were to suddenly melt, the sea level there would fall 100 meters.

    I get the idea from the video that this is a newly identified effect. This article 'seems' to validate that idea:


    The idea that Greenland has this effect on local sea level doesn't sound at all unreasonable to me, no different to underwater topology affecting the sea surface.

    However, in all my reading about the geoid and its relationship to MSL, I have never seen any reference to this effect. By geoid, I mean EGM96 which I *think* is the most current MSL approximating geoid. Bear in mind I am just a layperson with no expertise in this field, I am only reporting what I understand from what I've read.

    In reading about the geoid's surface shape and its relationship to the ellipsoid, generally the descriptions talk of the effect of gravity from the topology of the seafloor. As I understand it, the geoid and MSL are very close to each other, varying by no more than a meter or two. See this reference:


    My question then is - if the gravitational effect of Greenland on local sea levels is in the order of 100 meters, AND this effect has only recently been identified (eg circa 2010 or so it seems), how is it that the geoid and MSL are so closely aligned if calculation of the geoid back in 1996 did NOT include this effect?
  2. jcsd
  3. Oct 27, 2014 #2
    One-hundred millimeters? Possible, but doubtful. One-hundred meters? Not a chance. World sea levels are constantly being measured by various satellites. That kind of discrepancy from MSL would have been noted and commented on decades ago if it--in fact--existed.

    By the way, how does underwater topology affect MSL?

    The last 102 inter-glacials did not succeed in eliminating the Greenland ice cap. What did you envisage as causing to to suddenly disappear? If it did for some reason, any number of studies have concluded that mean sea level would rise, not sink.

    I think this is a case of mishearing or misinterpretation.
  4. Oct 27, 2014 #3
    I'm not saying that I think the ice cap can suddenly disappear. It was a thought experiment by the guy in the video. I may have misinterpreted but I didn't mishear. What he said in the video is that if the Greenland ice cap were to disappear, sea level around Greenland would drop 100 metres as a result of the change in gravity. He is arguing that the gravity of the ice cap's mass pulls the ocean to it, thus raising sea levels by 100 metres locally over what it would be without the ice cap. If it suddenly melted, the water would be distributed across the oceans with the main rise occurring around the equator due to rotation, while the local level would drop by 100 metres following the change in local gravity.

    I guess I may be misinterpreting things - the sea level local to Greenland being affected by the ice mass must already have been factored into calculations of the geoid, and clearly any measurement of local sea level would capture the actual level regardless of what might happen if the ice all melted away. This seems quite obvious so perhaps the 'new' thing about the idea of the drop in sea level is the realisation that if it all melted, it would not raise sea levels uniformly.

    Re underwater topology, my limited understanding of the geoid is that it is computed from satellite observations of gravity effects. It should be pretty close to actual mean sea level, and recent use of satellites to do detailed radar altimetry show that it is, or rather that mean sea level calculated from those observations is within 1-2 metres of the geoid. Sea level will reflect undersea topology, eg a large seamount will cause a piling up of water due to the gravitational effect of that mass.
  5. Oct 28, 2014 #4


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    The sea level local to Greenland is measured on tide gauges mounted on rocks along the coast of Greenland. If the Greenland ice sheet was to melt, the area of the Earth's crust we call Greenland would rise significantly as a result of the unloading. The tide gauges would therefore rise with the rock, out of the sea, so the sea level local to Greenland would appear to fall. Worldwide sea levels would rise slightly due to the Greenland meltwater being spread evenly across all oceans.

    All things are relative.
  6. Oct 28, 2014 #5
    Agreed but Mitrovika's thought experiment was purely in respect to meltwater distribution - I don't think he was including any land mass rebound. The effect he proposes is purely gravitational. Obviously if it really happened there would be a lot of other effects - the real point he is making is that without the ice sheets, sea level around Greenland would be 100 meters lower than now, while sea levels elsewhere would rise, perhaps as much as by 7 meters at the equator. All of which boils down to ocean piling up at coastlines due to the gravitational effect of that mass - the more massive the island/continent, the greater the pileup. I now realise this must already have been included in calculations of geoid/ellipsoid, I am just surprised by the scale.
  7. Oct 28, 2014 #6

    D H

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    Citation needed!

