Quasigeoid Model Research Articles

Application of GNSS-levelling for updating the base vertical network

Abstract This study explores the potential of GNSS-levelling to complement geometric levelling in the state levelling network, particularly outside the main lines. The Polish state levelling network plans to reduce the number of points from 40,000 to 16,000 during upcoming updates. GNSS-levelling is considered a cost-effective solution for filling gaps in the network, especially in rural areas. The experiment, commissioned by the Polish Head Office of Geodesy and Cartography, applied Polish geometric levelling accuracy criteria and tested them against GNSS-levelling. The goal was to develop a technique that an average surveying company could apply. The results showed that the initial hypothesis of GNSS-levelling’s suitability was not fully supported, primarily due to inconsistent vector repeatability. Accuracy could be improved by increasing the number of observation sessions or using specialized GNSS software while still maintaining cost-effectiveness. The experiment was conducted in an area where the state quasi-geoid model fits the levelling network with an accuracy of ±1 cm. Furthermore, the single vector solution (SVS) outperformed the each-to-each vector strategy (NET) in aligning with this network. Although challenges remain, GNSS-levelling demonstrates the potential and after refinement of techniques requirements, it is possible to obtain the main goal.

Enhancing Regional Quasi-Geoid Refinement Precision: An Analytical Approach Employing ADS80 Tri-Linear Array Stereoscopic Imagery and GNSS Gravity-Potential Leveling

This research investigates precision enhancement in regional quasi-geoid refinement through ADS80 tri-linear array scanning stereoscopic imagery for aerial triangulation coupled with GNSS gravity-potential modeling. By acquiring stereoscopic imagery and analyzing triangulation accuracy using an ADS80 camera, we performed this study over the Qinghai–Tibet Plateau’s elevated, desolate terrain, collecting 593 GNSS points following high-precision stereoscopic imagery modeling. By utilizing 12 gravity satellite models, we computed geoid heights and China’s 1985 Yellow Sea elevations for 28 benchmarks and GNSS points, thereby refining the Qinghai Province Quasi-Geoid Model (QPQM) using geometric techniques. The findings reveal that POS-assisted ADS80 stereoscopic imagery yields high-precision triangulation with maximal horizontal and elevation accuracies of 0.083/0.116 cm and 0.053/0.09 cm, respectively, across five control point arrangements. The RMSE of normal heights for 1985, processed via these GNSS points, achieved decimeter precision. By applying error corrections from benchmarks to the 1985 elevation data from gravity satellites and performing weighted averaging, the precision of EGM2008, SGG-UGM-2, and SGG-UGM-1 models improved to 8.61 cm, 9.09 cm, and 9.38 cm, respectively, surpassing the QPQM by 9.22 cm to 9.99 cm. This research demonstrates that the proposed methods can significantly enhance the precision of regional quasi-geoid surfaces. Additionally, these methods offer a novel approach for rapidly establishing regional quasi-geoid models in the uninhabited areas of the Qinghai–Tibet Plateau.

A conversion of the geoid to the quasigeoid at the Hong Kong territories

A levelling network was readjusted and a new geoid model compiled within the framework of geodetic vertical datum modernization at the Hong Kong territories. To accomplish all project objectives, the quasigeoid model has to be determined too. A quasigeoid model can be obtained from existing geoid model by applying the geoid-to-quasigeoid separation. The geoid-to-quasigeoid separation was traditionally computed as a function of the simple planar Bouguer gravity anomaly, while disregarding terrain geometry, topographic density variations, and vertical gravity changes due to mass density heterogeneities below the geoid surface. We applied this approximate method because orthometric heights of levelling benchmarks in Hong Kong were determined only approximately according to Helmert’s theory of orthometric heights. Considering a further improvement of the accuracy of orthometric heights by applying advanced numerical procedures, we determined the geoid-to-quasigeoid separation by applying an accurate method. The comparison of the accurately and approximately computed values of the geoid-to-quasigeoid separation revealed significant differences between them. The approximate values are all negative and reach -2.8 cm, whereas values from the accurate method vary between -4.1 and + 0.2 cm. In addition, we assessed the effect of anomalous topographic density on the geoid-to-quasigeoid separation by employing a newly developed digital rock density model. According to our estimates the effect of anomalous topographic density reaches a maximum value of 1.6 cm, reflecting a predominant presence of light volcanic rocks and sedimentary deposits at the Hong Kong territories. Our numerical findings indicate that the conversion between geoid and quasigeoid models should be done accurately, even in regions with a moderately elevated topography.

