Digital Elevation Models (DEMs) are fundamental components in geodetic computations, serving as key inputs in geoid modelling processes. Mostly, the freely available DEMs are used for geoid modelling without considering its impact on the developed geoid. Considering the criticality of terrain and downward continuation corrections calculated from DEMs, this research work explores the sensitivity of geoid models to variations in DEMs, aiming to elucidate the impact of different DEMs on the accuracy and precision of geoid modelling. The study aims at a comprehensive sensitivity analysis framework to assess the influence of DEM resolution, terrain representation, and fitting methods on regional geoid modelling in India. The selected study area consists of three states of India (Haryana, Punjab, and Himachal Pradesh) bounding approximately 169,500 km² of the area (73.5≤λ≤77.5 and 29≤ϕ≤33 of longitude and latitude, respectively) of vast topography including Indo-Gangetic Plain, Shivalik Hills, lofty hills, deep valleys, and verdant forests. This study employs Least Squares Modification of Stokes formula with Additive Corrections (LSMSAC) method developed by the Royal Institute of Technology, Sweden and evaluates four DEMs, Cartosat, Merit, Palsar and SRTM. For surface correction (fitting), 24 GNSS points are used with 4,5 & 7 parameter fitting models which is validated with 15 other GNSS point based on elementary statistics. This investigation offers insights into selection of an optimal DEM by obtaining RMSE between developed geoid using various DEMs and 15 GNSS points. Based on the obtained results by considering above-mentioned DEMs with various fitting models, the Cartosat DEM outperformed other DEMs by obtaining lowest RMSE (0.078603m) with 7 parameter fitting model. Surprisingly, the lowest RMSE (0.064557m) is obtained by Cartosat DEM with 4 parameter model which could be because of Cartosat DEM being an India specific DEM. While comparing the efficacy of developed geoid between globally available DEM, Merit performed best with lowest RMSE (0.078657m). Out of 90 combinations of each DEM for various sets of Degree/order of Global Geopotential model (GGM), integration cap size; the best result is obtained by 180 degree of GGM and 0.8 integration cap size for each DEM. Presented study improved our understanding in assessing the sensitivity of geoid models to various DEMs. This research aids geodesists, geophysicists, and remote sensing specialists in making informed decisions while selecting a suitable DEM for geoid computations. The findings presented in this paper contribute to the ongoing efforts to enhance the precision and reliability of geoid modelling techniques, ultimately improving our understanding of Earth's gravity field.

How to cite: Kumar, A., maurya, V., and dwivedi, R.: Sensitivity Analysis of Digital Elevation Models in Geoid Modelling for Indian region, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-1087, https://doi.org/10.5194/egusphere-egu24-1087, 2024.

Numerical methods like the Finite Element Methods (FEM) or Finite Element Methods (FVM) are widely used in many engineering applications to solve boundary value problems that are hard to find rigorous analytical solutions. These numerical methods have been also applied in geodesy in many previous studies regardless of its huge computation demands. They have arisen due to the fact that the upper boundary condition was usually set up at the satellite orbit level, hundreds of kilometers above the Earth. The relatively large distances between the bottom boundary Earth' s surface, and the upper boundary even exacerbates the computation loads because of the required discretization in between. Considering that many areas such as the US have uniformly distributed airborne gravity data that are just a few kilometers above the topography, we propose to move the upper boundary from the satellite orbit level to the mean flight level of the airborne gravimetry. The significant reduction in altitudes, dramatically saves the large computation demands in previous FEM or FVM computations. This paper demonstrates this benefit by using FVM for both simulated data and real data in the target area. In the simulated case, the FVM numerical results show that about an order of magnitude precision improvement can be obtained when moving the upper boundary from 250km to 10km, the maximum altitude of GRAV-D. For the real data sets, 2-3 cm level of accurate quasi geoid model can be obtained depending on different schemes used to model the topographic mass. The paper also demonstrates how to find the upper layer in case no airborne data is available. Last but not the least, this study provides a 3D representation of the entire local gravity field instead of a single 2D surface, the (quasi) geoid.

