Use of EGM08 model and shuttle radar topography mission data for geoid computation in the State of Rio de Janeiro, Brazil: A case study with Voronoi/Delaunay discretisations

The EGM08 geopotential model complete to degree and order 2159 was used in a remove-compute-restore (RCR) method for the geoid computation in the State of Rio de Janeiro, Brazil. Terrain and indirect effect corrections were computed using a 6-arcsec resolution DTE, derived from the TOPODATA Project (Shuttle Radar Topography Mission data) raised by the National Institute for Space Research. INPE, Brazil. We applied Voronoi/Delaunay discretisations for discrete Stokes integration. In these schemes, target area is partitioned into polygons/triangles, respectively, and the computation is carried out by point-wise numerical integration and no gridding is mandatory. For both procedures, the cells were produced using either observed gravity data combined with gridded Bouguer derived information. Particularly in Delaunay scheme, as the gravity anomalies are interpolated into the triangular cells, and geoid undulations are computed for their vertices, Stokes function singularity was gone. Externally estimated errors resulting from a comparison with GPS/leveling data were presented for both the schemes and classical ones, as well as for the EGM08 undulations. They yielded RMS differences equal to 0.105 m, 0.110 m, 0.110 m, 0.115 m and 0.228 m, respectively, for Voronoi, Delaunay, Voronoi/Delaunay with gridded-data alone and EGM08, computed between 32 GPS/leveling points.