A Direct Approach for Local Quasi-Geoid Modeling Based on Spherical Radial Basis Functions Using a Noisy Satellite-Only Global Gravity Field Model

A Direct Approach for Local Quasi-Geoid Modeling Based on Spherical Radial Basis Functions Using a Noisy Satellite-Only Global Gravity Field Model

A data-adaptive network design for the regional gravity field modelling using spherical radial basis functions

A high-precision regional gravity field model is significant in various geodesy applications. In the field of modelling regional gravity fields, the spherical radial basis functions (SRBFs) approach has recently gained widespread attention, while the modelling precision is primarily influenced by the base function network. In this study, we propose a method for constructing a data-adaptive network of SRBFs using a modified Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) algorithm, and the performance of the algorithm is verified by the observed gravity data in the Auvergne area. Furthermore, the turning point method is used to optimize the bandwidth of the basis function spectrum, which satisfies the demand for both high-precision gravity field and quasi-geoid modelling simultaneously. Numerical experimental results indicate that our algorithm has an accuracy of about 1.58 mGal in constructing the gravity field model and about 0.03 m in the regional quasi-geoid model. Compared to the existing methods, the number of SRBFs used for modelling has been reduced by 15.8%, and the time cost to determine the centre positions of SRBFs has been saved by 12.5%. Hence, the modified HDBSCAN algorithm presented here is a suitable design method for constructing the SRBF data adaptive network.

Results of creating an altitude-base using a local quasi-geoid model in the Republic of Lebanon

Results of creating an altitude-base using a local quasi-geoid model in the Republic of Lebanon

Potential of cold-atom airborne gravimetry to improve coastal gravity field and quasigeoid modelling

We investigate using the GIRAFE cold-atom gravimeter during an airborne gravity survey for improving gravity field and quasigeoid modelling. The study is conducted over the Bay of Biscay, France. Geoid/quasigeoid determination is usually a major challenge over such coastal areas due to scarce and inconsistent gravity data. In a first step, the GIRAFE dataset is analysed and compared with available surface gravity data as well as with global altimetry models from UCSD and DTU. The comparisons indicate that the DTU model is better than the UCSD model within around 10 km from the coastline. Furthermore, recent satellite altimeter missions significantly improve the altimetry models in coastal areas. A significant bias (− 4.00 mGal) in shipborne data is also found from this comparison. In a second step, eight quasigeoid solutions are calculated to evaluate the contribution of GIRAFE data. This contribution reaches 3 cm in terms of height anomaly for DTU21 while being much larger for UCSDv31 and shipborne data. Finally, the quasigeoid solutions are validated using GNSS-levelling data. The results indicate that using GIRAFE data improves by approximately 50% the quality of quasigeoid models over land near the coast. The highest accuracy, around 1 cm, is achieved when GIRAFE data are merged with refined gravity data. Importantly, the standard deviation is just 1.2 cm when compared with GNSS-levelling points if using only GIRAFE data over marine areas, which is very close to the 1 cm goal of geoid/quasigeoid model determination in modern geodesy. This study thus confirms the benefits of performing airborne gravity survey using quantum sensors.

