### Coordinate Changes or Not due to Changes in Elevation

I salute all respectable members of this great forumSomething came to my mind in which I believe experience members of this great forum will have answer to my thought.Does horizontal coordinate of a point changes dueto change in elevation of that particular point??If yes, why?If no, why?

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#### Replies

• THIS IS FOR ELIZABETH
ELIZABETH,
WHERE DID YOU GO? YOU SAID YOU HAD SOMETHING IMPORTANT TO SAY BUT YOU VANISHED. I SEE YOU ARE NO LONGER A MEMBER OF LSU. IF THIS IS NOT A SPAM POST, I WOULD LIKE TO HEAR WHAT YOU HAVE TO SAY.
• Charlie.

Thank you for sharing your experience with us as regards to Mean Sea Level (MSL). I love that...

I also appreciate the development in progress as regards to GRAV-D project in lieu of MSL.

I hope that will bring out good result.
• Oluwafemi,

Thanks, actually our current elevation reference datum is NAVD 88 which replaced NGVD' 29 years ago. It takes some in the bureaucracy quite a while to make a transition.

• David

You actually hit the point here. With your last step by step explanation.

As regards to Cartesian ellipsoidal coordinates, there is no Z. No doubt you are absolutely correct.

As regards to projected coordinates, you are absolutely right again when you said it is a mathematical trick so there is nothing like projected coordinates on site and the Z changes from point to point. In spite it is a mathematical trick to place the curve world into flat surface, remember that this mathematical trick is still adopted during projection (my zone fall into 32 and 33).

So when it comes to geographic coordinates which is our real coordinates as you said and you are right. We don't have problem with that.

But where the first problem occur with regard to your valuable explanation; is that you said, with precision leveling instruments we can get physical/orthometric height directly. I hope the precision leveling will be referenced to the Geoid directly as its benchmark not MSL because as far as the Geoid is concern, MSL can not be scientifically proved to be geoid approximation because the geoid itself is
an imaginary subsurface and it has only geophysical definition with a defined potential energy and it is considered to be irregular. Thus, difficult to define mathematically.

There is no problem in GPS giving us ellipsoidal height (h), But inaccurately to get Orthometric Height can never give us the correct answer to Geoid Undulations (N).

I repeat, our height should be normal to an accurate or approximate Geoid. The orthometric height derived today is error prone

Thus, your conclusion to the above question could be questionable and challenge by other expert in the science of geodesy.

Some will agree with your explanation that horizontal coordinates will change with change in elevation while some expert in the field of geodesy will not.

Conclusion:

There should be an accurate direct methodology in measuring and modeling the orthometric/physical height (H) normal to geoid directly. There should also be an accurate direct methodology in measuring and modeling geoid undulations (N). This will undoubtedly improve spatial data observation to the ever best standards.

Recommendation:

I recommended that this should be a research that should be theoretically and practically proven and acceptable. It will also lead to finding long term solution as far as direct measurement and modeling of orthometric height (H) and geiod undulations (N) and improve the practice of surveying and geospatial profession and eliminate all these mathematical tricks/assumptions in the field.
• Dear Oliwafemi:

Until I know, all the Datum based on MSL, have a value of the orthometric height for their reference. It is not relevance for us, because it is only a translation in height. So you can apply the old MSL or the MSL value plus the difference between the geoid and the MSL on the Datum reference.

The most relevant issue is that the way that the high precition levelling has been done: corrections on height, corrections to the string, corrections by gravity... give as a value of the Orthometric height (maybe a relative difference on it) between the Height Datum Reference and the closest benchmark to us. So using high precition level benchmark you are having orthometric height, and it is as accurate as we can. The only correction that you can do is with a very dense gravitational campaign in order to give gravity values to any high precition levelling benchmark.

Geoid is a geophysical concept, but has its own geometric definition... The problem is that there is not enough gravitational values to define it, only in small areas. And the second problem is that due to our internal composition, the geoid is moving constantly, so even having a goo gravitational campaign, you should updated regularly. But really, it shouldn´t be our concern as it will be a continuous phenomena, so that´s why MSL are, in fact, references. Because through the continuous monitoring, you can see the differences in the gravity. (Keep in mind that in this references, geodesics and geophysics, they are removing the tidal effects, waveing effects, rotational effects...)

