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# GEOID ELEVATION

Hello,

I am a novice surveyor learning about the geoid and its used in calculating elevation.  In my research I see the reference made to H=h-N and recognize the two paths to a point, one from the ellipsoid representing "h" and one from the geoid representing "H" orthometric height.  It appears to me that the significance of the two paths is having a redundant calculation for a point P on the ground.   Is my understanding correct or is there a greater purpose in calculating elevations for two different paths as shown in the attached pic.

This Content Originally Published by a land surveyor to Land Surveyors United Network

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### Replies to This Discussion

Mr. Turlington,

Redundant surveying observations are practically always beneficial.

The exact significance of your question is not clear to me.

The ellipsoid may be thought of like 3D graph paper. It is a man-made construct made as simple as possible for plotting positions on or near the earth.It is so simple it takes only two parameters to define it. There have been many attempts to define the ellipsoid over the centuries. After the advent of artificial satellites the knowledge of the shape of the earth has improved to the point that the last few iterations of refinement are miniscule. The most common ellipsoid in use today is GRS80.To be used as a datum a zero point for the longitude and the location of its origin  must be defined. Again the most frequent assignment is the Greenwich meridian and the center of mass of the Earth.

The geoid is a physical actuality. It is the surface of the points at which the gravitational potential is the strength of a reference - traditionally at or close to sea level. The geoid is not simple like the ellipsoid. It varies quite a bit from place to place depending on several factors, including latitude and the density of material under and around each point. It is not a mathematical surface.

What we did over the last few decades is to measure the gravity potential from place to place and developed something like a DEM of gravity potential - a geoid MODEL. The geoid model was not generally very useful until the popularity of GPS grew and its use for determining heights an elevations was desired.

GPS does not produce elevations. GPS gives excellent positions relative to the center of the earth and therefore, heights relative to the ellipsoid.The sole popular practical application of the geoid is to combine its model with GPS ellipsoid observations to approximate elevations (orthometric heights) by the formulae you illustrated.

I don't know if I addressed your interest, but I hope so.

JAC

Mr. Cavell,

Thank you for your feedback, and yes, your response is of much help.  I thought the value of ellipsoid height “h” and the geoid undulations value "N" are both provided by GPS.  As a novice, I do not see the significance in needing the Orhtometric height "H" unless it is to provide two paths for finding elevation for purposes of checks and balances.  I see that Leveling would provide the elevation above MSL and thus the orthometric height using traditional methods.  I assume the survey leveling approach is more time consuming and it is much quicker to just use GPS to subtract the geoid undulations “N” from the ellipsoid height "h" to arrive at the Orthometric height, assuming it is needed.  Is it common practice to use leveling in addition to calculating orthometric height as H=h-N as a redundant check or is it just one method of using GPS over traditional methods of leveling?

The principle difference is that Latitude, Longitude and Ellipsoid height are products of geometric geodesy; straightforward geometry, while orthometric, dynamic, normal and other heights (elevations) are products of physical geodesy; physical properties.

Orthometric height is what we call "elevation". In most cases it will help us predict what way water will flow and whether a building is plumb and won't topple.That isn't literally correct, for that we would look to Dynamic height, but that is minutia for most projects.

Locally, our instrumental measurements are controlled by local gravity via a plumb bob or level vial. So, locally we  are attached to down. AS we moved along in more extensive surveys, our instruments continued to be controlled by local gravity. With the advent of the EDM & GPS we began to reach beyond local and across changes in local gravity thereby confusing the notion of down over the whole of the project.

Additionally, government bureaucrats and design firm interns looking for specification came across geodetic terms and they were used as boilerplate in contracts and regulations. Therefore,requiring us to report results in a globally based datum or breach the law. The actual needs of a client are not a concern.

Leveling over any significant distance is an expensive prospect compared to using GNSS. NGS only very rarely utilizes field leveling any more. The Bluebook procedure assumes satellite positioning. The basis for the current realization of the NSRS is based on the positions and observations of CORS, in combination with other sophisticated geodetic techniques.

So, today I would not say using the geoid model is primarily used for redundancy. In most cases it is primary and local levels might be used to verify or tighten up the local differences within a project area.

JAC

Ok, so if I understand correctly, GNSS would use the Geoid as a reference surface for acquiring elevation, and the NAVD88 would be a reference for use with leveling?

Speaking literally, GNSS doesn't know which way is up. It circles the globe in all directions and generates 3-D X, Y, Z coordinates from the earth's center as origin. These coordinates are more easily understood when translated as Latitude, Longitude and Ellipsoid Height. GNSS is able to give one an Ellipsoid height.

Software (often within a hand held data collector) may use a model of the geoid to approximate the elevation (orthometric height).

So, while your work may depend on the geoid model. GNSS "knows" nothing about it.

JAC

When does NAVD88 come into play?

The NSRS is currently expressed in two datums as is traditional.

NAD83, the horizontal datum (LAT,LON, EL Ht) is geometric datum based on the Earth's center of mass and an arbitrary ellipsoid. Today is is much more a 3-D datum but it is geometric not physical. Your location in space is a geometric phenomenon.

NAVD88, the vertical datum (orthometric height or elevation) is a physical phenomenon dependent upon the distribution of mass most particularly near the surface of the earth. Its datum is the geoid,which  cannot be expressed in a mathematical closed form (formulas). Therefore it is modeled like a topo. Over time the models have become denser.

If one begins at a good BM with a orthometric height and conducts an accurate level survey the results will be in the NAVD88 datum because as the leveling proceeds the instruments align themselves with the geoid as one moves about.

The interest to the day-to-day surveyor became of interest when the EDM and then GPS allows making survey observations over great distances (greater than the underlying datums at the time). The users of GPS (or really their clients) wanted some way to use the GPS to establish elevation (orthometric heights) as easily as they could horizontal data.

During the cold war developments of geoid information was often Top Secret because the ballistic missiles depended upon it to be correctly aimed. Over time geoid models were made public and the NGS provided a model called Geoid12B for use in  North America.

So, to your question, if you make accurate GPS observations relative to NAD83, you may apply the geoid heights from the model (Geoid12B) to derive a reasonable approximation of orthometric height in NAVD88.

JAC

That is news to me, very interesting.  It was my impression that the geoid was associated to the ellipsoid and NAVD88 was based on a tide gauge in Quebec Canada, as an older vertical datum.  However, if I understand you correctly, the NAD83 and ellipsoid is one datum giving basis to lat-long and elevation, and the NAVD88 is a second datum tied to the geoid, as a vertical datum ?  So NAVD88 is only been around since the Geoid development in the cold war days ?

The geoid has always been with us. sea level approximates the geoid. I believe it was Gause  who spoke of it with the meaning we use today.

We were unable to develop a precise model of the geoid until first we had a precise geometric datum on which to describe it.

There were many local datums, but being local they didn't relate to each other well, if at all. We had to wait for artificial satellites before we could begin to determine the center of mass of the earth. Once we had a precise geometric datum a reasonable model of the geoid was possible.

The terrain is a real thing.

The ellipsoid is a mathematical construction. By convention the most used ones are meant to fit the shape of the earth well.

The geoid is a real thing.

The geoid models are models (thinnk DTM) developed by man to approximate the geoid.

JAC

sometime i used benchmark which are established by differential leveling and refererence to MSL. In the project site like construction project, levelling is the appropriate way, this is more applicable. Apple to apple.

If I am using differential leveling, does the NAVD88 Quebec tide datum represent the primary datum, or are there adjustments based on local tide datums typically ?

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