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<p>Various computational methods have been developed and applied to determine regional gravimetric geoid models with high accuracy using surface gravity and terrain data, while also often taking into consideration topographic mass density information. Helmert’s orthometric height is, on the other hand, until now solely used for practical realization of vertical geodetic controls in countries where the orthometric height is adopted for the definition of official height systems. Whereas small errors (at the level of a few centimetres) are reported for accurately determined regional gravimetric geoid models, errors in Helmert’s orthometric height reach several centimetres and decimetres already at levelling networks realized in lowlands and regions with moderately elevated topography. In mountainous regions with extremely elevated topography, these errors reach several metres. In Helmert’s definition of the orthometric height, the mean value of gravity within topographic masses is computed approximately from observed surface gravity by applying the Poincaré–Prey gravity gradient reduction, without applying complex computational methods that are used in the gravimetric geoid modelling. This approximation introduces errors due to assuming a constant topographic mass density and disregarding terrain geometry and mass density heterogeneities inside the geoid. Consequently, values of Helmert’s orthometric height are not consistent with accurately determined regional gravimetric geoid models and should not be fitted or combined with GNSS/levelling data. To address this theoretical inconsistency, we propose a computational scheme based on applying developed methods for consistent determination of the regional gravimetric geoid and orthometric height to achieve their full compatibility by means of improving the accuracy of the orthometric height. We demonstrate that computational methods applied in the regional gravimetric geoid modelling can be modified to determine also the accurate orthometric height, so that both quantities are computed consistently and simultaneously. We also show that the proposed computational scheme can be used for an accurate conversion of normal to orthometric heights by means of applying the geoid-to-quasigeoid separation. This allows an independent validation of regional gravimetric geoid models.</p>

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Consistent determination of the gravimetric geoid and orthometric height

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月23日

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  • Robert Tenzer,
  • Pavel Novák

摘要

Various computational methods have been developed and applied to determine regional gravimetric geoid models with high accuracy using surface gravity and terrain data, while also often taking into consideration topographic mass density information. Helmert’s orthometric height is, on the other hand, until now solely used for practical realization of vertical geodetic controls in countries where the orthometric height is adopted for the definition of official height systems. Whereas small errors (at the level of a few centimetres) are reported for accurately determined regional gravimetric geoid models, errors in Helmert’s orthometric height reach several centimetres and decimetres already at levelling networks realized in lowlands and regions with moderately elevated topography. In mountainous regions with extremely elevated topography, these errors reach several metres. In Helmert’s definition of the orthometric height, the mean value of gravity within topographic masses is computed approximately from observed surface gravity by applying the Poincaré–Prey gravity gradient reduction, without applying complex computational methods that are used in the gravimetric geoid modelling. This approximation introduces errors due to assuming a constant topographic mass density and disregarding terrain geometry and mass density heterogeneities inside the geoid. Consequently, values of Helmert’s orthometric height are not consistent with accurately determined regional gravimetric geoid models and should not be fitted or combined with GNSS/levelling data. To address this theoretical inconsistency, we propose a computational scheme based on applying developed methods for consistent determination of the regional gravimetric geoid and orthometric height to achieve their full compatibility by means of improving the accuracy of the orthometric height. We demonstrate that computational methods applied in the regional gravimetric geoid modelling can be modified to determine also the accurate orthometric height, so that both quantities are computed consistently and simultaneously. We also show that the proposed computational scheme can be used for an accurate conversion of normal to orthometric heights by means of applying the geoid-to-quasigeoid separation. This allows an independent validation of regional gravimetric geoid models.