With knowledge of geometry and density-distribution of topography, the residual terrain modelling (RTM) technique has been broadly applied in geodesy and geophysics for the determination of the high-frequency gravity field signals. Depending on the size of investigation areas, challenges in computational efficiency are encountered when using an ultra-high-resolution digital elevation model (DEM) in the Newtonian integration. For efficient and accurate gravity forward modelling in the spatial domain, we developed a new MATLAB-based program called, terrain gravity field (TGF). Our new software is capable of calculating the gravity field generated by an arbitrary topographic mass-density distribution. Depending on the attenuation character of gravity field with distance, the adaptive algorithm divides the integration masses into four zones, and adaptively combines four types of geometries (i.e., polyhedron, prism, tesseroid and point-mass) and DEMs with different spatial resolutions. Compared to some publicly available algorithms depending on one type of geometric approximation, this enables accurate modelling of gravity field and greatly reduces the computation time. Besides, the TGF software allows to calculate ten independent gravity field functionals, supports two types of density inputs (constant density value and digital density map), and considers the curvature of the Earth by involving spherical approximation and ellipsoidal approximation. Further to this, the TGF software is also capable of delivering the gravity field of full-scale topographic gravity field implied by masses between the Earth’s surface and mean sea level. In this contribution, the TGF software is introduced to the geoscience community and its capabilities are explained. Results from internal and external numerical validation experiments of TGF confirmed its accuracy at the sub-mGal level. Based on TGF, the trade-off between accuracy and efficiency, values for the spatial resolution and extension of topography models are recommended. The TGF software has been extensively tested and recently been applied in the SRTM2gravity project to convert the global 3” SRTM topography to implied gravity effects at 28 billion computation points. This confirms the capability of TGF for dealing with large datasets. Together with this paper, the TGF software will be released in the public domain for free use in geodetic and geophysical forward modelling computations.

SUMMARY: High resolution and accurate digital terrain models (DTMs) are frequently used as input data sets to define the topographic masses in gravity forward modelling, for example, for terrain corrections in the context of regional gravity modelling. However, over vegetated areas such as forests and scrublands, the radar- and image-based digital elevation models (DEMs) may contain a tree bias, and therefore do not represent the bare-ground surface. The presence of vegetation-induced signals in DEMs, denoted here the tree-canopy effect, will introduce errors in the gravity forward modelling. In this study, the role of the tree-canopy effect in gravity forward modelling calculations is numerically investigated. First, spectral forward modelling techniques were applied to analyse a global tree-canopy bias model with a horizontal resolution of 1 km x 1 km and to quantify its effect on global gravity forward modelling results. We demonstrate that tree-canopy signals in the DEM produce a positive bias in the topographic gravitational field over vegetated areas, with values ranging from 0 to ∼2.7 mGal for gravity disturbances. Second, the role of the tree-canopy effect in high-frequency gravity forward modelling is studied using well-known residual terrain modelling (RTM) techniques. As DEM data sets, we used the 3″ SRTM (Shuttle Radar Topography Mission Digital 9 m Elevation Database) V4.1 (containing vegetation biases) and the 3″ MERIT-DEM (Multi-Error-Removed Improved-Terrain Digital elevation model) as a representation of the bare-ground elevations. Using Tasmania and the Amazon rainforest regions as test areas with significant tree-canopy signals we show that the tree-height effect on RTM calculations is of high-frequency nature, with rather small signals which reach in extreme cases amplitudes of ∼1–2 mGal occurring at forest boundaries. Third, using ground gravity observations, validation experiments were performed over the Australian Alps, Tasmania and the Canadian Rocky Mountains. All validation experiments show that the bare-ground elevation model MERIT-DEM performs better than SRTM V4.1 in terms of reduction of the discrepancies between modelled and observed gravity values. As a general conclusion, bare-ground DEM models should be preferred in any gravity forward modelling application to avoid or reduce the tree-canopy effect.

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.

The Surface Water and Ocean Topography (SWOT) mission, initially designed to observe oceans and inland waters, proves valuable for mapping intertidal flat topography. This study presents a fusion method that integrates freely available SWOT interferometric altimetry data with Sentinel‐2 imagery. The density‐based spatial clustering of applications with noise algorithm is employed to accurately identify observation data located in the intertidal zone. Intertidal topography with a 10 m resolution were generated from L2_HR_PIXC data collected during SWOT's science phase (July 2023–October 2024) in the intertidal region along the coast of Jiangsu Province, China. These Digital Elevation Models were compared with laser altimetry observations from the ICESat‐2. SWOT observations show high accuracy, with RMSEs of 0.24 m (multi‐cycle) and 0.41 m (single‐cycle), confirming their potential for intertidal monitoring. This study presents a data processing strategy that does not rely on ground‐based observations, demonstrating potential for application in a broader range of regions.