RESUMOGPS sobre a rede de nivelamento geométrico para comparar com o modelo geoidal obtido. As anomalias de altura adicionadas de um termo de correção dependente da topografia derivadas do EGM2008 (grau 2190 e ordem 2159), GO_CONS_GCF_2_DIR_R2 (grau e ordem 240), GOCO02S (grau e ordem 250), EIGEN 51C (grau e ordem 359) e EIGEN 6C (grau e ordem 1420), bem como as alturas geoidais derivadas do MAPGEO2004 (antigo modelo oficial do IBGE) também foram comparadas com os pontos GPS sobre nivelamento.

An evaluation of recent GOCE geopotential models in BrazilSeveral global geopotential models based on Gravity field and steady-state Ocean Circulation Explorer (GOCE) data have been published in the last two years. Some of these models use combinations of different satellite missions, while others use only GOCE data. This paper presents the evaluation and analysis of each approach using GOCE data in the Southeast of Brazil. Two assessments have been made. We compared the geoid heights derived from GOCE-based models with the geoidal heights from 176 GPS stations on leveling benchmarks. The findings show an improvement in GOCE-based models TIM_R3 (0.40 m) and DIR_R3 (0.39 m) for degree and order 210 in relation to EGM2008 (0.44 m) in terms of RMS. For the other models the results did not exceed 0.44 m. The second evaluation reports the comparison in terms of gravity disturbances between terrestrial gravity data and the models. The results, in terms of RMS and up to degree and order 210, indicate slightly low GOCO 02S values (10.34 mGal), TIM_R2 (10.37 mGal) and TIM_R3 (10.47 mGal) compared to EGM2008 (10.66 mGal). We also applied the residual terrain model and, as a result, the RMS errors were reduced by ~35% (~6.0 mGal) in the entire area and by ~45% in the mountain region.

No abstract

No abstract

No abstract

The purpose of this manuscript is to compute and to evaluate the geoid model in the State of São Paulo from two methodologies (Stokes' integral through the Fast Fourier Transform -FFT and Least Squares Collocation -LSC). Another objective of this study is to verify the potentiality of GOCE-based. A special attention is given to GOCE mission. The theory related to Stokes' integral and Least Squares Collocation is also discussed in this work. The spectral decomposition was employed in the geoid models computation and the long wavelength component was represented by EGM2008 up to degree and order 150 and 360 and GOCE-based models up to 150. The models were compared in terms of geoid height residual and absolute and relative comparisons from GPS/leveling and the results show consistency between them. In addition, a comparison in the mountain regions was carried out to verify the methodologies behavior in this area; the results showed that LSC is less consistent than FFT. Keywords: Geodesy; Geoid Model; GOCE Mission; Gravity. Outro objetivo deste estudo é verificar a potencialidade dos modelos baseados no satélite GOCE. Uma atenção especial é dada à missão GOCE. A teoria relacionada à integral de Stokes e a LSC também é discutida nesse trabalho. A decomposição espectral foi empregada no cálculo dos modelos geoidais e os longos comprimentos de onda foram representados pelo EGM2008 até grau e ordem 150 e 360 e pelos modelos do GOCE até 150.Os modelos foram comparados em termos de resíduo da altura geoidal e de comparações absolutas e relativas a partir de pontos GPS sobre nivelamento, sendo que os resultados mostram consistência entre si. O modelo geoidal no Estado de São Paulo tem uma consistência de 0,20 m em relação aos pontos GPS sobre nivelamento. Uma comparação na região montanhosa também foi realizada para verificar o comportamento das metodologias naquela região; os resultados mostraram que a LSC é menos consistente do que a FFT.

No 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.