G1.5

The Rudzki inversion gravimetric reduction maps the Earth’s topographic masses inside the geoid in such a way that the inverted masses produce exactly the same potential as the topographic masses on the geoid. In other words, the indirect effect to the geoid is zero so that its computation is not needed. This paper proposes a geoid computation scheme that combines the Bouguer reduction and Rudzki inversion reduction under the spherical approximation and constant density assumption. The proposed computation scheme works with the Bouguer gravity field that is smooth and theoretically legitimate for the harmonic downward continuation. Then the Bouguer potential is compensated by the potential of the inverted masses, ensuring zero indirect effect to the geoid. The direct effect of the Rudzki inversion gravimetric reduction is added to the Bouguer gravity disturbance, resulting in the reduced gravity disturbance for geoid computation. A spherical harmonic reference gravity model is also developed so that the kernel modification/truncation can be applied to the Hotine integral. If the density of the topographic masses becomes available, the effect of density anomalies can be computed separately and added to the geoid computed under the constant density assumption. The combined ellipsoidal effect of the Bouguer and Rudzki inversion reduction should be insignificant because of the canceling effect between them.

How to cite: Wang, Y. M.: The Bouguer-Rudzki-Hotine scheme for geoid computations, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10202, https://doi.org/10.5194/egusphere-egu21-10202, 2021.

Topographic reduction is one of the most imperative steps in geoid modeling, where the gravity field inside the masses needs to be modeled. This is quite challenging because no one can measure gravity inside the topography at a desired resolution (only a very limited number of borehole gravity measurements are available in the whole world). Therefore, topographic mass modeling is usually treated either by the residual terrain modeling (RTM) or by the Helmert’s 2^nd condensation among other alternative reduction schemes. All of these topographic reductions need intense computation efforts for the integration of topographic mass induced gravity effects. Currently, the most popular tool for topographic mass modeling is the ‘tc’ program available in the GRAVSOFT package. In this program, the mass elements provided by a digital terrain model (DTM) are treated as rectangular prisms which cannot directly take the Earth curvature into account and suffer from geometrical shape change due to meridian convergence. In this study, the tesseroids which are naturally obtained from a DTM are employed and their gravity effects are precisely evaluated by numerical integrations. Four topographic mass integration schemes are proposed and programmed in FORTRAN. Their computational performances in computing the RTM effect, terrain correction, and total topographic effect with and without using parallelizing technique are tested in the Colorado area. Then they are applied to local geoid modeling to see the geoid model differences among these various integration schemes in the RTM case. The numerical findings reveal that: (1) The application of parallelization techniques can greatly reduce the computation time without the loss of any computation accuracy; (2) Among the four integration schemes, the maximum absolute difference of RTM effect, terrain correction, and total topographic effect is about 3 mm, 6 cm, and 7.5 cm for the height anomaly, and 4 mGal, 3 mGal, and 40 mGal for the gravity anomaly; (3) In the RTM case, the geoid model difference can reach a maximum of 1 cm in the target area, and a larger difference should be expected in areas with rougher terrain; (4) The effects on geoid models from mass density anomalies is bigger than the counterparts from DTM errors.

How to cite: Lin, M. and Li, X.: Comparison of different topographic mass integration schemes in topographic reduction and its impact on geoid modeling: a case study in the Colorado area, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6923, https://doi.org/10.5194/egusphere-egu21-6923, 2021.

For the upcoming North American-Pacific Geopotential Datum of 2022, the National Geodetic Survey (NGS), the Canadian Geodetic Survey (CGS) and the National Institute of Statistics and Geography of Mexico (INEGI) computed the first joint experimental gravimetric geoid model (xGEOID) on 1’x1’ grids that covers a region bordered by latitude 0 to 85 degree, longitude 180 to 350 degree east. xGEOID20 models are computed using terrestrial gravity data, the latest satellite gravity model GOCO06S, altimetric gravity data DTU15, and an additional nine airborne gravity blocks of the GRAV-D project, for a total of 63 blocks. In addition, a digital elevation model in a 3” grid was produced by combining MERIT, TanDEM-X, and USGS-NED and used for the topographic/gravimetric reductions. The geoid models computed from the height anomalies (NGS) and from the Helmert-Stokes scheme (CGS) were combined using two different weighting schemes, then evaluated against the independent GPS/leveling data sets. The models perform in a very similar way, and the geoid comparisons with the most accurate Geoid Slope Validation Surveys (GSVS) from 2011, 2014 and 2017 indicate that the relative geoid accuracy could be around 1-2 cm baseline lengths up to 300 km for these GSVS lines in the United States. The xGEOID20 A/B models were selected from the combined models based on the validation results. The geoid accuracies were also estimated using the forward modeling.