Прогнозування потенційних похибок аномалій висот глобальних моделей геоїда для різних систем припливів

The article presents the method of predicting the errors of height anomalies obtained from high-order global geoid models (EGM_2008, EIGEN_6C4, GECO, XGM2019e2159, SGG_UGM_2) and taking into account different tide systems (free/zero/mean-tide). A correct understanding of how much the choice of the global model height tide system affects the accuracy of calculating the normal heights of the Earth’s physical surface is an important component for obtaining reliable results. The purpose of the work is to predict the potential errors of height anomalies for three main concepts of tidal corrections (tidal systems) used in the creation of global geoid models. Method. The essence of the prediction method is to find a connection between the height anomalies of the global geoid models and the PL-quasi-geoid2021 regional quasi-geoid model. On the basis of the established connection, the prediction of potential errors of height anomalies was made, taking into account the choice of one or another system of tides. The prediction of the errors of height anomalies is implemented on the basis of 200 GNSS stations located on the territory of Ukraine and in the border sector. To find the connection between the heights of the global geoid models and the PL-quasi-geoid2021 regional model, a territory was allocated in the western border sector measuring 48°-52° in latitude and 21°-25° in longitude. For 36 GNSS stations located in the border area, a scale coefficient between global and regional height anomalies was found. Results. In the border sector, the factual errors of height anomalies are estimated at the level of 0.01-0.03 m based on the standard deviation and at the level of the mean square deviation of 0.17–0.18 m, 0.15-0.16 m, and 0.08–0.09 m for the free, zero and mean-tide systems, respectively. The standard deviations of the predicted potential errors for the border sector were 0.02-0.03 m, and the mean square values were 0.17–0.18 m, 0.13 m and 0.06 m for similar tidal systems. The residual errors of height anomalies for the border sector amounted to 0.03 m according to the standard and mean square deviation. Assessment of accuracy prediction of potential errors of height anomalies of models EGM_2008, EIGEN_6C4, GECO, XGM2019e2159, SGG_UGM_2 carried out on the basis of 200 GNSS stations was 0.03 m by standard deviation and 0.15 m (free-tide), 0.13 m (zero-tide) and 0.06 m (mean-tide) by mean square value. Scientific novelty. First implemented was the prediction of potential errors of height anomalies of global geoid models, which was performed by the scale factor for GNSS stations located on the territory of Ukraine and taking into account different tidal systems. Practical significance. The predicted errors of height anomalies make it possible to calculate the normal heights of GNSS stations and points on the Earth’s physical surface with an accuracy of about 3 cm. The obtained results allow the use of height anomalies of global geoid models of high order for more accurate geodetics work.

25 років Яворівському НГП – структура, використання, значення досліджень, перспективи

This paper presents detailed information about the stages of creation and directions of use of a special multifunctional standard scientific geodetic polygon (SGP) in Yavoriv district of Lviv region. The main purpose of the SGP is the metrological control of modern geodetic instruments and the testing of new technologies. The features of constructing geodetic networks, creating a local reference gravimetric network to refine the parameters of the global Earth gravimetric model, and constructing a quasi-geoid model with centimeter accuracy within the local polygon are described. The determination of high-precision astronomical coordinates and reference azimuths with an accuracy of 0.5–1.0, the creation of metrological objects of the NGP are outlined: the standard linear baseline (SLB) of original design and the fundamental geodetic network (FGN) for conducting special research and metrological verification of electronic theodolites, rangefinders, GNSS receivers, the development of a high-precision leveling network for studying accuracy and GNSS-leveling, etc. It provides information about multi-year experimental calibrations of the SLB using various methods and devices, and the first international intercomparisons on the SLB (working standard) in Ukraine, as well as multi-day GNSS observation campaigns at FGN points, the results of processing, and the achieved high accuracy. New experimental studies are related to improving the accuracy of FGN and GNSS leveling, new calibrations of SLB, including international intercomparisons, establishment of fundamental gravimetric points, optimization of the use of reference directions for metrological control and calibration of navigation equipment.

