Search Results (40)

Lago Argentino and Lago Viedma are large lakes fed by glaciers in Southern Patagonia, characterized by extraordinarily strong, persistent westerly winds and sharp gradients in regional relief, climate, and gravity field. We present operational models of spatio-temporal lake-level variations that represent instantaneous ellipsoidal lake-surface height as the superposition of three components: (i) a time-averaged lake-level topography derived from geoid modeling and ICESat-2 residuals, (ii) temporally varying water-volume changes in the lake estimated from tide gauge time series corrected for atmospherically driven perturbations, and (iii) a static hydrodynamic response to wind stress and air-pressure forcing. The atmospheric response is parametrized through empirically derived transfer functions obtained by regressing instantaneous lake-level anomalies against ERA5 wind and pressure fields, capturing wind-driven tilting. Standard deviations of ICESat-2 ATL13 elevations amount to 106 cm and 70 cm over Lago Argentino and Lago Viedma, respectively. The subtraction of our models reduces these standard deviations to 8 cm (Argentino) and 14 cm (Viedma). Surface waves incompletely averaged out within ICESat-2’s narrow footprint are identified as a principal source for the residual variability. A standard deviation of ATL13 elevations below 2 cm on calm days demonstrates ICESat-2’s unprecedented capability of monitoring water resources from space in a region of sparse hydrological infrastructure. Full article

This paper presents a methodological framework for integrating UAV-based photogrammetry and GIS technologies to generate a high-accuracy digital elevation model (DEM) for urban land-use planning. The study was conducted in an urbanized area characterized by heterogeneous topography, mixed vegetation cover, and fragmented land use, which complicate high-resolution terrain modeling. UAV surveys were performed using multiple photogrammetric blocks with centimeter-level ground sample distance and a dense ground control network supported by geoid-based height corrections. The resulting DEM was independently validated using control points derived from large-scale topographic data. The achieved vertical accuracy (RMSE ≈ 0.25 m) confirms the applicability of UAV-derived DEMs for large-scale mapping (1:1000–1:2000) and urban spatial analysis. Unlike studies focused on runoff simulation, this work emphasizes the accuracy-controlled generation and validation of DEMs as a primary spatial dataset for urban planning applications. The results demonstrate that DEM accuracy depends strongly on flight planning, ground control distribution, and hybrid automatic–manual point cloud refinement. Full article

Global Gravitational Models (GGMs) describe the Earth’s external gravitational field by a set of spherical harmonic (Stokes) coefficients. These coefficients are routinely used to compute the geoid model, while disregarding the upper continental crustal (i.e., topographic) masses above the geoid. Strictly speaking, however, these coefficients can describe only gravity field quantities at (or above) the Earth’s surface to satisfy Laplace’s equation. Consequently, the GGM coefficients cannot be used to define the geoid surface rigorously without accounting for the internal convergence domain and the gravitational effect of topographic masses. In most technical and scientific applications, the computation of the geoid model directly from the GGM coefficients has been accepted under the assumption that errors due to disregarding the internal convergence domain (inside the topographic masses) are typically less than a few centimeters (i.e., at the level of global geoid model uncertainties). In this study, we demonstrate that these errors reach several decimeters and even meters, with maxima in Tibet and Himalayas exceeding ~4 m. Moreover, relatively large errors, reaching decimeters, are already detected in regions with a moderately elevated topography. In scientific applications requiring a high accuracy, such errors cannot be ignored. Instead, GGM coefficients describing the Earth’s external gravitational field have to be corrected for the effect of (topographic) masses distributed above the geoid surface to obtain spherical harmonic coefficients that explicitly define the geoid globally. The explicit definition of the global geoid model in the spectral domain is derived in this study and used to compile spherical harmonic coefficients of the geoid up to degree/order 2160 from the EIGEN-6C4 global gravitational model. Full article