How to cite: Wang, Y. M., Li, X., Ahlgren, K., Krcmaric, J., Hardy, R., Veronneau, M., Huang, J., and Avalos, D.: The experimental geoid 2020 – the first joint geoid model for the North American and Pacific Geopotential Datum, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6011, https://doi.org/10.5194/egusphere-egu21-6011, 2021.

Within the GeoGravGOCE project, funded by the Hellenic Foundation for Research Innovation, one of the main goals is the investigation of downward continuation schemes for the GOCE Satellite Gravity Gradiometry (SGG) data. It is well known that once the original SGG observations have been filtered to the GOCE Measurement Band Width (MBW), in order to remove noise and long-wavelength correlated errors, a crucial point for gravity field and geoid determination refers to the combination of GOCE data with local gravity field information. One possible way to exploit GOCE data is to use them in a Spherical Harmonic Synthesis (SHS) to derive a GOCE-only and/or a combined Global Geopotential Model. Our aim is to overcome the inherent smoothing of SHS and use directly the SGG data in order to investigate their contribution to regional gravity field and geoid determination. For that, methods based on the input-output-system-theory (IOST) are used for the combination of heterogeneous data at the Earth’s surface and at the satellite altitude or a mean sphere. The GOCE Level 2 gradients are first processed, transformed and reduced to a mean orbit using the IOST methods and then are downward continued to the Earth’s surface with an iterative Monte Carlo method (simulated annealing - SA). In this work we present the theoretical background of the proposed methodology and key-concepts for its implementation.

How to cite: Tziavos, I. N., Natsiopoulos, D. A., Vergos, G. S., Pitenis, E. A., and Mamagiannou, E. G.: Theoretical frame for the application of IOST in the downward continuation of GOCE SGG data, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1968, https://doi.org/10.5194/egusphere-egu21-1968, 2021.

In the frame of the GeoGravGOCE project, funded by the Hellenic Foundation for Research Innovation, GOCE Satellite Gravity Gradiometry (SGG) data are to be used for regional geoid and gravity field refinement as well as for potential determination in the frame of the International Height Reference Frame (IHRF). An inherent step in the geoid computation with either stochastic or spectral methods is the reduction of the related disturbing potential functionals within the well-known Remove-Compute-Restore (RCR) procedure. In this work we evaluate the latest, Release 6 (R6), satellite only and combined Global Geopotential Models (GGMs) which rely solely on GOCE and on land gravity data. The evaluation is performed over the established network of 1542 GPS/Levelling benchmarks over Greece mainland (BMs), which have been used in the past for the evaluation of GOCE GGMs. We employ the spectral enhancement approach, during which the GOCE-based GGMs are evaluated every one degree to the maximum degree of expansion coupled by EGM2008 and high-frequency RTM effects. This synthesis resolves wavelengths corresponding to maximum degree 216,000, hence the omission error is at the few mm-level. TIM-R6, DIR-R6, GOCO06s and XGM2019e are evaluated using EGM2008 residuals to the GPS/Levelling as the ground truth. From the results achieved, the optimal combination degree of a GOCE-only GGM augmented with EGM2008 is selected to be used in the sequel as reference field for the practical determination of the gravimetric geoid over Greece.

How to cite: Vergos, G. S., Tziavos, I. N., Natsiopoulos, D. A., Mamagiannou, E. G., and Pitenis, E. A.: Evaluation of the latest GOCE GGMs in support of regional geoid modeling over Greece, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1648, https://doi.org/10.5194/egusphere-egu21-1648, 2021.

