Improved United States Gravimetric and Hybrid Geoids for 2003

A new gravimetric geoid, USGG2003, and a new hybrid geoid, USHG2003, were developed to replace the existing models (G99SSS and GEOID99, respectively) for the United States. USGG2003 was developed from much the same gravity data, however, significant improvements were made regarding the quality and use of DEM's in the remove-compute-restore technique. This one-arcminute model is in the ITRF00 reference frame, refers to a GRS-80 ellipsoid, and models the geopotential surface with W₀ = 62636856.88 m^2}/s{2. A comparison was made between geoid heights derived from USGG2003 and more than 11,000 GPS/leveling data in the Fall of 2003. The GPS/leveling data were from NOAA's National Geodetic Survey database and provided GPS-derived ellipsoidal heights (above NAD 83) on leveled bench marks (above NAVD 88). Due to the varying quality and distribution of the GPS/leveling data and systematic errors is USGG2003, significant differences occurred at short (100 km) and long (650 km) wavelengths. The complicated relationship between data of varying quality generated an empirical "curve" that could no longer be accurately fit by means of a single positive-definite matrix in Least Squares Collocation. An improved LSC methodology that used a combination of positive-definite matrices generated a mathematical model that better followed the empirical data. USHG2003 was created from a conversion surface developed from this improved LSC methodology using USGG2003 and the GPS/leveling from Fall 2003. Both GEOID99 and USHG2003 were compared to the GPS/leveling data from which they were respectively derived to check for any remaining signal or misfit. This misfit lowered from 4.6 cm (1σ ) for GEOID99 to about 2.8 cm (1σ ) for USHG2003. The misfit derived from both an uncorrelated signal (thought to derive from the random error in the GPS observations) and a correlated component (which could derive from any either the GPS or leveling adjustments as well as USGG2003). The correlated signal was about 2.5 cm (1σ ) with a 20 km correlation length for GEOID99, while it was less than 1.7 centimeter at 6 km for USHG2003. This improvement does not necessarily imply that more "noise" was incorporated into USHG2003. The shortest correlation length used in the improved LSC method was only 100 km, which is still a significant scale. Hence, USHG2003 is a better model for converting between the NAVD 88 and NAD 83 datums.