Local quasigeoid modelling in Slovakia using the finite volume method on the discretized Earth's topography

  • Róbert ČUNDERLÍK Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovak Republic
  • Matej MEDĽA Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovak Republic
  • Karol MIKULA Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovak Republic
Keywords: local quasigeoid modelling, fixed gravimetric boundary-value problem, finite volume method, unstructured computational mesh, GNSS-levelling test

Abstract

The paper presents local quasigeoid modelling in Slovakia using the finite volume method (FVM). FVM is used to solve numerically the fixed gravimetric boundary value problem (FGBVP) on a 3D unstructured mesh created above the real Earth's surface. Terrestrial gravimetric measurements as input data represent the oblique derivative boundary conditions on the Earth's topography. To handle such oblique derivative problem, its tangential components are considered as surface advection terms regularized by a surface diffusion. The FVM numerical solution is fixed to the GOCE-based satellite-only geopotential model on the upper boundary at the altitude of 230 km. The horizontal resolution of the 3D computational domain is 0.002 × 0.002 deg and its discretization in the radial direction is changing with altitude. The created unstructured 3D mesh of finite volumes consists of 454,577,577 unknowns. The FVM numerical solution of FGBVP on such a detailed mesh leads to large-scale parallel computations requiring 245 GB of internal memory. It results in the disturbing potential obtained in the whole 3D computational domain. Its values on the discretized Earth's surface are transformed into the local quasigeoid model that is tested at 404 GNSS/levelling benchmarks. The standard deviation of residuals is 2.8 cm and decreases to 2.6 cm after removing 9 identified outliers. It indicates high accuracy of the obtained FVM-based local quasigeoid model in Slovakia.

Author Biographies

Róbert ČUNDERLÍK, Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovak Republic

Department of Mathematics and Descriptive Geometry
Radlinského 11, 813 68 Bratislava, Slovak Republic

Matej MEDĽA, Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovak Republic

Department of Mathematics and Descriptive Geometry
Radlinského 11, 813 68 Bratislava, Slovak Republic

Karol MIKULA, Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovak Republic

Department of Mathematics and Descriptive Geometry
Radlinského 11, 813 68 Bratislava, Slovak Republic

Published
2020-09-22
How to Cite
ČUNDERLÍK, R., MEDĽA, M., & MIKULA, K. (2020). Local quasigeoid modelling in Slovakia using the finite volume method on the discretized Earth’s topography. Contributions to Geophysics and Geodesy, 50(3), 287-302. https://doi.org/10.31577/congeo.2020.50.3.1
Section
original research papers