Abstract: The extensive use of GNSS positioning, combined with the importance of precise geoid heights for transformation between geodetic and orthometric heights, brings up the discussion of the influence of data uncertainties and the use of variable density values on these estimates. In this sense, we analyze the influence of the topographic masses density distribution and the data uncertainty on the computation of orthometric and geoid heights in stations of the High Precision Altimetric Network of Brazil, considering the Helmert and Mader methods. For this, we use 569 stations whose values of geodetic and normal heights, gravity, and geopotential numbers are known. The results indicate that orthometric heights are more sensitive to density values and to greater heights than to the Helmert and Mader methods applied. Also, we verify that the normal and orthometric heights present significant differences for the analyzed stations, considering the high correlation between the heights, which provide small values of uncertainty. However, our analyses show that the use of the Mader method, along with variable density values, provides either more rigorous or more reliable results.

Abstract: In 2018, the Brazilian Institute of Geography and Statistics (IBGE) defined the normal height values and geopotential numbers for the High Precision Altimetric Network (HPAN), creating the need for developing procedures able to adapt works correlated with the Brazilian Geodetic System (BGS). In that context, and considering the state and municipal altimetric networks, it is necessary to estimate normal heights. To this end, this paper proposes to estimate normal height values and geopotential numbers for the Altimetric Network of the Federal District (AN-DF). Computational procedures involving the Least Squares Method were established and applied in a geometric levelling survey, which includes 200 stations distributed throughout the study area. The obtained results allowed estimating the normal heights of the network stations with accuracy up to 0.032m. However, because significant differences were found in the adjusted and known values of some used HPAN stations, we recommend a rigorous analysis of these stations before using them. In any case considering that the geometric levelling and the applied procedures were carried out correctly, it is suggested that the values estimated for all stations of the AN-DF in this work may be used.

Resumo: Existem diversas técnicas de determinação das alturas geoidais, seja utilizando os dados gravimétricos terrestres, os modelos do geopotencial, as componentes astro-geodésicas ou pela combinação deles. Dentre as técnicas utilizadas, uma que vêm sendo amplamente aplicada para a determinação precisa da altura geoidal é a Remoção-Cálculo-Restauração (RCR), que considera as componentes de curto, médio e longo comprimentos de onda, derivados de dados de altitude através de um Modelo Digital do Terreno (MDT), de dados gravimétricos terrestres e de modelos do geopotencial global, respectivamente. Para a aplicação desta técnica, torna-se necessário, primeiramente, adotar procedimentos para o cálculo de anomalias de gravidade, para em seguida calcular o modelo geoidal, considerando a integração dos diferentes comprimentos de onda citados e a compatibilização do modelo ao datum vertical adotado. Este trabalho apresenta uma revisão dos procedimentos adotados para cálculo de modelos geoidais, com base na técnica RCR e no método de condensação de Helmert, e suas aplicações para o cálculo de um modelo geoidal local no Distrito Federal, Brasil. Como resultado, o modelo geoidal local calculado para a área de estudo apresentou-se consistente com os valores disponíveis de alturas geoidais obtidas da associação do nivelamento geométrico com posicionamento GNSS (Global Navigation Satellite System).

Abstract: There are several techniques for determining geoid heights using ground gravity data, the geopotential models, the astro-geodetic components or a combination of them. Among the techniques used, the Remove-Compute-Restore (RCR) technique has been widely applied for the accurate determination of the geoid heights. This technique takes into account short, medium and long wavelength components derived from the elevation data obtained from Digital Terrain Models (DTM), ground gravity data and global geopotential models, respectively. This technique can be applied after adopting the procedures to compute gravity anomalies and, then, the geoid model, considering the integration of different wavelengths mentioned, and their compatibility with the vertical datum adopted. Thus, this paper presents the procedures, involving the RCR technique, following Helmert's condensation method, and its application to compute one local geoid model for the Federal District, Brazil. As a result, the local geoid model computed for the studied area was consistent with the available values of geoid heights derived from geometrical levelling technique supported by GNSS positioning.