Use H, Not Z

by Dave Doyle

During recent correspondence with a surveyor friend who was concerned about a positional difference he had observed at an old triangulation station, he sent me the following information: N = 213674.3282 m, E = 178633.4978 m, Z = 6.989 m.  Where the station is located is irrelevant. 

This type of a coordinate description is very common.  Whether the horizontal coordinates are State Plane, UTM, or some local coordinates is also irrelevant. 

What is relevant and wrong is his description of the height as “Z.”  I’ve heard surveyors express heights as Z countless times, and it’s wrong.  You might counter that what’s being described is a standard, three-dimensional Cartesian coordinate, and if this were a class in geometry you’d be right.

The general reference of Z as a height most often refers to the orthometric height value related to a vertical datum such as the National Geodetic Vertical Datum of 1929 (NGVD 29) or the North American Vertical Datum of 1988 (NAVD 88).  In this particular case it was the Puerto Rico Vertical Datum of 2009 (PRVD 09).  All of which are incorrect.   

In standard geodetic texts, articles, and presentations, orthometric heights are referred to as H. For example, reference the excellent article, “Defining Surfaces” by professor Charles Ghilani in our July issue.  As Dr. Ghilani notes, there are other heights as well: ellipsoid heights referenced as h and geoid heights as N.  Nowhere are heights referenced as Z. 

In geodesy, Z as a coordinate reference is reserved for the value of a point on the surface of the Earth directly north or south of the plane of the Equator as part of its Earth-Centered Earth Fixed three-dimensional coordinates.  The point referenced above would have a Z value of 1,953,823.627 m.
With the incredible technology of GNSS, the capacity for almost anyone to determine his or her three-dimensional position anywhere on the Earth is fairly trivial, yet we still see far too many instances of supposedly high-accuracy data sets that don’t match each other.  The reasons vary, but one is improper data element identification—metadata. 

As leaders in the geospatial community, surveyors need to ensure that they communicate the data they are providing accurately.  One very simple way to do this is to stop referring to orthometric heights as Z.  If you really need a letter, use H—that’s what it is.

—Dave

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