The Geoid can be define easily in a local form through a gravitational campaign but, as soon as we know that it´s value change... why to do it at big scale? It should be done when required

The orthometric height that we are using actually is a very good approximation to the real one, the only issue is that we should be close to a high precition level benchmark with a gravitational correction.

And regarding geodesic... (I´m a Geodesic Engineer too), any geodesic will tell you the same issue... as the gravity vector direction change with the height... sure... if you take your zenith direction and you try to keep the gravity vector, you will see that one kilometer above you it has been tilted, 2 km will be more tilted... So if the gravity in your zenith direction change, then the plan coordinates change with the height. Why? Because one kilometer above you, the gravity will be tilted to a point close to you, but not yours, so...which one will bring the Z coordinate? Your point, that is not matching with the gravity one kilometer above you, or the point close to yours that it´s matching with this alignment?

Think as a surveyor... We have many difficulties to try to absorve more!

Follow your local gravity always (except if you need a huge accuracy on a project with too much difference in level... more than 1000 m), follow the orthometric height, and if you think that you should consider this deviation, then make astronomical observation to get the deviation between you zenith and your lattitude.

There is a direct way to get the orthometric height normal to the geoid: high precition levelling plus gravitational corrections. There is a direct way to get the geoid ondulatios: same way that the one to get orthometric, plus GPS or geodetic/astronomical observation. In fact it is not too complicated, but the issue is that there is no too much relationship between surveyors, geodetics and geophysics. Anyone has his one market, and none of them are interested on getting a global definition of geoid.

This tricks/assumptions in the field are the ones that allows you to work with a Total Station or a GPS. If not, you equipment will be: differencial gravimeter (to check the gravitational difference against the closest gravitational station) + GPS (If you are interested to get the ellipsoidical height) + Theodolite (To determine the gravity vector) +... + huge knowledge of Survey, Geodetics, Geophysics, Astronomy, Cosmic Relativity...

I don´t know, but maybe this trick is more practical that the theoretical way.

• David,

Very interesting but I think it will take me a while to get my brain wrapped around all that (I am working on it). Here, the biggest thing elevations are used for is drainage & the reason it is desirable to have a universal datum is so we are all talking the same language. Of course, since geodetic coordinates are 3D, they are also essential for the adjustment of geodetic coordinates.

Another problem is government regulations. If you build something that doesn't comply with government regulations, you may have to move it which will likely cost somebody quite a lot of money.

Federal flood insurance regulations are tightly controlled in flood prone areas. They not only specify what the building elevations must be but also the datum that must be used. The surveyor assumes a lot of liability when he certifies an elevation.

I am a surveyor with a primary interest in complex boundary problems, mostly specific to local law. I am studying GPS & Geodetics because I think it will make me a better surveyor, not to mention that the common use of GPS & the resulting applications make such knowledge essential. Surveying is not what it was when I was licensed in 1983. Some things remain the same but the knowledge base a competent surveyor should have has increased drastically. Put another way, I don't want to be one of those surveyors using GPS  that really do not know what they are doing. I believe there are an alarming number of them out there.

It has been a pleasure discussing this with everybody &  I feel that I have learned a lot from it.

• David,

Thank you for your explanations, they are much appreciated. I mostly use OPUS static observations post processed by NGS for control. So far, the calculated ortho. elevations have checked very close to government bench marks.

When it comes to geodesy, I am still a student but I know a few things about ortho. datums. NGVD' 1929 was commonly called mean sea level (MSL), which it is not. It was based on mean sea level, however. NGS is working on a new datum called GRAV-D as I write this. Prototype orthometric heights are already being published. NGS says, "This height is subject to change as data & modeling for gravimetric geoid change throughout the lifetime of the GRAV-D project, or as new realizations of the ITF are adopted." FEMA is still using NGVD' 29 in some areas. The trouble with tidal bench marks is the data is only good at the tide gauge where it was measured. If you run levels between tidal bench marks along the coast you will find that they usually don't agree as  MSL varies from location to location.

• Sigh!
The horizontal coordinates meant to the above question are for the following coordinate system:

Cartesian ellipsoidal coordinates

Projected coordinates

Geographic coordinate.