How to cite: Li, X., Cunderlik, R., Lin, M., Macak, M., Zahorec, P., Papco, J., Minarechova, Z., Krcmaric, J., and Roman, D.: FVM: A Good Match to Airborne Gravimetry?, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-1346, https://doi.org/10.5194/egusphere-egu24-1346, 2024.

This groundbreaking study addresses the imperative to comprehend gravity shifts resulting from Groundwater Storage (GWS) variations in the Arabian Peninsula. Despite the critical importance of water resource sustainability and its relationship with gravity, limited research emphasizes the need for expanded exploration. The investigation explores the impact of GWS extraction on the gravity field, utilizing Gravity Recovery and Climate Experiment (GRACE) and Global Land Data Assimilation System (GLDAS) data in addition to validation using WaterGAP Global Hydrology Model (WGHM). Spanning April 2002 to June 2023, the study predicts GWS trends over the next decade using the Seasonal Autoregressive Integrated Moving Average (SARIMA) model.  The comprehensive time-series Analysis reveals a huge GRACE-derived GWS trend about -4.90±0.32 mm/year during the period of study. This significantly influences the gravity anomaly GA values, demonstrating a corresponding fluctuation in GWS time series. The projected GWS indicates a depletion rate of 14.51 km³/year over the next decade. The correlation between GWS and GA is substantial at 0.80, while GA and rainfall correlation is negligible due to low precipitation rates. Employing multiple linear regression explains 80.61% of the variance in gravity anomaly due to GWS, precipitation, and evapotranspiration. The study investigates climate change factors—precipitation, temperature, and evapotranspiration—providing a holistic understanding of forces shaping GWS variations. Precipitation and evapotranspiration exhibit nearly equal values, limiting GWS replenishment opportunities. This research holds significance in studying extensive GWS withdrawal in the Arabian Peninsula, particularly concerning crust mass stability. Integrating GRACE and hydrological models’ datasets furnishes a comprehensive understanding, contributing valuable foresight into the future trajectory of GWS. The results illuminate intricate relationships between GWS, gravity anomalies, and climate factors, presenting a robust framework for sustainable water resource management. 

How to cite: Mohasseb, H. A., Shen, W., Abd-Elmotaal, H. A., and Jiao, J.: Assessing Groundwater Sustainability in the Arabian Peninsula and its Impact on Gravity Fields through GRACE Measurements , EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-2185, https://doi.org/10.5194/egusphere-egu24-2185, 2024.

Although machine learning has become increasingly important in geodesy related fields such as geophysics, seismology and remote sensing, its applications in geodesy, especially in physical geodesy, are still in its early stages. The main reason for this can be attributed to the black box nature of pure data-driven machine learning, which lacks physical interpretability and credibility, making it difficult for machine learning approaches to be used in physical geodesy that takes reliability and accuracy as its core criteria. Physics-Informed Neural Networks (PINNs) is a class of deep learning algorithms aims to seamlessly integrate data and physical prior knowledge including ordinary or partial differential equations, it can yield more physically interpretable machine learning models that provide robust and accurate predictions. We present the PINN approach for gravimetric geoid modeling from Earth gravity model, terrestrial and airborne gravity datasets. A convolutional neural network (CNN) deep learning architecture is used, gravity measurements and physical laws are integrated by embedding the Laplace’s equation of disturbing potential and the fundamental equation of gravity anomaly into the loss function of the neural network using automatic differentiation. The PINN based geoid computation approach is tested in the area of the Colorado 1-cm geoid experiment. Simulated gravity observations and GNSS leveling derived geoid heights based on EIGEN-6C4 are used to validate the theoretical correctness and validity of the proposed PINN approach, and its performance on precise geoid modeling in this challenging area is evaluated using the actual terrestrial and airborne gravity observations, GNSS leveling measured geoid heights and high resolution DEM provided by NGS/NOAA.