This study presents the digitization and integration of Kazakhstan’s legacy gravimetric maps at a scale of 1:200,000 into a modern geospatial database using ArcGIS. The primary objective was to convert analog gravity data into a structured, queryable, and spatially analyzable digital format to support contemporary geoscientific applications, including geoid modeling and regional geophysical analysis. The project addresses critical gaps in national gravity coverage, particularly in underrepresented regions such as the Caspian Sea basin and the northeastern frontier, thereby enhancing the accessibility and utility of gravity data for multidisciplinary research. The methodology involved a systematic workflow: assessment and selection of gravimetric maps, raster image enhancement, georeferencing, and digitization of observation points and anomaly values. Elevation data and terrain corrections were incorporated where available, and metadata fields were populated with information on the methods and accuracy of elevation determination. Gravity anomalies were recalculated, including Bouguer anomalies (with densities of 2.67 g/cm³ and 2.30 g/cm³), normal gravity, and free-air anomalies. A unified ArcGIS geodatabase was developed, containing spatial and attribute data for all digitized surveys. The final deliverables include a 1:1,000,000-scale gravimetric map of free-air gravity anomalies for the entire territory of Kazakhstan, a comprehensive technical report, and supporting cartographic products. The project adhered to national and international geophysical mapping standards and utilized validated interpolation and error estimation techniques to ensure data quality. The validation process by the modern gravimetric surveys also confirmed the validity and reliability of the digitized historical data. This digitization effort significantly modernizes Kazakhstan’s gravimetric infrastructure, providing a robust foundation for geoid modeling, tectonic studies, and resource exploration. Full article

Orthometric heights are practically determined from levelling and gravity measurements by applying orthometric corrections to levelled height differences. Currently, Helmert’s definition of orthometric heights is mostly used, with the mean gravity computed only approximately from observed surface gravity by applying the Poincaré–Prey gravity reduction. In this study, we apply the state-of-the-art method for the orthometric height determination and demonstrate its practical applicability. The method utilizes advanced numerical procedures to account for the topographic relief and mass density variations, while adopting the Earth’s spherical approximation. The non-topographic contribution of masses inside the geoid is evaluated by solving geodetic boundary-values problems. We apply this method for the first time to practically determine the orthometric heights of levelling benchmarks from levelling and gravity measurements and digital terrain and rock density models. The results obtained after the readjustment of newly determined orthometric heights at the levelling network covering Hong Kong territories are compared with Helmert’s orthometric heights. This comparison revealed that errors in Helmert’s orthometric heights vary between −3.13 and 0.95 cm. Such errors are very significant when compared to accurate values of the cumulative orthometric correction between −1.88 and 0.84 cm. Moreover, large errors (up to 1 cm) already occur at levelling benchmarks at very low elevations (<100 m). These findings demonstrate that the accurate determination of orthometric heights is crucial, even for regions with moderately elevated topography. Full article

Developing a high-precision regional geoid model is a key element in modernizing Kazakhstan’s vertical reference framework and ensuring consistent GNSS-based height determination. However, the mountainous terrain of southeastern Kazakhstan, characterized by strong topographic gradients and sparse terrestrial gravity coverage, poses significant modelling challenges. This study presents the first AI-enhanced hybrid geoid model developed for the Almaty region, integrating classical gravimetric modelling with modern machine-learning simulation. The baseline solution was computed using the Least-Squares Modification of Stokes’ Formula with Additive Corrections, combining digitized Soviet-era terrestrial gravity data, the global geopotential model XGM2019e_2159, and the FABDEM 30 m digital elevation model. Validation using GNSS/levelling benchmarks revealed a systematic bias of −0.06 m and an RMS of 0.08 m. To improve the fit between modelled and observed undulations, three machine-learning regressors—Gaussian Process Regression (GPR), Support Vector Regression (SVR), and LSBoost—were applied to model the residual correction surface. Among them, SVR provided the best held-out performance (RMSE = 0.04 m), while LOOCV, 10-fold and spatial CV confirmed stable generalization across terrain regimes. The resulting hybrid model, designated N_ALM2025, achieved centimetre-level consistency with GNSS/levelling data. The results demonstrate that integrating classical geoid computation with AI-based residual modelling provides an efficient computational framework for high-precision geoid determination in complex mountainous environments. Full article

