Preliminary Results of Spatial Modelling of GPS/Levelling Heights: A Local Quasi-Geoid/Geoid for the Lisbon Area
Taking GPS-measured ellipsoidal heights with in situ measured gravity values, levelling-measured heights, and knowing the difference between normal gravity potential and geoidal potential, the calculation of normal heights is possible. The difference betw
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Preliminary Results of Spatial Modelling of GPS/Levelling Heights: A Local Quasi-Geoid/Geoid for the Lisbon Area A.P. Falcão, J. Matos, A. Gonçalves, J. Casaca, and J. Sousa
Abstract Taking GPS-measured ellipsoidal heights with in situ measured gravity values, levellingmeasured heights, and knowing the difference between normal gravity potential and geoidal potential, the calculation of normal heights is possible. The difference between normal and ellipsoidal heights allows the computation of gravity anomalies and geoid undulation, and thus the calculation of quasi-geoid and geoid surfaces, to serve practical applications such as large scale map production and engineering applications. In this work an evaluation of the spatial interpolation techniques used in the quasi-geoid/ geoid local calculation methods is presented. Deterministic interpolators (Inverse Power of Distance – IPD and Radial Basis Functions– RBF), and probabilistic interpolators (Ordinary Kriging – OrdK and Kriging with External Drift – KED) were tested. The sample used in this study is from a 34 km × 28 km area including Lisbon, which includes 25 levelling heights and gravity values measured by the Instituto Geográfico Português, and the related ellipsoidal heights, measured with a LEICA AX1200 double-frequency GPS receiver.
43.1 Introduction The definition of a common height reference system in the European space has deserved attention in latest EUREF promoted symposia. Resolution no. 3 of the
A.P. Falcão () Departamento de Engenharia Civil e Arquitectura (DECivil), Instituto Superior Técnico, Universidade Técnica de Lisboa, Lisboa 1049-001, Portugal e-mail: [email protected]
2007 London symposium describes the definition and realization of the EVRS (European Vertical Reference System) as a priority. The height systems are traditionally based on tide gauge observations, which differ from the geoid due to ocean currents, temperature, pressure, salinity and other local conditions (Fotopoulos, 2003). The definition and choice of the reference surface for height representation is not consensual and has been widely discussed in the geodetic community, with several authors to address this problem (Hannah, 2001; NOAA, 1998; Featherstone and Kuhn, 2006). As an alternative to the geoid, many countries use the quasi-geoid as reference. According to the official data published by EUREF, several height reference systems coexist, using normal, orthometric and normal-orthometric heights (Jekeli, 2000). In the Portuguese mainland, the official height system is relative to the tide gauge in Cascais, fixed in 1938, and therefore official heights are geopotential related (Casaca, 2007). The objective of this work is to present a preliminary quasi-geoid for the Lisbon area, obtained by several interpolation functions and to compare their results. The test area is 34 km × 28 km, and includes Lisbon, where 19 benchmarks (obtained by levelling) and 6 geodetic marks of the geodetic network (for which the orthometric height and gravity values are known) were
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