(changes since last update are shown in RED)
The USGG2003 geoid model is a purely gravimetric, geocentric geoid model covering the Conterminous United States. Input data for USGG2003 consisted of:
Using EGM96 as an underlying long wavelength model, USGG2003 was computed using a 1-D FFT remove/compute/restore application of the spherical Stokes integral, where Faye anomalies approximated Helmert anomalies. In computing USGG2003, the geopotential value of the geoid was chosen as W0= 62636856.88 m2 / s2. The USGG2003 geoid undulations refer to a geocentric GRS-80 ellipsoid. USGG2003 was computed on a 1 x 1 arc minute grid, covering the Conterminous United States in the region 24-58 N latitude and 230-300 E longitude.
USGG2003 was generated in much the same manner as G99SSS (click here for more details on the generating of G99SSS). The biggest difference between G99SSS and USGG2003 is that the altimeter-derived gravity data were used from GSFC00.1 instead of KMS98. This resulted in a significant improvement in the comparison of USGG2003 to the GPSBM2003 data. The overall standard deviation dropped from 40 cm to 30 cm in the state of Florida. Other changes occurred all along the East coast and parts of the West coast. As the intent is to have a better forward model of the gravity field, the use of the GSFC00.1 data was adopted.
The GEOID03 geoid model is (in the Conterminous United States) a hybrid geoid model, combining the gravimetric geoid USGG2003 with datum transformations and NAD 83 GPS ellipsoid heights on NAVD 88 leveled bench marks (GPSBM2003).
In addition to the gravimetric geoid model USGG2003, the GEOID03 model consisted of the following input:
The USGG2003 geoid undulations were compared nationally with GPSBM2003. After removing a 55 cm bias and a trend (0.15 ppm, 332 degrees azimuth), an 13.8 cm RMS difference remained. For a discussion of how this signal may have originated, see the technical details of GEOID99. The focus here is on how the signal was treated differently for GEOID03 than for GEOID99 using a multi-matrix Least Squares Collocation method.
Instead of fitting a single Gaussian function to the signal implied by the empirical data, two such functions were created and added. The first function had a correlation length of 650 km and a signal amplitude of (11.2 cm)2. The second had a correlation length of 60 km and an amplitude of (8.1 cm)2. In the below images, the first shows the fit selected for GEOID99 while the second shows that for GEOID03.
Clearly, then the second fit is better. This improved fit reflects the modeling of data at varying quality and spatial distribution. The results show a significantly improved fit between GEOID03 and the GPSBM2003 data. The grid generated by the multi-matrix Least Squares Collocation method, along with the bias, trend and ITRF00/NAD 83 transformation were used to compute a conversion surface which when removed from USGG2003 yields GEOID03. GEOID03 undulations have a 2.4 cm RMS difference when compared to the GPSBM2003 data, which represents 50% improvement over the GEOID99 model.
Furthermore, the actual geoid error is under 1.0 cm. The total misfit
between the data is a combination of the uncorrelated signal deriving from the
GPS observations (random error) and a correlated signal that could derive
from either GPS or leveling data as well as USGG2003. The uncorrelated
signal is about 2.1 cm. Note how there is a spike on the y-axis where the
data auto-correlate. This spike represents the uncorrelated signal, because
random error at one point does not impact the signal at another. In the below
figure, the correlated signal can be projected into the y-axis at about 1.0
cm of signal. Hence, the actual geoid error is 1.0 cm for one sigma or 2.0
cm for 2 sigma (95% confidence level). This relationship is expressed through
the variances (the squares of the numbers discussed here).
Total Signal = Uncorrelated + Correlated
(2.4 cm)2 = (2.1 cm)2 + (1.0 cm)2