Accurate geoid determination is essential for height system unification and for converting Global Navigation Satellite System (GNSS) ellipsoidal heights to orthometric heights. This study demonstrates a national-scale workflow that integrates digitized Soviet-era gravimetric maps at 1:200,000 scale with modern satellite and ancillary datasets to compute a high-resolution gravimetric geoid for Kazakhstan. Legacy gravity maps were systematically digitized, harmonized, and quality-controlled, then integrated with a global geopotential model (XGM2019e_2159) for long-wavelength information and a digital elevation model (FABDEM) for terrain corrections. Geoid computation employed the Least-Squares Modification of Stokes’ Formula, with spectral testing used to select optimal parameters; external control and validation relied on an extensive set of GNSS observations and geometric levelling benchmarks from the national network. The resulting geoid surface captures the country’s full topographic range, from the Caspian Depression to the Tien Shan and Altai. After regression-based removal of residual tilts linked to distortions in the Baltic 1977 height system, we achieved a root-mean-square error of 0.066 m. The integrated use of 1:200,000 gravity maps and modern satellite-derived models yields accuracy improvements over widely used global solutions, establishing a consistent vertical reference for Kazakhstan and supporting datum modernization, GNSS-based heighting, infrastructure development, and environmental monitoring. These results show that digitized Soviet-era gravity maps, when fused with modern satellite datasets, can provide robust, high-accuracy geoid solutions. Full article

Determining a high-precision national geoid is a fundamental step in modernizing Kazakhstan’s vertical reference system. However, the country’s vast territory, complex topography, and limited coverage of modern terrestrial and airborne gravimetric surveys present significant challenges. In this context, Soviet-era gravimetric maps at a 1:200,000 scale remain the only consistent nationwide data source, yet their reliability has not previously been rigorously assessed within modern gravity standards. This study presents the first comprehensive validation of Soviet-era gravimetric surveys using two independent approaches. The first approach is about the comparison of gravity anomalies with the global geopotential models EGM2008, EIGEN-6C4 and XGM2019e_2159. The second approach is about the direct evaluation against absolute gravity measurements from the newly established Qazaqstan Gravity Reference Frame (QazGRF). The analysis demonstrates that, after applying systematic corrections, the Soviet-era gravimetric survey retains high information content. The mean discrepancy with QazGRF measurements is 0.7 mGal with a standard deviation of 2.5 mGal, and more than 90% of the evaluated points deviate by less than ±5 mGal. Larger inconsistencies, up to 20 mGal, are confined to mountainous and geophysically complex regions. In addition, several artifacts inherent to the global models were identified, suggesting that the integration of validated regional gravimetric data can also support future improvements of global gravity models. A key finding was the detection of an artifact in the global models on sheet M43. Its presence was confirmed by comparison with terrestrial gravimetric data and inter-model differences. It was established that the anomaly is caused by inaccuracies in the terrestrial “fill-in” component of the EGM2008 model, which subsequently inherited by later global solutions. The results confirm that Soviet gravimetric maps, once critically re-evaluated and tied to absolute observations, can be effectively integrated with global models. This integration delivers reliable, high-resolution inputs for regional gravity-field modeling. It establishes a robust scientific and practical foundation for constructing the first national geoid of Kazakhstan and for implementing a unified state coordinate and height system. It also helps enhance the accuracy of global geopotential models. Full article

This study examines the influence of gravity on different height systems by integrating Global Navigation Satellite Systems (GNSS), leveling, and gravimetric measurements. Although the theoretical influence of gravity on height systems is well known, empirical studies that quantify these effects along steep terrain are rare—particularly within the Croatian reference systems. Geometric leveling, recognized for its precision in geodesy, was employed alongside gravimetric data to analyze the relationship between gravity variations and height differences. The research was conducted along Sljeme Road on Mt. Medvednica, Croatia, where altitude-dependent gravity effects were systematically investigated along an elevation profile with a height difference of about 650 m. GNSS measurements provided positional coordinates referenced to the Croatian Terrestrial Reference System 1996 (HTRS96) (EPSG:4888), while leveling and gravimetric data were analyzed within the Croatian Height Reference System 1971 (HVRS71) (EPSG:5610) and Croatian Gravimetric Reference System 2003 (HGRS03), respectively. The results demonstrate that differences between geometric and normal–orthometric heights become more pronounced at higher elevations but remain at the millimeter level. Notably, the impact of gravity is evident in normal and orthometric heights, with differences from geometric heights reaching up to 3.7 cm at the highest points. Additionally, a comparison between normal and orthometric heights reveals that at the beginning of the leveling line, the difference is around 4 mm. However, as the elevation increases, this difference grows, reaching over 1 cm at the end of the leveling line. The study also confirms the theoretical correlation between the geoid–quasigeoid height difference and terrain elevation, with increasing differences observed at higher altitudes. To examine the consistency of different height determination methods, two approaches were applied: one based on adjustment within the geopotential system, and the other involving direct adjustment in the desired height system, with specific height corrections applied. The results confirmed that the height differences between the two methods were 0, to the tenth of a millimeter, indicating that both methods provided identical results. These findings contribute to a deeper understanding of geodetic height systems and the role of gravity in height determination. Full article