    Greenland ice cores don't go back that far in time, and there have been a number of super interglacials (Marine Isotope Stages 11, 31, 49, 55, 77, 87, 91, and 93) during which climate was mild for an extended period of time. The Greenland ice sheet underwent massive collapse during MIS 11. The further back in time one goes the less certain things look. From everything I've read, the permanence of the Greenland and West Antarctica ice sheets is not a given. It's only the East Antarctica Ice Sheet that can be said with some certainty to have been a permanent fixture for the last sixty million years.

    You are misinterpreting the cited video. I think everyone in this thread, including the OP, is misinterpreting the cited video. Mitrovica is not claiming that the Greenland ice sheet will collapse. He's merely asking what sea levels would look like if the Greenland ice sheet magically melted overnight.

    That takes a long, long time in human terms. Lands in the far north are still rebounding despite the fact that it's been 12000 or so years since the end of the last glaciation. The immediate response to one of the major ice sheets magically melting overnight would be essentially zero isostatic rebound. The meltwaters would form a constant geopotential surface very quickly, but the rebound would be delayed by thousands of years.

    That depends on what you mean by "spread evenly across all oceans." It would certainly be "spread evenly across the oceans" in terms of geopotential. That's what the geoid represents. The main point of Mitrovica's work (along with many others) is that spreading the water "evenly across all oceans" can result in rather uneven sea level rises.

    Mitrovica's "what if" scenario in that video is intentionally intended to illustrate that sea level rise is not evenly distributed across all the oceans, at least not in terms of which of Helsinki, New York City, or Sao Paulo suffers the greatest sea level rise. More importantly, by observing where sea levels are rising and where they are falling gives a hint as to which ice sheet is melting the most.

    Variations in sea level rise around the globe provide a fingerprint of which ice sheet is experiencing the greatest melting. If you query "sea level fingerprint" at scholar.google.com you'll see that a whole lot of work has been done in this area since the start of the millennium.
  8. Oct 28, 2014 #7
    Yes, that's what I now understand he is saying. Really all he's observing is that for any volume of ocean, the geopotential surface it would approximate to would vary depending on the arrangement of land masses (and any ice masses). I guess when it boils down to it, I was just surprised by the scale of the effect of Greenland's ice sheet - I wouldn't have imagined that it alone could pull enough water to it to cause a piling up of as much as 100 meters.

    I am also surprised that the very small melt relatively speaking to date could affect sea levels in such a way as to provide a 'finger print'. I don't know the volume of water each year being returned to the ocean, nor how quick its spread. But given the majority of sea rise is supposed to be thermal expansion, the contribution of Greenland ice melt must be very small when spread over the entire globe. To say nothing of the extent to which the ice mass is changing - what is the percentage change in total mass from ice melt annually?

    In the video Mitrovica states this addresses the 'European tide gauge problem" (which I have never heard of). This isn't a case of sort of begging the question is it? I guess I'll have to have a look over at Google Scholar.
  9. Oct 28, 2014 #8
    PS I think too I misunderstood the relationship between the reference ellipsoid and the geoid. I thought 'the' ellipsoid was fixed with respect to the earth's centre at all times and conditions and all geoids would relate to that, but a quick dig just now suggests that the ellipsoid is the best fit to the chosen geoid, so of course whatever the arrangement of land masses and their effect on the ocean's surface would be implicit in the resulting ellipsoid/geoid.
  10. Oct 28, 2014 #9

    D H

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    You're still looking at it a bit confusingly. Look at it instead as asking what happens if all that ice melts overnight.

    One way to model this instantaneous melting (and I don't know if this is what Mitrovica did) is to add a chunk of positive mass (water) to the oceans to represent the influx of melted ice and to add an equal but opposite chunk of negative mass to the Greenland ice sheet to represent the melt itself. The water added to the ocean will raise the geoid globally, but the negative mass added to Greenland depresses the geoid in the vicinity of Greenland. The drop in sea level due to the depression of the geoid wins over the global rise in sea level near Greenland. Its the other way around along the coastline of Brazil.

