STUDY OF CORRECTIONS TO OBTAIN THE RIGOROUS ORTHOMETRIC HEIGHT

Autores

¹Albarici, F.L.; ²Foroughi, I.; ³Santos, M.C.; ⁴Guimarães, G.N.; ⁵Trabanco, J.L.A.; ⁶Kingdon, R.; ⁷Vanícěk, P.

¹IFSULDEMINAS Email: fabio.albarici@ifsuldeminas.edu.br
²UNIVERSITY OF NEW BRUNSWICK Email: i.foroughi@unb.ca
³UNIVERSITY OF NEW BRUNSWICK Email: msantos@unb.ca
⁴UNIVERSIDADE FEDERAL DE UBERLÂNDIA Email: gabriel@ufu.br
⁵FEC/UNICAMP Email: trabanco@fec.unicamp.br
⁶UNIVERSITY OF NEW BRUNSWICK Email: robert.kingdon@unb.ca
⁷UNIVERSITY OF NEW BRUNSWICK Email: vanicek@unb.ca

Resumo

The height systems in South American countries are not consistent, some are based on normal height and some on orthometric height. Due to these problems, the countries in South America have been trying to homogenize their height datum. The height system in Brazil is defined as normal-orthometric height. According to IBGE, (2011) only the non-parallelism corrections of equipotential surfaces were applied to GNSS/leveling network of Brazil. The objective of this research is to calculate the Helmert orthometric heights of the GNSS/Leveling points covering the city of Campinas/SP, and then convert them to rigorous orthometric heights. The geopotential numbers were calculated for all points along with Helmert orthometric and normal Heights were obtained. For converting Helmert to rigorous orthometric heights, the corrections are: (1) Second-order correction for normal gravity; (2) Second-order correction for the Bouguer shell; (3) The geoid-generated gravity disturbance; (4) The terrain/roughness-generated gravity; (5) The lateral variation of topographical mass–density (Santos et al, 2006). The results show that terms 1 and 2 have a small magnitude and in practice their results can be neglected, where statistically their minimum, maximum, mean and standard deviation are respectively: -0.0120 mm; -0.0050 mm; 0.0070 mm; 0.00167 m and -0.0110 mm; -0.0040 mm; -0.0069 mm; 0.0016 mm. The 3th corrective term has the highest correction values and these values have a great correlation with the terrain. The highest values is the correction are at the highest altitudes, having minimum and maximum values of -1.245 mm and 2.622 mm, mean -0.0069 mm and deviation standard of 0.0016 mm. The 4th term usually corresponds to the second major correction, but in this case specifically, the area is limited and does not have a large variation in the terrain, with the minimum and maximum values being -0.0097 m; 0.0008 m, with mean and standard deviation at -0.0016 m and 0.0020 m, respectively. And finally the term 5 which is the third largest correction with a minimum of -0.0128 m, maximum of 0.0027 m, average of -0.0057 m and standard deviation 0.0042 m. By the numerical analysis performed in points distributed around the city of Campinas/SP, it can be concluded that the largest and smallest corrections applied to the Helmert’s heights were 1.52 and 0.23 centimeters. These corrections were calculated individually where corrections (1) and (2) have no contribution because they are very small, but corrections (3), (4) and (5) have the greatest contribution in obtaining the rigorous orthometric height.

Keywords

Orthometric height; GNSS/levelling; Geopotential Numbers

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