Error propagation for the Molodensky G1 term

McCubbine, Jack; Featherstone, Will; Brown, N. J.

doi:10.1007/s00190-018-1211-6

Cited by 6 publications

(5 citation statements)

References 34 publications

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“…Molodensky free air anomalies are 'reconstructed' on the topography by applying a reverse planar simple Bouguer correction with the height of each DEM element. Faye gravity anomalies are computed by adding the planar terrain correction from the same DEM as an approximation of the Molodensky G1 term, recently including error propagation (McCubbine et al 2017(McCubbine et al , 2019. These are then block-averaged (GMT routine blockmean) to determine surface-mean Faye gravity anomalies as approximations of Molodensky anomalies for subsequent quasigeoid computation.…”

Section: The Cut Approachmentioning

confidence: 99%

Empirical comparison between stochastic and deterministic modifiers over the French Auvergne geoid computation test-bed

et al. 2021

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Since 2006, several different groups have computed geoid and/or quasigeoid (quasi/geoid) models for the Auvergne test area in central France using various approaches. In this contribution, we compute and compare quasigeoid models for the Auvergne test area using Curtin University of Technology's and the Swedish Royal Institute of Technology's approaches. These approaches differ in many ways, such as their treatment of the input data, choice of type of spherical harmonic model (combined or satellite-only), form and sequence of correction terms applied, and different modified Stokes's kernels (deterministic or stochastic). We have also compared our new results with most of the previously reported studies over Auvergne in order to seek any improvements with respect to time [exceptions are when different subsets of data have been used]. All studies considered here have compared the computed quasi/geoid models with the same 75 GPS-levelling heights over Auvergne. The standard deviation for almost all of the computations (without any fitting) is of the order of 30-40 mm, so there is not yet any clear indication whether any approach is necessarily better than any other nor improving over time. We also recommend more universal standardisation on the presentation of quasi/geoid comparisons with GPS-levelling data so that results from different studies over the same areas can be compared more objectively.

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Section: The Cut Approachmentioning

confidence: 99%

Empirical comparison between stochastic and deterministic modifiers over the French Auvergne geoid computation test-bed

et al. 2021

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“…The height anomaly / quasigeoid is the solution to the Molodensky boundary value problem and the solution can be obtained by using Stokes's integral with the Molodensky gravity anomaly on the Earth's surface (Molodensky et al 1960Heiskanen and Moritz 1967). The gravitational effect of topography is expressed as an infinite power series of convolution integrals of the Molodensky free air anomalies and normal heights (McCubbine et al, 2019). For regional quasigeoid computations only the first term, 𝐺 1 (Eq.…”

Section: Planar Terrain Corrections Versus the Molodensky G Seriesmentioning

confidence: 99%

“…Standard deviations (m) of gravimetric quasigeoid models for parameter sweeps of FEO kernel modification degree and spherical integration cap radius versus GNSS-levelling data after removal of a tilted plane using the G1 term (solid lines) and the planar terrain corrections, both determined from 1'×1' grids. From McCubbine et al (2019) To investigate this issue, we further recomputed both the terrain corrections and 𝐺 1 terms using a block-averaged DEM and 1 arc minute grid (equivalent to the resolution of the AGQG2017 model) and produced another suite of quasigeoid models. While in this instance the Molodensky gravity anomaly with the 𝐺 1 terms gave the superior fit to the GDA2020 ellipsoidal heights minus AHD heights, using the 1 arc second planar terrain correction still gave the best result (Fig 2 .3.1).…”

Section: < Accepted Manuscript >mentioning

confidence: 99%

Australian quasigeoid modelling: Review, current status and future plans

McCubbine¹,

Featherstone²,

Brown³

2021

Terr. Atmos. Ocean. Sci.

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We review the history of quasi/geoid modelling in Australia, from the first model produced in 1967 to the most recent AGQG2017. b) The results of more than 10,000 trial quasigeoid solutions are presented, computed to assess whether methods used to produce AGQG2017 could be improved. c) Details of a new Australian vertical reference system, and future planned efforts to improve the underlying quasigeoid model are given.

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“…In order to further reduce geoid errors, it is favorable to set up a formal error budget, i.e., to investigate each contributing element to the observed discrepancies. Consequently, the estimation of reliable formal geoid errors has gained interest (e.g., Ågren and Sjöberg 2014;Farahani et al 2017;Featherstone et al 2018;Gerlach et al 2019;Goli et al 2019;McCubbine et al 2019;Slobbe et al 2019).…”

Section: Introductionmentioning

confidence: 99%

Error propagation in regional geoid computation using spherical splines, least-squares collocation, and Stokes’s formula

Ophaug

Gerlach

2020

J Geod

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Current International Association of Geodesy efforts within regional geoid determination include the comparison of different computation methods in the quest for the “1-cm geoid.” Internal (formal) and external (empirical) approaches to evaluate geoid errors exist, and ideally they should agree. Spherical radial base functions using the spline kernel (SK), least-squares collocation (LSC), and Stokes’s formula are three commonly used methods for regional geoid computation. The three methods have been shown to be theoretically equivalent, as well as to numerically agree on the millimeter level in a closed-loop environment using synthetic noise-free data (Ophaug and Gerlach in J Geod 91:1367–1382, 2017. 10.1007/s00190-017-1030-1). This companion paper extends the closed-loop method comparison using synthetic data, in that we investigate and compare the formal error propagation using the three methods. We use synthetic uncorrelated and correlated noise regimes, both on the 1-mGal ($$=10^{-5}~{\mathrm {m s}}^{-2}$$ = 10 - 5 m s - 2 ) level, applied to the input data. The estimated formal errors are validated by comparison with empirical errors, as determined from differences of the noisy geoid solutions to the noise-free solutions. We find that the error propagations of the methods are realistic in both uncorrelated and correlated noise regimes, albeit only when subjected to careful tuning, such as spectral band limitation and signal covariance adaptation. For the SKs, different implementations of the L-curve and generalized cross-validation methods did not provide an optimal regularization parameter. Although the obtained values led to a stabilized numerical system, this was not necessarily equivalent to obtaining the best solution. Using a regularization parameter governed by the agreement between formal and empirical error fields provided a solution of similar quality to the other methods. The errors in the uncorrelated regime are on the level of $$\sim $$ ∼ 5 mm and the method agreement within 1 mm, while the errors in the correlated regime are on the level of $$\sim $$ ∼ 10 mm, and the method agreement within 5 mm. Stokes’s formula generally gives the smallest error, closely followed by LSC and the SKs. To this effect, we note that error estimates from integration and estimation techniques must be interpreted differently, because the latter also take the signal characteristics into account. The high level of agreement gives us confidence in the applicability and comparability of formal errors resulting from the three methods. Finally, we present the error characteristics of geoid height differences derived from the three methods and discuss them qualitatively in relation to GNSS leveling. If applied to real data, this would permit identification of spatial scales for which height information is preferably derived by spirit leveling or GNSS leveling.

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Error propagation for the Molodensky G1 term

Cited by 6 publications

References 34 publications

Empirical comparison between stochastic and deterministic modifiers over the French Auvergne geoid computation test-bed

Empirical comparison between stochastic and deterministic modifiers over the French Auvergne geoid computation test-bed

Australian quasigeoid modelling: Review, current status and future plans

Error propagation in regional geoid computation using spherical splines, least-squares collocation, and Stokes’s formula

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