In each of those coordinates system listed above, what will happen to the horizontal coordinates derived from those coordinates system due to changes in elevation of same observed point (decrease or increase)

Hence, I think the issue has to be tackle from thoroughly understanding of the elevation/height system in geodesy; since the study is basically on changes in elevation/height (decrease or increase)

Thus, the H = h - N which is the fundamental equation in height in Geodesy

Where 'h' is the ellipsoidal/geometric height (normal to ellipsoid)

Where 'H' is the Orthometric height (normal to geiod)

Where 'N' is the geoid undulations (separation of ellipsoid from geoid)

Unfortunately, neither the orthometric height (H) nor the geoid undulation (N) can be observed directly.

As a matter of that, the determination of the coordinates of a point on the earth surface with high accuracy is a real contemporary challenges not to talk of coordinates of changes in elevation of same observed point.

This has constitute into having different theory of answers to the above question.

With the aid of GPS observation, today we are able to observe ellipsoidal/geometric height (h) which is normal to the ellipsoid.

Height/elevation has to be normal to geoid, so now combine with local height/elevation (datum) we have orthometric height

Orthometric height by its definition, is the physical height (H) of a point, is the distance between the point and the geoid surface. Unfortunately, where our problems lies now globally which has constitute different theory of answers to the question above is that there is no direct methodology known to compute the orthometric height (H) directly. The geoid itself is an imaginary subsurface and it has only geophysical definition with a defined potential energy.

The classical leveling technique long away, the water surface of the earth was considered as a homogenous equipotential surface and a datum for vertical observations. Hence, most of the height measurements were measured by leveling from the Mean Sea Level (MSL). Scientists and engineers strongly criticize the leveling for a one reason, because its uses horizontal plan (datum) for relative height difference while the datum used for height is the geoid which is not horizontal, rather it’s irregular.

Another area to be address is to have direct methodology to measure the separation of ellipsoid from geoid (Geoid Undulations 'N')

I strongly believe there are problems for researchers to solve in the field of geodesy which remain the ultimate backbone to surveying and geospatial profession.
• Step by step:

Cartesian ellipsoidal coordinates: You can have a ellipsoidal coordinate through lat and long, but there is no height. It is a mathematic trick for us, but the normal to a ellipsoid is not the normal to an ellipsoid one meter above... that´s why it is not used.

Projected coordinates: There is no projected coordinates. You have a reality that usually, we are approaching by proyecting this reality in some surfaces that can be planar-developmented. Again, it is a mathematical trick in order to put something curve (our ground) into something flat, our design. But there is no projected coordinates on site, why? Because, as with the ellipsoidal coordinates, there is no Z direction. You are assuming that it is normal to X-Y, but in your projected reality, Z direction change for any single point. (Think on UTM and you will see it)

Geographical coordinates: That´s our real coordinates. But we can´t staying taking a look to the stars every time that we need a new station, that´s why we are considering a celestial sphere, an ellipsoid, a proyection system... Because it is not simple, for a big scale, to match our curved reality with our design on a cartesian XYZ system.

On the equation H=h+N, H it is easilly determined but high prec. levelling, the issue is that we need to correct our observations. h can be determined by GPS observation, so then you can get N.

The problem arise when you need to get a accurate value, because your GPS is solving the 3D intersection to give you your position, but, if you need something real accurate, then you need post process. When you need to get a good orthometric height, you need corrections through a gravity campaign, and usually, surveyors/geodetics and geophysicists, we are not close enough...

So, it is not a real problem, the issue is that the people involved any one is searching for his interests: surveyors for a quick and accurate work, geodetics for a good geodetic network and new ellipsoidal models, and geophysicists working mainly for mining and petrol industries, not real interested in absolute and relative gravitational campaign.

And regarding the question of this post...

With our actual reference system, datums and projections: YES, THE HORIZONTAL COORDINATES OF ONE POINT CAN CHANGE WITH THE HEIGHT!!!

Why?

Simple, because with our actual instrumentation, we are always working with local gravity, and we should work with the normal to the Geoid. Meanwhile, we will use orthometrics plus local gravity as an approximation to geoid height.

• Thanks to the big men in the heart of science (geodesy) of Surveying and Geospatial profession.

They all share their knowledge as far as geodesy is concern to make their points.

I strongly believe that hundreds of people have learn one, two or more things from their contributions.

Once again, thank you all for devoting your precious time to shed more light to the science of surveying (geodesy)

We appreciate you all!
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