Abstract
Abstract The combination of physical and geometric heights, required for geodetic purposes, uses Global Geopotential Models (GGMs), local geoid, or quasigeoid models. The geoid height and the height anomaly, provided by GGMs, are not accurate enough for most engineering applications. Considering the normal height system of Brazil and the physical concepts of the involved reference surfaces, a quasigeoid model is more appropriate than the current Brazilian geoid model MAPGEO2015. This paper shows the determination of the geoid and the quasigeoid models for São Paulo state using the updated gravimetric data and the new system of the normal height of the 2018 Brazilian Vertical Reference Frame (BVRF). The computation of the quasigeoid model was performed by numerical integration through the Fast Fourier Transform (FFT). The Molodensky gravity anomaly was determined in a 5’ grid and reduced and restored using the Residual Terrain Model (RTM) technique and the XGM2019e GGM truncated at degree and order 250 and 720. The geoid model was derived from the Bouguer gravity anomalies. The quasigeoid model validation has shown a Root Mean Square (RMS) difference of 18 cm compared with the Global Positioning System (GPS) measurements in the levelling network.
Highlights
From a physical point of view, the Earth is described by the geoid which is an equipotential surface of the gravity field, best approximated in nature by the mean sea level
Due to the mathematical and physical concepts involved, for compatibility purposes, it is recommended that the system of normal height uses a quasigeoid model
In this sense and considering the present scenario, in which MAPGEO2015 has a 30 cm of Root Mean Square (RMS) difference with the BVFR, a quasi geoid model is most suitable because it is closer to the normal heights system
Summary
From a physical point of view, the Earth is described by the geoid which is an equipotential surface of the gravity field, best approximated in nature by the mean sea level. Its resolution is related to the height concepts, which should be analyzed from the physical and geometric perspectives, considering the reference surface of altimetric measurements and interpreting its meaning as the reference surface of the gravity field (Blitzkow, Campos, and De Freitas 2004). Due to the mathematical and physical concepts involved, for compatibility purposes, it is recommended that the system of normal height uses a quasigeoid model In this sense and considering the present scenario, in which MAPGEO2015 has a 30 cm of RMS difference with the BVFR, a quasi geoid model is most suitable because it is closer to the normal heights system. This paper aimed to estimate the geoid and quasigeoid models for the São Paulo state using the normal height from the 2018 BVRF and the updated gravimetric data (Silva et al 2020). An analysis has been made comparing the normal heights which are given for the levelling network points
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