Sub-centimetre geoid

Foroughi, Ismael; Vaníček, Petr; Kingdon, Robert; Goli, Mehdi; Sheng, Michael; Afrasteh, Yosra; Novák, Pavel; Santos, Marcelo C.

doi:10.1007/s00190-018-1208-1

Cited by 33 publications

(15 citation statements)

References 22 publications

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“…For example, Janák et al (2017) demonstrated than when the approach is correctly applied the computed geoid is of the same or perhaps better accuracy than the results of other techniques. Furthermore, Foroughi et al (2017) provide an assessment on the optimal combination of satellite data and terrestrial data and most recently they showed new advances on the algorithm for downward continuation using Least Squares and showed the likelihood of obtaining a sub-centimetric geoid (Foroughi et al, 2019). All these findings and developments assure a very precise geoid determination using the Stokes-Helmert approach.…”

Section: Literature Reviewmentioning

confidence: 92%

“…The fundamental theory behind the Stokes-Helmert approach of performing the Stokes integration in the Helmert space was introduced by Vaníček and Kleusberg (1987). Since this time, the approach is being perfected through a series of improvement to provide a very accurate determination of a gravimetric geoid (Foroughi et al, 2019;Kingdon and Vaníček, 2011;Tenzer et al, 2003a;Tenzer et al, 2003b). Modern testing of the approach had been done in the last years.…”

Section: Literature Reviewmentioning

confidence: 99%

“…All these findings and developments assure a very precise geoid determination using the Stokes-Helmert approach. In the current work, the improvements carried out by Foroughi et al (2019) were not included because of the time period of this project.…”

Section: Literature Reviewmentioning

confidence: 99%

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A regional Stokes-Helmert geoid determination for Costa Rica (GCR-RSH-2020): computation and evaluation

Garbanzo-León

Fernández

Sánchez

et al. 2020

Contrib. Geophys. Geod.

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GNSS observations are a common solution for outdoor positioning around the world for coarse and precise applications. However, GNSS produces geodetic heights, which are not physically meaningful, limiting their functionality in many engineering applications. In Costa Rica, there is no regional model of the geoid, so geodetic heights (h) cannot be converted to physically meaningful orthometric heights (H). This paper describes the computation of a geoid model using the Stokes-Helmert approach developed by the University of New Brunswick. We combined available land, marine and satellite gravity data to accurately represent Earth's high frequency gravity field over Costa Rica. We chose the GOCO05s satellite-only global geopotential model as a reference field for our computation. With this combination of input data, we computed the 2020 Regional Stokes-Helmert Costa Rican Geoid (GCR-RSH-2020). To validate this model, we compared it with 4 global combined geopotential models (GCGM): EGM2008, Eigen6C-4, GECO and SGG-UM-1 finding an average difference of 5 cm. GECO and SGG-UM-1 are more similar to the GCR-RSH-2020 based on the statistics of the difference between models and the shape of the histogram of differences. The computed geoid also showed a shift of 7 cm when compared to the old Costa Rican height system but presented a slightly better fit with that system than the other models when looking at the residuals. In conclusion, GCR-RSH-2020 presents a consistent behaviour with the global models and the Costa Rican height systems. Also, the lowest variance suggests a more accurate determination when the bias is removed.

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Section: Literature Reviewmentioning

confidence: 92%

Section: Literature Reviewmentioning

confidence: 99%

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A regional Stokes-Helmert geoid determination for Costa Rica (GCR-RSH-2020): computation and evaluation

Garbanzo-León

Fernández

Sánchez

et al. 2020

Contrib. Geophys. Geod.

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“…1a), majorly located in Colorado, USA. It is a mountainous area, with an average elevation of 2017 m. The highest location reaches 4386 m, the lowest 932 m. The eastern part of the study area is more flat than the western and the central part, while it is still higher than 1000 m. The larger the topographic heights are, the worse the accuracy of the geoid becomes (Foroughi et al 2019). Thus, this is a challenging study area, due to the rugged terrain, high elevation, and varying gravity field.…”

Section: Study Area and Datamentioning

confidence: 99%

Regional gravity field refinement for (quasi-) geoid determination based on spherical radial basis functions in Colorado