Whilst GOCE SGG data have been widely processed and used in geodetic research, one of the key points of their use is to have a one-stop software for their pre-processing and basic manipulations in terms of frame transformations and filtering operations. Within the GeoGravGOCE project, funded by the Hellenic Foundation for Research Innovation, the main goal is the optimal combination of GOCE Satellite Gravity Gradiometry (SGG) data with in-situ observations for geoid determination. During the project development, it became apparent that GOCE SGG data after using the GOCEPARSER, had to be pre- and post-processed via several own-developed routines in order to perform data quality checks, data consistency tests, reference frame transformations, data reductions and filtering. With that in mind, a standalone open-source software has been developed in MATLAB consisting of a Graphical User Interface (GUI) to perform the aforementioned operation. The software is divided in four tabs and is designed to process the original GOCE gravity gradients, which are the second-order derivatives of the gravitational potential. The first tab of the software is designed to allow the pre-processing of the Level 2 Electrostatic Gravity Gradiometer nominal gravity gradients (EGG_NOM) and Satellite to Satellite Tracking Precise Science Orbits (SST_PSO) products. The second tab enables the transformation of gravity gradients from a Global Geopotential Model (GGM) from the Local North Oriented Frame (LNOF) to the Gradiometer Reference Frame (GRF). The third tab provides filtering options for the reduced SGG observations and encompasses three different methods: Finite Impulse Response (FIR), Infinite Impulse Response (IIR), and Wavelet Multi-Resolution Analysis (WL-MRA). Finally, the fourth tab allows the transformation of SGG data from the GRF to the LNOF and vice versa. In this work, we present the basic software development procedure and outline its basic functionality and results.

How to cite: Mamagiannou, E. M. G., Pitenis, E. A., Natsiopoulos, D. A., Vergos, G. S., and Tziavos, I. N.: GeoGravGOCE: A GOCE SGG processing software for datum transformations and filtering, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1680, https://doi.org/10.5194/egusphere-egu21-1680, 2021.

Physical heights, e.g. orthometric and normal heights, are, so far, practically considered as static heights in the majority of land areas over the world. They were traditionally determined without considering the dynamic processes of the Earth induced from temporal mass variations within the Earth’s system. The Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) satellite missions provided unique data that allow the estimation of temporal variations of geoid heights and vertical deformations of the Earth’s surface, and thereby the dynamics of physical heights. They revealed that for the large river basin of a strong hydrological signal (e.g. the Amazon river basin), peak to peak variations of orthometric/normal height changes reach 8 cm. The objective of this research is to discuss the need of considering the dynamics of physical heights for the determination of accurate orthometric/normal heights. An approach to determine the dynamics of physical heights using the release 6 (RL06) GRACE-based Global Geopotential Models (GGMs) as well as load Love numbers from the Preliminary Reference Earth Model (PREM) was proposed. Then, the dynamics of orthometric/normal heights was modelled and predicted using the seasonal decomposition (SD) method. The proposed approach was tested over the area of Poland. The main findings reveal that the dynamics of orthometric/normal heights over the area investigated reach the level of a couple of centimetres and can be modelled and predicted with a millimetre accuracy using the SD method. Accurate orthometric/normal heights can be obtained by combining modelled dynamics of orthometric/normal heights with static orthometric/normal heights referred to a specific reference epoch.

Keywords: dynamics of physical heights, GRACE, accurate orthometric/normal heights, temporal variations of geoid/quasigeoid heights, vertical deformations of the Earth’s surface

How to cite: Godah, W., Szelachowska, M., and Krynski, J.: On the dynamics of physical heights and their use for the determination of accurate orthometric/normal heights, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2110, https://doi.org/10.5194/egusphere-egu21-2110, 2021.