How to cite: Jiang, T., Tu, Z., and Dang, Y.: Physics-Informed Neural Networks for geoid modeling: preliminary results in Colorado, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-4068, https://doi.org/10.5194/egusphere-egu24-4068, 2024.

The coverage of the gravity data plays an important role in the geoid determination process. Still some parts in the world have poor gravity data coverage, with sometimes, large data gaps, e.g., Africa. In this paper we study the effect of implementing Moho depths on the gravity interpolation at large data gaps. For this reason, and in order to qualify that effect, an artificial data gap has been made in the gravity data set of Austria (originally with perfect gravity data coverage). The outcome of the present study is essential for the IAG sub-commission on the gravity and geoid in Africa in order to determine the African geoid from the available data sets with the best possible precision. The gravity interpolation has been made at the original omitted data points at the data gap with and without the Moho information. The interpolated gravity has thus been compared to the original omitted data values for both cases to determine the effect of using Moho depths on gravity interpolation. The results are shown and comprehensively discussed.

How to cite: Abd-Elmotaal, H. and Kühtreiber, N.: Effect of Implementing Moho Depths on Gravity Interpolation at Large Data Gaps , EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-4477, https://doi.org/10.5194/egusphere-egu24-4477, 2024.

The combination of satellite positioning techniques (e.g., GPS) and high-resolution geoid or quasi-geoid models provides an alternative to the expensive and time-consuming spirit leveling for the determination of physical heights. The reliability of the physical heights thus undergoes the same accuracy limitations of the (quasi-) geoid models. However, in many regions, especially developing or newly industrializing countries, there is no reliable regional gravity model, due to the low availability or quality of surface gravity data. This study tackles such challenges in a case study in the northwestern part of South America and provides the first up-to-date high-resolution Colombian quasi-geoid model.

This region is a challenging study area with coastlines on both the Pacific and the Atlantic Ocean and rugged topography with high elevation reaching more than 5,000 m. Available terrestrial and airborne data were collected during the last eight decades, which frequently contain systematic errors and biases and the corresponding metadata is missing. We develop approaches to validate and improve the quality of old gravity datasets. They are then combined with a global gravity model (GGM) and topography models, which play an important role in mountainous areas, within the remove-compute-restore (RCR) procedure. In the offshore area, satellite altimetry-derived gravity data are additionally incorporated, which are obtained from the latest release of the DTU (Technical University of Denmark) gravity anomaly grid, DTU21GRA.

The computed quasi-geoid model is thoroughly validated with independent GPS/leveling data. It delivers an STD of 15.76 cm in comparison to the GPS/leveling data, which is 36% smaller than that obtained from the latest South American quasi-geoid model QGEIOD2021 (24.51 cm). Five recent high-resolution GGMs, namely EGM2008, EIGEN6C4, GECO, SGG-UGM-1, and XGM2019 are also validated using the same GPS/leveling data. They deliver STD values of 28.09 cm, 21.10 cm, 20.39 cm, 20.93 cm, and 17.86 cm, respectively, which are averagely 38% larger than that of our computation.

How to cite: Liu, Q., Schmidt, M., and Sánchez, L.: Methods for geoid determination in regions with challenging data quality and coverage, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5383, https://doi.org/10.5194/egusphere-egu24-5383, 2024.

We have analysed the digital elevation models (DEMs) published in recent years and merged them to create a new elevation grid together with complementary Earth’s relief model for bedrock, surface, bathymetry, ice surface, and ice thickness. Although each model is unique in its own, the merged grid is able to provide seamless elevation information based on a common reference surface globally with high spatial resolution as required for various geoscience applications. We present how the merging procedure was carried out, how the accuracy of the model was evaluated and for which application areas it is intended. Our aim is to disseminate the use of a homogeneous and a consistent elevation model that is particularly suitable for geodetic applications in all parts of the world, including global and regional geoid calculations. The DEMs and associated auxiliary files included in the merged product are: TanDEM-X 90m over all dry land and ice-covered regions, ETOPO2022, GEBCO-2022 and GEBCO-2023 over land and ocean, BedMachineGreenland-v5 over Greenland, BedMachineAntarctica-v3 over Antarctica, GLOBathy (the Global Lakes Bathymetry Dataset) over lakes globally. Masks for ocean, dry land, lakes, islands in the lakes, ponds on the islands, ice-covered land, ice-covered shelves, the area outside Greenland and the ice-covered lake Vostok (Antarctica) were taken into account in the merging. This complete model is anticipated to provide a standardized DEM for various applications in geodesy and geophysics.  Our future plans include high resolution topographic gravity field modelling using this consolidated 30 arc-second digital elevation model and laterally varying global density data.