Methodology of Applying Inverse Distance Weighting Interpolation Method in Determining Normal Heights

This article explores the application of the Inverse Distance Weighting (IDW) interpolation method in determining normal heights, utilizing a network of points with measured ellipsoidal and normal heights by the use of GNSS/levelling method. The IDW method, which assumes that points closer to each other are more alike, is employed to locate points within the correct quadrant and calculate their normal height based on the determined average height anomaly across the entire area. The accuracy of this method is validated using check points. The article further discusses the methodology of normal height determination at a country level by using generated coefficients, representing the average difference between various height-systems, which could be used as an integral to the interpolation methods used for generating a refined Digital Elevation Model (DEM) across the country. This study contributes to the ongoing discourse on the effective use of interpolation methods in geospatial analysis and DEM generation. It provides valuable insights into the practical application of the IDW method and its potential for enhancing the accuracy of normal height determination and DEM refinement. Importantly, such methods hold significant value for countries lacking gravimetric data, as they provide a viable means of determining normal heights in the absence of a local quasi geoid model.

High-resolution regional gravity field modeling in data-challenging regions for the realization of geopotential-based height systems

Modern height systems are based on the combination of satellite positioning and gravity field models of high resolution. However, in many regions, especially developing or newly industrializing countries, there is no (reliable) regional gravity model at all, due to challenges such as limited data availability, unknown/low data quality, and missing metadata. This paper addresses this issue in a case study of Colombia, where eight decades of historical terrestrial and airborne gravity measurements are available but widely contain systematic errors, outliers, and biases. Correspondingly, processing strategies and structures are proposed and applied to validate and improve the quality of old gravity datasets. A novel method is developed based on spherical radial basis functions (SRBFs) for estimating biases, which are found in different airborne surveys with values exceeding 40 mGal. The validity of this bias estimation method is demonstrated both by a simulation test and by the evaluation of the airborne data in comparison to the SATOP (SAtellite-TOPography) model, which merges the satellite-only global gravity model GOCO06s with the Earth2014 topography model. The terrestrial and airborne data are then combined with a global gravity model (GGM), ultra-high-resolution topography models, as well as altimetry-derived gravity anomalies from DTU21GRA for the offshore areas. The results are presented in terms of height anomalies (QGeoidCOL2023), and they are thoroughly validated using GPS/leveling data both in the absolute and relative manner. The standard deviation in comparison to the GPS/leveling data after applying a correction surface to account for the datum inconsistencies amounts to 15.76 cm, which is 27% smaller compared to the mean standard deviation value given by five recent high-resolution GGMs, and 36% smaller than the one delivered by the latest South American quasi-geoid model QGEOID2021. The relative validation results show that QGeoidCOL2023 performs better, i.e., delivers lower RMS errors than the GGMs and QGEOID2021 in all the baseline length groups. These results indicate the validity and benefits of the developed methods and procedures, which can be used for other data-challenging areas to facilitate the realization of geopotential-based height systems.Graphical

Результаты астрономического нивелирования на Московской аттракции с использованием астроизмерителя

In this paper, the quasi-geoid elevations along the profile of the Moscow attraction are calculated based on the astronomical leveling method – according to the components of the deflection of vertical, which were measured using the zenith camera of the FSUE "VNIIF-TRI". The length of the profile is approximately 93 km. The error in the final excess of the quasi-geoid for the attraction profile, obtained from the mentioned measurements, was about 13 mm. The results are compared with a digital model of quasi-geoid heights, which has a relative error of ~4 cm in the Moscow region. Juxtaposition of the quasi-geoid elevations gave an average difference of –1,8 cm and its standard deviation of 1,9 cm. The dependence of the quasi-geoid final excess for the attraction profile on the points’ number used (lengths of segments) and the measurement area anomaly were studied. For the Moscow attraction, which is a medium-anomalous region, it was found out that the optimal distance between surveyed points should not exceed 13 km. The method of astronomical leveling using a zenith camera can be used for metrological support and independent control of quasigeoid models obtained through other methods, for example, gravimetric ones

Validation of a tailored gravity field model for precise quasigeoid modelling over selected sites in Cameroon and South Africa

