The one labeled NUKE must be close to the Donald C. Cook Nuclear Plant near Bridgman, Michigan.?ÿ Lived within ten miles of that facility for four years.?ÿ Now everyone knows what is wrong with me and why I glow in the dark.
Nice find. Unlike some other pairs mentioned, this clearly shows what the OP wanted to find.
Looking at your second pair, I was reminded of some time in Chicago at Meigs Field. It was great place to fly into when visiting the city. Looking at current aerial photography no trace of the airport is evident. Nice park though.
I attach two graphics showing heights for your four points as both dynamic and IGLD85 heights.?ÿ
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I was surprised the datasheets did not include dynamic heights for all the points.?ÿ
There are a number of papers on adequacy of Helmert heights and possible alternative reductions.?ÿ
Two additional issues are the use of GPS-derived orthometric heights: a hybrid model incorporates a corrector service from GPS on BMs posing a separability problem and users of published NAVD88 heights on datasheets should be aware of the LVL_DH TOOL.
Good stuff! Not sure if NRCan has a similar LVL_DH tool.
I'm well down the Sunday afternoon rabbit hole now - even found these guys from 10 years ago... ?????ÿ
https://surveyorconnect.com/community/surveying-geomatics/helmert-orthometric-corrections-long/
(Update) After replying, ?ÿI re-read the original post. I note that the OP author uses ??H (geoid)? when he clearly means H (orthometric) as he explains that he wants an example to show that differences in ellipsoid heights do NOT represent the same physical relationship as the differences in orthometric heights do. That said...
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Reviewing posts on this topic, I took a look at the two points whose PIDs you provide. From their datasheets, I extract the following heights (in meters):
For AD9143 ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ For AA9807
h = +3.756 ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ -1.176
H = +31.68 ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ+26.72
N = -27.908 ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ -27.888
The differences, in the sense AD9143 to AA9807:
dh = -4.932
dH = -4.96
As the OP wanted examples of two points whose dh and DH differ in sign this is NOT the case between your two points. The fact that the dN is positive is not responsive to his question. FWIW, the H values for the two points were derived from h and N.?ÿ
I note as well that in your first point on this topic acknowledges that the ??...ellipsoid and geoid are independent...? . Here you seem to argue that ?ÿellipsoid heights and geoid heights are distances to the same ellipsoid. This implies to me that you feel that the geoid can be defined geometrically.
Orthometric heights have been linked to ??mean sea level? and similar systems long before the ellipsoid became useful for heighting. NGVD29 was defined with respect to tide gauges along the N. American coast.?ÿ
The definition used for NGS for the geoid is ??An equipotential surface of the Earth??s gravity field that represents, in a least squares sense, global mean sea level.? See the NGS Glossary for quibbles about this definition. https://www.ngs.noaa.gov/CORS-Proxy/Glossary/xml/NGS_Glossary.xml
NAVD 88 heights are a type of orthometric heights and are the distance along the curved plumb line from the geoid to the point of interest on the terrain. Importantly the instruments used for differential leveling are with respect to the plumb line (direction of gravity).
Ellipsoid heights in respect to say, NAD83, are not determined with respect to the plumb line but the normal to the ellipsoid. See the graphic ??Physical Height Systems? in my post at 2318 on 24 April.
The quantity reported as the geoid height is the distance from the ellipsoid to the Wo value adopted for the zero surface for the geoid.?ÿ
The fundamental relationship between the three heights is: h - H - N = 0 (assuming all are without error). We can directly measure h by GPS observations. We can measure H by leveling with respect to a system defined with respect to Wo. We can determine the ellipsoid-geoid separation by rearranging the relationship above to solve for N. This is the rationale for the GPS on BM effort at NGS. NGS has since the 1990s created gravimetric geoid models. BTW, the newest I heard was that modelers were planning to incorporate ellipsoidal harmonics rather than spheroidal into the latest modeling.?ÿ
Also, I noticed this document providing technical details about the upcoming new vertical datum.?ÿ
Having gone on too long, I stop.
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Yes, there is a conflict between the OP's words and his symbols. I answered his question in terms of his words; you answered it in terms of his symbols. I think that you interpreted his meaning correctly.
That said, note that my examples compared dh to dN, not dh to dH. I think that you will find opposite directions for the former quantities in both examples.
No, I don't believe that the geoid can be defined geometrically. Note that you stated that the ellipsoid height, the distance from a geometric shape to the surface, is a geometric height. The ellipsoid is geometric, the surface is not, so you are saying that the distance from a geometric surface to a non-geometric surface is a geometric distance. I merely extended that definition to geoid height, another example of a distance from a geometric shape to a non-geometric shape.
Yes, I do believe that ellipsoid height and geoid height are measured to the same ellipsoid.
Now, your statement about NGVD 29 is misleading. From NGS: "The datum was not mean sea level, the geoid, or any other equipotential surface. Therefore, it was renamed in 1973, the National Geodetic Vertical Datum on (sic) 1929." Thus, while orthometric height has been linked to "sea level" for centuries, often one tide gauge or a rough estimate with no gauge, NGVD 29 was known to not represent mean sea level.
Thank you for commenting. This is a very valuable discussion.
Apologies if I got things backwards.
Yes I meant "H" to mean height above the geoid (orthometric), which isn't the same thing a "geoid height". Although I have always used 'geoid undulation" rather than geoid height.
I appreciate everybody's input here.
My reply to your post was due to my trying to understand what I was missing when looking at your two points. I missed that your were comparing the signs of the dh and dN.
As to the comment on my statement ?? NGVD29 was defined with respect to tide gauges along the N. American coast.??ÿ?ÿThis is not equivalent to stating that it was defined with respect to mean sea level.?ÿ
The fact that it was only until 1973 that the ??mean sea level? name was changed to NGVD is an indication to me that the intent was to tie the national vertical network to mean sea level. The name change was the result of the accumulation of data showing that mean sea level differs from location to location.
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While there are a number of NGS papers and presentations of NGVD29 and NAVD88 available from their site, I like papers on the very similar vertical network in Australia. I especially like the papers available through Prof. Featherstone?? s ( Curtin University in Australia) web site: ?ÿ ?ÿ ?ÿ ?ÿ
https://staffportal.curtin.edu.au/staff/profile/view/W.Featherstone/?ÿ ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ ?ÿ
The paper shown below is relevant to this discussion.?ÿ
?ÿAs for the description of the relationship of the geoid to the ellipsoid, I think the paper above explains better than I that relationship.?ÿ
My digression to the 1929 US national vertical network was an attempt to indicate that height systems did not involve the ellipsoid until modern GPS. In fact, one reason for the HARN reobservation campaigns of the late 90??s early 2000??s was to provide good quality usable ellipsoid heights. The use of GNSS on all types of sensor systems does make ellipsoid heights ubiquitous.
BTW, the ??Prince of Mathematics? C.F. Gauss proposed the use of the surface of the oceans as the ??mathematical figure of the earth? a term later named the ??geoid.? See ??Physical Geodesy? by Heiskanen and Moritz (1966 reprinted in 2000). An excellent reference for the topic.
Trying not to get too deep into the weeds... and yet... ?ÿ?ÿ
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No problem. I understood what you meant. I am happy that you got some real world examples. I too have problems with the term ??geoid height.?
Reading ??Geodesy? by Lu,Qu and Qiao (2014) I note that he uses the term ??geodetic height? to refer to heights wrt the ellipsoid. As if things were not confusing enough.