A precise gravimetric geoid model in a mountainous area with scarce gravity data: a case study in central Turkey

Abbak, Ramazan Alpay; Sjöberg, Lars E.; Ellmann, Artu; Ustun, Aydin

doi:10.1007/s11200-011-9001-0

Cited by 24 publications

(15 citation statements)

References 19 publications

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“…in Sweden (Nahavandchi, 1998), Zambia (Nsombo, 1998), Baltic countries (Ellmann, 2001(Ellmann, , 2004, Greece (Daras, 2008), Sudan (Abdalla, 2009;Abdalla and Fairhead, 2011), Kazakhstan (Inerbayeva, 2010), New Zealand (Abdalla and Tenzer, 2011). Moreover, this method shows excellent results in the mountainous areas as shown in the studies conducted over Ethiopia (Hunegnaw, 2001), Iran mountains (Kiamehr, 2006), over Mount Kilimanjaro in Tanzania (Ulotu, 2009) and over the area of Konya in central Turkey (Abbak et al, 2012).…”

Section: R a F T 1 Introductionmentioning

confidence: 83%

Implementation of a rigorous least-squares modification of Stokes’ formula to compute a gravimetric geoid model over Saudi Arabia (SAGEO13)

Abdalla

Mogren

2015

Can. J. Earth Sci.

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A gravimetric geoid model (SAGEO13) is computed for the Kingdom of Saudi Arabia using a rigorous stochastic computational method. The computational methodology is based on a combination of least-squares (LS) modification of Stokes’ formula and the additive corrections for topographic, ellipsoidal, atmospheric, and downward continuation effects on the geoid solution. In this study, we used terrestrial gravity data, a digital elevation model (SRTM3), and seven global geopotential models (GGMs) to compute a new geoid model for Saudi Arabia. The least-squares coefficients are derived based on the optimisation of the input modification parameters. The gravimetric solution and its additive corrections are computed based on the optimum LS coefficients. Compared to GPS-levelling data, SAGEO13 shows a fit of 18 cm (RMS) after using a 4-parameter fitting model.

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Section: R a F T 1 Introductionmentioning

confidence: 83%

Implementation of a rigorous least-squares modification of Stokes’ formula to compute a gravimetric geoid model over Saudi Arabia (SAGEO13)

Abdalla

Mogren

2015

Can. J. Earth Sci.

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“…Among the different approaches used in the determination of the gravimetric geoid either at regional or local scale, the best known method in the literatures is the Remove-Compute-Restore (R-C-R) approach as argued by [14]. Although there is no consensus as to the best approach because proponents of each method prefer theirs over the others [15], the R-C-R method is the method adopted for this study.…”

Section: Methodsmentioning

confidence: 99%

Modelling Orthometric Heights from a Combination of Ellipsoidal Heights and Gravimetric Geoid Model in Rivers State, Nigeria

Jackson¹,

Moka²

2020

IJG

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Many applications in geodesy, hydrography and engineering require geoid-related heights. Spirit leveling which is the traditional means of obtaining geoid-or mean sea level-related heights is slow, time-consuming and costly. Global Navigation Satellite Systems (GNSS) offer faster and relatively cheaper way of obtaining geoid-related heights when geoidal undulation is applied to ellipsoidal heights. However, difficulties involved in determining acceptable geoid height have seriously hampered the application of GNSS for leveling in Rivers State, thus necessitating the need to develop an acceptable geoid model which will serve as a means of conversion of GNSS-delivered ellipsoidal heights to their orthometric heights equivalent. In pursuance of this objective, a detailed gravimetric geoid has been evaluated for Rivers State, Nigeria. The computation of the geoid was carried out by the traditional remove-restore procedure. The Earth Geopotential Model 2008 (EGM08) was applied as the reference field for both the remove and restore parts of the procedures; spherical Fast Fourier Transform (FFT) was employed for the evaluation of the Molodenskii's integral formula for the height anomaly, (ζ) to yield the quasi-geoid; while the Residual Terrain Modelling (RTM) was done by prism integration. The classical gravimetric geoid over Rivers State was obtained from the rigorously evaluated quasi-geoid by adding the quasi-geoid to geoid (N − ζ) correction it. The minimum and maximum geoid height values are 18.599 m and 20.114 m respectively with standard deviation of 0.345 m across the study area. Comparison of the gravimetric geoidal heights with the GPS/Leveling-derived geoidal heights of 13 stations across Rivers State, Nigeria showed that the absolute agreement with respect to the How to cite this paper: JacksonGPS/leveling datum is generally better than 7 cm root mean squares (r.m.s) error. Results also showed that combining both GPS heights and the computed Rivers State geoid model can give orthometric heights accurate to 3 cm post-fit using a 4-parameter empirical model. The geoid model can thus serve as a good alternative to traditional leveling when used with GPS leveling, particularly for third order leveling in the study area.

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“…The KTH method has been used to compute the Swedish national quasigeoid (Ågren et al 2009b), the Nordic Geodetic Commission 2015 quasigeoid (Ågren et al 2016). The KTH approach has received much wider application than the CUT approach, with quasi/geoid models for the Baltic countries (Ellmann 2004), Iran (Kiamehr 2006), Tanzania (Ulotu 2009), Greece (Daras et al 2010), Kazakhstan (Inerbayeva 2010), Sudan (Abdalla and Fairhead 2011),New Zealand (Abdalla and Tenzer 2011), central Turkey (Abbak et al 2012), Moldova (Danila 2012), Saudia Arabia (Abdalla and Mogren 2015), Uganda (Ssengendo 2015), Poland (Kuczynska-Siehien et al 2016), peninsular Malaysia (Pa'suya et al 2019, Estonia (Ellmann et al 2019) and Jilin province in China (Wu et al 2020).…”

Section: The Kth 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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A precise gravimetric geoid model in a mountainous area with scarce gravity data: a case study in central Turkey

Cited by 24 publications

References 19 publications

Implementation of a rigorous least-squares modification of Stokes’ formula to compute a gravimetric geoid model over Saudi Arabia (SAGEO13)

Implementation of a rigorous least-squares modification of Stokes’ formula to compute a gravimetric geoid model over Saudi Arabia (SAGEO13)

Modelling Orthometric Heights from a Combination of Ellipsoidal Heights and Gravimetric Geoid Model in Rivers State, Nigeria

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

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