Comparisons of geoid models over Alaska computed with different Stokes' kernel modifications

Li, X.; Wang, Y.

doi:10.2478/v10156-010-0016-1

Cited by 9 publications

(7 citation statements)

References 14 publications

(14 reference statements)

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“…The use of the unmodified [spherical] Stokes kernel (zero on the X-axis in Figure 9) gives worse results because it is not as powerful a filter as the modified kernels (cf. Vanicek and Featherstone 1998), and is consistent with results found in Australia (e.g., Featherstone et al 1998Featherstone et al , 2011Featherstone et al , 2017 and elsewhere (e.g., Li and Wang 2011). The preferred quasigeoid solution was computed with an integration cap of 2.5 degrees and a Wong and Gore (1969) modification degree of 160.…”

Section: Discussionsupporting

confidence: 79%

“…Moreover, quasigeoid solutions determined using modification degrees greater than 120 produced unreliable solutions, where the standard deviation of the quasigeoid/GPS-levelling differences varied drastically and were highly sensitive to the choice of integration cap. This is due to the instability of this kernel for high modification degrees, as noted in Featherstone (2003); also see Li and Wang (2011). We obtained more consistent results for the higher modification degrees using the Wong and Gore (1969) modified kernel.…”

Section: Discussionsupporting

confidence: 60%

See 1 more Smart Citation

The New Zealand gravimetric quasigeoid model 2017 that incorporates nationwide airborne gravimetry

McCubbine

Amos²,

Tontini

et al. 2017

J Geod

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A one arc-minute resolution gravimetric quasigeoid model has been computed for New Zealand, covering the region 25°S to 60°S and 160°E to 170°W. It was calculated by Wong-Gore modified Stokes integration using the removecompute-restore technique with the EIGEN-6C4 global gravity model as the reference field. The gridded gravity data used for the computation consisted of 40,677 land gravity observations, satellite-altimetry-derived marine gravity anomalies, historical shipborne marine gravity observations and, importantly, approximately one million new airborne gravity observations. The airborne data were collected with the specific intention of reinforcing the shortcomings of the existing data in areas of rough topography inaccessible to land gravimetry and in coastal areas where shipborne gravimetry cannot be collected and altimeter-derived gravity anomalies are generally poor. The new quasigeoid has a nominal precision of ±48 mm on comparison to GPS-levelling data, which is approximately 14 mm less than its predecessor NZGeoid09.

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Section: Discussionsupporting

confidence: 79%

Section: Discussionsupporting

confidence: 60%

The New Zealand gravimetric quasigeoid model 2017 that incorporates nationwide airborne gravimetry

McCubbine

Amos²,

Tontini

et al. 2017

J Geod

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show abstract

“…If the condition numbers are used, it can be shown that the matrix of normal equations for Molodensky coefficients is always well conditioned. More recently, Li and Wang (2011) determined that Alaskan geoid models computed from the spheroidal Molodensky modification coefficients were variable depending on the choices of ψ o and L. They, however, used the real rather than a synthetic field for their tests and such results should have been expected. Table 2 Condition numbers for the combinations tested in this paper Another, perhaps more plausible, explanation is the size of the integration domain ψ o in relation to the choice of L. Specifically, if a small ψ o is used, the NZ integration cannot sense lower frequencies that may have not been removed by the degree-L RF.…”

Section: The ψ O and L Invariance Enigmamentioning

confidence: 99%

Testing Stokes-Helmert geoid model computation on a synthetic gravity field: experiences and shortcomings

et al. 2013

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We report on testing the UNB (University of New Brunswick) software suite for accurate regional geoid model determination by use of Stokes-Helmert's method against an Australian synthetic field (ASF) as "ground truth". This testing has taken several years and has led to discoveries of several significant errors (larger than 5mm in the resulting geoid models) both in the UNB software as well as the ASF. It was our hope that, after correcting the errors in UNB software, we would be able to come up with some definite numbers as far as the achievable accuracy for a geoid model computed by the UNB software. Unfortunately, it turned out that the ASF contained errors, some of as yet unknown origin, that will have to be removed before that ultimate goal can be reached. Regardless, the testing has taught us some valuable lessons, which we describe in this paper. As matters stand now, it seems that given errorless gravity data on 1' by 1' grid, a digital elevation model of a reasonable accuracy and no topographical density variations, the Stokes-Helmert approach as realised in the UNB software suite is capable of delivering an accuracy of the geoid model of no constant bias, standard deviation of about 25 mm and a maximum range of about 200 mm. We note that the UNB software suite does not use any corrective measures, such as biases and tilts or surface fitting, so the resulting errors reflect only the errors in modelling the geoid.

