Ellipsoidal heights and engineering applications

As the GPS surveying techniques started showing promise of high accuracy geodetic positioning in the early 1990s, few “open-minded” geodesists realized the possibility of using ellipsoidal heights in place of orthometric heights. Many conceptual approaches were mentioned and proposed in various applications. However, Steinberg and Papo were the fi rst to publish a paper entitled “Ellipsoidal Heights: The Future of Vertical Geodetic Control” (GPS World, Vol. 9, No. 2, 1998). As could be expected, Petr Vanicek, a geodesy professor, was quick to downplay the proposed new “type” of vertical control (GPS World, Vol. 9, No. 4, 1998). It seems that Steinberg and Papo did not “defend” their new proposal. Thus, in this paper, a review has been made to check and comment on Vanicek’s example against the ellipsoidal heights, reference to orthometric islands, and issuance of a warning for non-dissemination of ellipsoidal heights to Canadian users.

Facts to note

The following geodetic facts are pointed for users to have better appreciation for the new approach:

1. As MSL is not an equipotential surface, it cannot be considered as a zero reference for orthometric heights and depths for all areas, land or ocean.

2. MSL has “slope” along coasts, both in E-W and N-S directions. Thus, a zero elevation does not necessarily coincide with MSL. 3. There are coastal points along Caspian Sea and Dead Sea, which have negative heights (-H) or are below “sea level”.

4. Two points on a “level” surface can have “different” heights (H).

Observations on Vanicek’s Opposition (GPS World, Vol. 9, No. 4, 1998):

a. Warning for Non-dissemination of ellipsoidal heights (h) – It seems that this warning was issued based on old traditional usage and also on fear of mix up by the users. Instead, if a review and check had made of the new idea, the warning would not have been needed (Coordinates, Vol. 1, No. 3, 2005).

b. Example of negative ellipsoidal heights along the coastline for an engineer, who wants to plan port facilities – Engineers have worked in the past and still work routinely with negative MSL heights along the North Sea in The Netherlands. Thus, the negative comment does not prove anything against the proposed use of ellipsoidal heights. Interestingly, the traditional geodesists accept negative MSL elevations along Caspian Sea and never question how a seacoast can be below “sea level”!

c. Orthometric Islands and chart datum – It is diffi cult to understand why this topic was brought out against the ellipsoid heights.

In a nutshell, fi rst Prof. Vanicek should have been open to the proposal of two researchers, checked it with the real data, and then commented accordingly. He just chose to downplay his futuristic colleagues in old traditionalistic approach.

Checking real data sets

Here, the first step was to collect the real geodetic data, viz., “h, H, and N” (Note: The GPS surveyed heights “h” do not require any theoretical models and approximations). The data sets were obtained from the U.S. National Geodetic Survey (NGS) for eleven States, viz., Washington, California, Texas, Nevada, Colorado, New Mexico, Virginia, Tennessee, Georgia, New York, and Kansas. Here, the criteria was terrain variation from mountainous to fl at plain and the area covered to have good geographical distributed over the country. For linear distances up to 3-5 km between two points, the differentials “Δh” and “ΔH” differed from each other by 1-3 cm. Thus, the important point to note is that the zero references for “h and H” are different, but the “Δh” and “ΔH” are the same for practical usage.Here, a very important point to note is that in extremely flat areas the difference between Δh and ΔH will be practically ZERO. Thus, an engineer will be able to use ellipsoidal heights with confi dence.

Non-engineering applications revisited

In the paper entitled “When ellipsoidal heights will do the job, why not use them!” (Coordinates, Vol. 1, No. 3, 2005), the use of ellipsoidal heights (h) in non-engineering applications was discussed and explained with full supporting “How to” use them methods and algorithms. No negative critique in writing has been received except on ellipsoid height contours. This critique was that such contours would not work in “general planning” for engineering projects. A double “check” is provided in the following Section.

Engineering applications one by one

Let us now check a number of engineering applications, which we could identify:

1. Ellipsoidal contours on maps – The minimum contour interval (CI) is generally 2 m (or more). In such a case, the accuracy of height information is taken as half the “CI” or ± 1 m (or more). Thus, as there is practically no difference between “Δh” and “ΔH”, all road construction work and general planning for canals, pipe lines, etc., can be done with confi dence.

2. GPS surveyed “Δh” with accuracy of 1 in 1 million or better – Using for section by section of up to 500-600 meters in length, the ellipsoidal “Δh” will work in canal and pipeline projects even in extremely fl at terrains. However, a few small sections of spirit leveling can be done as “check ups”. These “spot” checks will help during transitioning from the OLD approach and to develop confi dence in the NEW usage.

Conclusions

To use ellipsoidal heights, first we all need to change our predetermined attitude. Then, accurately surveyed “h and Δh” will do all jobs, including engineering. However, in extremely flat terrain areas, where accurate “slope” is critically vital, a few sections of differential spirit leveling can be carried out as check ups, especially during transition. It will build up confi dence. This usage of GPS surveyed accurate ellipsoidal heights will be signifi cantly cost effective and time saving for any project.