Estimation of the longitude bias of the NWL9D coordinate system from deflections of the vertical, satellite altimetry and high degree spherical harmonic expansions

Abstract

TheNWL9D (orNSWC9Z2) coordinate system is known to have thex andy coordinates of its origin approximately1 or2 meters from the Earth’s gravity center, but its zero meridian plane is supposed to form an angle (Δλ) of−0″.5 to−0″.8 with the astronomical (Greenwich) zero meridian plane. If biased geodetic longitudes are used for the calculation of an astrogeodetic geoid profile at, e.g., latitude φ=30° extending1000 km, then the geoid undulation differences between the two endpoints will differ more than2 m from the true geoid. This error will easily show up by comparison with a geoid calculated from a high-degree spherical harmonic expansion or the approximately observed geoid undulations obtained from satellite altimetry. This gives a possibility for determining Δλ as the correction (−cos φ·Δλ) which gives the best least squares agreement between the deflections of the vertical and other gravity field-dependent quantities.

An estimation of Δλ has been made using least squares collocation, because this method gives result which fulfil a least squares minimum principle. The following datasets were used.

• (A) 301 deflections of the vertical in an area with latitude between29° and33°, and east longitude between264° and279° along the coastline of the Gulf of Mexico.

• (B) coefficients to maximal degree180 of two spherical harmonic expansions, and

• (C) sea-surface heights determined from satellite altimetry along the same coastline treated as if they were biased geoid undulations.

The deflections were used with the coefficients alone or combined with the sea-surface heights. A value of Δλ=−0″.55±0″.08 was obtained for the data combination which gave the smallest standard deviation. This result is not significantly different from the value of Δλ=−0″.50 adopted for the transformation between the North American Datum, 1983 andNWL9D (NSWC9Z2).