Abstract In this study, a tailored gravity-field model is developed to fit and recover local terrestrial gravity data by integrating gravity from global gravity-field models, residual gravity derived from topographic data and observed terrestrial gravity over two study sites in Africa (Cameroon and South Africa). During the modelling phase, two-thirds of the terrestrial gravity data is utilised, reserving the remaining one-third for validation purposes. Additionally, an independent validation is conducted by comparing computed quasigeoid models (derived from tailored gravity data) with height anomalies from GPS/levelling data over the two study sites. The accuracy of the tailored gravity model in reproducing observed gravity data is noteworthy, with a ±8.9 mGal accuracy for the study site in South Africa at 2867 test points and a ±10.4 mGal accuracy for the study site in Cameroon at 637 test points. Comparing height anomalies from GPS/levelling with the SATGQG quasigeoid model (developed from tailored gravity data) and the recent CDSM09A quasigeoid model at 11 GPS/levelling data points reveals comparable accuracies of ±0.10 m and ±0.05 m, for SATGQG and CDSM09A, respectively for the site in South Africa. For the Cameroon site, the differences between height anomalies from GPS/levelling and the CTGQG quasigeoid model (developed from tailored gravity data), along with the recent CGM20 quasigeoid model at 38 GPS/levelling data points, show practically equal accuracies of ±0.15 m for CTGQG and ±0.11 m for CGM20. These findings underscore the potential of tailored gravity-field model in developing accurate quasigeoid models, particularly in regions with limited gravity data coverage. This approach holds promise for gravity recovery and precise geoid modelling in developing countries and regions with insufficient coverage of terrestrial gravity data.

RETRACTED: The creation of quasigeoid model by local method in the territory of the Republic of Armenia

See the retraction notice BIO Web of Conferences 116, 00001 (2024), https://doi.org/10.1051/bioconf/202411600001

High-Accuracy Quasi-Geoid Determination Using Molodensky’s Series Solutions and Integrated Gravity/GNSS/Leveling Data

This study presents a methodology for constructing a quasi-geoid model with millimeter-level accuracy over the Shangyu area in China, following the guidelines of the International Association of Geodesy Joint Working Group 2.2.2, known as “The 1 cm geoid experiment”. Our approach combines two steps to ensure exceptional accuracy. First, we employ Molodensky’s theory to model the gravity field, accounting for non-level surfaces and considering complex terrain effects. Through an exhaustive analysis of these influential factors, we implement a comprehensive suite of applicable formulae within Molodensky’s series solution, enabling a thorough assessment of their impacts on height anomalies within the gravimetric quasi-geoid model. Second, we utilize a hybrid method that involves a multi-surface function using the least-squares method and a robust estimation technique. This approach enables the interpolation of quasi-geoid heights by incorporating ellipsoidal and leveling normal heights, as well as gravimetric quasi-geoid data. Through a numerical example, we demonstrate the efficiency of our solution concept, achieving an accuracy of 0.79 cm compared to independent global navigation satellite system (GNSS)/leveling measurements. By developing this methodology, our study contributes to the advancement of geodesy research and provides a valuable methodology for creating highly precise quasi-geoid models in geodetic applications.

A first step towards a national realisation of the international height reference system in Sweden with a comparison to RH 2000

Abstract The International Height Reference System (IHRS) was defined by the International Association of Geodesy in 2015. Since then, the international geodetic community has been working on the specification and establishment of its realisation, the International Height Reference Frame (IHRF). This frame will primarily be realised by geopotential numbers (or physical heights) in a sparse global reference network. In Sweden, only one such global station is planned. Regional and national realisations (or densifications) computed in accordance with the IHRS definition are needed to enable the best possible unification of height datums. The main purpose of this article is to make a case study for Sweden regarding the national realisation of IHRS and to investigate in what way preliminary IHRF differs from the current Swedish levelling-based realisation of the European Vertical Reference System, RH 2000. The two different quasigeoid models that we consider best over Sweden at the present time are used to compute the preliminary IHRS realisations in the study. The realisations are compared to each other and to RH 2000. It is shown that a very significant part of the difference to RH 2000 is due to the different postglacial land uplift epochs, permanent tide concepts, and zero levels. The standard deviation for the difference between one of the preliminary national IHRS realisations and RH 2000 is reduced from 75.5 to 19.2 mm after correction of the postglacial land uplift and permanent tide effects. The corresponding mean differences are –208.5 and –454.7 mm, respectively. The magnitude of the mean difference thus increases when the corrections in question are applied.