How to cite: Förste, C., Abrykosov, O., and Ince, E. S.: A consolidated 30 Arc-second Global Digital Elevation Model for Geodesy and Geophysics, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-8340, https://doi.org/10.5194/egusphere-egu24-8340, 2024.

Many geodetic-related observations nowadays require a precise local geoid height that is as accurate as sub-centimeters. Here, we develop a method to combine global Earth Gravitational Model (EGM), Digital Terrain Model (DTM), as well as highly accurate local gravity and Global Navigation Satellite System (GNSS) observations to achieve this goal. We carried out several observation campaigns to obtain high space resolution and high accuracy gravity and GNSS data. Firstly, we analyze the accuracy of the commonly used methods such as those that use EGM only or use EGM and DTM combined. Then we test our method with a synthetic earth that was developed with EGM, DTM, and local high-resolution topography. Our results should that, the high degree EGM-only geoid has a mean error of tens of centimeters; the geoid from combined EGM and DTM can achieve accuracy of several centimeters; and if we want to have a local geoid with deviations less than sub-centimeter, high accurate observations with space resolution as high as 1"x1" are needed.

How to cite: Huang, J., Zheng, G., Yushan, A., and Qiu, B.: Observation requirements for precise determination of local (quasi)geoid, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-14283, https://doi.org/10.5194/egusphere-egu24-14283, 2024.

In the frame of the GeoNetGNSS project, funded by the European Union and National Funds through the Region of Central Macedonia (RCM) in Northern Greece, regional gravimetric and hybrid geoid models have been determined with the main goal being to support a newly established network of Continuously Operating Reference Stations (CORS). The main aim was to assist everyday surveying purposes by delivering accurate orthometric heights based on GNSS/Levelling, i.e., determining orthometric heights without the need to carry out levelling. With that in mind, a regional gravimetric geoid was determined based on historical and newly acquired high-accuracy and density gravity data, employing the Remove-Compute-Restore (RCR) technique and both stochastic and spectral evaluations of Stokes’ integral. Consequently, a hybrid deterministic and stochastic approach was used to model the residuals of the gravimetric geoid solution relative to available GNSS/Levelling geoid heights. The latter refer to 533 geodetic benchmarks in the entire study area, where accurate static GNSS observations and orthometric heights from the Hellenic Military Geographic Service (HMGS) were available. Various parametric models ranging from simple north-south bias and tilt to 2^nd and 3^rd order degree polynomial models were evaluated in terms of the fit residual absolute and relative differences. After the deterministic fit, a collocation approach employing exponential and 2^nd order Gauss-Markov covariance functions was used to model the stochastic residuals. Finally, the hybrid deterministic and stochastic corrector surface, provided as grid corrections for the entire area under study, has been determined to accommodate user needs for orthometric height determination. From the results acquired, absolute differences of the order of 1-2 cm and relative ones at the 3-4 ppm have been achieved after validation against independent GNSS/Levelling observations.

How to cite: Natsiopoulos, D. A., Vergos, G., Mamagiannou, E. G., Tzanou, E. A., Triantafyllou, A. I., Tziavos, I. N., Ramnalis, D., and Polychronos, V.: Refinements of regional gravimetric and hybrid geoid models in support of the GeoNetGNSS CORS network in Northern Greece, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-17974, https://doi.org/10.5194/egusphere-egu24-17974, 2024.