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Section 4: Surveying Vertical Networks with GPS

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The use of GPS for vertical network surveys requires an understanding of the relationship between conventional and GPS height systems and to the problems unique to the vertical component of a GPS measurement.

Conventional trigonometric, spirit, or compensator leveling measures the relative elevations of points above an undulating equipotential surface called the geoid, which is close to, but not the same as, “mean sea level.” The model of this undulated geoid surface, currently in use by TxDOT, is the GEOID03. TxDOT uses the NAVD88 vertical datum for orthometric height (elevation) measurements from this geoid surface (GEOID03) and it has superseded the old NGVD datum of 1929. Elevations measured by conventional leveling are orthometric heights.


Ellipsoid Measurements

In contrast, GPS measures the relative heights of points above a smooth, mathematically simple surface called an ellipsoid. An example of an ellipsoidal reference surface is GRS80, the defining ellipsoid for NAD 83. Elevations derived from GPS measurements are ellipsoidal heights minus the separation between the geoid and ellipsoid.

The ellipsoidal (h) and orthometric (H) heights are closely related by the geoid height (N), the separation between the two reference surfaces, as shown in Figure 4-4 below. Geoid heights can be derived from GPS observations on bench marks, where both the ellipsoidal and orthometric heights have been measured for the same point. A network of GPS bench mark observations, gravity observations, and elevation models are used to develop a geoid model. From this model, geoid heights at other points in the area can be estimated. The accuracy of these geoid heights is dependant upon the accuracies of the various measurements used to construct the model.

Relationship between ellipsoidal (h), orthometric
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Figure 4-4. Relationship between ellipsoidal (h), orthometric (H), and geoid (N) heights.

Note that in the continental United States the ellipsoid is above the geoid; therefore N in Figure 4-4 is negative. Also, note that the height equation h = H + N is only an approximation as the orthometric height is measured along a curved plumb line normal to the geoid surface, while the ellipsoidal and geoid heights are measured along straight lines normal to the ellipsoid surface. For land surveying applications, the height error associated with this approximation will always be less than one centimeter.

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Height Component

The height component of a GPS survey measurement is also affected by relatively poor geometric strength for trilateration, as the earth blocks all satellite signals from the hemisphere below the horizon. This imbalance makes ranging much more critical for determining vertical. Slight ranging errors from multipath or atmospheric conditions are more problematic with this poor geometry.

Accordingly, GPS height accuracies for a survey are typically 1½ - 2 times poorer GPS horizontal accuracies, depending on data quality and baseline length. Increased redundancy of observations under independent conditions is useful for identifying errors.

Because of the need for four (4) or more vertical control points (and in some cases, all four quadrants) to establish good GPS elevations, many times it will be more economical to run conventional level loops.

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