Improving Orthometric Heights Using Precise GPS Measurements

The vertical component obtained from the Global Positioning System (GPS) observations is from the ellipsoid (a mathematical surface), and therefore needs to be converted to the orthometric height, which is from the geoid (represented by the mean sea level). The common practice is to use existing bench marks (around the four corners of a project area and interpolate for the rest of the area), but in many areas bench marks may not be available, in which case an existing geoid undulation is used. Present available global geoid undulation values are not generally as detailed as needed, and in many areas they are not known better than ±1 to ±5 m, because of many limitations. This article explains the difficulties encountered in obtaining precise geoid undulation with some example computations, and proposes a technique of applying corrections to the best available global geoid undulations using detailed free-air gravity anomalies (within a 2° × 2° area) to get relative centimeter accuracy. Several test computations have been performed to decide the optimal block sizes and the effective spherical distances to compute the regional and the local effects of gravity anomalies on geoid undulations by using the Stokes integral. In one test computation a 2° × 2° area was subdivided into smaller surface elements. A difference of 37.34 ± 1.6 cm in geoid undulation was obtained over the same 2° × 2° area when 1° × 1° block sizes were replaced by a combination of 5' × 5' and 1' × 1' subdivision integration elements (block sizes).