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“…where ψ 0 is the spherical cap distance of the truncation radius, L is the degree of Molodensky modification (Molodensky et al 1962), which should be set smaller than n max , p is the degree of Wong and Gore modification (Wong and Gore, 1969), which is set equal to L in practice, t k is the kth Vanicek and Kleusberg modification coefficient (Vanićek and Kleusberg 1987), P k is the kth degree Legendre function. The application of Wong and Gore modification replaces the low-degree contributions from terrestrial gravity data with those from the GGM, whereas those of Molodensky modification and Vanićek and Kleusberg modification minimize the L 2 norm of the error kernel for the selected ψ 0 and L (Li and Wang, 2011). Therefore, unlike the Meissl kernel (namely L = 0), the FEO kernel not only reduces the truncation error but also optimally combines terrestrial gravity data with the GGM when the appropriate modification parameters (ψ 0 and L) are selected.…”

Section: Residual Cogeoid Heightmentioning

confidence: 99%

Refinement of a gravimetric geoid model for Japan using GOCE and an updated regional gravity field model

Matsuo

Kuroishi

2020

Earth Planets Space

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We developed a refined gravimetric geoid model for Japan on a 1 × 1.5 arc-minute (2 km) grid from a GOCE-based satellite-only global geopotential model and a regional gravity field model updated in this study. First, we have constructed a regional gravity field model for Japan using updated gravity datasets together with a residual terrain model: 323,431 land gravity data, 77,389 shipborne marine gravity data, and Sandwell's v28.1 altimetry-derived global marine gravity model. Then, the geoid was determined with the gravity field model. The methodology for gravimetric geoid determination was based on the remove-compute-restore technique with Helmert's second method of condensation of topography (Stokes-Helmert scheme). Here, the hybrid Meissl-Molodensky modified spheroidal Stokes kernel was employed to minimize the truncation error under an appropriate combination of different kinds of gravity data. In addition, a high-resolution GSI-DEM on a 0.4 × 0.4 arc-second (10 m) grid, together with the SRTM-DEM on a 7.5 × 11.25 arc-second (250 m) grid, was utilized for precisely applying terrain correction to the regional gravity field model. Consequently, we created a gravimetric geoid model for Japan, consistent with 971 GNSS/leveling geoid heights distributed over the four main islands of Japan with a standard deviation of 5.7 cm, showing a considerable improvement by 2.3 cm over the previous model (JGEOID2008). However, there remain some areas with large discrepancies between the computed and GNSS/leveling geoid heights in northern Japan (Hokkaido), mountainous areas in central Japan, and some coastal regions. Since terrestrial gravity data are especially sparse in these areas, we speculated that the largeness of the geoid discrepancies there could be partly attributed to the insufficient coverage and accuracy of gravity data. The Geospatial Information Authority of Japan has started airborne gravity surveys to be covered over the Japanese Islands, and in future, we plan to develop a geoid model for Japan further accurately by incorporating airborne gravity data to come.

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Comparisons of geoid models over Alaska computed with different Stokes' kernel modifications

Cited by 9 publications

References 14 publications

The New Zealand gravimetric quasigeoid model 2017 that incorporates nationwide airborne gravimetry

The New Zealand gravimetric quasigeoid model 2017 that incorporates nationwide airborne gravimetry

Testing Stokes-Helmert geoid model computation on a synthetic gravity field: experiences and shortcomings

Refinement of a gravimetric geoid model for Japan using GOCE and an updated regional gravity field model

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