PL-geoid2021: A quasigeoid model for Poland developed using geophysical gravity data inversion technique

This paper presents the results of research and analyses related to the development of a new quasigeoid model fitted to GNSS/levelling data for the area of Poland (PL-geoid2021). The model was determined employing two procedures based on the Geophysical Gravity data Inversion technique (GGI method): procedure A consisted of the determination of the gravimetric quasigeoid model in the first step and its subsequent fitting to GNSS/levelling data in the second step, and procedure B consisted of a one-step determination of the model fitted to GNSS/levelling data. Both models were developed using the global geopotential model SGG-UGM-2 and gravity data covering the area of Poland, and slightly extend beyond Poland's southern and northern borders. The average model was adopted as the final model. It was demonstrated that the accuracy of the gravimetric quasigeoid model had a very low dependence on the reference topographic mass density model used. On the basis of this model, the GNSS/levelling datasets were also assessed and outliers were identified. The estimated accuracy of the gravimetric model, determined based on four GNSS/levelling datasets, was in the range of ± 1.2 to ± 1.7 cm, in terms of the standard deviation of the differences between the measured and model-determined height anomalies. Due to partial lack of gravity data just beyond the Polish border, the edge effect was also analysed. The accuracy of the final quasigeoid model (estimated in the same way as the gravimetric model) ranges from ± 1.0 to ± 1.2 cm. It should be noted, however, that this assessment is not fully independent because three of the four sets of GNSS/levelling points used for it, were also used to build the final model.

Variance–covariance analysis of two high-resolution regional least-squares quasi-geoid models

This paper investigates the full variance–covariance (VC) matrix of two high-resolution regional quasi-geoid models, utilizing a spherical radial basis function parameterization. Model parameters were estimated using weighted least-squares techniques and variance component estimation (VCE) for data weighting. The first model, known as the “RCR model,” is computed through the remove–compute–restore method, incorporating various local gravity and radar altimeter datasets. The second model, the “combined model,” includes the GOCO05s satellite-only global geopotential model as an additional dataset with a full-noise VC matrix. Validation of the noise VC matrix scaling for each quasi-geoid model is achieved by comparing observed and formal noise standard deviations of differences between geometric and gravimetric height anomalies at GPS height markers in the Netherlands. Analysis of the noise VC matrix of height anomalies at grid nodes reveals significantly smaller formal noise standard deviations for the RCR model compared to the combined model. This difference is attributed to VCE assigning larger weights to the GOCO05s dataset, which exhibits greater noise standard deviations for the specific spatial scales used. Additionally, the formal noise standard deviations of height anomaly differences, relevant for GNSS-heighting, favor the RCR model. However, the disparity between the two models is smaller than implied by the height anomaly noise standard deviations. This is due to the combined model’s noise autocorrelation function displaying a longer correlation length (67 km) in contrast to the RCR model’s (17 km). Consequently, the combined model exhibits a greater reduction in noise variance for height anomaly differences relative to white noise compared to the RCR model.