Liu¹,

Schmidt²,

Sánchez³

et al. 2020

J Geod

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This study presents a solution of the ‘1 cm Geoid Experiment’ (Colorado Experiment) using spherical radial basis functions (SRBFs). As the only group using SRBFs among the fourteen participated institutions from all over the world, we highlight the methodology of SRBFs in this paper. Detailed explanations are given regarding the settings of the four most important factors that influence the performance of SRBFs in gravity field modeling, namely (1) the choosing bandwidth, (2) the locations of the SRBFs, (3) the type of the SRBFs as well as (4) the extensions of the data zone for reducing the edge effect. Two types of basis functions covering the same spectral range are used for the terrestrial and the airborne measurements, respectively. The non-smoothing Shannon function is applied to the terrestrial data to avoid the loss of spectral information. The cubic polynomial (CuP) function which has smoothing features is applied to the airborne data as a low-pass filter for filtering the high-frequency noise. Although the idea of combining different SRBFs for different observations was proven in theory to be possible, it is applied to real data for the first time, in this study. The RMS error of our height anomaly result along the GSVS17 benchmarks w.r.t the validation data (which is the mean results of the other contributions in the ‘Colorado Experiment’) drops by 5% when combining the Shannon function for the terrestrial data and the CuP function for the airborne data, compared to those obtained by using the Shannon function for both the two data sets. This improvement indicates the validity and benefits of using different SRBFs for different observation types. Global gravity model (GGM), topographic model, the terrestrial gravity data, as well as the airborne gravity data are combined, and the contribution of each data set to the final solution is discussed. By adding the terrestrial data to the GGM and the topographic model, the RMS error of the height anomaly result w.r.t the validation data drops from 4 to 1.8 cm, and it is further reduced to 1 cm by including the airborne data. Comparisons with the mean results of all the contributions show that our height anomaly and geoid height solutions at the GSVS17 benchmarks have an RMS error of 1.0 cm and 1.3 cm, respectively; and our height anomaly results give an RMS value of 1.6 cm in the whole study area, which are all the smallest among the participants.

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“…It was concluded that 3.5 km data spacing with an accuracy of 1.5 mGal is needed to achieve a 5 mm quasi-geoid model over the Netherlands. Foroughi et al (2019) tested the possibility of achieving sub-centimetre accuracy in gravimetric geoid computation using the Stokes-Helmert's by spherical approximations of the UNB (University of New Brunswick) approach. As a means of testing the accuracy of the proposed method, the uncertainties in the computed geoid were computed with respect to uncertainties in the downward continuation vis-à-vis the near zone (NZ) contribution, far zone (FZ) contribution, reference spheroid and transformation of the co-geoid back to the real space.…”

Section: Introductionmentioning

confidence: 99%

Gravity data requirements for decimetre accuracy regional geoid using Stokes' Remove Compute Restore technique in Nigeria

Odumosu

Nnam

2020

Contrib. Geophys. Geod.

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The need for dense and accurate gravity data cannot be overemphasised in the development of a precise gravimetric geoid model. Unfortunately, the field observations required are costly, and labour-intensive hence the need to ascertain via numerical simulations the appropriate field specifications before embarking on them. This paper presents an experimental study on the gravimetric data specifications (spatial resolution and data accuracy) required for achieving decimetre-level accuracy geoid using the conventional Stokes' Remove Compute Restore (RCR) method in Nigeria. A two-step solution approach was used in this study. The steps were determination of the (i) effect of data spacing by a comparative assessment of computation results obtained by using gravity data at four user determined intervals and (ii) effect of observation accuracy by numerical simulation using error propagation analysis. The data intervals (3′×3′, 5′×5′, 10′×10′ and 20′×20′) were selected from a combination of 1815 terrestrial FA anomaly points merged with EGM2008 derived FA anomaly covering the study area. Also, observational errors investigated were 0 mGal, 0.1 mGal, 0.5 mGal, 1 mGal and 5 mGal. The study was conducted in Nigeria having a total land area of approximately 923,768 km2. The study established that gravimetric geoid accuracy improves substantially as the spatial resolution and accuracy of the gravity data improves. Also, the study identified that data spacing contributes more to the overall geoid error than data accuracy. In addition, the study observed that hilly regions should have denser data spacing than plain areas. Within the test region, a data spacing of 3′×3′ with gravity observational errors 5 mGal was found to produce an acceptable gravimetric geoid. The produced gravimetric geoid had a pre-fit Root Mean Square Error (RMSE) of 15.6 cm when compared with GNSS-Levelling data at 27 stations located evenly across the study area.

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Sub-centimetre geoid

Cited by 33 publications

References 22 publications

A regional Stokes-Helmert geoid determination for Costa Rica (GCR-RSH-2020): computation and evaluation

A regional Stokes-Helmert geoid determination for Costa Rica (GCR-RSH-2020): computation and evaluation

Regional gravity field refinement for (quasi-) geoid determination based on spherical radial basis functions in Colorado

Gravity data requirements for decimetre accuracy regional geoid using Stokes' Remove Compute Restore technique in Nigeria

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