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Determining a gravimetric geoid for the Paraná State by using minimum square collocatin

Rafael Santos Genro, Márcia Cristina Lopes Quintas


Recently, geoidal models have been developed in order to transform ellipsoidal
heights provided by GPS measurements to orthometric heights. The objective of
this work is to calculate a gravimetric geoid model for Parana State, which is
located between latitudes –27o to –22o and longitudes –55o to –47,5o. The traditional
Remove-Restore technique for geoid computation is used in this study, in which the
method of Least-Squares Collocation is used. To achieve this goal, the following
information are used: EGM96 to the global geopotential model (degree and order
360); 42.135 gravimetric observations; digital terrain model SRTM with resolution
of 1’ (around 1850 m) and 245 benchmarks (RRNN) observed with geodetic GPS
receiver. The final resolution of the gravimetric geoid computed to Parana State is
5’ (around 10 km), having an absolute error of 30 cm (with 68% of confidence) and
a relative error of 2 ppm, that is, 2 mm/km. Besides, an interpolation program of
geoidal heights was developed, which was called GEOIDEPR2006(CMQ), and
geodetic coordinates referred to Brazilian Geodetic System (Sistema Geodésico
Brasileiro - SIRGAS2000) have been used as input data.


gravimetric geoid; geoidal height; Least-Squares Collocation; geóide gravimétrico; altura geoidal; Colocação por Mínimos