Can someone give me a real world example of 2 points on the surface of the earth where delta h (ellipsoid) from A to B is positive, while delta H (geoid) from A to B is negative - hence water would flow "uphill" on the ellipsoid?
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I'd take a look at the Bonneville Salt Flats area East of Wendover Utah.?ÿ
Water does not flow up hill, since up a hill is defined on the geoid. Just because a point has a greater positive value above the ellipsoid does not mean it is up hill from some other point with a lesser positive value. I have never considered I should look for such points but if I were it would be along the Jersey Shore where the geoid is below the ellipsoid. Technically water flows from a place of higher gravitational energy to a place of lower gravitational energy. Hills are defined by gravitational energy and gravity does not necessarily mean straight down. An ellipsoid is a smooth mathematical construct approximating a gross view of the earth's surface. The geoid is a very non-smooth surface approximating a minuscule view of the earth's surface.
Paul in PA
Doubtful you can find an area that the geoid height changes fast enough to overcome tension and friction enough to get the water to flow along an ellipsoid height contour line. But I live where the Geoid height changes .5'/mile on average heading towards a mountain range. That is fast for geoid height changes, but I wouldn't want my sewer lines to be that flat.?ÿ
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It's obvious that all water should flow to the poles, North and South, from the Equator due to the Equator being farther from the center of the Earth, right? ???? ???? ???? ???? ?????ÿ
That's why I put "uphill" in quotation marks - I understand all you say.
I am looking for such points to prove why we need geoid models rather than just using ellipsoid elevations. When this idea is mooted, it is usually pointed out that it could lead to water flowing "uphill" scenarios. I am just curious for an actual location where this situation exists.
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Think of it using first principals. Every location does this along a contour line perpendicular to the slope of the Geoid Model.?ÿ
It's obvious that all water should flow to the poles, North and South, from the Equator due to the Equator being farther from the center of the Earth, right? ???? ???? ???? ???? ?????ÿ
Yup, except centrifugal force affects sea level and closely negates the pole-equator center of the earth distance difference.?ÿ Apparently the Mississippi is a large scale river which actually flows uphill because of its massive N-S extent and near zero gradient:
Mississippi ?ÿ ?ÿ ?ÿ ?ÿ I'm not endorsing this article's conclusions, just pointing it out.
I faintly recall an old ACSM journal article that posited water could flow uphill in smaller locales due to massive Geoid undulations?ÿ which were not modelled in early Geoids.?ÿ Can't find the cite.?ÿ
Anywhoo, I'll assert that a terrestrial spirit levelling is the gold standard which defines "downhill", and there are some curious situations where hydraulic considerations allow a canal to be at zero slope for tens of miles yet still "push" the water through, even at an inch or two "uphill" gradient.?ÿ?ÿ
DK9983 and FY1129.?ÿ It's probably not unusual. The ellipsoid and the geoid are independent of each other, so there's no real reason to expect them to change in concert from point. Ellipsoid height is terrain-dependent while geoid height is gravity-dependent.
This was the only pair I tested. The terrain in NC rises from sea level to over 6,000 feet from east to west, so, even within the same Piedmont NC county, there will likely be a change in EH from east to west.
The geoid, on the other hand, is a function of gravity, which doesn't necessarily follow terrain.
Thanks, now sorry, but how do I look them up? I went to NGS site and typed them in, but I'm Canadian so not familiar with the process!
Go here:
https://geodesy.noaa.gov/datasheets/
Scroll down and on the right-hand side of the screen, find PIDs-Permanent Identifiers. Click the text icon and enter the identifiers (PIDs) in my post.?ÿ
On the next screen, choose Select All, and you should be in business.
Interesting concept, thanks for bringing it up.
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http://www.ngs.noaa.gov/cgi-bin/ds_mark.prl?PidBox=DK9983
http://www.ngs.noaa.gov/cgi-bin/ds_mark.prl?PidBox=FY1129
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One of the key points to remember when dealing with the three height systems: orthometric, ellipsoid and geoid (distance from the ellipsoid to the geoid) is that they are NOT parallel.?ÿ
I read into your question a belief that ellipsoid height differences can replace orthometric height differences. I attempt to explain wh this is not true.
Ellipsoid heights are geometric and do not account for gravity. An ellipsoid height is the distance from the surface of the ellipsoid to the point of interest.?ÿ
Orthometric heights like NAVD88 take geometric differences from field leveling and apply a number of corrections including accounting for mass density. The equation for Helmert heights is H = C/(g+0.0424H) where g is surface gravity and the factor 0.0424 is used to address the issue of the density of underlying rock.
Examine the following graphics that explain the issue.
?ÿCan one find areas where the dh (difference in ellipsoid heights) and dH (difference in orthometric heights) have opposite signs? As Loyal posts there are some parts of the country like Wendover, UT where this occurs.
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Well, geoid heights are geometric, too, because they're distances to a geometric shape, the ellipsoid. Assigning gravity to geoid heights while ignoring gravity in orthometric heights does not make one geometric and the other not.?ÿ
Again, situations where ellipsoid heights change positively or negatively while geoid heights change negatively or positively are not rare nor are they confined to limited areas. Consider, for example, AD9143 and AA9807, both near the international airport in Orlando (MCO -- Mickey's Corporate Office).
While both heights are distances to the same ellipsoid, they otherwise move independently. This uncorrelated movement between the two is one reason why ellipsoid heights cannot replace orthometric heights.
It is true, though, that water does not flow on the ellipsoid nor on the geoid.
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Thanks everyone!
To look for a real life situation where water flows against the Ellipsoid slope I would first look at canals and ditches near mountain ranges. They will flow downstream from a POD along a valley cut into the side of the valley wall, cross the ridge between the next valley and flow upstream into the next valley. All at very gentle grades. Just off the top of my head I would think the water flowing towards the mountain could actually flow up the ellipsoid hill.?ÿ
Found this online and worth reading.
http://kejian1.cmatc.cn/vod/comet/GIS/gravity_intro_2/navmenu.php_tab_1_page_3_5_0_type_flash.htm
Here are a couple real-world pairs of interest, spanning across Lake Michigan. Units are meters.
Ben
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From West to East.
PID : DG4988
Name : WIND POINT GPS
Ortho Ht (H) : 180.71
Ellip Ht (h) : 145.796
Geoid Ht (N) : -34.869
PID : OL0375
Name : K 317
Ortho Ht (H) : 180.364
Ellip Ht (h) : 146.754
Geoid Ht (N) : -33.667
Delta Ortho Ht (dH) = -0.346
Delta Ellip Ht (dh) = +0.958
Delta Geoid Ht (dN) = +1.202
Distance = 130 km
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From East to West.
PID : ME3336
Name : NUKE
Ortho Ht (H) : 180.5
Ellip Ht (h) : 146.585
Geoid Ht (N) : -33.961
PID : AC9170
Name : DALEY
Ortho Ht (H) : 180.5
Ellip Ht (h) : 146.861
Geoid Ht (N) : -33.589
Delta Ortho Ht (dH) = 0.0
Delta Ellip Ht (dh) = +0.276
Delta Geoid Ht (dN) = +0.372
Distance = 87 km
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Datasheets.
https://www.ngs.noaa.gov/cgi-bin/ds_mark.prl?PidBox=DG4988
https://www.ngs.noaa.gov/cgi-bin/ds_mark.prl?PidBox=OL0375
https://www.ngs.noaa.gov/cgi-bin/ds_mark.prl?PidBox=ME3336
https://www.ngs.noaa.gov/cgi-bin/ds_mark.prl?PidBox=AC9170