In the frame of the IAG Subcommission 2.4f “Gravity and Geoid in Antarctica” (AntGG) a first Antarctic-wide grid of ground-based gravity anomalies was released in 2016 (Scheinert et al. 2016). That data set was provided with a grid space of 10 km and covered about 73% of the Antarctic continent. Since then a considerably amount of new data has been made available, mainly collected by means of airborne gravimetry. Regions which were formerly void of any terrestrial gravity observations and have now been surveyed include especially the polar data gap originating from GOCE satellite gravimetry. Thus, it is timely to come up with an updated and enhanced regional gravity field solution for Antarctica. For this, we aim to improve further aspects in comparison to the AntGG 2016 solution: The grid spacing will be enhanced to 5 km. Instead of providing gravity anomalies only for parts of Antarctica, now the entire continent should be covered. In addition to the gravity anomaly also a regional geoid solution should be provided along with further desirable functionals (e.g. gravity anomaly vs. disturbance, different height levels).

We will discuss the expanded AntGG data base which now includes terrestrial gravity data from Antarctic surveys conducted over the past 40 years. The methodology applied in the analysis is based on the remove-compute-restore technique. Here we utilize the newly developed combined spherical-harmonic gravity field model SATOP1 (Zingerle et al. 2019) which is based on the global satellite-only model GOCO05s and the high-resolution topographic model EARTH2014. We will demonstrate the feasibility to adequately reduce the original gravity data and, thus, to also cross-validate and evaluate the accuracy of the data especially where different data set overlap. For the compute step the recently developed partition-enhanced least-squares collocation (PE-LSC) has been used (Zingerle et al. 2021, in review; cf. the contribution of Zingerle et al. in the same session). This method allows to treat all data available in Antarctica in one single computation step in an efficient and fast way. Thus, it becomes feasible to iterate the computations within short time once any input data or parameters are changed, and to easily predict the desirable functionals also in regions void of terrestrial measurements as well as at any height level (e.g. gravity anomalies at the surface or gravity disturbances at constant height).

We will discuss the results and give an outlook on the data products which shall be finally provided to present the new regional gravity field solution for Antarctica. Furthermore, implications for further applications will be discussed e.g. with respect to geophysical modelling of the Earth’s interior (cf. the contribution of Schaller et al. in session G4.3).

How to cite: Scheinert, M., Zingerle, P., Schaller, T., Pail, R., and Willberg, M.: Towards an updated, enhanced regional gravity field solution for Antarctica, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9873, https://doi.org/10.5194/egusphere-egu21-9873, 2021.

In the last decade, big efforts have been undertaken in terms of gravity surveys in the Southeast part of Brazil. First of all, São Paulo state has gravity data coverage quite completed in terms of 5’ resolution. Second, in the last few years, some field works have been carried out in Minas Gerais state. The purpose of gravity densification is not only to improve the quality of geoid (quasi-geoid) models in Brazil, but also to contribute to the geodetic infrastructure, in particular, at the moment, for the establishment of the International Height Reference Frame, where two of six planned stations are located in the densification area. These efforts resulted in the computation of two quasi-geoid models in the Southeast region of Brazil. The decision is to compute a quasi-geoid instead of a geoid model, once since 2018, the Brazilian vertical system is based on normal heights. The Minas Gerais model was computed using Least Squares Collocation, via Fast Collocation. The spectral decomposition was employed in the technique for quasi-geoid model computation, where the reference field was represented by XGM2019 up to degree and order 200. The model was compared with GNSS/leveling in order to check the consistency of two different data sets. Two quasi-geoidal models for the São Paulo state have been computed. Numerical integration through the Fast Fourier Transform (FFT) was used to perform the integral. The Molodensky gravity anomaly was determined in a 5’ grid, reduced and restored using the Residual Terrain Model (RTM) technique and the XGM2019 with the degree and order 250 and 720. The validation for the São Paulo quasi-geoid model is based on the GNSS measurements in the leveling network too.  The Digital Terrain Model SRTM15 plus was used in the continent and the ocean areas in both states.

How to cite: Silva, V., Guimarães, G., Blitkow, D., and Matos, A. C.: New geoid models computation in the Southeast part of Brazil, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3284, https://doi.org/10.5194/egusphere-egu21-3284, 2021.