    While there is no such thing as negative mass, this mathematical trick of negative mass works quite nicely in a lot of applications.
  11. Oct 28, 2014 #10
    DH, aren't we saying the same thing? In essence, I am saying that the geoid would change in response to the changed mass of Greenland and the addition of volume to the ocean, and that's what you are saying. So I am not sure where the confusion arises.

    Does this suggest a misunderstanding by me about what the geoid represents? remember, I have no special expertise in this regard, I can only go on what I've read and how I understand that.

    My understanding is that 'the' geoid that mostly closely approximates mean sea level demonstrates undulations from the reference ellipsoid. Or put another way, the ellipsoid fits the geoid without the undulations. The undulationa arise from the changes in gravitational acceleration and vector deriving from the actual surface arrangement.

    To me this means that mean sea level is that level the oceans would assume without the perturbing influences of waves, tides etc. The ocean would in that unperturbed state be essentially 'flat' at all points with respect to local gravitation. The geoid is a computed surface that most closely matches that ocean surface.

    Now the geoid by that nature must be dynamic over time - ie if the surface arrangement changes, for example changes in crustal density or the removal of ice masses, the mean sea surface level, or shape, would change to match. It would still be 'flat' at each point, but the radius at those points would change.

    So taking our example of the conversion of the ice mass of Greenland to water and adding it instantly to the oceans, the oceans would seek equilibrium and Greenland would be much less massive. MSL (the geoid) would change such that its surface would remain flat locally, but its shape would change - that is, its radius at any point would change. That change represents both the distribution of the additional volume as well as the distribution of the equipotential surface arising from the changes in gravitational acceleration and vector.

    Or as you say, add sea surface height from the added volume, and depress the local sea level from the negative mass at Greenland.

    Have I got that concept largely correct? By the way, at no time in that description am I talking about relative sea level as measured by local tide gauges.

    If I have that right, then my comment really is that I am surprised at the scale of the effect of the negative mass. Mitrovica is saying that the effect of the negative mass is in the order of a reduction of 100 meters of radius of the geoid at the greenland coast. Actually, he's saying it's even more than that, because the additional volume must be distributed across the entire surface and then offset locally by the negative mass. So he could be arguing for an actual reduction in radius of over 100 meters compared to the elliposid. Given that the deviation of the geoid from the ellipsoid is in the order of +/- 100 meters globally at present, that seems a big change for losing just the Greenland ice cap. It must be way more massive than I'd have imagined.
  12. Nov 1, 2014 #11


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    I can't answer all of your questions, but I can answer some:

    Not sure where you get 2010, but the article you linked, discussing the anomaly being 10x larger than expected is from 2003. EGM84 is the original geoid model, which as I understand has been more or less continuously updated since the project began. Current version is 2008: http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008/

    This is from the wiki article, but appears to be the latest version:

    Frankly, I was also very surprised at the magnitude of the effect, but if we compare that to the radius of the earth, it is actually pretty small percentagewise. But I also have difficulty understanding how the effect was not noticed soon after the GPS system went online in the late 1980s. Now, until "selective availability" was discontinued in 2000, civilian GPS would not have been accurate enough to notice this, but Navy ships spend a lot of time in the North Sea and I would have expected a GPS expert would have noticed and understood what he was seeing. I will say, though, that as a run-of-the-mill Navy navigator in the early 2000s, I pretty much ignored the altitude data the GPS gave us. That said, "noticing" and actively studying are two different things.

    What I'm not clear on though is the deviation between the 1996 and 2004 versions: was it really a factor of 10? And if so, why? This is a military project, so I'm wondering if there was some secrecy involved (related to the shutoff of selective availability).

    I would be curious to know if we have any PF users from New Guinea who could stand on a beach and tell us what their GPS says.
    Last edited: Nov 1, 2014
  13. Nov 1, 2014 #12


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    Conveniently enough, here's an online calculator that outputs the deviations for EGM2008, 96 and 84 versus WGS84:
    http://geographiclib.sourceforge.net/cgi-bin/GeoidEval?input=60 -20&option=Submit

    I entered in a bunch of coordinates I though might show the discrepancy and am seeing very little. For example, what I linked above should give you 60N, 20W, and the elevations are 60.66, 60.69 & 60.30 meters, for 2008, 1996 and 1984 respectively.

