Improvement of a high resolution geoid height model in the United States by GPS height on NAVD 88 benchmarks

A geoid model, G9501, is computed on a 3' grid using over 1.5 million gravity data from the NGS database and from the Defense Mapping Agency. Computation involves a spherical approximation to perform the linearized Molodensky integration by a 2-D FFT. The integration computes a high frequency correction to an underlying OSU91A height anomaly surface. The output grid of height anomalies are then converted into the final geoid grid. A terrain correction grid at 30 resolution was computed by FFT with a spherical approximation of the classical terrain correction integral. Intercomparison with 1889 NAD 83 (86) GPS benchmarks with NAVD 88 Helmert heights identified a 24.8 cm RMS variation about a tilted plane trend of 0.36 ppm. This tilt is almost completely described by the datum difference between the NAD 83 (86) system and the ITRF93(1995.0) reference frame. A simple, empirical covariance function with a very long characteristic length, L=500 km, was found to fit the detrended differences between the geoid model and the GPS benchmarks. A least-squares collocation predictor lead to the development of a smooth datum corrector surface. Applying this surface to the geoid model produced a new geoid model, G9501C. This model is biased relative to a geocentric geoid, but it successfully relates the NAD 83 (86) datum to the NAVD 88 datum. Evaluation of the covariances of the differences between G9501C and the GPS benchmarks indicates an accuracy of 2.6 cm RMS with a characteristic length of L=40 km. The covariances also show a Gaussian noise source of 6.4 cm RMS. This is primarily error in GPS ellipsoid height, and is due to a variety of sources, including GPS data reduction and analysis procedures. Conversion of the datum corrector surface to a geocentric form, verifies a - 72 cm bias in NAVD 88 seen by Rapp (1995).