Consistent determination of the gravimetric geoid and orthometric height

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F25%3A43975325" target="_blank" >RIV/49777513:23520/25:43975325 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00190-025-01959-1" target="_blank" >https://link.springer.com/article/10.1007/s00190-025-01959-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00190-025-01959-1" target="_blank" >10.1007/s00190-025-01959-1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Consistent determination of the gravimetric geoid and orthometric height

Popis výsledku v původním jazyce

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 centimeters) are reported for accurately determined regional gravimetric geoid models, errors in Helmert’s orthometric height reach several centimeters and decimeters already at levelling networks realized in lowlands and regions with moderately elevated topography. In mountainous regions with extremely elevated topography, these errors reach several meters. 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 heights 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 also 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.

Název v anglickém jazyce

Consistent determination of the gravimetric geoid and orthometric height

Popis výsledku anglicky

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 centimeters) are reported for accurately determined regional gravimetric geoid models, errors in Helmert’s orthometric height reach several centimeters and decimeters already at levelling networks realized in lowlands and regions with moderately elevated topography. In mountainous regions with extremely elevated topography, these errors reach several meters. 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 heights 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 also 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10508 - Physical geography

Projekt

<a href="/cs/project/GA23-07031S" target="_blank" >GA23-07031S: Elipsoidické modelování planetárních gravitačních polí</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

JOURNAL OF GEODESY

ISSN

0949-7714

e-ISSN

1432-1394

Svazek periodika

99

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

33

Strana od-do

nestránkováno

Kód UT WoS článku

001534296400003

EID výsledku v databázi Scopus

2-s2.0-105011359919