Gravity anomalies play critical roles in geological analysis, geodynamic monitoring, and precise geoid modeling. Obtaining accurate gravity data is challenging, particularly in inaccessible or sparsely covered regions. This study evaluates machine learning (ML) methods—Support Vector Regression (SVR), Gaussian Process Regression (GPR), and Ensemble of Trees—for predicting gravity anomalies in southeastern Kazakhstan and compares their effectiveness with traditional Kriging interpolation. A dataset, consisting of the simple Bouguer anomaly values, latitude, longitude, elevation, normal gravity, and terrain corrections derived from historical maps at a scale of 1:200,000, was utilized. Models were trained and validated using cross-validation techniques, with performance assessed by statistical metrics (RMSE, MAE, R²) and spatial error analysis. Results indicated that the Exponential GPR model demonstrated the highest predictive accuracy, outperforming other ML methods, with 72.9% of predictions having errors below 1 mGal. Kriging showed comparable accuracy and superior robustness against extreme errors. Most prediction errors from all methods were spatially associated with mountainous regions featuring significant elevation changes. While this study demonstrated the effectiveness of machine learning methods for gravity anomaly prediction, their accuracy decreases in complex terrain, indicating the need for further research to improve model performance in such environments. Full article

Astrogeodetic deflections of the vertical (DoVs) are close indicators of the slope of the geoid. Thus, DoVs observed along horizontal profiles may be integrated to create geoid undulation profiles. In this study, we collected DoV data in the Eastern Swiss Alps using a Swiss Digital Zenith Camera, the COmpact DIgital Astrometric Camera (CODIAC), and two total station-based QDaedalus systems. In the mountainous terrain of the Eastern Swiss Alps, the geoid profile was established at 15 benchmarks over a two-week period in June 2021. The elevation along the profile ranges from 1185 to 1800 m, with benchmark spacing ranging from 0.55 km to 2.10 km. The DoV, gravity, GNSS, and levelling measurements were conducted on these 15 benchmarks. The collected gravity data were primarily used for corrections of the DoV-based geoid profiles, accounting for variations in station height and the geoid-quasigeoid separation. The GNSS/levelling and DoV data were both used to compute geoid heights. These geoid heights are compared with the Swiss Geoid Model 2004 (CHGeo2004) and two global gravity field models (EGM2008 and XGM2019e). Our study demonstrates that absolute geoid heights derived from GNSS/leveling data achieve centimeter-level accuracy, underscoring the precision of this method. Comparisons with CHGeo2004 predictions reveal a strong correlation, closely aligning with both GNSS/leveling and DoV-derived results. Additionally, the differential geoid height analysis highlights localized variations in the geoid surface, further validating the robustness of CHGeo2004 in capturing fine-scale geoid heights. These findings confirm the reliability of both absolute and differential geoid height calculations for precise geoid modeling in complex mountainous terrains. Full article

