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

The physical heights definition of heights, proposed by Helmert in 1890 is one of the commonly used heights systems in practice. In Helmert’s definition, the mean value of gravity along plumbline is computed by simplifying the topography with a Bouguer shell containing masses with mean density value. Although this approximation might be accurate enough many purposes, a more rigorous definition can be determined by considering the effects of terrain, topographic mass density variation, and masses contained in the geoid the mean gravity value along the plumbline. The purpose of this paper is to compute the corrections for the Helmert’s definition of the orthometric heights to obtain the rigorous orthometric heights in the state of São Paulo and adjacent states and to evaluate these corrections. The heights system used in Brazil (until July 2018) and some South American countries is normal-orthometric heights, therefore the corrections needs to be applied accordingly. Our numerical results show that there are significant differences between the normal-orthometric and rigorous orthometric heights, with maximum values of ~ 0.4 m, minimum of ~ -0.8 m and mean value of ~ -0.32 m. There are larger differences between normal-orthometric and normal height than the ones between normal and rigorous definition of orthometric heights.