Experiences with the RTM Method in Local Quasi-Geoid Modeling

In local quasi-geoid modeling, the residual terrain modeling (RTM) method is often used to remove short-wavelength gravity field signals from the measured gravity on the ground in order to obtain a regularized and smooth gravity field that is suited for field interpolation and modeling. Accurate computation of RTM corrections plays a crucial role in computing an accurate local quasi-geoid, and it requires a set of fine-tuned parameters, including the combination of DEMs with different resolutions for suitably representing the real topography, the choice of integration radius for properly defining the extent of the computation zone, and the determination of reference topography to properly describe the RTM-reduced Earth’s surface. To our knowledge, this has not been systematically documented, despite its obvious importance. This study aims to systematically investigate the impact of these factors on RTM correction computation and, consequently, on local quasi-geoid modeling to provide practical guidelines for real-world applications. The tesseroid-based gravity forward modeling technique is employed to investigate the following issues existing in the practical use of the RTM method: ① Can the combination of a high-resolution DEM and a DEM with a lower resolution replace the single use of the high-resolution DEM for RTM correction computation while maintaining accuracy and improving efficiency? If it does, how do I properly choose the resolution of this coarse DEM as well as the integration radius r1 for the inner zone and r2 for the outer zone? ② How large would the differences between the RTM corrections computed by three types of reference topographies, which are obtained from the direct averaging (DA) approach, the moving averaging (MA) approach, and the spherical harmonic (SH) approach, be, and how large would their impact on quasi-geoid modeling be? To obtain objective findings, two research regions were selected for this investigation. One is the Colorado test area (USA) with rugged terrain, and the other is the Auvergne test area (France) with moderate terrain. The main numerical findings are: (1) the combination of the 3” resolution DEM (inner zone) and the 30″ resolution DEM (outer zone) is sufficient for accurate and efficient RTM correction computation; (2) if the resolution of the reference topography is 5′ or slightly lower, all three types of reference topographies are able to obtain local quasi-geoid models at a similar accuracy level, while the values of r1 and r2 are preferred to be at least 20 km and 111 km, respectively; (3) if the reference topography has a resolution of 30′ or lower, the MA or SH reference topography is recommended, especially for the latter one, and the values of r1 and r2 are suggested to be at least 20 km and 222 km, respectively. The above numerical findings can be taken as a reference for local quasi-geoid determination in areas with different topographic regimes than the two selected test areas.

Performance evaluation of high/ultra-high-degree global geopotential models over Vietnam using GNSS/leveling data

The availability of many high-degree Global Geopotential Models (GGMs), namely EGM2008, EIGEN-6C4, GECO, SGG-UGM-1, SGG-UGM-2, XGM2019e_2159, and GGMPlus, challenges users regarding which model is best for Vietnam. This study, therefore, evaluates their performance by comparing them with GNSS/leveling data over Vietnam. Results show that their absolute and relative performances are largely independent of topographic conditions and geographical location and can be ranked into three classes: (1) XGM2019e_2159 has the highest accuracy, (2) the models EIGEN-6C4, GECO, SGG-UGM-1, SGG-UGM-2, and GGMPlus, have a very similar level of medium accuracy, while (3) EGM2008 is found to be the least accurate. In an absolute sense, the differences between GNSS/leveling and EGM2008-based height anomalies have a standard deviation (STD) of 0.290 ± 0.010 m, whereas, for XGM2019e_2159, this is 0.156 ± 0.006 m. All other models have STDs of (0.18–0.19) ± 0.007 m. Regarding relative performance without fitting, all GGMs have comparable accuracies for baseline length of 5–20 km, while for baselines longer than 20 km, the STD of XGM2019e_2159 is 1.5 ppm–0.5 ppm (approximately 19%–40%) lower compared with EGM2008, and 0.5 ppm–0.25 ppm (approximately 7%–36%) lower compared with EIGEN6C4, GECO, SGG-UGM-1, SGG-UGM-2, and GGMPlus. In addition, the STDs decrease significantly from 20 to 12 ppm in the range of 5–10 km, slightly from 12 to 6 ppm for 10–35 km, very slightly from 6 to 2.5 ppm for 35–200 km, and then remain almost unchanged for longer baselines. After fitting, the relative accuracies of all GGMs are at the same level with negligible STD/RMSE values. Furthermore, only EGM2008 experiences significant regional differences, while other GGMs show more homogeneous spatial variation of absolute accuracy over Vietnam. These findings can contribute to the development of local quasigeoid models in Vietnam and may be helpful with the improvement of GGMs in the future.