A conventional value for the geoid reference potential $$W_{0}$$ W 0

Sánchez, Laura; Čunderlík, Róbert; Dayoub, Nadim; Mikula, Karol; Minarechová, Zuzana; Šíma, Z.; Vatrt, Viliam; Vojtíšková, Marie

doi:10.1007/s00190-016-0913-x

Cited by 69 publications

(72 citation statements)

References 59 publications

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“…Although the classical geodetic geoid definition and the IAG 2015 resolution both refer to the worldwide mean ocean surface, so far no adopted standards exist for the definition of MSL, the handling of time-dependent terms (e.g. due to global sea level rise), and the derivation of W 0 , where the latter value can be determined in principle from satellite altimetry and a global geopotential model (see Burša et al 1999or Sánchez et al 2016. Furthermore, the IHRS value for the reference potential is inconsistent with the corresponding value W 0 used for the definition of TT (see also Sect.…”

Section: Discussionmentioning

confidence: 99%

Geodetic methods to determine the relativistic redshift at the level of 10 $$^{-18}$$ - 18 in the context of international timescales: a review and practical results

Denker

Timmen

Voigt

et al. 2017

J Geod

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The frequency stability and uncertainty of the latest generation of optical atomic clocks is now approaching the one part in 10 18 level. Comparisons between earthbound clocks at rest must account for the relativistic redshift of the clock frequencies, which is proportional to the corresponding gravity (gravitational plus centrifugal) potential difference. For contributions to international timescales, the relativistic redshift correction must be computed with respect to a conventional zero potential value in order to be consistent with the definition of Terrestrial Time. To benefit fully from the uncertainty of the optical clocks, the gravity potential must be determined with an accuracy of about 0.1 m 2 s −2 , equivalent to about 0.01 m in height. This contribution focuses on the static part of the gravity field, assuming that temporal variations are accounted for separately by appropriate reductions. Two geodetic approaches are investigated for the derivation of gravity potential values: geometric levelling and the Global Navigation Satellite Systems (GNSS)/geoid approach. Geometric levelling gives potential differences with millimetre uncertainty over shorter distances (several kilometres), but is susceptible to systematic errors at the decimetre level over large distances. The GNSS/geoid approach gives absolute gravity potential values, but with an uncertainty corresponding to about 2 cm in height. For large distances, the GNSS/geoid approach should therefore be better than geometric levelling. This is demonstrated by the results from practical investigations related to three clock sites in Germany and one in France. The estimated uncertainty for the relativistic redshift correction at each site is about 2 × 10 −18 .

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Section: Discussionmentioning

confidence: 99%

Geodetic methods to determine the relativistic redshift at the level of 10 $$^{-18}$$ - 18 in the context of international timescales: a review and practical results

Denker

Timmen

Voigt

et al. 2017

J Geod

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“…with a constant W 0 = 6.263 685 34 × 10 7 m 2 s −2 , which complies with modern conventions [13,14]. The numerical value of W 0 is chosen in a way to have the geoid coincide best with the mean sea level at rest and a history of measurements and previous conventions, see Ref.…”

Section: A Newtonian Geoidmentioning

confidence: 99%

“…The numerical value of W 0 is chosen in a way to have the geoid coincide best with the mean sea level at rest and a history of measurements and previous conventions, see Ref. [14]. In contrast to usual geodetic formulations, we use a negative potential such that our convention in Eq.…”

Section: A Newtonian Geoidmentioning

confidence: 99%

Relativistic geoid: Gravity potential and relativistic effects

et al. 2020

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The Earth's geoid is one of the most important fundamental concepts to provide a gravity fieldrelated height reference in geodesy and associated sciences. To keep up with the ever-increasing experimental capabilities and to consistently interpret high-precision measurements without any doubt, a relativistic treatment of geodetic notions (including the geoid) within Einstein's theory of General Relativity is inevitable. Building on the theoretical construction of isochronometric surfaces and the so-called redshift potential for clock comparison, we define a relativistic gravity potential as a generalization of known (post-)Newtonian notions. This potential exists for any stationary configuration and rigidly co-rotating observers. It is the same as realized by local plumb lines. In a second step, we employ the gravity potential to define the relativistic geoid in direct analogy to the Newtonian understanding. In the respective limits, it allows to recover well-known (post-) Newtonian results. For a better illustration and proper interpretation of the general relativistic gravity potential and geoid, we consider some particular examples. Explicit results are derived for exact vacuum solutions to Einstein's field equation as well as a parametrized post-Newtonian model. Comparing the Earth's Newtonian geoid to its relativistic generalization is a very subtle problem. However, an isometric embedding into Euclidean three-dimensional space can solve it and allows a genuinely intrinsic comparison. With this method, the leading-order differences are determined, which are at the mm-level.

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“…In the ideal case, without irregularities of topographic densities, the two potentials are equal (W o = U o ). As a primary parameter for the definition of the reference (zero-height) surface with respect to Earth's body (which provides an absolute definition to the vertical datum of a height system), a global estimation of W o is required [64].…”

Section: Synthesis Of the Gravity Field Parameters Using Ggms Sphericmentioning

confidence: 99%

An Assessment of the GOCE High-Level Processing Facility (HPF) Released Global Geopotential Models with Regional Test Results in Turkey

2020

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The launch of dedicated satellite missions at the beginning of the 2000s led to significant improvement in the determination of Earth gravity field models. As a consequence of this progress, both the accuracies and the spatial resolutions of the global geopotential models increased. However, the spectral behaviors and the accuracies of the released models vary mainly depending on their computation strategies. These strategies are briefly explained in this article. Comprehensive quality assessment of the gravity field models by means of spectral and statistical analyses provides a comparison of the gravity field mapping accuracies of these models, as well as providing an understanding of their progress. The practical benefit of these assessments by means of choosing an optimal model with the highest accuracy and best resolution for a specific application is obvious for a broad range of geoscience applications, including geodesy and geophysics, that employ Earth gravity field parameters in their studies. From this perspective, this study aims to evaluate the GOCE High-Level Processing Facility geopotential models including recently published sixth releases using different validation methods recommended in the literature, and investigate their performances comparatively and in addition to some other models, such as GOCO05S, GOGRA04S and EGM2008. In addition to the validation statistics from various countries, the study specifically emphasizes the numerical test results in Turkey. It is concluded that the performance improves from the first generation RL01 models toward the final RL05 models, which were based on the entire mission data. This outcome was confirmed when the releases of different computation approaches were considered. The accuracies of the RL05 models were found to be similar to GOCO05S, GOGRA04S and even to RL06 versions but better than EGM2008, in their maximum expansion degrees. Regarding the results obtained from these tests using the GPS/leveling observations in Turkey, the contribution of the GOCE data to the models was significant, especially between the expansion degrees of 100 and 250. In the study, the tested geopotential models were also considered for detailed geoid modeling using the remove-compute-restore method. It was found that the best-fitting geopotential model with its optimal expansion degree (please see the definition of optimal degree in the article) improved the high-frequency regional geoid model accuracy by almost 15%.

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A conventional value for the geoid reference potential $$W_{0}$$ W 0

Cited by 69 publications

References 59 publications

Geodetic methods to determine the relativistic redshift at the level of 10 $$^{-18}$$ - 18 in the context of international timescales: a review and practical results

Geodetic methods to determine the relativistic redshift at the level of 10 $$^{-18}$$ - 18 in the context of international timescales: a review and practical results

Relativistic geoid: Gravity potential and relativistic effects

An Assessment of the GOCE High-Level Processing Facility (HPF) Released Global Geopotential Models with Regional Test Results in Turkey

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