    -5, +143 gives a discrepancy between 1984 and the newer ones, but still not that big: 80.9, 80.5 & 77.6
    Last edited: Nov 1, 2014
  14. Nov 1, 2014 #13


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    I am afraid this can be misleading, or at least may need reading the manual to be sure we know what we are being told. As far as I remember Garmin 60CSx doesn't show "true" height - it has a barometric sensor and requires calibration.
  15. Nov 1, 2014 #14


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    And, a little more....
    So I've read your article. It mentions a satellite named TOPEX/Poseiden, which would have definitively answered this question soon after launch in 1992, if there was still an unanswered discrepancy then, but the wording of the sentence implies that the discrepancy was already known, before the satellite was launched:
    "These measurements have demonstrated that neither human error nor GPS inaccuracies are responsible for the sometimes substantial discrepancies between ellipsoid and MSL measurements."

    Indeed, the thesis sentence of the article implies it was GPS itself that revealed the discrepancy -- which likely would have happened as they were setting up the system in the early 1980s. So I think some of the intro to the article is a bit sensationally worded and glossed over regarding the timing of the findings.
  16. Nov 1, 2014 #15


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    First, see my edit to my post. You responded before I could fix a major geography fail....

    I guess I would not be surprised if an aviation GPS would use a barometric altimeter. I do know, however, that my phone does not. Let's run a little trial:

    Without telling you precisely where my house is, the GPS coordinates are about 40.2N, 75.5W. My phone says the elevation is 86 meters (accuracy: 3m) and I'm on the second floor, so figure more like 82m. Google Earth says 84 meters (I verified that Google Eath uses WGS84). The geoid calculator says the deviation here is -35 meters.

    Now, this doesn't exactly help our matching experiment but it does suggest that anyone near a beach should be able to see the discrepancy. I have noted the discrepancy before though when near/on the ocean, but never knew what the cause was: I'd always assumed it was a GPS error (I thought I'd heard the altitude was much less accurate than the lat/long). I'll be driving nearer to the ocean next week and I'll see if I can do another check.
  17. Nov 1, 2014 #16


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    Vertical ionospheric delay cannot be fully compensated for because we have no GPS satellites underground.
  18. Nov 2, 2014 #17


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    The GPS gear I work with on a daily basis has good accuracy
    less than 10 mm in vertical or horizontal

    I always find that the vertical error is usually at least double the horizontal as seen in the attached screen shot of one of my customers units on test


  19. Nov 2, 2014 #18


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    I thought RTK was a differential GPS mode. Unfortunately, differential GPS referenced to a nearby fixed station cannot be used to measure global deviations from the ellipsoid, it is used to eliminate geoid, tidal and ionospheric effects. If the GPS reference station was not local then you would see the difference between the Earth's surface responding to tidal forces and the regional variation in ionospheric propagation delay.
  20. Nov 2, 2014 #19

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    Once again, this is a calculated result for a hypothetical event.

    That said, about 14,000 years ago a large amount of ice (sea level rise of about 20 meters) occurred over a very short span of time, 200 to 500 years. Compared to the 4,000 year rebound time, that 200 to 500 years was nearly instantaneous. The response to that meltwater 1A event was recorded in coral beds and can still be seen today. This response yields a "sea level fingerprint" that indicate which ice sheets melted. Today we're seeing a rapid melting of some of the ice sheets. The non-uniform changes in sea level help pinpoint which ice sheets are melting. You'll get lots of hits if you go to scholar.google.com and search for "sea level fingerprint," starting with the 2002 paper by Clark, et al. "Sea-level fingerprinting as a direct test for the source of global meltwater pulse IA." Science 295.5564 (2002): 2438-2441.

    Original? Not by a long shot!

    The concept of a geoid dates back to the early 1800s. George Stokes developed a mechanism for calculating the geoid in 1849: Stokes, G. G., 1849: On the variation of gravity at the surface of the Earth. Trans Cambridge Phil. Soc., 672. It was a bit unwieldy (especially without computers), and it was a bit difficult to generate a global model, but people did work on this. Development ramped up massively with artificial satellite and digital computers. People have been developing satellite-based gravity models (and hence geoids) pretty much since the onset of the satellite era.
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