The U.S. Is Getting Shorter (article discussion)

I was reading this NYT article today about how the US is updating how heights are measured across the country:

I didn’t realize how complicated of a question “What’s the height of this point” really is. Even with GPS it isn’t so straightforward:

… a height measured only by GPS could be badly inaccurate. An engineer who laid pipe only using GPS, without measuring local variations in the effect of gravity, might not get water to flow where it was supposed to go.

This made me really curious: if you’re working on an application in Cesium, do you usually use the heights as returned by CesiumJS (relative to the WGS84 Ellipsoid) or do you convert it to some vertical datum, or augment it with height information from local sources? Or do you need to convert it to height relative to sea level?

I’d love to hear what kind of work people are doing if you run into the challenges this article talks about, or anything else about the article you want to discuss!


Fascinating read, Omar! I was quite impressed by the complexity of the problem.

I’m a bit skeptical about the modernized heights in Texas affecting whether or not homes are in floodplains, though: the relative heights aren’t changing, so if the dry land is dropping a few feet, it seems like the nearby river would, too.

I really liked the conclusion that the earth is dynamic, even in our lifetimes, with heights affected by oil drilling, glaciers melting, etc. It reminded me of Cataclysms on the Columbia, a book I read years ago about the Missoula Floods that carved out the Columbia River Gorge. It’s been decades since I read it, so I hope this is a fair representation, but according to the book there are these two competing schools of thought in geology that have taken turns dominating the discipline: one that Earth changes gradually, like sandstone wearing away one grain at a time, and the other that Earth changes abruptly, with meteor crashes and massive earthquakes. Of course both types of change are at work, but on my tiny human scale it’s hard to not think of the hills as everlasting and immovable. So even as I read this article about heights I was expecting them to say this new method will give us the ultimate standard for terrain heights, when in fact I should have known that can never be definitive.

Hi Omar
Thank you for the article!
Yes, I think this is indeed a very important topic for many use-cases: Going back and forth between WGS84 and EGM96 is quite often required. Currently, I am using the GeographicLib to achieve that. If there would be a conversion within Cesium, that would be very handy!
However, my concern is the following: For really high resolution e.g. grid of 1’, the geoid data files become quite large (EGM2008-1 is about 470MB). Thus, it probably would not be possible to ship that within Cesium itself but rather have a service on ION for instance…just a preliminary thought (I don’t know whether that is possible at all).
Looking forward to hear your catch on this and also whether there is some more interest in that matter.
Best, Tim

That’s a good question! From what I understood, it isn’t just a problem of shifting everything by some constant amount. You might have a piece of land that is now considered 3 feet lower, relative to sea level. So the body of water is still your zero point, but the new method of computing heights might change different areas around it in different ways.

Glad you liked it, thanks for sharing that link! I think a conversion service like that as part of Cesium ion could be very useful, especially if the required database files are so large and if others commonly have this need as well.

Say a ball rolls (or water flows) from point A to point B due to gravity.

Both points (and every point in between) have identical:
-gravity vectors (scale and direction)
-elevation (distance from reference ellipsoid)

I don’t know if I’d consider point B to be at a lower level than the other points, at least not in a traditional sense. Rather the component of the gravity vector perpendicular to the normal of the surface causes the horizontal force.

Perhaps lower level in a local flow sense?

Local as you can’t really compare sites at totally different parts of the planet to each-other, as resultant gravity is the sum of gravity pulls of local sources in addition to the rest of the planet. It would be neat to see flow direction arrows shown on tiles.

It would also be interesting to approximate local gravity sources using a handful of gravity points located at various positions (slightly underground), each with a certain amount of mass. Have one massive one at the center of the planet that’s like 95%+ of the entire mass. The more points you have the more accurate, but perhaps you can get close enough using just a few. From these you can calculate local flow.

EDIT: just came across this article that came out today

" Scientists detect unexpected widespread structures near Earth’s core"

Apparently Earth’s core isn’t so uniform, though being so close to the Earth’s center it may not have a large local effect on the surface. I wonder how uniform the Earth’s mantle is, density wise, which would have a greater affect at the surface consisting of 70% of Earth’s mass (crust is less than 1% of Earth’s mass.)


While doing a little research on what might affect local gravity the most, I came across some interesting facts:

The sea floor crust is mostly 10km thick.

Sea thickness is never more than around 10km

So that means seafloor+sea is never more than 20km total thickness.

Continents never rise more than 9km above the top of the sea (Everest at 8.8km.)

So if the bottom of the continental crust were to match the bottom of the sea floor crust, continental crust couldn’t exceed 29km, but it does in many places. This means that continental crust descents deeper into the mantle ellipsoid of the earth than does the seafloor crust. The crust of the Himalayan mountain range is 70km thick, and it rises no more than 9km over the top of the sea. That means roughly 50km of that crust resides under the bottom of sea floor crust! So as 2 plates smash together, much more buckles under than over sea level, before melting back into the mantle.

I suppose continents very slowly plow through seafloor crust similar to an icebreaker ship breaking through sheets of ice, resulting in earthquakes and volcanic activity. Instead of floating on water they float on mantle. Mid ocean ridges being where resulting cracks are quickly filled in with magma coming up then cooling into new crust.

Some density values (higher the density the lower you go)
1027 kg/m^3 average ocean density
2850 kg/m^3 average crust density (I’ve read sea floor crust is slightly less dense than continental)
3300 kg/m^3 average mantle density

While the crust of the Earth is no more than 1% of the Earth’s total mass, it’s the closest to surface, so it might have enough of a gravity effect to noticeably alter the flow of water due to density variations. The mantle might not be so uniform in density either but the effects of mantle variations would be less due to the distance.

addendum (6-14-2020):

3D gravity data

While searching for information on vector gravimeters I came across these links

It would appear that the vast majority of data is taken from at least hundreds if not thousands of feet in the air. If these measurements were made in conjunction with surface (and perhaps even sub surface) measurements, one might be able to create a decent 3D gravity map.

This vector gravity data could be fed to a computer program to determine what configuration of say a few dozen mass points with any mass and any location (in 3D space) would most closely cause the resultant gravity vector data at each measurement point.

This 3D gravity map might allow a sort of GPS in underground tunnels. Satellite GPS won’t work underground as the ground absorbs the Electro Magnetic waves. One could correlate changes in the gravity vector while traveling in a tunnel to a 3D gravity map to determine exactly where they are in the tunnel.

1 Like

This sounds like the next big thing :smiley: - is this something anyone’s working on?

Not that I’m aware of, maybe because there aren’t all that many long tunnel systems out there and gravity maps are currently only created from aircraft elevations as far as I know. Data would be limited to just a gravity vector at each spot, but as you travel you should be able correlate a group of these vectors collected at various distance intervals to figure out where you when compared to a gravity map, or at least narrow it down to a few possible locations that could create these readings.

Though with constructed tunnels I’m sure they’d add some sort of location markers along the way to track position (I suppose the same could be added to natural tunnels.)