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Effect of great lakes on gravity reduction and geoid determination caused by unclassified DTMs: case study for Lake Victoria, Africa

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Abstract

The determination of the gravimetric geoid is based on the magnitude of gravity observed at the topographic surface of the Earth. In order to satisfy Laplace’s equation, the masses between the surface of the Earth and the geoid must be removed or shifted inside the geoid. Then the gravity values have to be reduced to the geoid, forming the boundary values on the boundary surface. Gravity reduction techniques with unclassified height models usually presume that positive elevations are reserved for positive rock topography. Great lakes, however, are filled with water and may be situated partially or fully above sea level. In case of Lake Victoria, the whole lake including its bed floor is situated above sea level, i. e., having positive elevation (orthometric height). This leads to an obvious error in the topographic-isostatic reduction using, for example, the TC program (Forsberg in A study of terrain reductions, density anomalies and geophysical inversion methods in gravity, 1984; Forsberg and Tscherning in Sansò F, Rummel R (eds) Geodetic boundary value problems in view of the one centimeter geoid, Lecture notes in earth sciences. vol 65, pp 239–272, 1997. https://doi.org/10.1007/BFb0011707) by assuming rock topography filling the lake instead of water. The aim of this paper is to determine the effect of Lake Victoria on gravity reduction and geoid computation in Africa, as a prototype of the effect of great lakes on gravity reduction and geoid determination. The results prove that the masses of Lake Victoria have significant effect both on the reduced anomalies and on the computed geoid, which then have to be considered for precise geoid determination with correct density values.

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Data availability

There are no gravity data used for the current research. The used height models are directly generated from the ASTER-GDEM and DTM2006.0 models, which are freely available from earthexplorer.usgs.gov and earth-info.nga.mil, respectively.

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Acknowledgements

This project was supported financially by the Science and Technology Fund (STDF), Egypt, Grant No. 7944. The support by the International Association of Geodesy (IAG), the International Union of Geodesy and Geophysics (IUGG) and the DAAD (German Academic Exchange Service) is gratefully acknowledged. The authors would like to thank the editor of the current paper and three anonymous reviewers for their useful comments.

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HA proposed the idea. HA, KS, MA and BH developed the algorithms. HA and KS designed the software. HA, KS and MA performed the computations. HA, KS, MA and BH analyzed the results. HA and MA drafted the illustrations. HA and KS wrote the manuscript. BH corrected the manuscript.

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Correspondence to Hussein A. Abd-Elmotaal.

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Abd-Elmotaal, H.A., Seitz, K., Ashry, M. et al. Effect of great lakes on gravity reduction and geoid determination caused by unclassified DTMs: case study for Lake Victoria, Africa. J Geod 94, 97 (2020). https://doi.org/10.1007/s00190-020-01410-7

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