Sub-centimetre geoid

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F19%3A43952650" target="_blank" >RIV/49777513:23520/19:43952650 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00190-018-1208-1" target="_blank" >https://link.springer.com/article/10.1007/s00190-018-1208-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00190-018-1208-1" target="_blank" >10.1007/s00190-018-1208-1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Sub-centimetre geoid

Popis výsledku v původním jazyce

When a generation ago, Martinec and Vaníček revived and improved the classical Stokes-Helmert technique for computing the geoid, “the geoid was dead!” according to some and the quasigeoid reigned supreme. When they stated that it would be possible to compute the geoid with an “error of the order of one centimetre”, the statement was not universally accepted, basically for two reasons: the effect of the topographic mass density on observed gravity could not be evaluated to a high enough accuracy and “the downward continuation of gravity anomalies should never be invoked as a solution method without adding an adjective like ‘regularized’ ”. Now, 25 years later, we are at the end of the road: we have shown on an example of the area of Auvergne, France, where there is an excellent gravity coverage, both accurate and dense, as well as all the supporting data, that the geoid couldan be indeed evaluated to a sub-centimetre accuracy. That does not mean that the geoid can be provided to this accuracy everywhere in the world, though. The accuracy of the geoid deteriorates over areas with higher topographical heights and with the gravity data coverage and accuracy worse than those of Auvergne. To achieve the sub-centimetre accuracy of the geoid, we had to advance modelling the effect of the topographic mass density, discover a solid spherical Bouguer anomaly, develop the probabilistic downward continuation approach, incorporate improved satellite determined global gravitational models, and to introduce a whole host of smaller improvements. Having taken the standard deviation of the observed gravity values to be 0.5 mGal, according to Institute Geographique Nationale (Duquenne, 2007), we obtained the standard deviation of the gravity anomalies continued downward to the geoid to be in average 3-times larger than those of the surface anomalies with large spikes underneath the highest topographic points. The standard deviations of resulting geoidal heights range from a few millimetres to just over 6 cm for the highest topographic points in the Alps (just short of 2000 m). The mean standard deviations of the geoidal heights for the whole region is only 0.6 cm, which should be considered quite reasonable even if one acknowledges that Auvergne is mostly flat. As one should expect, the main contributory factors to these uncertainties are the Poisson probabilistic downward continuation process, with the maximum standard deviation of just short of 6 cm (an average of 2.5 mm) and the topographical density uncertainties, with the maximum of 5.6 cm (the average value of 3.0 mm). The comparison of our geoidal height with the testing geoidal heights, obtained for the set of the 75 control points (regularly spaced throughout the region), show a mean shift of 13 cm which is believed to reflect the displacement of the French vertical datum from the geoid due to Sea Surface Topography. The mean root square error of the misfit is 3.3 cm. This misfit, together with the estimated accuracy of our geoid, indicate that the mean standard deviation of the “test geoid” is about 3 cm, which makes it about 5 times less accurate than the Stokes-Helmert computed geoid. Thus, it does not seem to make sense, at least in regions well covered by relatively accurate gravimetric data, to use the GNSS/lLevelling-implied geoid to “test” the accuracy of (Stokes-Helmert’s) geoid computed from terrestrial gravity data. Such a test is still valid for checking the physical validity of the Stokes-Helmert technique, though.

Název v anglickém jazyce

Sub-centimetre geoid

Popis výsledku anglicky

When a generation ago, Martinec and Vaníček revived and improved the classical Stokes-Helmert technique for computing the geoid, “the geoid was dead!” according to some and the quasigeoid reigned supreme. When they stated that it would be possible to compute the geoid with an “error of the order of one centimetre”, the statement was not universally accepted, basically for two reasons: the effect of the topographic mass density on observed gravity could not be evaluated to a high enough accuracy and “the downward continuation of gravity anomalies should never be invoked as a solution method without adding an adjective like ‘regularized’ ”. Now, 25 years later, we are at the end of the road: we have shown on an example of the area of Auvergne, France, where there is an excellent gravity coverage, both accurate and dense, as well as all the supporting data, that the geoid couldan be indeed evaluated to a sub-centimetre accuracy. That does not mean that the geoid can be provided to this accuracy everywhere in the world, though. The accuracy of the geoid deteriorates over areas with higher topographical heights and with the gravity data coverage and accuracy worse than those of Auvergne. To achieve the sub-centimetre accuracy of the geoid, we had to advance modelling the effect of the topographic mass density, discover a solid spherical Bouguer anomaly, develop the probabilistic downward continuation approach, incorporate improved satellite determined global gravitational models, and to introduce a whole host of smaller improvements. Having taken the standard deviation of the observed gravity values to be 0.5 mGal, according to Institute Geographique Nationale (Duquenne, 2007), we obtained the standard deviation of the gravity anomalies continued downward to the geoid to be in average 3-times larger than those of the surface anomalies with large spikes underneath the highest topographic points. The standard deviations of resulting geoidal heights range from a few millimetres to just over 6 cm for the highest topographic points in the Alps (just short of 2000 m). The mean standard deviations of the geoidal heights for the whole region is only 0.6 cm, which should be considered quite reasonable even if one acknowledges that Auvergne is mostly flat. As one should expect, the main contributory factors to these uncertainties are the Poisson probabilistic downward continuation process, with the maximum standard deviation of just short of 6 cm (an average of 2.5 mm) and the topographical density uncertainties, with the maximum of 5.6 cm (the average value of 3.0 mm). The comparison of our geoidal height with the testing geoidal heights, obtained for the set of the 75 control points (regularly spaced throughout the region), show a mean shift of 13 cm which is believed to reflect the displacement of the French vertical datum from the geoid due to Sea Surface Topography. The mean root square error of the misfit is 3.3 cm. This misfit, together with the estimated accuracy of our geoid, indicate that the mean standard deviation of the “test geoid” is about 3 cm, which makes it about 5 times less accurate than the Stokes-Helmert computed geoid. Thus, it does not seem to make sense, at least in regions well covered by relatively accurate gravimetric data, to use the GNSS/lLevelling-implied geoid to “test” the accuracy of (Stokes-Helmert’s) geoid computed from terrestrial gravity data. Such a test is still valid for checking the physical validity of the Stokes-Helmert technique, though.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10508 - Physical geography

Projekt

<a href="/cs/project/GA18-06943S" target="_blank" >GA18-06943S: Teorie zpracování gradientů geopotenciálu vyšších řádů a jejich použití v geodézii</a><br>

Návaznosti

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

Rok uplatnění

2019

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

—

Svazek periodika

93

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

20

Strana od-do

849-868

Kód UT WoS článku

000467249800005

EID výsledku v databázi Scopus

2-s2.0-85056487956