The isle of Gavdos, and its wider area, is one of the few places worldwide where the calibration and validation of altimetric satellites has been carried out during the last, more than, two decades using dedicated techniques at sea and on land. The sea-surface calibration employed for the determination of the bias in the satellite altimeter’s sea-surface height relies on the use of a gravimetric geoid in collocation with data from tide gauges, permanent global navigation satellite system (GNSS) receivers, as well as meteorological and oceanographic sensors. Hence, a high-accuracy and high-resolution gravimetric geoid model in the vicinity of Gavdos and its surrounding area is of vital importance. The existence of such a geoid model resides in the availability of reliable, in terms of accuracy, and dense, in terms of spatial resolution, gravity data. The isle of Gavdos presents varying topographic characteristics with heights larger than 400 m within small spatial distances of ~7 km. The small size of the island and the significant bathymetric variations in its surrounding marine regions make the determination of the gravity field and the geoid a challenging task. Given the above, the objective of the present work was two-fold. First, to collect new land gravity data over the isle of Gavdos in order to complete the existing database and cover parts of the island where voids existed. Relative gravity campaigns have been designed to cover as homogenously as possible the entire island of Gavdos and especially areas where the topographic gradient is large. The second focus was on the determination of a high-resolution, $1\prime \times 1\prime$, and high-accuracy gravimetric geoid for the wider Gavdos area, which will support activities on the determination of the absolute altimetric bias. The relative gravity campaigns have been designed and carried out employing a CG5 relative gravity meter along with geodetic grade GNSS receivers to determine the geodetic position of the acquired observations. Geoid determination has been based on the newly acquired and historical gravity data, GNSS/Leveling observations, and topography and bathymetry databases for the region. The modeling was based on the well-known remove–compute–restore (RCR) method, employing least-squares collocation (LSC) and fast Fourier transform (FFT) methods for the evaluation of the Stokes’ integral. Modeling of the long wavelength contribution has been based on EIGEN6c4 and XGM2019e global geopotential models (GGMs), while for the contribution of the topography, the residual terrain model correction has been employed using both the classical, space domain, and spectral approaches. From the results achieved, the final geoid model accuracy reached the ±1–3 cm level, while in terms of the absolute differences to the GNSS/Leveling data per baseline length, 28.4% of the differences were below the $1\mathrm{c}\mathrm{m}\sqrt{S_{ij} \left[\mathrm{k}\mathrm{m}\right]}$ level and 55.2% below the $2\mathrm{c}\mathrm{m}\sqrt{S_{ij} \left[\mathrm{k}\mathrm{m}\right]}$. The latter improved drastically to 52.8% and 81.1%, respectively, after deterministic fit to GNSS/Leveling data, while in terms of the relative differences, the final geoid reaches relative uncertainties of 11.58 ppm (±1.2 cm) for baselines as short as 0–10 km, which improves to 10.63 ppm (±1.1 cm) after the fit. Full article

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. Full article

This article investigates the role of different approaches and interpolation methods in gridding terrestrial gravity anomalies. In this regard, first of all, simple and complete Bouguer anomalies are considered in gravity data gridding. In the comparison results of gridding these two Bouguer anomaly datasets, the effect of the high-frequency contribution of topographic gravitation (by means of the terrain correction) is clarified. After that, the role of the used interpolation algorithm on the resulting grid of mean gravity anomalies and hence on the geoid modeling accuracy is inspected. For this purpose, four different interpolation methods including geostatistical Kriging, nearest neighbor, inverse distance to a power (IDP), and artificial neural networks (ANNs) are applied. Here, the IDP and nearest neighbor methods represent simple-structured algorithms among the interpolation methods tested in this study. The ANN method, on the other hand, is preferred as a complex, optimization-based soft computing method that has been applied in recent years. In addition, the geostatistical Kriging method is one of the conventional methods that is mostly applied for gridding gravity data in geodesy and geophysics. The calculated gravity anomalies in grids are employed in high-resolution geoid model computations using the least squares modifications of Stokes formula with additive corrections (LSMSA) technique. The investigations are carried out using the test datasets of Auvergne, France that are provided by the International Service for the Geoid for scientific research. It is concluded that the interpolation algorithms affect the gravity gridding results and hence the geoid model determination. The ANN method does not provide superior results compared to the conventional algorithms in gravity gridding. The geoid model with 4.1 cm accuracy is computed in the test area. Full article

The determination of the geoid–quasigeoid separation (GQS) is most often based on the use of Bouguer gravity anomalies or disturbances with additional corrections, which allow for the determination of so-called complete or accurate GQS values. This study presents analyses related to an attempt to determine accurate GQS values using the GGI approach (based on the geophysical gravity inversion technique). This approach allows for the modeling of various parameters of the gravity field, and it also enables the determination of the GQS or geoid undulations. Such capabilities of the method have not yet been tested. In this study, the details of the GGI solution in terms of determining the GQS and the first results from tests performed in the area of the Colorado 1 cm geoid computation experiment are presented. The GQS values determined by the GGI approach were compared with the reference values determined previously using the complete classical approach. The differences between the compared values were small, with a standard deviation of 0.007 m, and the maximum differences reached 0.075 m. The analyses also revealed the significant impact of changes in the density of topographic masses on both the geoid undulations and GQS values determined using the GGI approach. Full article